TSTP Solution File: ITP241^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP241^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 03:24:25 EDT 2023
% Result : Theorem 116.77s 117.01s
% Output : Proof 116.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.53/2.56 % Problem : ITP241^3 : TPTP v8.1.2. Released v8.1.0.
% 2.53/2.56 % Command : do_cvc5 %s %d
% 2.57/2.77 % Computer : n032.cluster.edu
% 2.57/2.77 % Model : x86_64 x86_64
% 2.57/2.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.57/2.77 % Memory : 8042.1875MB
% 2.57/2.77 % OS : Linux 3.10.0-693.el7.x86_64
% 2.57/2.77 % CPULimit : 300
% 2.57/2.77 % WCLimit : 300
% 2.57/2.77 % DateTime : Sun Aug 27 14:57:32 EDT 2023
% 2.57/2.77 % CPUTime :
% 5.13/5.45 %----Proving TH0
% 5.13/5.46 %------------------------------------------------------------------------------
% 5.13/5.46 % File : ITP241^3 : TPTP v8.1.2. Released v8.1.0.
% 5.13/5.46 % Domain : Interactive Theorem Proving
% 5.13/5.46 % Problem : Sledgehammer problem VEBT_Pred 00822_049130
% 5.13/5.46 % Version : [Des22] axioms.
% 5.13/5.46 % English :
% 5.13/5.46
% 5.13/5.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.13/5.46 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.13/5.46 % Source : [Des22]
% 5.13/5.46 % Names : 0069_VEBT_Pred_00822_049130 [Des22]
% 5.13/5.46
% 5.13/5.46 % Status : Theorem
% 5.13/5.46 % Rating : 1.00 v8.1.0
% 5.13/5.46 % Syntax : Number of formulae : 11233 (5702 unt; 988 typ; 0 def)
% 5.13/5.46 % Number of atoms : 27840 (12143 equ; 0 cnn)
% 5.13/5.46 % Maximal formula atoms : 71 ( 2 avg)
% 5.13/5.46 % Number of connectives : 115572 (2836 ~; 515 |;1734 &;99970 @)
% 5.13/5.46 % ( 0 <=>;10517 =>; 0 <=; 0 <~>)
% 5.13/5.46 % Maximal formula depth : 39 ( 6 avg)
% 5.13/5.46 % Number of types : 85 ( 84 usr)
% 5.13/5.46 % Number of type conns : 4523 (4523 >; 0 *; 0 +; 0 <<)
% 5.13/5.46 % Number of symbols : 907 ( 904 usr; 61 con; 0-8 aty)
% 5.13/5.46 % Number of variables : 26014 (2358 ^;22889 !; 767 ?;26014 :)
% 5.13/5.46 % SPC : TH0_THM_EQU_NAR
% 5.13/5.46
% 5.13/5.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.13/5.46 % from the van Emde Boas Trees session in the Archive of Formal
% 5.13/5.46 % proofs -
% 5.13/5.46 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.13/5.46 % 2022-02-17 23:44:43.999
% 5.13/5.46 %------------------------------------------------------------------------------
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% 5.13/5.46 code_integer: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Extended____Nat__Oenat,type,
% 5.13/5.46 extended_enat: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__List__Olist_I_Eo_J,type,
% 5.13/5.46 list_o: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Complex__Ocomplex,type,
% 5.13/5.46 complex: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 5.13/5.46 set_o: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__String__Ochar,type,
% 5.13/5.46 char: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Real__Oreal,type,
% 5.13/5.46 real: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Rat__Orat,type,
% 5.13/5.46 rat: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Num__Onum,type,
% 5.13/5.46 num: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Nat__Onat,type,
% 5.13/5.46 nat: $tType ).
% 5.13/5.46
% 5.13/5.46 thf(ty_n_t__Int__Oint,type,
% 5.13/5.46 int: $tType ).
% 5.13/5.46
% 5.13/5.46 % Explicit typings (904)
% 5.13/5.46 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 5.13/5.46 archim2889992004027027881ng_rat: rat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
% 5.13/5.46 archim7802044766580827645g_real: real > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 5.13/5.46 archim3151403230148437115or_rat: rat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 5.13/5.46 archim6058952711729229775r_real: real > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 5.13/5.46 archim7778729529865785530nd_rat: rat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 5.13/5.46 archim8280529875227126926d_real: real > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 5.13/5.46 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 5.13/5.46 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.13/5.46 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.13/5.46 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 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 ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.13/5.46 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.13/5.46 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.13/5.46 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.13/5.46 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.13/5.46 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.13/5.46 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.13/5.46 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.13/5.46 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Binomial_Obinomial,type,
% 5.13/5.46 binomial: nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 5.13/5.46 gbinomial_complex: complex > nat > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 5.13/5.46 gbinomial_int: int > nat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 5.13/5.46 gbinomial_nat: nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 5.13/5.46 gbinomial_rat: rat > nat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 5.13/5.46 gbinomial_real: real > nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 5.13/5.46 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 5.13/5.46 bit_and_not_num: num > num > option_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.13/5.46
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% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
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% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
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% 5.13/5.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.13/5.46
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% 5.13/5.46
% 5.13/5.46 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,
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% 5.13/5.46
% 5.13/5.46 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,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
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% 5.13/5.46 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_GCD_Obezw,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_GCD_Obezw__rel,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_GCD_Ogcd__nat__rel,type,
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% 5.13/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
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% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 ring_18347121197199848620nteger: int > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.13/5.46 ring_17405671764205052669omplex: int > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.13/5.46 ring_1_of_int_int: int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.13/5.46 ring_1_of_int_rat: int > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.13/5.46 ring_1_of_int_real: int > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 5.13/5.46 inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.13/5.46 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.13/5.46 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.46 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.13/5.46 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.13/5.46 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.13/5.46 append_int: list_int > list_int > list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.13/5.46 append_nat: list_nat > list_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 5.13/5.46 drop_nat: nat > list_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 5.13/5.46 fold_int_int: ( int > int > int ) > list_int > int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 5.13/5.46 last_nat: list_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.13/5.46 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.13/5.46 cons_int: int > list_int > list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.13/5.46 cons_nat: nat > list_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.13/5.46 nil_int: list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.13/5.46 nil_nat: list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.13/5.46 hd_nat: list_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.13/5.46 set_o2: list_o > set_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.13/5.46 set_complex2: list_complex > set_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.13/5.46 set_int2: list_int > set_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 5.13/5.46 set_list_nat2: list_list_nat > set_list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.13/5.46 set_nat2: list_nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.13/5.46 set_real2: list_real > set_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.13/5.46 tl_nat: list_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.13/5.46 list_update_o: list_o > nat > $o > list_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.13/5.46 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.13/5.46 list_update_int: list_int > nat > int > list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.13/5.46 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.13/5.46 list_update_real: list_real > nat > real > list_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001_Eo,type,
% 5.13/5.46 nth_o: list_o > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.13/5.46 nth_complex: list_complex > nat > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.13/5.46 nth_int: list_int > nat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 5.13/5.46 nth_list_nat: list_list_nat > nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.13/5.46 nth_nat: list_nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.13/5.46 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.13/5.46 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.13/5.46 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.13/5.46 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.13/5.46 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.13/5.46 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.13/5.46 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.13/5.46 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.13/5.46 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.13/5.46 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.13/5.46 nth_real: list_real > nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.13/5.46 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.13/5.46 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.13/5.46 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.13/5.46 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.13/5.46 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.13/5.46 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.13/5.46 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.13/5.46 replicate_o: nat > $o > list_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.13/5.46 replicate_complex: nat > complex > list_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.13/5.46 replicate_int: nat > int > list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.13/5.46 replicate_nat: nat > nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.13/5.46 replicate_real: nat > real > list_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.13/5.46 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.13/5.46 take_nat: nat > list_nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oupt,type,
% 5.13/5.46 upt: nat > nat > list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oupto,type,
% 5.13/5.46 upto: int > int > list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oupto__aux,type,
% 5.13/5.46 upto_aux: int > int > list_int > list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_List_Oupto__rel,type,
% 5.13/5.46 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_OSuc,type,
% 5.13/5.46 suc: nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.13/5.46 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.13/5.46 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.13/5.46 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 semiri4939895301339042750nteger: nat > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.13/5.46 semiri8010041392384452111omplex: nat > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.13/5.46 semiri1314217659103216013at_int: nat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.13/5.46 semiri1316708129612266289at_nat: nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.13/5.46 semiri681578069525770553at_rat: nat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.13/5.46 semiri5074537144036343181t_real: nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.13/5.46 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.13/5.46 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.13/5.46 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.13/5.46 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.13/5.46
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.13/5.46
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% 5.13/5.46
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% 5.13/5.46
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% 5.13/5.46
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% 5.13/5.46
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% 5.13/5.46 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.13/5.46
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% 5.13/5.46 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
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% 5.13/5.46 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,
% 5.13/5.46 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.13/5.46 size_size_list_real: list_real > nat ).
% 5.13/5.46
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.13/5.46 size_size_num: num > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.13/5.46 nat_list_encode: list_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.13/5.46 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.13/5.46 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Oset__decode,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.13/5.46 nat_set_encode: set_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.13/5.46 nat_triangle: nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_NthRoot_Oroot,type,
% 5.13/5.46 root: nat > real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_NthRoot_Osqrt,type,
% 5.13/5.46 sqrt: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_OBitM,type,
% 5.13/5.46 bitM: num > num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oinc,type,
% 5.13/5.46 inc: num > num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.13/5.46 neg_nu7009210354673126013omplex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.13/5.46 neg_numeral_dbl_int: int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.13/5.46 neg_numeral_dbl_rat: rat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.13/5.46 neg_numeral_dbl_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.13/5.46 neg_nu6511756317524482435omplex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.13/5.46 neg_nu3811975205180677377ec_int: int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.13/5.46 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.13/5.46 neg_nu6075765906172075777c_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.13/5.46 neg_nu8557863876264182079omplex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.13/5.46 neg_nu5851722552734809277nc_int: int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.13/5.46 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.13/5.46 neg_nu8295874005876285629c_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.13/5.46 neg_numeral_sub_int: num > num > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onum_OBit0,type,
% 5.13/5.46 bit0: num > num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onum_OBit1,type,
% 5.13/5.46 bit1: num > num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onum_OOne,type,
% 5.13/5.46 one: num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.13/5.46 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onum_Osize__num,type,
% 5.13/5.46 size_num: num > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onum__of__nat,type,
% 5.13/5.46 num_of_nat: nat > num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 numera6620942414471956472nteger: num > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.13/5.46 numera6690914467698888265omplex: num > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.13/5.46 numera1916890842035813515d_enat: num > extended_enat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.13/5.46 numeral_numeral_rat: num > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Opow,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Opred__numeral,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Num_Osqr,type,
% 5.13/5.46 sqr: num > num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Complex__Ocomplex_M_Eo_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Int__Oint_M_Eo_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
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% 5.13/5.46
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% 5.13/5.46
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% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.13/5.46 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.13/5.46 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 5.13/5.46 product_Pair_num_num: num > num > product_prod_num_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.13/5.46 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.13/5.46 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.13/5.46 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.13/5.46 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.13/5.46 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.13/5.46 produc8678311845419106900er_nat: ( code_integer > nat ) > ( code_integer > nat ) > produc8923325533196201883nteger > product_prod_nat_nat ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc127349428274296955eger_o: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc2592262431452330817omplex: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8763457246119570046nteger > set_complex ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc8604463032469472703et_int: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc8763457246119570046nteger > set_int ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc3558942015123893603et_nat: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > set_nat ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc815715089573277247t_real: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > set_real ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc8289552606927098482et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc7773217078559923341nt_int > set_nat ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.13/5.46 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.13/5.46 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.13/5.46 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.13/5.46 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.13/5.46 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.13/5.46 produc8580519160106071146omplex: ( int > int > set_complex ) > product_prod_int_int > set_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 5.13/5.46 produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.46 produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc1656060378719767003at_nat: ( int > int > set_Pr1261947904930325089at_nat ) > product_prod_int_int > set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.13/5.46 produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.13/5.46 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.13/5.46 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.13/5.46 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.13/5.46 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.13/5.46 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.13/5.46 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.13/5.46 product_fst_int_int: product_prod_int_int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.13/5.46 product_snd_int_int: product_prod_int_int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_OAbs__Rat,type,
% 5.13/5.46 abs_Rat: product_prod_int_int > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_OFract,type,
% 5.13/5.46 fract: int > int > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_OFrct,type,
% 5.13/5.46 frct: product_prod_int_int > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_ORep__Rat,type,
% 5.13/5.46 rep_Rat: rat > product_prod_int_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.13/5.46 field_5140801741446780682s_real: set_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Onormalize,type,
% 5.13/5.46 normalize: product_prod_int_int > product_prod_int_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Oof__int,type,
% 5.13/5.46 of_int: int > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Opcr__rat,type,
% 5.13/5.46 pcr_rat: product_prod_int_int > rat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Opositive,type,
% 5.13/5.46 positive: rat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Oquotient__of,type,
% 5.13/5.46 quotient_of: rat > product_prod_int_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rat_Oratrel,type,
% 5.13/5.46 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_OReal,type,
% 5.13/5.46 real2: ( nat > rat ) > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_Ocauchy,type,
% 5.13/5.46 cauchy: ( nat > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_Opcr__real,type,
% 5.13/5.46 pcr_real: ( nat > rat ) > real > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_Opositive,type,
% 5.13/5.46 positive2: real > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_Orealrel,type,
% 5.13/5.46 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_Orep__real,type,
% 5.13/5.46 rep_real: real > nat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real_Ovanishes,type,
% 5.13/5.46 vanishes: ( nat > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.13/5.46 real_V2521375963428798218omplex: set_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.13/5.46 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.13/5.46 real_V7735802525324610683m_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.13/5.46 real_V4546457046886955230omplex: real > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.13/5.46 real_V2046097035970521341omplex: real > complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.13/5.46 real_V1485227260804924795R_real: real > real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.13/5.46 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.13/5.46 divide1717551699836669952omplex: complex > complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.13/5.46 divide_divide_int: int > int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.13/5.46 divide_divide_nat: nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.13/5.46 divide_divide_rat: rat > rat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.13/5.46 divide_divide_real: real > real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.13/5.46 dvd_dvd_complex: complex > complex > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.13/5.46 dvd_dvd_int: int > int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.13/5.46 dvd_dvd_nat: nat > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.13/5.46 dvd_dvd_rat: rat > rat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.13/5.46 dvd_dvd_real: real > real > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.13/5.46 modulo_modulo_int: int > int > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.13/5.46 modulo_modulo_nat: nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.13/5.46 zero_n356916108424825756nteger: $o > code_integer ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.13/5.46 zero_n1201886186963655149omplex: $o > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.13/5.46 zero_n2684676970156552555ol_int: $o > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.13/5.46 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.13/5.46 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.13/5.46 zero_n3304061248610475627l_real: $o > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.13/5.46 suminf_complex: ( nat > complex ) > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.13/5.46 suminf_int: ( nat > int ) > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.13/5.46 suminf_nat: ( nat > nat ) > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.13/5.46 suminf_real: ( nat > real ) > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.13/5.46 summable_complex: ( nat > complex ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.13/5.46 summable_int: ( nat > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.13/5.46 summable_nat: ( nat > nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.13/5.46 summable_real: ( nat > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.13/5.46 sums_complex: ( nat > complex ) > complex > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.13/5.46 sums_int: ( nat > int ) > int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.13/5.46 sums_nat: ( nat > nat ) > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.13/5.46 sums_real: ( nat > real ) > real > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001_Eo,type,
% 5.13/5.46 collect_o: ( $o > $o ) > set_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.13/5.46 collect_complex: ( complex > $o ) > set_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.13/5.46 collect_int: ( int > $o ) > set_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.13/5.46 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.13/5.46 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.13/5.46 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.13/5.46 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.13/5.46 collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.13/5.46 collect_nat: ( nat > $o ) > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
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% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.46 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_OCollect_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.13/5.46 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
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% 5.13/5.46 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.46 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.13/5.46 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.13/5.46 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.13/5.46 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.13/5.46 set_or1266510415728281911st_int: int > int > set_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.13/5.46 set_or7049704709247886629st_num: num > num > set_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.13/5.46 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.13/5.46 set_or1222579329274155063t_real: real > real > set_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.13/5.46 set_or4662586982721622107an_int: int > int > set_int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.13/5.46 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.13/5.46 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
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% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Extended____Nat__Oenat,type,
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% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
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% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
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% 5.13/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.13/5.46 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.13/5.46 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.13/5.46 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.13/5.46 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.13/5.46 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.13/5.46 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.13/5.46 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.46 topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.13/5.46 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.13/5.46 topolo2815343760600316023s_real: real > filter_real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.13/5.46 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oarccos,type,
% 5.13/5.46 arccos: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.13/5.46 arcosh_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oarcsin,type,
% 5.13/5.46 arcsin: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oarctan,type,
% 5.13/5.46 arctan: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.13/5.46 arsinh_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.13/5.46 artanh_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.13/5.46 cos_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.13/5.46 cos_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.13/5.46 cos_coeff: nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
% 5.13/5.46 cosh_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.13/5.46 cosh_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 5.13/5.46 cot_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.13/5.46 cot_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.13/5.46 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.13/5.46 diffs_int: ( nat > int ) > nat > int ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.13/5.46 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.13/5.46 diffs_real: ( nat > real ) > nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.13/5.46 exp_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.13/5.46 exp_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.13/5.46 ln_ln_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Olog,type,
% 5.13/5.46 log: real > real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Opi,type,
% 5.13/5.46 pi: real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.13/5.46 powr_real: real > real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.13/5.46 sin_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.13/5.46 sin_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.13/5.46 sin_coeff: nat > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 5.13/5.46 sinh_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.13/5.46 sinh_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.13/5.46 tan_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.13/5.46 tan_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.13/5.46 tanh_complex: complex > complex ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.13/5.46 tanh_real: real > real ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.13/5.46 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.13/5.46 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.13/5.46 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.13/5.46 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.13/5.46 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.13/5.46 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.13/5.46 vEBT_VEBT_high: nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.13/5.46 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.13/5.46 vEBT_VEBT_low: nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.13/5.46 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.13/5.46 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.13/5.46 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.13/5.46 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.13/5.46 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.13/5.46 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.13/5.46 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.13/5.46 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.13/5.46 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.13/5.46 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.13/5.46 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.13/5.46 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.13/5.46 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.13/5.46 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.13/5.46 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.13/5.46 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.13/5.46 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.13/5.46 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.13/5.46 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.13/5.46 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.13/5.46 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.13/5.46 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.13/5.46 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.13/5.46 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.13/5.46 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.13/5.46 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.13/5.46 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.13/5.46 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.13/5.46 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.13/5.46 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.13/5.46 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.13/5.46 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.13/5.46 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.13/5.46 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.13/5.46 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.13/5.46 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.13/5.46 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.13/5.46 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.13/5.46 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.13/5.46 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.13/5.46 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.13/5.46 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001_Eo,type,
% 5.13/5.46 member_o: $o > set_o > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.13/5.46 member_complex: complex > set_complex > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Int__Oint,type,
% 5.13/5.46 member_int: int > set_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.13/5.46 member_list_o: list_o > set_list_o > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.13/5.46 member_list_int: list_int > set_list_int > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.13/5.46 member_list_nat: list_nat > set_list_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.13/5.46 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Nat__Onat,type,
% 5.13/5.46 member_nat: nat > set_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Num__Onum,type,
% 5.13/5.46 member_num: num > set_num > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.46 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Rat__Orat,type,
% 5.13/5.46 member_rat: rat > set_rat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Real__Oreal,type,
% 5.13/5.46 member_real: real > set_real > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.46 member_set_nat: set_nat > set_set_nat > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.13/5.46 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_deg____,type,
% 5.13/5.46 deg: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_m____,type,
% 5.13/5.46 m: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_ma____,type,
% 5.13/5.46 ma: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_maxy____,type,
% 5.13/5.46 maxy: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_mi____,type,
% 5.13/5.46 mi: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_na____,type,
% 5.13/5.46 na: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_pr____,type,
% 5.13/5.46 pr: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_res____,type,
% 5.13/5.46 res: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_summary____,type,
% 5.13/5.46 summary: vEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_treeList____,type,
% 5.13/5.46 treeList: list_VEBT_VEBT ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_xa____,type,
% 5.13/5.46 xa: nat ).
% 5.13/5.46
% 5.13/5.46 thf(sy_v_za____,type,
% 5.13/5.46 za: nat ).
% 5.13/5.46
% 5.13/5.46 % Relevant facts (10205)
% 5.13/5.46 thf(fact_0_maxt__corr__help,axiom,
% 5.13/5.46 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 5.13/5.46 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.46 => ( ( ( vEBT_vebt_maxt @ T )
% 5.13/5.46 = ( some_nat @ Maxi ) )
% 5.13/5.46 => ( ( vEBT_vebt_member @ T @ X )
% 5.13/5.46 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % maxt_corr_help
% 5.13/5.46 thf(fact_1_max__in__set__def,axiom,
% 5.13/5.46 ( vEBT_VEBT_max_in_set
% 5.13/5.46 = ( ^ [Xs: set_nat,X2: nat] :
% 5.13/5.46 ( ( member_nat @ X2 @ Xs )
% 5.13/5.46 & ! [Y: nat] :
% 5.13/5.46 ( ( member_nat @ Y @ Xs )
% 5.13/5.46 => ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % max_in_set_def
% 5.13/5.46 thf(fact_2_min__in__set__def,axiom,
% 5.13/5.46 ( vEBT_VEBT_min_in_set
% 5.13/5.46 = ( ^ [Xs: set_nat,X2: nat] :
% 5.13/5.46 ( ( member_nat @ X2 @ Xs )
% 5.13/5.46 & ! [Y: nat] :
% 5.13/5.46 ( ( member_nat @ Y @ Xs )
% 5.13/5.46 => ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % min_in_set_def
% 5.13/5.46 thf(fact_3_True,axiom,
% 5.13/5.46 ( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.46 = pr ) ).
% 5.13/5.46
% 5.13/5.46 % True
% 5.13/5.46 thf(fact_4__092_060open_062Some_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_092_060close_062,axiom,
% 5.13/5.46 ( ( some_nat @ maxy )
% 5.13/5.46 = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ pr ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % \<open>Some maxy = vebt_maxt (treeList ! pr)\<close>
% 5.13/5.46 thf(fact_5__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.13/5.46 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.13/5.46
% 5.13/5.46 % \<open>2 \<le> deg\<close>
% 5.13/5.46 thf(fact_6_abe,axiom,
% 5.13/5.46 vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % abe
% 5.13/5.46 thf(fact_7__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
% 5.13/5.46 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.46 = na ) ).
% 5.13/5.46
% 5.13/5.46 % \<open>deg div 2 = n\<close>
% 5.13/5.46 thf(fact_8_False,axiom,
% 5.13/5.46 za != mi ).
% 5.13/5.46
% 5.13/5.46 % False
% 5.13/5.46 thf(fact_9_bit__split__inv,axiom,
% 5.13/5.46 ! [X: nat,D: nat] :
% 5.13/5.46 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.13/5.46 = X ) ).
% 5.13/5.46
% 5.13/5.46 % bit_split_inv
% 5.13/5.46 thf(fact_10_abc,axiom,
% 5.13/5.46 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ na ).
% 5.13/5.46
% 5.13/5.46 % abc
% 5.13/5.46 thf(fact_11__092_060open_062high_Az_A_Ideg_Adiv_A2_J_A_092_060le_062_Apr_092_060close_062,axiom,
% 5.13/5.46 ord_less_eq_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ pr ).
% 5.13/5.46
% 5.13/5.46 % \<open>high z (deg div 2) \<le> pr\<close>
% 5.13/5.46 thf(fact_12_semiring__norm_I85_J,axiom,
% 5.13/5.46 ! [M: num] :
% 5.13/5.46 ( ( bit0 @ M )
% 5.13/5.46 != one ) ).
% 5.13/5.46
% 5.13/5.46 % semiring_norm(85)
% 5.13/5.46 thf(fact_13_semiring__norm_I83_J,axiom,
% 5.13/5.46 ! [N: num] :
% 5.13/5.46 ( one
% 5.13/5.46 != ( bit0 @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % semiring_norm(83)
% 5.13/5.46 thf(fact_14_numeral__le__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.13/5.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_le_iff
% 5.13/5.46 thf(fact_15_numeral__le__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.13/5.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_le_iff
% 5.13/5.46 thf(fact_16_numeral__le__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_le_iff
% 5.13/5.46 thf(fact_17_numeral__le__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.13/5.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_le_iff
% 5.13/5.46 thf(fact_18_numeral__Bit0__div__2,axiom,
% 5.13/5.46 ! [N: num] :
% 5.13/5.46 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.46 = ( numeral_numeral_nat @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_Bit0_div_2
% 5.13/5.46 thf(fact_19_numeral__Bit0__div__2,axiom,
% 5.13/5.46 ! [N: num] :
% 5.13/5.46 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.13/5.46 = ( numeral_numeral_int @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_Bit0_div_2
% 5.13/5.46 thf(fact_20_divide__numeral__1,axiom,
% 5.13/5.46 ! [A: complex] :
% 5.13/5.46 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.13/5.46 = A ) ).
% 5.13/5.46
% 5.13/5.46 % divide_numeral_1
% 5.13/5.46 thf(fact_21_divide__numeral__1,axiom,
% 5.13/5.46 ! [A: real] :
% 5.13/5.46 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.13/5.46 = A ) ).
% 5.13/5.46
% 5.13/5.46 % divide_numeral_1
% 5.13/5.46 thf(fact_22_divide__numeral__1,axiom,
% 5.13/5.46 ! [A: rat] :
% 5.13/5.46 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.13/5.46 = A ) ).
% 5.13/5.46
% 5.13/5.46 % divide_numeral_1
% 5.13/5.46 thf(fact_23__092_060open_062pr_A_060_Ahigh_Az_A_Ideg_Adiv_A2_J_A_092_060Longrightarrow_062_AFalse_092_060close_062,axiom,
% 5.13/5.46 ~ ( ord_less_nat @ pr @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % \<open>pr < high z (deg div 2) \<Longrightarrow> False\<close>
% 5.13/5.46 thf(fact_24_verit__eq__simplify_I8_J,axiom,
% 5.13/5.46 ! [X22: num,Y2: num] :
% 5.13/5.46 ( ( ( bit0 @ X22 )
% 5.13/5.46 = ( bit0 @ Y2 ) )
% 5.13/5.46 = ( X22 = Y2 ) ) ).
% 5.13/5.46
% 5.13/5.46 % verit_eq_simplify(8)
% 5.13/5.46 thf(fact_25_semiring__norm_I87_J,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ( bit0 @ M )
% 5.13/5.46 = ( bit0 @ N ) )
% 5.13/5.46 = ( M = N ) ) ).
% 5.13/5.46
% 5.13/5.46 % semiring_norm(87)
% 5.13/5.46 thf(fact_26_numeral__eq__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ( numera6690914467698888265omplex @ M )
% 5.13/5.46 = ( numera6690914467698888265omplex @ N ) )
% 5.13/5.46 = ( M = N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_eq_iff
% 5.13/5.46 thf(fact_27_numeral__eq__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ( numeral_numeral_real @ M )
% 5.13/5.46 = ( numeral_numeral_real @ N ) )
% 5.13/5.46 = ( M = N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_eq_iff
% 5.13/5.46 thf(fact_28_numeral__eq__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ( numeral_numeral_rat @ M )
% 5.13/5.46 = ( numeral_numeral_rat @ N ) )
% 5.13/5.46 = ( M = N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_eq_iff
% 5.13/5.46 thf(fact_29_numeral__eq__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ( numeral_numeral_nat @ M )
% 5.13/5.46 = ( numeral_numeral_nat @ N ) )
% 5.13/5.46 = ( M = N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_eq_iff
% 5.13/5.46 thf(fact_30_numeral__eq__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ( numeral_numeral_int @ M )
% 5.13/5.46 = ( numeral_numeral_int @ N ) )
% 5.13/5.46 = ( M = N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_eq_iff
% 5.13/5.46 thf(fact_31_order__refl,axiom,
% 5.13/5.46 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 5.13/5.46
% 5.13/5.46 % order_refl
% 5.13/5.46 thf(fact_32_order__refl,axiom,
% 5.13/5.46 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.13/5.46
% 5.13/5.46 % order_refl
% 5.13/5.46 thf(fact_33_order__refl,axiom,
% 5.13/5.46 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.13/5.46
% 5.13/5.46 % order_refl
% 5.13/5.46 thf(fact_34_order__refl,axiom,
% 5.13/5.46 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.13/5.46
% 5.13/5.46 % order_refl
% 5.13/5.46 thf(fact_35_order__refl,axiom,
% 5.13/5.46 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.13/5.46
% 5.13/5.46 % order_refl
% 5.13/5.46 thf(fact_36_dual__order_Orefl,axiom,
% 5.13/5.46 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.refl
% 5.13/5.46 thf(fact_37_dual__order_Orefl,axiom,
% 5.13/5.46 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.refl
% 5.13/5.46 thf(fact_38_dual__order_Orefl,axiom,
% 5.13/5.46 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.refl
% 5.13/5.46 thf(fact_39_dual__order_Orefl,axiom,
% 5.13/5.46 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.refl
% 5.13/5.46 thf(fact_40_dual__order_Orefl,axiom,
% 5.13/5.46 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.refl
% 5.13/5.46 thf(fact_41_maxt__member,axiom,
% 5.13/5.46 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.13/5.46 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.46 => ( ( ( vEBT_vebt_maxt @ T )
% 5.13/5.46 = ( some_nat @ Maxi ) )
% 5.13/5.46 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % maxt_member
% 5.13/5.46 thf(fact_42_member__correct,axiom,
% 5.13/5.46 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.46 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.46 => ( ( vEBT_vebt_member @ T @ X )
% 5.13/5.46 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % member_correct
% 5.13/5.46 thf(fact_43__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.13/5.46 ~ ! [Maxy: nat] :
% 5.13/5.46 ( ( some_nat @ Maxy )
% 5.13/5.46 != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ pr ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % \<open>\<And>thesis. (\<And>maxy. Some maxy = vebt_maxt (treeList ! pr) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.13/5.46 thf(fact_44_numeral__less__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.13/5.46 = ( ord_less_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_less_iff
% 5.13/5.46 thf(fact_45_numeral__less__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.13/5.46 = ( ord_less_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_less_iff
% 5.13/5.46 thf(fact_46_numeral__less__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.46 = ( ord_less_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_less_iff
% 5.13/5.46 thf(fact_47_numeral__less__iff,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.13/5.46 = ( ord_less_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % numeral_less_iff
% 5.13/5.46 thf(fact_48_semiring__norm_I71_J,axiom,
% 5.13/5.46 ! [M: num,N: num] :
% 5.13/5.46 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.13/5.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.13/5.46
% 5.13/5.46 % semiring_norm(71)
% 5.13/5.46 thf(fact_49_semiring__norm_I68_J,axiom,
% 5.13/5.46 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.13/5.46
% 5.13/5.46 % semiring_norm(68)
% 5.13/5.46 thf(fact_50_semiring__norm_I69_J,axiom,
% 5.13/5.46 ! [M: num] :
% 5.13/5.46 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.13/5.46
% 5.13/5.46 % semiring_norm(69)
% 5.13/5.46 thf(fact_51__C5_Ohyps_C_I9_J,axiom,
% 5.13/5.46 ord_less_eq_nat @ mi @ ma ).
% 5.13/5.46
% 5.13/5.46 % "5.hyps"(9)
% 5.13/5.46 thf(fact_52_less__shift,axiom,
% 5.13/5.46 ( ord_less_nat
% 5.13/5.46 = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_shift
% 5.13/5.46 thf(fact_53_lesseq__shift,axiom,
% 5.13/5.46 ( ord_less_eq_nat
% 5.13/5.46 = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % lesseq_shift
% 5.13/5.46 thf(fact_54_verit__comp__simplify1_I1_J,axiom,
% 5.13/5.46 ! [A: real] :
% 5.13/5.46 ~ ( ord_less_real @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % verit_comp_simplify1(1)
% 5.13/5.46 thf(fact_55_verit__comp__simplify1_I1_J,axiom,
% 5.13/5.46 ! [A: rat] :
% 5.13/5.46 ~ ( ord_less_rat @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % verit_comp_simplify1(1)
% 5.13/5.46 thf(fact_56_verit__comp__simplify1_I1_J,axiom,
% 5.13/5.46 ! [A: num] :
% 5.13/5.46 ~ ( ord_less_num @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % verit_comp_simplify1(1)
% 5.13/5.46 thf(fact_57_verit__comp__simplify1_I1_J,axiom,
% 5.13/5.46 ! [A: nat] :
% 5.13/5.46 ~ ( ord_less_nat @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % verit_comp_simplify1(1)
% 5.13/5.46 thf(fact_58_verit__comp__simplify1_I1_J,axiom,
% 5.13/5.46 ! [A: int] :
% 5.13/5.46 ~ ( ord_less_int @ A @ A ) ).
% 5.13/5.46
% 5.13/5.46 % verit_comp_simplify1(1)
% 5.13/5.46 thf(fact_59_lt__ex,axiom,
% 5.13/5.46 ! [X: real] :
% 5.13/5.46 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 5.13/5.46
% 5.13/5.46 % lt_ex
% 5.13/5.46 thf(fact_60_lt__ex,axiom,
% 5.13/5.46 ! [X: rat] :
% 5.13/5.46 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 5.13/5.46
% 5.13/5.46 % lt_ex
% 5.13/5.46 thf(fact_61_lt__ex,axiom,
% 5.13/5.46 ! [X: int] :
% 5.13/5.46 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 5.13/5.46
% 5.13/5.46 % lt_ex
% 5.13/5.46 thf(fact_62_gt__ex,axiom,
% 5.13/5.46 ! [X: real] :
% 5.13/5.46 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.13/5.46
% 5.13/5.46 % gt_ex
% 5.13/5.46 thf(fact_63_gt__ex,axiom,
% 5.13/5.46 ! [X: rat] :
% 5.13/5.46 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.13/5.46
% 5.13/5.46 % gt_ex
% 5.13/5.46 thf(fact_64_gt__ex,axiom,
% 5.13/5.46 ! [X: nat] :
% 5.13/5.46 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.13/5.46
% 5.13/5.46 % gt_ex
% 5.13/5.46 thf(fact_65_gt__ex,axiom,
% 5.13/5.46 ! [X: int] :
% 5.13/5.46 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.13/5.46
% 5.13/5.46 % gt_ex
% 5.13/5.46 thf(fact_66_dense,axiom,
% 5.13/5.46 ! [X: real,Y4: real] :
% 5.13/5.46 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.46 => ? [Z: real] :
% 5.13/5.46 ( ( ord_less_real @ X @ Z )
% 5.13/5.46 & ( ord_less_real @ Z @ Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % dense
% 5.13/5.46 thf(fact_67_dense,axiom,
% 5.13/5.46 ! [X: rat,Y4: rat] :
% 5.13/5.46 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.46 => ? [Z: rat] :
% 5.13/5.46 ( ( ord_less_rat @ X @ Z )
% 5.13/5.46 & ( ord_less_rat @ Z @ Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % dense
% 5.13/5.46 thf(fact_68_less__imp__neq,axiom,
% 5.13/5.46 ! [X: real,Y4: real] :
% 5.13/5.46 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.46 => ( X != Y4 ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_imp_neq
% 5.13/5.46 thf(fact_69_less__imp__neq,axiom,
% 5.13/5.46 ! [X: rat,Y4: rat] :
% 5.13/5.46 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.46 => ( X != Y4 ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_imp_neq
% 5.13/5.46 thf(fact_70_less__imp__neq,axiom,
% 5.13/5.46 ! [X: num,Y4: num] :
% 5.13/5.46 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.46 => ( X != Y4 ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_imp_neq
% 5.13/5.46 thf(fact_71_less__imp__neq,axiom,
% 5.13/5.46 ! [X: nat,Y4: nat] :
% 5.13/5.46 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.46 => ( X != Y4 ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_imp_neq
% 5.13/5.46 thf(fact_72_less__imp__neq,axiom,
% 5.13/5.46 ! [X: int,Y4: int] :
% 5.13/5.46 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.46 => ( X != Y4 ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_imp_neq
% 5.13/5.46 thf(fact_73_order_Oasym,axiom,
% 5.13/5.46 ! [A: real,B: real] :
% 5.13/5.46 ( ( ord_less_real @ A @ B )
% 5.13/5.46 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % order.asym
% 5.13/5.46 thf(fact_74_order_Oasym,axiom,
% 5.13/5.46 ! [A: rat,B: rat] :
% 5.13/5.46 ( ( ord_less_rat @ A @ B )
% 5.13/5.46 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % order.asym
% 5.13/5.46 thf(fact_75_order_Oasym,axiom,
% 5.13/5.46 ! [A: num,B: num] :
% 5.13/5.46 ( ( ord_less_num @ A @ B )
% 5.13/5.46 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % order.asym
% 5.13/5.46 thf(fact_76_order_Oasym,axiom,
% 5.13/5.46 ! [A: nat,B: nat] :
% 5.13/5.46 ( ( ord_less_nat @ A @ B )
% 5.13/5.46 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % order.asym
% 5.13/5.46 thf(fact_77_order_Oasym,axiom,
% 5.13/5.46 ! [A: int,B: int] :
% 5.13/5.46 ( ( ord_less_int @ A @ B )
% 5.13/5.46 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % order.asym
% 5.13/5.46 thf(fact_78_ord__eq__less__trans,axiom,
% 5.13/5.46 ! [A: real,B: real,C: real] :
% 5.13/5.46 ( ( A = B )
% 5.13/5.46 => ( ( ord_less_real @ B @ C )
% 5.13/5.46 => ( ord_less_real @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_eq_less_trans
% 5.13/5.46 thf(fact_79_ord__eq__less__trans,axiom,
% 5.13/5.46 ! [A: rat,B: rat,C: rat] :
% 5.13/5.46 ( ( A = B )
% 5.13/5.46 => ( ( ord_less_rat @ B @ C )
% 5.13/5.46 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_eq_less_trans
% 5.13/5.46 thf(fact_80_ord__eq__less__trans,axiom,
% 5.13/5.46 ! [A: num,B: num,C: num] :
% 5.13/5.46 ( ( A = B )
% 5.13/5.46 => ( ( ord_less_num @ B @ C )
% 5.13/5.46 => ( ord_less_num @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_eq_less_trans
% 5.13/5.46 thf(fact_81_ord__eq__less__trans,axiom,
% 5.13/5.46 ! [A: nat,B: nat,C: nat] :
% 5.13/5.46 ( ( A = B )
% 5.13/5.46 => ( ( ord_less_nat @ B @ C )
% 5.13/5.46 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_eq_less_trans
% 5.13/5.46 thf(fact_82_ord__eq__less__trans,axiom,
% 5.13/5.46 ! [A: int,B: int,C: int] :
% 5.13/5.46 ( ( A = B )
% 5.13/5.46 => ( ( ord_less_int @ B @ C )
% 5.13/5.46 => ( ord_less_int @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_eq_less_trans
% 5.13/5.46 thf(fact_83_ord__less__eq__trans,axiom,
% 5.13/5.46 ! [A: real,B: real,C: real] :
% 5.13/5.46 ( ( ord_less_real @ A @ B )
% 5.13/5.46 => ( ( B = C )
% 5.13/5.46 => ( ord_less_real @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_less_eq_trans
% 5.13/5.46 thf(fact_84_ord__less__eq__trans,axiom,
% 5.13/5.46 ! [A: rat,B: rat,C: rat] :
% 5.13/5.46 ( ( ord_less_rat @ A @ B )
% 5.13/5.46 => ( ( B = C )
% 5.13/5.46 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_less_eq_trans
% 5.13/5.46 thf(fact_85_ord__less__eq__trans,axiom,
% 5.13/5.46 ! [A: num,B: num,C: num] :
% 5.13/5.46 ( ( ord_less_num @ A @ B )
% 5.13/5.46 => ( ( B = C )
% 5.13/5.46 => ( ord_less_num @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_less_eq_trans
% 5.13/5.46 thf(fact_86_ord__less__eq__trans,axiom,
% 5.13/5.46 ! [A: nat,B: nat,C: nat] :
% 5.13/5.46 ( ( ord_less_nat @ A @ B )
% 5.13/5.46 => ( ( B = C )
% 5.13/5.46 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_less_eq_trans
% 5.13/5.46 thf(fact_87_ord__less__eq__trans,axiom,
% 5.13/5.46 ! [A: int,B: int,C: int] :
% 5.13/5.46 ( ( ord_less_int @ A @ B )
% 5.13/5.46 => ( ( B = C )
% 5.13/5.46 => ( ord_less_int @ A @ C ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % ord_less_eq_trans
% 5.13/5.46 thf(fact_88_less__induct,axiom,
% 5.13/5.46 ! [P: nat > $o,A: nat] :
% 5.13/5.46 ( ! [X3: nat] :
% 5.13/5.46 ( ! [Y5: nat] :
% 5.13/5.46 ( ( ord_less_nat @ Y5 @ X3 )
% 5.13/5.46 => ( P @ Y5 ) )
% 5.13/5.46 => ( P @ X3 ) )
% 5.13/5.46 => ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % less_induct
% 5.13/5.46 thf(fact_89_antisym__conv3,axiom,
% 5.13/5.46 ! [Y4: real,X: real] :
% 5.13/5.46 ( ~ ( ord_less_real @ Y4 @ X )
% 5.13/5.46 => ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.13/5.46 = ( X = Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % antisym_conv3
% 5.13/5.46 thf(fact_90_antisym__conv3,axiom,
% 5.13/5.46 ! [Y4: rat,X: rat] :
% 5.13/5.46 ( ~ ( ord_less_rat @ Y4 @ X )
% 5.13/5.46 => ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.13/5.46 = ( X = Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % antisym_conv3
% 5.13/5.46 thf(fact_91_antisym__conv3,axiom,
% 5.13/5.46 ! [Y4: num,X: num] :
% 5.13/5.46 ( ~ ( ord_less_num @ Y4 @ X )
% 5.13/5.46 => ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.13/5.46 = ( X = Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % antisym_conv3
% 5.13/5.46 thf(fact_92_antisym__conv3,axiom,
% 5.13/5.46 ! [Y4: nat,X: nat] :
% 5.13/5.46 ( ~ ( ord_less_nat @ Y4 @ X )
% 5.13/5.46 => ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.13/5.46 = ( X = Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % antisym_conv3
% 5.13/5.46 thf(fact_93_antisym__conv3,axiom,
% 5.13/5.46 ! [Y4: int,X: int] :
% 5.13/5.46 ( ~ ( ord_less_int @ Y4 @ X )
% 5.13/5.46 => ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.13/5.46 = ( X = Y4 ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % antisym_conv3
% 5.13/5.46 thf(fact_94_linorder__cases,axiom,
% 5.13/5.46 ! [X: real,Y4: real] :
% 5.13/5.46 ( ~ ( ord_less_real @ X @ Y4 )
% 5.13/5.46 => ( ( X != Y4 )
% 5.13/5.46 => ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % linorder_cases
% 5.13/5.46 thf(fact_95_linorder__cases,axiom,
% 5.13/5.46 ! [X: rat,Y4: rat] :
% 5.13/5.46 ( ~ ( ord_less_rat @ X @ Y4 )
% 5.13/5.46 => ( ( X != Y4 )
% 5.13/5.46 => ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % linorder_cases
% 5.13/5.46 thf(fact_96_linorder__cases,axiom,
% 5.13/5.46 ! [X: num,Y4: num] :
% 5.13/5.46 ( ~ ( ord_less_num @ X @ Y4 )
% 5.13/5.46 => ( ( X != Y4 )
% 5.13/5.46 => ( ord_less_num @ Y4 @ X ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % linorder_cases
% 5.13/5.46 thf(fact_97_linorder__cases,axiom,
% 5.13/5.46 ! [X: nat,Y4: nat] :
% 5.13/5.46 ( ~ ( ord_less_nat @ X @ Y4 )
% 5.13/5.46 => ( ( X != Y4 )
% 5.13/5.46 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % linorder_cases
% 5.13/5.46 thf(fact_98_linorder__cases,axiom,
% 5.13/5.46 ! [X: int,Y4: int] :
% 5.13/5.46 ( ~ ( ord_less_int @ X @ Y4 )
% 5.13/5.46 => ( ( X != Y4 )
% 5.13/5.46 => ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % linorder_cases
% 5.13/5.46 thf(fact_99_mem__Collect__eq,axiom,
% 5.13/5.46 ! [A: int,P: int > $o] :
% 5.13/5.46 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.13/5.46 = ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % mem_Collect_eq
% 5.13/5.46 thf(fact_100_mem__Collect__eq,axiom,
% 5.13/5.46 ! [A: nat,P: nat > $o] :
% 5.13/5.46 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.13/5.46 = ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % mem_Collect_eq
% 5.13/5.46 thf(fact_101_mem__Collect__eq,axiom,
% 5.13/5.46 ! [A: complex,P: complex > $o] :
% 5.13/5.46 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.13/5.46 = ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % mem_Collect_eq
% 5.13/5.46 thf(fact_102_mem__Collect__eq,axiom,
% 5.13/5.46 ! [A: real,P: real > $o] :
% 5.13/5.46 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.13/5.46 = ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % mem_Collect_eq
% 5.13/5.46 thf(fact_103_mem__Collect__eq,axiom,
% 5.13/5.46 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.13/5.46 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.13/5.46 = ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % mem_Collect_eq
% 5.13/5.46 thf(fact_104_mem__Collect__eq,axiom,
% 5.13/5.46 ! [A: list_nat,P: list_nat > $o] :
% 5.13/5.46 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.13/5.46 = ( P @ A ) ) ).
% 5.13/5.46
% 5.13/5.46 % mem_Collect_eq
% 5.13/5.46 thf(fact_105_Collect__mem__eq,axiom,
% 5.13/5.46 ! [A2: set_int] :
% 5.13/5.46 ( ( collect_int
% 5.13/5.46 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.13/5.46 = A2 ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_mem_eq
% 5.13/5.46 thf(fact_106_Collect__mem__eq,axiom,
% 5.13/5.46 ! [A2: set_nat] :
% 5.13/5.46 ( ( collect_nat
% 5.13/5.46 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.13/5.46 = A2 ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_mem_eq
% 5.13/5.46 thf(fact_107_Collect__mem__eq,axiom,
% 5.13/5.46 ! [A2: set_complex] :
% 5.13/5.46 ( ( collect_complex
% 5.13/5.46 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.13/5.46 = A2 ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_mem_eq
% 5.13/5.46 thf(fact_108_Collect__mem__eq,axiom,
% 5.13/5.46 ! [A2: set_real] :
% 5.13/5.46 ( ( collect_real
% 5.13/5.46 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.13/5.46 = A2 ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_mem_eq
% 5.13/5.46 thf(fact_109_Collect__mem__eq,axiom,
% 5.13/5.46 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.13/5.46 ( ( collec3392354462482085612at_nat
% 5.13/5.46 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 5.13/5.46 = A2 ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_mem_eq
% 5.13/5.46 thf(fact_110_Collect__mem__eq,axiom,
% 5.13/5.46 ! [A2: set_list_nat] :
% 5.13/5.46 ( ( collect_list_nat
% 5.13/5.46 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 5.13/5.46 = A2 ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_mem_eq
% 5.13/5.46 thf(fact_111_Collect__cong,axiom,
% 5.13/5.46 ! [P: nat > $o,Q: nat > $o] :
% 5.13/5.46 ( ! [X3: nat] :
% 5.13/5.46 ( ( P @ X3 )
% 5.13/5.46 = ( Q @ X3 ) )
% 5.13/5.46 => ( ( collect_nat @ P )
% 5.13/5.46 = ( collect_nat @ Q ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_cong
% 5.13/5.46 thf(fact_112_Collect__cong,axiom,
% 5.13/5.46 ! [P: complex > $o,Q: complex > $o] :
% 5.13/5.46 ( ! [X3: complex] :
% 5.13/5.46 ( ( P @ X3 )
% 5.13/5.46 = ( Q @ X3 ) )
% 5.13/5.46 => ( ( collect_complex @ P )
% 5.13/5.46 = ( collect_complex @ Q ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_cong
% 5.13/5.46 thf(fact_113_Collect__cong,axiom,
% 5.13/5.46 ! [P: real > $o,Q: real > $o] :
% 5.13/5.46 ( ! [X3: real] :
% 5.13/5.46 ( ( P @ X3 )
% 5.13/5.46 = ( Q @ X3 ) )
% 5.13/5.46 => ( ( collect_real @ P )
% 5.13/5.46 = ( collect_real @ Q ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_cong
% 5.13/5.46 thf(fact_114_Collect__cong,axiom,
% 5.13/5.46 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.13/5.46 ( ! [X3: product_prod_nat_nat] :
% 5.13/5.46 ( ( P @ X3 )
% 5.13/5.46 = ( Q @ X3 ) )
% 5.13/5.46 => ( ( collec3392354462482085612at_nat @ P )
% 5.13/5.46 = ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_cong
% 5.13/5.46 thf(fact_115_Collect__cong,axiom,
% 5.13/5.46 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.13/5.46 ( ! [X3: list_nat] :
% 5.13/5.46 ( ( P @ X3 )
% 5.13/5.46 = ( Q @ X3 ) )
% 5.13/5.46 => ( ( collect_list_nat @ P )
% 5.13/5.46 = ( collect_list_nat @ Q ) ) ) ).
% 5.13/5.46
% 5.13/5.46 % Collect_cong
% 5.13/5.46 thf(fact_116_dual__order_Oasym,axiom,
% 5.13/5.46 ! [B: real,A: real] :
% 5.13/5.46 ( ( ord_less_real @ B @ A )
% 5.13/5.46 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.asym
% 5.13/5.46 thf(fact_117_dual__order_Oasym,axiom,
% 5.13/5.46 ! [B: rat,A: rat] :
% 5.13/5.46 ( ( ord_less_rat @ B @ A )
% 5.13/5.46 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.asym
% 5.13/5.46 thf(fact_118_dual__order_Oasym,axiom,
% 5.13/5.46 ! [B: num,A: num] :
% 5.13/5.46 ( ( ord_less_num @ B @ A )
% 5.13/5.46 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.asym
% 5.13/5.46 thf(fact_119_dual__order_Oasym,axiom,
% 5.13/5.46 ! [B: nat,A: nat] :
% 5.13/5.46 ( ( ord_less_nat @ B @ A )
% 5.13/5.46 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.13/5.46
% 5.13/5.46 % dual_order.asym
% 5.13/5.46 thf(fact_120_dual__order_Oasym,axiom,
% 5.13/5.47 ! [B: int,A: int] :
% 5.13/5.47 ( ( ord_less_int @ B @ A )
% 5.13/5.47 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.asym
% 5.13/5.47 thf(fact_121_dual__order_Oirrefl,axiom,
% 5.13/5.47 ! [A: real] :
% 5.13/5.47 ~ ( ord_less_real @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.irrefl
% 5.13/5.47 thf(fact_122_dual__order_Oirrefl,axiom,
% 5.13/5.47 ! [A: rat] :
% 5.13/5.47 ~ ( ord_less_rat @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.irrefl
% 5.13/5.47 thf(fact_123_dual__order_Oirrefl,axiom,
% 5.13/5.47 ! [A: num] :
% 5.13/5.47 ~ ( ord_less_num @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.irrefl
% 5.13/5.47 thf(fact_124_dual__order_Oirrefl,axiom,
% 5.13/5.47 ! [A: nat] :
% 5.13/5.47 ~ ( ord_less_nat @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.irrefl
% 5.13/5.47 thf(fact_125_dual__order_Oirrefl,axiom,
% 5.13/5.47 ! [A: int] :
% 5.13/5.47 ~ ( ord_less_int @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.irrefl
% 5.13/5.47 thf(fact_126_exists__least__iff,axiom,
% 5.13/5.47 ( ( ^ [P2: nat > $o] :
% 5.13/5.47 ? [X4: nat] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: nat > $o] :
% 5.13/5.47 ? [N2: nat] :
% 5.13/5.47 ( ( P3 @ N2 )
% 5.13/5.47 & ! [M2: nat] :
% 5.13/5.47 ( ( ord_less_nat @ M2 @ N2 )
% 5.13/5.47 => ~ ( P3 @ M2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % exists_least_iff
% 5.13/5.47 thf(fact_127_linorder__less__wlog,axiom,
% 5.13/5.47 ! [P: real > real > $o,A: real,B: real] :
% 5.13/5.47 ( ! [A3: real,B2: real] :
% 5.13/5.47 ( ( ord_less_real @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: real] : ( P @ A3 @ A3 )
% 5.13/5.47 => ( ! [A3: real,B2: real] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_wlog
% 5.13/5.47 thf(fact_128_linorder__less__wlog,axiom,
% 5.13/5.47 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.13/5.47 ( ! [A3: rat,B2: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 5.13/5.47 => ( ! [A3: rat,B2: rat] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_wlog
% 5.13/5.47 thf(fact_129_linorder__less__wlog,axiom,
% 5.13/5.47 ! [P: num > num > $o,A: num,B: num] :
% 5.13/5.47 ( ! [A3: num,B2: num] :
% 5.13/5.47 ( ( ord_less_num @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: num] : ( P @ A3 @ A3 )
% 5.13/5.47 => ( ! [A3: num,B2: num] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_wlog
% 5.13/5.47 thf(fact_130_linorder__less__wlog,axiom,
% 5.13/5.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.13/5.47 ( ! [A3: nat,B2: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 5.13/5.47 => ( ! [A3: nat,B2: nat] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_wlog
% 5.13/5.47 thf(fact_131_linorder__less__wlog,axiom,
% 5.13/5.47 ! [P: int > int > $o,A: int,B: int] :
% 5.13/5.47 ( ! [A3: int,B2: int] :
% 5.13/5.47 ( ( ord_less_int @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: int] : ( P @ A3 @ A3 )
% 5.13/5.47 => ( ! [A3: int,B2: int] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_wlog
% 5.13/5.47 thf(fact_132_order_Ostrict__trans,axiom,
% 5.13/5.47 ! [A: real,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ord_less_real @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans
% 5.13/5.47 thf(fact_133_order_Ostrict__trans,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans
% 5.13/5.47 thf(fact_134_order_Ostrict__trans,axiom,
% 5.13/5.47 ! [A: num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_num @ B @ C )
% 5.13/5.47 => ( ord_less_num @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans
% 5.13/5.47 thf(fact_135_order_Ostrict__trans,axiom,
% 5.13/5.47 ! [A: nat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_nat @ B @ C )
% 5.13/5.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans
% 5.13/5.47 thf(fact_136_order_Ostrict__trans,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_int @ B @ C )
% 5.13/5.47 => ( ord_less_int @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans
% 5.13/5.47 thf(fact_137_not__less__iff__gr__or__eq,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.13/5.47 = ( ( ord_less_real @ Y4 @ X )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_less_iff_gr_or_eq
% 5.13/5.47 thf(fact_138_not__less__iff__gr__or__eq,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.13/5.47 = ( ( ord_less_rat @ Y4 @ X )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_less_iff_gr_or_eq
% 5.13/5.47 thf(fact_139_not__less__iff__gr__or__eq,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.13/5.47 = ( ( ord_less_num @ Y4 @ X )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_less_iff_gr_or_eq
% 5.13/5.47 thf(fact_140_not__less__iff__gr__or__eq,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.13/5.47 = ( ( ord_less_nat @ Y4 @ X )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_less_iff_gr_or_eq
% 5.13/5.47 thf(fact_141_not__less__iff__gr__or__eq,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.13/5.47 = ( ( ord_less_int @ Y4 @ X )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_less_iff_gr_or_eq
% 5.13/5.47 thf(fact_142_dual__order_Ostrict__trans,axiom,
% 5.13/5.47 ! [B: real,A: real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ B @ A )
% 5.13/5.47 => ( ( ord_less_real @ C @ B )
% 5.13/5.47 => ( ord_less_real @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans
% 5.13/5.47 thf(fact_143_dual__order_Ostrict__trans,axiom,
% 5.13/5.47 ! [B: rat,A: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ B @ A )
% 5.13/5.47 => ( ( ord_less_rat @ C @ B )
% 5.13/5.47 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans
% 5.13/5.47 thf(fact_144_dual__order_Ostrict__trans,axiom,
% 5.13/5.47 ! [B: num,A: num,C: num] :
% 5.13/5.47 ( ( ord_less_num @ B @ A )
% 5.13/5.47 => ( ( ord_less_num @ C @ B )
% 5.13/5.47 => ( ord_less_num @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans
% 5.13/5.47 thf(fact_145_dual__order_Ostrict__trans,axiom,
% 5.13/5.47 ! [B: nat,A: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_nat @ C @ B )
% 5.13/5.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans
% 5.13/5.47 thf(fact_146_dual__order_Ostrict__trans,axiom,
% 5.13/5.47 ! [B: int,A: int,C: int] :
% 5.13/5.47 ( ( ord_less_int @ B @ A )
% 5.13/5.47 => ( ( ord_less_int @ C @ B )
% 5.13/5.47 => ( ord_less_int @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans
% 5.13/5.47 thf(fact_147_order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [A: real,B: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_not_eq
% 5.13/5.47 thf(fact_148_order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_not_eq
% 5.13/5.47 thf(fact_149_order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_not_eq
% 5.13/5.47 thf(fact_150_order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_not_eq
% 5.13/5.47 thf(fact_151_order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_not_eq
% 5.13/5.47 thf(fact_152_dual__order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [B: real,A: real] :
% 5.13/5.47 ( ( ord_less_real @ B @ A )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_not_eq
% 5.13/5.47 thf(fact_153_dual__order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [B: rat,A: rat] :
% 5.13/5.47 ( ( ord_less_rat @ B @ A )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_not_eq
% 5.13/5.47 thf(fact_154_dual__order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [B: num,A: num] :
% 5.13/5.47 ( ( ord_less_num @ B @ A )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_not_eq
% 5.13/5.47 thf(fact_155_dual__order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [B: nat,A: nat] :
% 5.13/5.47 ( ( ord_less_nat @ B @ A )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_not_eq
% 5.13/5.47 thf(fact_156_dual__order_Ostrict__implies__not__eq,axiom,
% 5.13/5.47 ! [B: int,A: int] :
% 5.13/5.47 ( ( ord_less_int @ B @ A )
% 5.13/5.47 => ( A != B ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_not_eq
% 5.13/5.47 thf(fact_157_linorder__neqE,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 => ( ~ ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neqE
% 5.13/5.47 thf(fact_158_linorder__neqE,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 => ( ~ ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neqE
% 5.13/5.47 thf(fact_159_linorder__neqE,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 => ( ~ ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ord_less_num @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neqE
% 5.13/5.47 thf(fact_160_linorder__neqE,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 => ( ~ ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neqE
% 5.13/5.47 thf(fact_161_linorder__neqE,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 => ( ~ ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neqE
% 5.13/5.47 thf(fact_162_order__less__asym,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym
% 5.13/5.47 thf(fact_163_order__less__asym,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym
% 5.13/5.47 thf(fact_164_order__less__asym,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym
% 5.13/5.47 thf(fact_165_order__less__asym,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym
% 5.13/5.47 thf(fact_166_order__less__asym,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym
% 5.13/5.47 thf(fact_167_linorder__neq__iff,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 = ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 | ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neq_iff
% 5.13/5.47 thf(fact_168_linorder__neq__iff,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 = ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 | ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neq_iff
% 5.13/5.47 thf(fact_169_linorder__neq__iff,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 = ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 | ( ord_less_num @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neq_iff
% 5.13/5.47 thf(fact_170_linorder__neq__iff,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 = ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 | ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neq_iff
% 5.13/5.47 thf(fact_171_linorder__neq__iff,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( X != Y4 )
% 5.13/5.47 = ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 | ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_neq_iff
% 5.13/5.47 thf(fact_172_order__less__asym_H,axiom,
% 5.13/5.47 ! [A: real,B: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym'
% 5.13/5.47 thf(fact_173_order__less__asym_H,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym'
% 5.13/5.47 thf(fact_174_order__less__asym_H,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym'
% 5.13/5.47 thf(fact_175_order__less__asym_H,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym'
% 5.13/5.47 thf(fact_176_order__less__asym_H,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_asym'
% 5.13/5.47 thf(fact_177_order__less__trans,axiom,
% 5.13/5.47 ! [X: real,Y4: real,Z2: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_real @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_real @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_trans
% 5.13/5.47 thf(fact_178_order__less__trans,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,Z2: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_rat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_rat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_trans
% 5.13/5.47 thf(fact_179_order__less__trans,axiom,
% 5.13/5.47 ! [X: num,Y4: num,Z2: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_num @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_num @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_trans
% 5.13/5.47 thf(fact_180_order__less__trans,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_trans
% 5.13/5.47 thf(fact_181_order__less__trans,axiom,
% 5.13/5.47 ! [X: int,Y4: int,Z2: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_int @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_trans
% 5.13/5.47 thf(fact_182_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: real,F: real > real,B: real,C: real] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_183_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_184_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: num,F: real > num,B: real,C: real] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_185_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_186_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: int,F: real > int,B: real,C: real] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_187_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_188_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_189_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_190_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_191_ord__eq__less__subst,axiom,
% 5.13/5.47 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_less_subst
% 5.13/5.47 thf(fact_192_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_193_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_194_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > num,C: num] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_195_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_196_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > int,C: int] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_197_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_198_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_199_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_200_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_201_ord__less__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_less_eq_subst
% 5.13/5.47 thf(fact_202_order__less__irrefl,axiom,
% 5.13/5.47 ! [X: real] :
% 5.13/5.47 ~ ( ord_less_real @ X @ X ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_irrefl
% 5.13/5.47 thf(fact_203_order__less__irrefl,axiom,
% 5.13/5.47 ! [X: rat] :
% 5.13/5.47 ~ ( ord_less_rat @ X @ X ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_irrefl
% 5.13/5.47 thf(fact_204_order__less__irrefl,axiom,
% 5.13/5.47 ! [X: num] :
% 5.13/5.47 ~ ( ord_less_num @ X @ X ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_irrefl
% 5.13/5.47 thf(fact_205_order__less__irrefl,axiom,
% 5.13/5.47 ! [X: nat] :
% 5.13/5.47 ~ ( ord_less_nat @ X @ X ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_irrefl
% 5.13/5.47 thf(fact_206_order__less__irrefl,axiom,
% 5.13/5.47 ! [X: int] :
% 5.13/5.47 ~ ( ord_less_int @ X @ X ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_irrefl
% 5.13/5.47 thf(fact_207_order__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: real > real,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_208_order__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_209_order__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: num > real,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_210_order__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_211_order__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: int > real,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_int @ B @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_212_order__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_213_order__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_214_order__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_215_order__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_216_order__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_int @ B @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst1
% 5.13/5.47 thf(fact_217_order__less__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_218_order__less__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_219_order__less__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > num,C: num] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_220_order__less__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_221_order__less__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > int,C: int] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_222_order__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_223_order__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_224_order__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_225_order__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_226_order__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_subst2
% 5.13/5.47 thf(fact_227_order__less__not__sym,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_not_sym
% 5.13/5.47 thf(fact_228_order__less__not__sym,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_not_sym
% 5.13/5.47 thf(fact_229_order__less__not__sym,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_not_sym
% 5.13/5.47 thf(fact_230_order__less__not__sym,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_not_sym
% 5.13/5.47 thf(fact_231_order__less__not__sym,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_not_sym
% 5.13/5.47 thf(fact_232_order__less__imp__triv,axiom,
% 5.13/5.47 ! [X: real,Y4: real,P: $o] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_real @ Y4 @ X )
% 5.13/5.47 => P ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_triv
% 5.13/5.47 thf(fact_233_order__less__imp__triv,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,P: $o] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_rat @ Y4 @ X )
% 5.13/5.47 => P ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_triv
% 5.13/5.47 thf(fact_234_order__less__imp__triv,axiom,
% 5.13/5.47 ! [X: num,Y4: num,P: $o] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_num @ Y4 @ X )
% 5.13/5.47 => P ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_triv
% 5.13/5.47 thf(fact_235_order__less__imp__triv,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,P: $o] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_nat @ Y4 @ X )
% 5.13/5.47 => P ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_triv
% 5.13/5.47 thf(fact_236_order__less__imp__triv,axiom,
% 5.13/5.47 ! [X: int,Y4: int,P: $o] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_int @ Y4 @ X )
% 5.13/5.47 => P ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_triv
% 5.13/5.47 thf(fact_237_linorder__less__linear,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 )
% 5.13/5.47 | ( ord_less_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_linear
% 5.13/5.47 thf(fact_238_linorder__less__linear,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 )
% 5.13/5.47 | ( ord_less_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_linear
% 5.13/5.47 thf(fact_239_linorder__less__linear,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 )
% 5.13/5.47 | ( ord_less_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_linear
% 5.13/5.47 thf(fact_240_linorder__less__linear,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 )
% 5.13/5.47 | ( ord_less_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_linear
% 5.13/5.47 thf(fact_241_linorder__less__linear,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 )
% 5.13/5.47 | ( ord_less_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_less_linear
% 5.13/5.47 thf(fact_242_order__less__imp__not__eq,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( X != Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq
% 5.13/5.47 thf(fact_243_order__less__imp__not__eq,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( X != Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq
% 5.13/5.47 thf(fact_244_order__less__imp__not__eq,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( X != Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq
% 5.13/5.47 thf(fact_245_order__less__imp__not__eq,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( X != Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq
% 5.13/5.47 thf(fact_246_order__less__imp__not__eq,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( X != Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq
% 5.13/5.47 thf(fact_247_order__less__imp__not__eq2,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( Y4 != X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq2
% 5.13/5.47 thf(fact_248_order__less__imp__not__eq2,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( Y4 != X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq2
% 5.13/5.47 thf(fact_249_order__less__imp__not__eq2,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( Y4 != X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq2
% 5.13/5.47 thf(fact_250_order__less__imp__not__eq2,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( Y4 != X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq2
% 5.13/5.47 thf(fact_251_order__less__imp__not__eq2,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( Y4 != X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_eq2
% 5.13/5.47 thf(fact_252_order__less__imp__not__less,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_less
% 5.13/5.47 thf(fact_253_order__less__imp__not__less,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_less
% 5.13/5.47 thf(fact_254_order__less__imp__not__less,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_less
% 5.13/5.47 thf(fact_255_order__less__imp__not__less,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_less
% 5.13/5.47 thf(fact_256_order__less__imp__not__less,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_not_less
% 5.13/5.47 thf(fact_257_order__le__imp__less__or__eq,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_imp_less_or_eq
% 5.13/5.47 thf(fact_258_order__le__imp__less__or__eq,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_set_nat @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_imp_less_or_eq
% 5.13/5.47 thf(fact_259_order__le__imp__less__or__eq,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_imp_less_or_eq
% 5.13/5.47 thf(fact_260_order__le__imp__less__or__eq,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_imp_less_or_eq
% 5.13/5.47 thf(fact_261_order__le__imp__less__or__eq,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_imp_less_or_eq
% 5.13/5.47 thf(fact_262_order__le__imp__less__or__eq,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_imp_less_or_eq
% 5.13/5.47 thf(fact_263_linorder__le__less__linear,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.47 | ( ord_less_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_less_linear
% 5.13/5.47 thf(fact_264_linorder__le__less__linear,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 | ( ord_less_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_less_linear
% 5.13/5.47 thf(fact_265_linorder__le__less__linear,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 | ( ord_less_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_less_linear
% 5.13/5.47 thf(fact_266_linorder__le__less__linear,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 | ( ord_less_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_less_linear
% 5.13/5.47 thf(fact_267_linorder__le__less__linear,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 | ( ord_less_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_less_linear
% 5.13/5.47 thf(fact_268_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_269_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_270_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > real,C: real] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_271_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_272_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: int,B: int,F: int > real,C: real] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_273_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_274_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_275_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_276_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_277_order__less__le__subst2,axiom,
% 5.13/5.47 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst2
% 5.13/5.47 thf(fact_278_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_279_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_280_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_281_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_282_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_283_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: real,F: num > real,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_284_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_285_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: num,F: num > num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_286_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_287_order__less__le__subst1,axiom,
% 5.13/5.47 ! [A: int,F: num > int,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_subst1
% 5.13/5.47 thf(fact_288_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_289_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_290_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_291_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_292_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_293_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > real,C: real] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_294_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_295_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_296_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_297_order__le__less__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst2
% 5.13/5.47 thf(fact_298_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: real > real,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_299_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_300_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: num > real,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_301_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_302_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: real,F: int > real,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_int @ B @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_303_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ! [X3: real,Y3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_304_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_305_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_306_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_307_order__le__less__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_int @ B @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_subst1
% 5.13/5.47 thf(fact_308_order__less__le__trans,axiom,
% 5.13/5.47 ! [X: real,Y4: real,Z2: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_real @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_real @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_trans
% 5.13/5.47 thf(fact_309_order__less__le__trans,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat,Z2: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_set_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_trans
% 5.13/5.47 thf(fact_310_order__less__le__trans,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,Z2: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_rat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_rat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_trans
% 5.13/5.47 thf(fact_311_order__less__le__trans,axiom,
% 5.13/5.47 ! [X: num,Y4: num,Z2: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_num @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_num @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_trans
% 5.13/5.47 thf(fact_312_order__less__le__trans,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_trans
% 5.13/5.47 thf(fact_313_order__less__le__trans,axiom,
% 5.13/5.47 ! [X: int,Y4: int,Z2: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_int @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le_trans
% 5.13/5.47 thf(fact_314_order__le__less__trans,axiom,
% 5.13/5.47 ! [X: real,Y4: real,Z2: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_real @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_real @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_trans
% 5.13/5.47 thf(fact_315_order__le__less__trans,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat,Z2: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_set_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_set_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_trans
% 5.13/5.47 thf(fact_316_order__le__less__trans,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,Z2: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_rat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_rat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_trans
% 5.13/5.47 thf(fact_317_order__le__less__trans,axiom,
% 5.13/5.47 ! [X: num,Y4: num,Z2: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_num @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_num @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_trans
% 5.13/5.47 thf(fact_318_order__le__less__trans,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_trans
% 5.13/5.47 thf(fact_319_order__le__less__trans,axiom,
% 5.13/5.47 ! [X: int,Y4: int,Z2: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_int @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less_trans
% 5.13/5.47 thf(fact_320_order__neq__le__trans,axiom,
% 5.13/5.47 ! [A: real,B: real] :
% 5.13/5.47 ( ( A != B )
% 5.13/5.47 => ( ( ord_less_eq_real @ A @ B )
% 5.13/5.47 => ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_neq_le_trans
% 5.13/5.47 thf(fact_321_order__neq__le__trans,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat] :
% 5.13/5.47 ( ( A != B )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_neq_le_trans
% 5.13/5.47 thf(fact_322_order__neq__le__trans,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( A != B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_neq_le_trans
% 5.13/5.47 thf(fact_323_order__neq__le__trans,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( A != B )
% 5.13/5.47 => ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ord_less_num @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_neq_le_trans
% 5.13/5.47 thf(fact_324_order__neq__le__trans,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( A != B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_neq_le_trans
% 5.13/5.47 thf(fact_325_order__neq__le__trans,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( A != B )
% 5.13/5.47 => ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( ord_less_int @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_neq_le_trans
% 5.13/5.47 thf(fact_326_order__le__neq__trans,axiom,
% 5.13/5.47 ! [A: real,B: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.47 => ( ( A != B )
% 5.13/5.47 => ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_neq_trans
% 5.13/5.47 thf(fact_327_order__le__neq__trans,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( ( A != B )
% 5.13/5.47 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_neq_trans
% 5.13/5.47 thf(fact_328_order__le__neq__trans,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( A != B )
% 5.13/5.47 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_neq_trans
% 5.13/5.47 thf(fact_329_order__le__neq__trans,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( A != B )
% 5.13/5.47 => ( ord_less_num @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_neq_trans
% 5.13/5.47 thf(fact_330_order__le__neq__trans,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( A != B )
% 5.13/5.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_neq_trans
% 5.13/5.47 thf(fact_331_order__le__neq__trans,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( ( A != B )
% 5.13/5.47 => ( ord_less_int @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_neq_trans
% 5.13/5.47 thf(fact_332_order__less__imp__le,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_le
% 5.13/5.47 thf(fact_333_order__less__imp__le,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_set_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_le
% 5.13/5.47 thf(fact_334_order__less__imp__le,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_le
% 5.13/5.47 thf(fact_335_order__less__imp__le,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_num @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_le
% 5.13/5.47 thf(fact_336_order__less__imp__le,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_le
% 5.13/5.47 thf(fact_337_order__less__imp__le,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_int @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_imp_le
% 5.13/5.47 thf(fact_338_linorder__not__less,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_eq_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_less
% 5.13/5.47 thf(fact_339_linorder__not__less,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_less
% 5.13/5.47 thf(fact_340_linorder__not__less,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_less
% 5.13/5.47 thf(fact_341_linorder__not__less,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_less
% 5.13/5.47 thf(fact_342_linorder__not__less,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_less
% 5.13/5.47 thf(fact_343_linorder__not__le,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_real @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_le
% 5.13/5.47 thf(fact_344_linorder__not__le,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_rat @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_le
% 5.13/5.47 thf(fact_345_linorder__not__le,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_num @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_le
% 5.13/5.47 thf(fact_346_linorder__not__le,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_nat @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_le
% 5.13/5.47 thf(fact_347_linorder__not__le,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_int @ X @ Y4 ) )
% 5.13/5.47 = ( ord_less_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_not_le
% 5.13/5.47 thf(fact_348_order__less__le,axiom,
% 5.13/5.47 ( ord_less_real
% 5.13/5.47 = ( ^ [X2: real,Y: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ X2 @ Y )
% 5.13/5.47 & ( X2 != Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le
% 5.13/5.47 thf(fact_349_order__less__le,axiom,
% 5.13/5.47 ( ord_less_set_nat
% 5.13/5.47 = ( ^ [X2: set_nat,Y: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.13/5.47 & ( X2 != Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le
% 5.13/5.47 thf(fact_350_order__less__le,axiom,
% 5.13/5.47 ( ord_less_rat
% 5.13/5.47 = ( ^ [X2: rat,Y: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.13/5.47 & ( X2 != Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le
% 5.13/5.47 thf(fact_351_order__less__le,axiom,
% 5.13/5.47 ( ord_less_num
% 5.13/5.47 = ( ^ [X2: num,Y: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X2 @ Y )
% 5.13/5.47 & ( X2 != Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le
% 5.13/5.47 thf(fact_352_order__less__le,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [X2: nat,Y: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.13/5.47 & ( X2 != Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le
% 5.13/5.47 thf(fact_353_order__less__le,axiom,
% 5.13/5.47 ( ord_less_int
% 5.13/5.47 = ( ^ [X2: int,Y: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X2 @ Y )
% 5.13/5.47 & ( X2 != Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_less_le
% 5.13/5.47 thf(fact_354_order__le__less,axiom,
% 5.13/5.47 ( ord_less_eq_real
% 5.13/5.47 = ( ^ [X2: real,Y: real] :
% 5.13/5.47 ( ( ord_less_real @ X2 @ Y )
% 5.13/5.47 | ( X2 = Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less
% 5.13/5.47 thf(fact_355_order__le__less,axiom,
% 5.13/5.47 ( ord_less_eq_set_nat
% 5.13/5.47 = ( ^ [X2: set_nat,Y: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ X2 @ Y )
% 5.13/5.47 | ( X2 = Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less
% 5.13/5.47 thf(fact_356_order__le__less,axiom,
% 5.13/5.47 ( ord_less_eq_rat
% 5.13/5.47 = ( ^ [X2: rat,Y: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X2 @ Y )
% 5.13/5.47 | ( X2 = Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less
% 5.13/5.47 thf(fact_357_order__le__less,axiom,
% 5.13/5.47 ( ord_less_eq_num
% 5.13/5.47 = ( ^ [X2: num,Y: num] :
% 5.13/5.47 ( ( ord_less_num @ X2 @ Y )
% 5.13/5.47 | ( X2 = Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less
% 5.13/5.47 thf(fact_358_order__le__less,axiom,
% 5.13/5.47 ( ord_less_eq_nat
% 5.13/5.47 = ( ^ [X2: nat,Y: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X2 @ Y )
% 5.13/5.47 | ( X2 = Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less
% 5.13/5.47 thf(fact_359_order__le__less,axiom,
% 5.13/5.47 ( ord_less_eq_int
% 5.13/5.47 = ( ^ [X2: int,Y: int] :
% 5.13/5.47 ( ( ord_less_int @ X2 @ Y )
% 5.13/5.47 | ( X2 = Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_le_less
% 5.13/5.47 thf(fact_360_dual__order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [B: real,A: real] :
% 5.13/5.47 ( ( ord_less_real @ B @ A )
% 5.13/5.47 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_order
% 5.13/5.47 thf(fact_361_dual__order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [B: set_nat,A: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ B @ A )
% 5.13/5.47 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_order
% 5.13/5.47 thf(fact_362_dual__order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [B: rat,A: rat] :
% 5.13/5.47 ( ( ord_less_rat @ B @ A )
% 5.13/5.47 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_order
% 5.13/5.47 thf(fact_363_dual__order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [B: num,A: num] :
% 5.13/5.47 ( ( ord_less_num @ B @ A )
% 5.13/5.47 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_order
% 5.13/5.47 thf(fact_364_dual__order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [B: nat,A: nat] :
% 5.13/5.47 ( ( ord_less_nat @ B @ A )
% 5.13/5.47 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_order
% 5.13/5.47 thf(fact_365_dual__order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [B: int,A: int] :
% 5.13/5.47 ( ( ord_less_int @ B @ A )
% 5.13/5.47 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_implies_order
% 5.13/5.47 thf(fact_366_order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [A: real,B: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_order
% 5.13/5.47 thf(fact_367_order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ A @ B )
% 5.13/5.47 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_order
% 5.13/5.47 thf(fact_368_order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_order
% 5.13/5.47 thf(fact_369_order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_order
% 5.13/5.47 thf(fact_370_order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_order
% 5.13/5.47 thf(fact_371_order_Ostrict__implies__order,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_implies_order
% 5.13/5.47 thf(fact_372_dual__order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_real
% 5.13/5.47 = ( ^ [B3: real,A4: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.13/5.47 & ~ ( ord_less_eq_real @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_not
% 5.13/5.47 thf(fact_373_dual__order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_set_nat
% 5.13/5.47 = ( ^ [B3: set_nat,A4: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 5.13/5.47 & ~ ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_not
% 5.13/5.47 thf(fact_374_dual__order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_rat
% 5.13/5.47 = ( ^ [B3: rat,A4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.13/5.47 & ~ ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_not
% 5.13/5.47 thf(fact_375_dual__order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_num
% 5.13/5.47 = ( ^ [B3: num,A4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.13/5.47 & ~ ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_not
% 5.13/5.47 thf(fact_376_dual__order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [B3: nat,A4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.13/5.47 & ~ ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_not
% 5.13/5.47 thf(fact_377_dual__order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_int
% 5.13/5.47 = ( ^ [B3: int,A4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.13/5.47 & ~ ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_not
% 5.13/5.47 thf(fact_378_dual__order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [B: real,A: real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_real @ C @ B )
% 5.13/5.47 => ( ord_less_real @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans2
% 5.13/5.47 thf(fact_379_dual__order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.13/5.47 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans2
% 5.13/5.47 thf(fact_380_dual__order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [B: rat,A: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_rat @ C @ B )
% 5.13/5.47 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans2
% 5.13/5.47 thf(fact_381_dual__order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [B: num,A: num,C: num] :
% 5.13/5.47 ( ( ord_less_num @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_num @ C @ B )
% 5.13/5.47 => ( ord_less_num @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans2
% 5.13/5.47 thf(fact_382_dual__order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [B: nat,A: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_nat @ C @ B )
% 5.13/5.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans2
% 5.13/5.47 thf(fact_383_dual__order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [B: int,A: int,C: int] :
% 5.13/5.47 ( ( ord_less_int @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_int @ C @ B )
% 5.13/5.47 => ( ord_less_int @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans2
% 5.13/5.47 thf(fact_384_dual__order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [B: real,A: real,C: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.47 => ( ( ord_less_real @ C @ B )
% 5.13/5.47 => ( ord_less_real @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans1
% 5.13/5.47 thf(fact_385_dual__order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_set_nat @ C @ B )
% 5.13/5.47 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans1
% 5.13/5.47 thf(fact_386_dual__order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [B: rat,A: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.47 => ( ( ord_less_rat @ C @ B )
% 5.13/5.47 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans1
% 5.13/5.47 thf(fact_387_dual__order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [B: num,A: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.13/5.47 => ( ( ord_less_num @ C @ B )
% 5.13/5.47 => ( ord_less_num @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans1
% 5.13/5.47 thf(fact_388_dual__order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [B: nat,A: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_nat @ C @ B )
% 5.13/5.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans1
% 5.13/5.47 thf(fact_389_dual__order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [B: int,A: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.47 => ( ( ord_less_int @ C @ B )
% 5.13/5.47 => ( ord_less_int @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_trans1
% 5.13/5.47 thf(fact_390_dual__order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_real
% 5.13/5.47 = ( ^ [B3: real,A4: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_order
% 5.13/5.47 thf(fact_391_dual__order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_set_nat
% 5.13/5.47 = ( ^ [B3: set_nat,A4: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_order
% 5.13/5.47 thf(fact_392_dual__order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_rat
% 5.13/5.47 = ( ^ [B3: rat,A4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_order
% 5.13/5.47 thf(fact_393_dual__order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_num
% 5.13/5.47 = ( ^ [B3: num,A4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_order
% 5.13/5.47 thf(fact_394_dual__order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [B3: nat,A4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_order
% 5.13/5.47 thf(fact_395_dual__order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_int
% 5.13/5.47 = ( ^ [B3: int,A4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.strict_iff_order
% 5.13/5.47 thf(fact_396_dual__order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_real
% 5.13/5.47 = ( ^ [B3: real,A4: real] :
% 5.13/5.47 ( ( ord_less_real @ B3 @ A4 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.order_iff_strict
% 5.13/5.47 thf(fact_397_dual__order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_set_nat
% 5.13/5.47 = ( ^ [B3: set_nat,A4: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ B3 @ A4 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.order_iff_strict
% 5.13/5.47 thf(fact_398_dual__order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_rat
% 5.13/5.47 = ( ^ [B3: rat,A4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ B3 @ A4 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.order_iff_strict
% 5.13/5.47 thf(fact_399_dual__order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_num
% 5.13/5.47 = ( ^ [B3: num,A4: num] :
% 5.13/5.47 ( ( ord_less_num @ B3 @ A4 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.order_iff_strict
% 5.13/5.47 thf(fact_400_dual__order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_nat
% 5.13/5.47 = ( ^ [B3: nat,A4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ B3 @ A4 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.order_iff_strict
% 5.13/5.47 thf(fact_401_dual__order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_int
% 5.13/5.47 = ( ^ [B3: int,A4: int] :
% 5.13/5.47 ( ( ord_less_int @ B3 @ A4 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.order_iff_strict
% 5.13/5.47 thf(fact_402_dense__le__bounded,axiom,
% 5.13/5.47 ! [X: real,Y4: real,Z2: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ! [W: real] :
% 5.13/5.47 ( ( ord_less_real @ X @ W )
% 5.13/5.47 => ( ( ord_less_real @ W @ Y4 )
% 5.13/5.47 => ( ord_less_eq_real @ W @ Z2 ) ) )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_le_bounded
% 5.13/5.47 thf(fact_403_dense__le__bounded,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,Z2: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ! [W: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X @ W )
% 5.13/5.47 => ( ( ord_less_rat @ W @ Y4 )
% 5.13/5.47 => ( ord_less_eq_rat @ W @ Z2 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_le_bounded
% 5.13/5.47 thf(fact_404_dense__ge__bounded,axiom,
% 5.13/5.47 ! [Z2: real,X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.13/5.47 => ( ! [W: real] :
% 5.13/5.47 ( ( ord_less_real @ Z2 @ W )
% 5.13/5.47 => ( ( ord_less_real @ W @ X )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ W ) ) )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_ge_bounded
% 5.13/5.47 thf(fact_405_dense__ge__bounded,axiom,
% 5.13/5.47 ! [Z2: rat,X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.13/5.47 => ( ! [W: rat] :
% 5.13/5.47 ( ( ord_less_rat @ Z2 @ W )
% 5.13/5.47 => ( ( ord_less_rat @ W @ X )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ W ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_ge_bounded
% 5.13/5.47 thf(fact_406_order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_real
% 5.13/5.47 = ( ^ [A4: real,B3: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.13/5.47 & ~ ( ord_less_eq_real @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_not
% 5.13/5.47 thf(fact_407_order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_set_nat
% 5.13/5.47 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 5.13/5.47 & ~ ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_not
% 5.13/5.47 thf(fact_408_order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_rat
% 5.13/5.47 = ( ^ [A4: rat,B3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.13/5.47 & ~ ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_not
% 5.13/5.47 thf(fact_409_order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_num
% 5.13/5.47 = ( ^ [A4: num,B3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.13/5.47 & ~ ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_not
% 5.13/5.47 thf(fact_410_order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [A4: nat,B3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.13/5.47 & ~ ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_not
% 5.13/5.47 thf(fact_411_order_Ostrict__iff__not,axiom,
% 5.13/5.47 ( ord_less_int
% 5.13/5.47 = ( ^ [A4: int,B3: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.13/5.47 & ~ ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_not
% 5.13/5.47 thf(fact_412_order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [A: real,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_real @ B @ C )
% 5.13/5.47 => ( ord_less_real @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans2
% 5.13/5.47 thf(fact_413_order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.13/5.47 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans2
% 5.13/5.47 thf(fact_414_order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans2
% 5.13/5.47 thf(fact_415_order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [A: num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ord_less_num @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans2
% 5.13/5.47 thf(fact_416_order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [A: nat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans2
% 5.13/5.47 thf(fact_417_order_Ostrict__trans2,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.47 => ( ord_less_int @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans2
% 5.13/5.47 thf(fact_418_order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [A: real,B: real,C: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.47 => ( ( ord_less_real @ B @ C )
% 5.13/5.47 => ( ord_less_real @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans1
% 5.13/5.47 thf(fact_419_order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_set_nat @ B @ C )
% 5.13/5.47 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans1
% 5.13/5.47 thf(fact_420_order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_rat @ B @ C )
% 5.13/5.47 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans1
% 5.13/5.47 thf(fact_421_order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [A: num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_num @ B @ C )
% 5.13/5.47 => ( ord_less_num @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans1
% 5.13/5.47 thf(fact_422_order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [A: nat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_nat @ B @ C )
% 5.13/5.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans1
% 5.13/5.47 thf(fact_423_order_Ostrict__trans1,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_int @ B @ C )
% 5.13/5.47 => ( ord_less_int @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_trans1
% 5.13/5.47 thf(fact_424_order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_real
% 5.13/5.47 = ( ^ [A4: real,B3: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_order
% 5.13/5.47 thf(fact_425_order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_set_nat
% 5.13/5.47 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_order
% 5.13/5.47 thf(fact_426_order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_rat
% 5.13/5.47 = ( ^ [A4: rat,B3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_order
% 5.13/5.47 thf(fact_427_order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_num
% 5.13/5.47 = ( ^ [A4: num,B3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_order
% 5.13/5.47 thf(fact_428_order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [A4: nat,B3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_order
% 5.13/5.47 thf(fact_429_order_Ostrict__iff__order,axiom,
% 5.13/5.47 ( ord_less_int
% 5.13/5.47 = ( ^ [A4: int,B3: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.13/5.47 & ( A4 != B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.strict_iff_order
% 5.13/5.47 thf(fact_430_order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_real
% 5.13/5.47 = ( ^ [A4: real,B3: real] :
% 5.13/5.47 ( ( ord_less_real @ A4 @ B3 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.order_iff_strict
% 5.13/5.47 thf(fact_431_order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_set_nat
% 5.13/5.47 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.13/5.47 ( ( ord_less_set_nat @ A4 @ B3 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.order_iff_strict
% 5.13/5.47 thf(fact_432_order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_rat
% 5.13/5.47 = ( ^ [A4: rat,B3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ A4 @ B3 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.order_iff_strict
% 5.13/5.47 thf(fact_433_order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_num
% 5.13/5.47 = ( ^ [A4: num,B3: num] :
% 5.13/5.47 ( ( ord_less_num @ A4 @ B3 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.order_iff_strict
% 5.13/5.47 thf(fact_434_order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_nat
% 5.13/5.47 = ( ^ [A4: nat,B3: nat] :
% 5.13/5.47 ( ( ord_less_nat @ A4 @ B3 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.order_iff_strict
% 5.13/5.47 thf(fact_435_order_Oorder__iff__strict,axiom,
% 5.13/5.47 ( ord_less_eq_int
% 5.13/5.47 = ( ^ [A4: int,B3: int] :
% 5.13/5.47 ( ( ord_less_int @ A4 @ B3 )
% 5.13/5.47 | ( A4 = B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.order_iff_strict
% 5.13/5.47 thf(fact_436_not__le__imp__less,axiom,
% 5.13/5.47 ! [Y4: real,X: real] :
% 5.13/5.47 ( ~ ( ord_less_eq_real @ Y4 @ X )
% 5.13/5.47 => ( ord_less_real @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_le_imp_less
% 5.13/5.47 thf(fact_437_not__le__imp__less,axiom,
% 5.13/5.47 ! [Y4: rat,X: rat] :
% 5.13/5.47 ( ~ ( ord_less_eq_rat @ Y4 @ X )
% 5.13/5.47 => ( ord_less_rat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_le_imp_less
% 5.13/5.47 thf(fact_438_not__le__imp__less,axiom,
% 5.13/5.47 ! [Y4: num,X: num] :
% 5.13/5.47 ( ~ ( ord_less_eq_num @ Y4 @ X )
% 5.13/5.47 => ( ord_less_num @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_le_imp_less
% 5.13/5.47 thf(fact_439_not__le__imp__less,axiom,
% 5.13/5.47 ! [Y4: nat,X: nat] :
% 5.13/5.47 ( ~ ( ord_less_eq_nat @ Y4 @ X )
% 5.13/5.47 => ( ord_less_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_le_imp_less
% 5.13/5.47 thf(fact_440_not__le__imp__less,axiom,
% 5.13/5.47 ! [Y4: int,X: int] :
% 5.13/5.47 ( ~ ( ord_less_eq_int @ Y4 @ X )
% 5.13/5.47 => ( ord_less_int @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_le_imp_less
% 5.13/5.47 thf(fact_441_less__le__not__le,axiom,
% 5.13/5.47 ( ord_less_real
% 5.13/5.47 = ( ^ [X2: real,Y: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ X2 @ Y )
% 5.13/5.47 & ~ ( ord_less_eq_real @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_le_not_le
% 5.13/5.47 thf(fact_442_less__le__not__le,axiom,
% 5.13/5.47 ( ord_less_set_nat
% 5.13/5.47 = ( ^ [X2: set_nat,Y: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.13/5.47 & ~ ( ord_less_eq_set_nat @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_le_not_le
% 5.13/5.47 thf(fact_443_less__le__not__le,axiom,
% 5.13/5.47 ( ord_less_rat
% 5.13/5.47 = ( ^ [X2: rat,Y: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.13/5.47 & ~ ( ord_less_eq_rat @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_le_not_le
% 5.13/5.47 thf(fact_444_less__le__not__le,axiom,
% 5.13/5.47 ( ord_less_num
% 5.13/5.47 = ( ^ [X2: num,Y: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X2 @ Y )
% 5.13/5.47 & ~ ( ord_less_eq_num @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_le_not_le
% 5.13/5.47 thf(fact_445_less__le__not__le,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [X2: nat,Y: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.13/5.47 & ~ ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_le_not_le
% 5.13/5.47 thf(fact_446_less__le__not__le,axiom,
% 5.13/5.47 ( ord_less_int
% 5.13/5.47 = ( ^ [X2: int,Y: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X2 @ Y )
% 5.13/5.47 & ~ ( ord_less_eq_int @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_le_not_le
% 5.13/5.47 thf(fact_447_dense__le,axiom,
% 5.13/5.47 ! [Y4: real,Z2: real] :
% 5.13/5.47 ( ! [X3: real] :
% 5.13/5.47 ( ( ord_less_real @ X3 @ Y4 )
% 5.13/5.47 => ( ord_less_eq_real @ X3 @ Z2 ) )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_le
% 5.13/5.47 thf(fact_448_dense__le,axiom,
% 5.13/5.47 ! [Y4: rat,Z2: rat] :
% 5.13/5.47 ( ! [X3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ X3 @ Y4 )
% 5.13/5.47 => ( ord_less_eq_rat @ X3 @ Z2 ) )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_le
% 5.13/5.47 thf(fact_449_dense__ge,axiom,
% 5.13/5.47 ! [Z2: real,Y4: real] :
% 5.13/5.47 ( ! [X3: real] :
% 5.13/5.47 ( ( ord_less_real @ Z2 @ X3 )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ X3 ) )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_ge
% 5.13/5.47 thf(fact_450_dense__ge,axiom,
% 5.13/5.47 ! [Z2: rat,Y4: rat] :
% 5.13/5.47 ( ! [X3: rat] :
% 5.13/5.47 ( ( ord_less_rat @ Z2 @ X3 )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ X3 ) )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % dense_ge
% 5.13/5.47 thf(fact_451_antisym__conv2,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.47 => ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv2
% 5.13/5.47 thf(fact_452_antisym__conv2,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ~ ( ord_less_set_nat @ X @ Y4 ) )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv2
% 5.13/5.47 thf(fact_453_antisym__conv2,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv2
% 5.13/5.47 thf(fact_454_antisym__conv2,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv2
% 5.13/5.47 thf(fact_455_antisym__conv2,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv2
% 5.13/5.47 thf(fact_456_antisym__conv2,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv2
% 5.13/5.47 thf(fact_457_antisym__conv1,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ~ ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv1
% 5.13/5.47 thf(fact_458_antisym__conv1,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat] :
% 5.13/5.47 ( ~ ( ord_less_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv1
% 5.13/5.47 thf(fact_459_antisym__conv1,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ~ ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv1
% 5.13/5.47 thf(fact_460_antisym__conv1,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ~ ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv1
% 5.13/5.47 thf(fact_461_antisym__conv1,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ~ ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv1
% 5.13/5.47 thf(fact_462_antisym__conv1,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ~ ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym_conv1
% 5.13/5.47 thf(fact_463_nless__le,axiom,
% 5.13/5.47 ! [A: real,B: real] :
% 5.13/5.47 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.13/5.47 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.13/5.47 | ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nless_le
% 5.13/5.47 thf(fact_464_nless__le,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat] :
% 5.13/5.47 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 5.13/5.47 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 | ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nless_le
% 5.13/5.47 thf(fact_465_nless__le,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.13/5.47 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 | ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nless_le
% 5.13/5.47 thf(fact_466_nless__le,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.13/5.47 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.13/5.47 | ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nless_le
% 5.13/5.47 thf(fact_467_nless__le,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.13/5.47 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 | ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nless_le
% 5.13/5.47 thf(fact_468_nless__le,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.13/5.47 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.13/5.47 | ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nless_le
% 5.13/5.47 thf(fact_469_leI,axiom,
% 5.13/5.47 ! [X: real,Y4: real] :
% 5.13/5.47 ( ~ ( ord_less_real @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_real @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % leI
% 5.13/5.47 thf(fact_470_leI,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ~ ( ord_less_rat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % leI
% 5.13/5.47 thf(fact_471_leI,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ~ ( ord_less_num @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % leI
% 5.13/5.47 thf(fact_472_leI,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ~ ( ord_less_nat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % leI
% 5.13/5.47 thf(fact_473_leI,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ~ ( ord_less_int @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % leI
% 5.13/5.47 thf(fact_474_leD,axiom,
% 5.13/5.47 ! [Y4: real,X: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_real @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % leD
% 5.13/5.47 thf(fact_475_leD,axiom,
% 5.13/5.47 ! [Y4: set_nat,X: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_set_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % leD
% 5.13/5.47 thf(fact_476_leD,axiom,
% 5.13/5.47 ! [Y4: rat,X: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_rat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % leD
% 5.13/5.47 thf(fact_477_leD,axiom,
% 5.13/5.47 ! [Y4: num,X: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_num @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % leD
% 5.13/5.47 thf(fact_478_leD,axiom,
% 5.13/5.47 ! [Y4: nat,X: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % leD
% 5.13/5.47 thf(fact_479_leD,axiom,
% 5.13/5.47 ! [Y4: int,X: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_int @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % leD
% 5.13/5.47 thf(fact_480_verit__comp__simplify1_I3_J,axiom,
% 5.13/5.47 ! [B4: real,A5: real] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_real @ B4 @ A5 ) )
% 5.13/5.47 = ( ord_less_real @ A5 @ B4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(3)
% 5.13/5.47 thf(fact_481_verit__comp__simplify1_I3_J,axiom,
% 5.13/5.47 ! [B4: rat,A5: rat] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_rat @ B4 @ A5 ) )
% 5.13/5.47 = ( ord_less_rat @ A5 @ B4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(3)
% 5.13/5.47 thf(fact_482_verit__comp__simplify1_I3_J,axiom,
% 5.13/5.47 ! [B4: num,A5: num] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_num @ B4 @ A5 ) )
% 5.13/5.47 = ( ord_less_num @ A5 @ B4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(3)
% 5.13/5.47 thf(fact_483_verit__comp__simplify1_I3_J,axiom,
% 5.13/5.47 ! [B4: nat,A5: nat] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_nat @ B4 @ A5 ) )
% 5.13/5.47 = ( ord_less_nat @ A5 @ B4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(3)
% 5.13/5.47 thf(fact_484_verit__comp__simplify1_I3_J,axiom,
% 5.13/5.47 ! [B4: int,A5: int] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_int @ B4 @ A5 ) )
% 5.13/5.47 = ( ord_less_int @ A5 @ B4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(3)
% 5.13/5.47 thf(fact_485_le__num__One__iff,axiom,
% 5.13/5.47 ! [X: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ one )
% 5.13/5.47 = ( X = one ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_num_One_iff
% 5.13/5.47 thf(fact_486_order__antisym__conv,axiom,
% 5.13/5.47 ! [Y4: set_nat,X: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ Y4 @ X )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym_conv
% 5.13/5.47 thf(fact_487_order__antisym__conv,axiom,
% 5.13/5.47 ! [Y4: rat,X: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.13/5.47 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym_conv
% 5.13/5.47 thf(fact_488_order__antisym__conv,axiom,
% 5.13/5.47 ! [Y4: num,X: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ Y4 @ X )
% 5.13/5.47 => ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym_conv
% 5.13/5.47 thf(fact_489_order__antisym__conv,axiom,
% 5.13/5.47 ! [Y4: nat,X: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ Y4 @ X )
% 5.13/5.47 => ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym_conv
% 5.13/5.47 thf(fact_490_order__antisym__conv,axiom,
% 5.13/5.47 ! [Y4: int,X: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ Y4 @ X )
% 5.13/5.47 => ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 = ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym_conv
% 5.13/5.47 thf(fact_491_linorder__le__cases,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ~ ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_cases
% 5.13/5.47 thf(fact_492_linorder__le__cases,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ~ ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_cases
% 5.13/5.47 thf(fact_493_linorder__le__cases,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ~ ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_cases
% 5.13/5.47 thf(fact_494_linorder__le__cases,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ~ ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_le_cases
% 5.13/5.47 thf(fact_495_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_496_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_497_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_498_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_499_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_500_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_501_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_502_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_503_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_504_ord__le__eq__subst,axiom,
% 5.13/5.47 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ( F @ B )
% 5.13/5.47 = C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_subst
% 5.13/5.47 thf(fact_505_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_506_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_507_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_508_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_509_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_510_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: num,F: num > num,B: num,C: num] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_511_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_512_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: int,F: num > int,B: num,C: num] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_513_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_514_ord__eq__le__subst,axiom,
% 5.13/5.47 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.13/5.47 ( ( A
% 5.13/5.47 = ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_subst
% 5.13/5.47 thf(fact_515_linorder__linear,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 | ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_linear
% 5.13/5.47 thf(fact_516_linorder__linear,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 | ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_linear
% 5.13/5.47 thf(fact_517_linorder__linear,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 | ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_linear
% 5.13/5.47 thf(fact_518_linorder__linear,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 | ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_linear
% 5.13/5.47 thf(fact_519_verit__la__disequality,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 | ~ ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_la_disequality
% 5.13/5.47 thf(fact_520_verit__la__disequality,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 | ~ ( ord_less_eq_num @ A @ B )
% 5.13/5.47 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_la_disequality
% 5.13/5.47 thf(fact_521_verit__la__disequality,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 | ~ ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_la_disequality
% 5.13/5.47 thf(fact_522_verit__la__disequality,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 | ~ ( ord_less_eq_int @ A @ B )
% 5.13/5.47 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_la_disequality
% 5.13/5.47 thf(fact_523_order__eq__refl,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat] :
% 5.13/5.47 ( ( X = Y4 )
% 5.13/5.47 => ( ord_less_eq_set_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_eq_refl
% 5.13/5.47 thf(fact_524_order__eq__refl,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( X = Y4 )
% 5.13/5.47 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_eq_refl
% 5.13/5.47 thf(fact_525_order__eq__refl,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( X = Y4 )
% 5.13/5.47 => ( ord_less_eq_num @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_eq_refl
% 5.13/5.47 thf(fact_526_order__eq__refl,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( X = Y4 )
% 5.13/5.47 => ( ord_less_eq_nat @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_eq_refl
% 5.13/5.47 thf(fact_527_order__eq__refl,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( X = Y4 )
% 5.13/5.47 => ( ord_less_eq_int @ X @ Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_eq_refl
% 5.13/5.47 thf(fact_528_order__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_529_order__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_530_order__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_531_order__subst2,axiom,
% 5.13/5.47 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_532_order__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_533_order__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_534_order__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_535_order__subst2,axiom,
% 5.13/5.47 ! [A: num,B: num,F: num > int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_536_order__subst2,axiom,
% 5.13/5.47 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_537_order__subst2,axiom,
% 5.13/5.47 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst2
% 5.13/5.47 thf(fact_538_order__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_539_order__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_540_order__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_541_order__subst1,axiom,
% 5.13/5.47 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_542_order__subst1,axiom,
% 5.13/5.47 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_543_order__subst1,axiom,
% 5.13/5.47 ! [A: num,F: num > num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_544_order__subst1,axiom,
% 5.13/5.47 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_545_order__subst1,axiom,
% 5.13/5.47 ! [A: num,F: int > num,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.47 => ( ! [X3: int,Y3: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_546_order__subst1,axiom,
% 5.13/5.47 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_547_order__subst1,axiom,
% 5.13/5.47 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ! [X3: num,Y3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.13/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_subst1
% 5.13/5.47 thf(fact_548_Orderings_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 5.13/5.47 & ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % Orderings.order_eq_iff
% 5.13/5.47 thf(fact_549_Orderings_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: rat,B3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.13/5.47 & ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % Orderings.order_eq_iff
% 5.13/5.47 thf(fact_550_Orderings_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: num,B3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.13/5.47 & ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % Orderings.order_eq_iff
% 5.13/5.47 thf(fact_551_Orderings_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: nat,B3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.13/5.47 & ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % Orderings.order_eq_iff
% 5.13/5.47 thf(fact_552_Orderings_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: int,B3: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.13/5.47 & ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % Orderings.order_eq_iff
% 5.13/5.47 thf(fact_553_antisym,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym
% 5.13/5.47 thf(fact_554_antisym,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym
% 5.13/5.47 thf(fact_555_antisym,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ A )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym
% 5.13/5.47 thf(fact_556_antisym,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym
% 5.13/5.47 thf(fact_557_antisym,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_int @ B @ A )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % antisym
% 5.13/5.47 thf(fact_558_dual__order_Otrans,axiom,
% 5.13/5.47 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.13/5.47 => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.trans
% 5.13/5.47 thf(fact_559_dual__order_Otrans,axiom,
% 5.13/5.47 ! [B: rat,A: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_rat @ C @ B )
% 5.13/5.47 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.trans
% 5.13/5.47 thf(fact_560_dual__order_Otrans,axiom,
% 5.13/5.47 ! [B: num,A: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_num @ C @ B )
% 5.13/5.47 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.trans
% 5.13/5.47 thf(fact_561_dual__order_Otrans,axiom,
% 5.13/5.47 ! [B: nat,A: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_nat @ C @ B )
% 5.13/5.47 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.trans
% 5.13/5.47 thf(fact_562_dual__order_Otrans,axiom,
% 5.13/5.47 ! [B: int,A: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_int @ C @ B )
% 5.13/5.47 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.trans
% 5.13/5.47 thf(fact_563_dual__order_Oantisym,axiom,
% 5.13/5.47 ! [B: set_nat,A: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.antisym
% 5.13/5.47 thf(fact_564_dual__order_Oantisym,axiom,
% 5.13/5.47 ! [B: rat,A: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.antisym
% 5.13/5.47 thf(fact_565_dual__order_Oantisym,axiom,
% 5.13/5.47 ! [B: num,A: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.antisym
% 5.13/5.47 thf(fact_566_dual__order_Oantisym,axiom,
% 5.13/5.47 ! [B: nat,A: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.antisym
% 5.13/5.47 thf(fact_567_dual__order_Oantisym,axiom,
% 5.13/5.47 ! [B: int,A: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.47 => ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( A = B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.antisym
% 5.13/5.47 thf(fact_568_dual__order_Oeq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 5.13/5.47 & ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.eq_iff
% 5.13/5.47 thf(fact_569_dual__order_Oeq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: rat,B3: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.13/5.47 & ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.eq_iff
% 5.13/5.47 thf(fact_570_dual__order_Oeq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: num,B3: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.13/5.47 & ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.eq_iff
% 5.13/5.47 thf(fact_571_dual__order_Oeq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: nat,B3: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.13/5.47 & ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.eq_iff
% 5.13/5.47 thf(fact_572_dual__order_Oeq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [A4: int,B3: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.13/5.47 & ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % dual_order.eq_iff
% 5.13/5.47 thf(fact_573_linorder__wlog,axiom,
% 5.13/5.47 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.13/5.47 ( ! [A3: rat,B2: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: rat,B2: rat] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_wlog
% 5.13/5.47 thf(fact_574_linorder__wlog,axiom,
% 5.13/5.47 ! [P: num > num > $o,A: num,B: num] :
% 5.13/5.47 ( ! [A3: num,B2: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: num,B2: num] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_wlog
% 5.13/5.47 thf(fact_575_linorder__wlog,axiom,
% 5.13/5.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.13/5.47 ( ! [A3: nat,B2: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: nat,B2: nat] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_wlog
% 5.13/5.47 thf(fact_576_linorder__wlog,axiom,
% 5.13/5.47 ! [P: int > int > $o,A: int,B: int] :
% 5.13/5.47 ( ! [A3: int,B2: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( ! [A3: int,B2: int] :
% 5.13/5.47 ( ( P @ B2 @ A3 )
% 5.13/5.47 => ( P @ A3 @ B2 ) )
% 5.13/5.47 => ( P @ A @ B ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % linorder_wlog
% 5.13/5.47 thf(fact_577_order__trans,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat,Z2: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_eq_set_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_trans
% 5.13/5.47 thf(fact_578_order__trans,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,Z2: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_rat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_eq_rat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_trans
% 5.13/5.47 thf(fact_579_order__trans,axiom,
% 5.13/5.47 ! [X: num,Y4: num,Z2: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_num @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_eq_num @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_trans
% 5.13/5.47 thf(fact_580_order__trans,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_nat @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_eq_nat @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_trans
% 5.13/5.47 thf(fact_581_order__trans,axiom,
% 5.13/5.47 ! [X: int,Y4: int,Z2: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_int @ Y4 @ Z2 )
% 5.13/5.47 => ( ord_less_eq_int @ X @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_trans
% 5.13/5.47 thf(fact_582_order_Otrans,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.13/5.47 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.trans
% 5.13/5.47 thf(fact_583_order_Otrans,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.trans
% 5.13/5.47 thf(fact_584_order_Otrans,axiom,
% 5.13/5.47 ! [A: num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.trans
% 5.13/5.47 thf(fact_585_order_Otrans,axiom,
% 5.13/5.47 ! [A: nat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.trans
% 5.13/5.47 thf(fact_586_order_Otrans,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.47 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order.trans
% 5.13/5.47 thf(fact_587_order__antisym,axiom,
% 5.13/5.47 ! [X: set_nat,Y4: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ Y4 @ X )
% 5.13/5.47 => ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym
% 5.13/5.47 thf(fact_588_order__antisym,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_rat @ Y4 @ X )
% 5.13/5.47 => ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym
% 5.13/5.47 thf(fact_589_order__antisym,axiom,
% 5.13/5.47 ! [X: num,Y4: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_num @ Y4 @ X )
% 5.13/5.47 => ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym
% 5.13/5.47 thf(fact_590_order__antisym,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_nat @ Y4 @ X )
% 5.13/5.47 => ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym
% 5.13/5.47 thf(fact_591_order__antisym,axiom,
% 5.13/5.47 ! [X: int,Y4: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ( ( ord_less_eq_int @ Y4 @ X )
% 5.13/5.47 => ( X = Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_antisym
% 5.13/5.47 thf(fact_592_ord__le__eq__trans,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.13/5.47 => ( ( B = C )
% 5.13/5.47 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_trans
% 5.13/5.47 thf(fact_593_ord__le__eq__trans,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.47 => ( ( B = C )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_trans
% 5.13/5.47 thf(fact_594_ord__le__eq__trans,axiom,
% 5.13/5.47 ! [A: num,B: num,C: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.13/5.47 => ( ( B = C )
% 5.13/5.47 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_trans
% 5.13/5.47 thf(fact_595_ord__le__eq__trans,axiom,
% 5.13/5.47 ! [A: nat,B: nat,C: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.47 => ( ( B = C )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_trans
% 5.13/5.47 thf(fact_596_ord__le__eq__trans,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.47 => ( ( B = C )
% 5.13/5.47 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_le_eq_trans
% 5.13/5.47 thf(fact_597_ord__eq__le__trans,axiom,
% 5.13/5.47 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.13/5.47 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_trans
% 5.13/5.47 thf(fact_598_ord__eq__le__trans,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.47 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_trans
% 5.13/5.47 thf(fact_599_ord__eq__le__trans,axiom,
% 5.13/5.47 ! [A: num,B: num,C: num] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.13/5.47 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_trans
% 5.13/5.47 thf(fact_600_ord__eq__le__trans,axiom,
% 5.13/5.47 ! [A: nat,B: nat,C: nat] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_trans
% 5.13/5.47 thf(fact_601_ord__eq__le__trans,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( A = B )
% 5.13/5.47 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.47 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % ord_eq_le_trans
% 5.13/5.47 thf(fact_602_order__class_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [X2: set_nat,Y: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.13/5.47 & ( ord_less_eq_set_nat @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_class.order_eq_iff
% 5.13/5.47 thf(fact_603_order__class_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [X2: rat,Y: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.13/5.47 & ( ord_less_eq_rat @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_class.order_eq_iff
% 5.13/5.47 thf(fact_604_order__class_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [X2: num,Y: num] :
% 5.13/5.47 ( ( ord_less_eq_num @ X2 @ Y )
% 5.13/5.47 & ( ord_less_eq_num @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_class.order_eq_iff
% 5.13/5.47 thf(fact_605_order__class_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [X2: nat,Y: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.13/5.47 & ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_class.order_eq_iff
% 5.13/5.47 thf(fact_606_order__class_Oorder__eq__iff,axiom,
% 5.13/5.47 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.13/5.47 = ( ^ [X2: int,Y: int] :
% 5.13/5.47 ( ( ord_less_eq_int @ X2 @ Y )
% 5.13/5.47 & ( ord_less_eq_int @ Y @ X2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % order_class.order_eq_iff
% 5.13/5.47 thf(fact_607_le__cases3,axiom,
% 5.13/5.47 ! [X: rat,Y4: rat,Z2: rat] :
% 5.13/5.47 ( ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_rat @ Y4 @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_rat @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_rat @ X @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_rat @ X @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_rat @ Z2 @ Y4 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_rat @ Z2 @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_rat @ Y4 @ X ) )
% 5.13/5.47 => ( ( ( ord_less_eq_rat @ Y4 @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_rat @ Z2 @ X ) )
% 5.13/5.47 => ~ ( ( ord_less_eq_rat @ Z2 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_rat @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_cases3
% 5.13/5.47 thf(fact_608_le__cases3,axiom,
% 5.13/5.47 ! [X: num,Y4: num,Z2: num] :
% 5.13/5.47 ( ( ( ord_less_eq_num @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_num @ Y4 @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_num @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_num @ X @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_num @ X @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_num @ Z2 @ Y4 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_num @ Z2 @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_num @ Y4 @ X ) )
% 5.13/5.47 => ( ( ( ord_less_eq_num @ Y4 @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_num @ Z2 @ X ) )
% 5.13/5.47 => ~ ( ( ord_less_eq_num @ Z2 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_num @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_cases3
% 5.13/5.47 thf(fact_609_le__cases3,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ( ord_less_eq_nat @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_nat @ Y4 @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_nat @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_nat @ X @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_nat @ X @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_nat @ Z2 @ Y4 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_nat @ Y4 @ X ) )
% 5.13/5.47 => ( ( ( ord_less_eq_nat @ Y4 @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_nat @ Z2 @ X ) )
% 5.13/5.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_nat @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_cases3
% 5.13/5.47 thf(fact_610_le__cases3,axiom,
% 5.13/5.47 ! [X: int,Y4: int,Z2: int] :
% 5.13/5.47 ( ( ( ord_less_eq_int @ X @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_int @ Y4 @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_int @ Y4 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_int @ X @ Z2 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_int @ X @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_int @ Z2 @ Y4 ) )
% 5.13/5.47 => ( ( ( ord_less_eq_int @ Z2 @ Y4 )
% 5.13/5.47 => ~ ( ord_less_eq_int @ Y4 @ X ) )
% 5.13/5.47 => ( ( ( ord_less_eq_int @ Y4 @ Z2 )
% 5.13/5.47 => ~ ( ord_less_eq_int @ Z2 @ X ) )
% 5.13/5.47 => ~ ( ( ord_less_eq_int @ Z2 @ X )
% 5.13/5.47 => ~ ( ord_less_eq_int @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_cases3
% 5.13/5.47 thf(fact_611_nle__le,axiom,
% 5.13/5.47 ! [A: rat,B: rat] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.13/5.47 = ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.47 & ( B != A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nle_le
% 5.13/5.47 thf(fact_612_nle__le,axiom,
% 5.13/5.47 ! [A: num,B: num] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.13/5.47 = ( ( ord_less_eq_num @ B @ A )
% 5.13/5.47 & ( B != A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nle_le
% 5.13/5.47 thf(fact_613_nle__le,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.13/5.47 = ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.47 & ( B != A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nle_le
% 5.13/5.47 thf(fact_614_nle__le,axiom,
% 5.13/5.47 ! [A: int,B: int] :
% 5.13/5.47 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.13/5.47 = ( ( ord_less_eq_int @ B @ A )
% 5.13/5.47 & ( B != A ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % nle_le
% 5.13/5.47 thf(fact_615_verit__comp__simplify1_I2_J,axiom,
% 5.13/5.47 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(2)
% 5.13/5.47 thf(fact_616_verit__comp__simplify1_I2_J,axiom,
% 5.13/5.47 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(2)
% 5.13/5.47 thf(fact_617_verit__comp__simplify1_I2_J,axiom,
% 5.13/5.47 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(2)
% 5.13/5.47 thf(fact_618_verit__comp__simplify1_I2_J,axiom,
% 5.13/5.47 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(2)
% 5.13/5.47 thf(fact_619_verit__comp__simplify1_I2_J,axiom,
% 5.13/5.47 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.13/5.47
% 5.13/5.47 % verit_comp_simplify1(2)
% 5.13/5.47 thf(fact_620_verit__eq__simplify_I10_J,axiom,
% 5.13/5.47 ! [X22: num] :
% 5.13/5.47 ( one
% 5.13/5.47 != ( bit0 @ X22 ) ) ).
% 5.13/5.47
% 5.13/5.47 % verit_eq_simplify(10)
% 5.13/5.47 thf(fact_621_div__le__dividend,axiom,
% 5.13/5.47 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.13/5.47
% 5.13/5.47 % div_le_dividend
% 5.13/5.47 thf(fact_622_div__le__mono,axiom,
% 5.13/5.47 ! [M: nat,N: nat,K: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.47 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % div_le_mono
% 5.13/5.47 thf(fact_623_maxt__corr,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( vEBT_vebt_maxt @ T )
% 5.13/5.47 = ( some_nat @ X ) )
% 5.13/5.47 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % maxt_corr
% 5.13/5.47 thf(fact_624_maxt__sound,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.13/5.47 => ( ( vEBT_vebt_maxt @ T )
% 5.13/5.47 = ( some_nat @ X ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % maxt_sound
% 5.13/5.47 thf(fact_625__092_060open_062high_Ares_A_Ideg_Adiv_A2_J_A_061_Apr_092_060close_062,axiom,
% 5.13/5.47 ( ( vEBT_VEBT_high @ res @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.47 = pr ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>high res (deg div 2) = pr\<close>
% 5.13/5.47 thf(fact_626_greater__shift,axiom,
% 5.13/5.47 ( ord_less_nat
% 5.13/5.47 = ( ^ [Y: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % greater_shift
% 5.13/5.47 thf(fact_627_mint__corr__help,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = ( some_nat @ Mini ) )
% 5.13/5.47 => ( ( vEBT_vebt_member @ T @ X )
% 5.13/5.47 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mint_corr_help
% 5.13/5.47 thf(fact_628_aaa,axiom,
% 5.13/5.47 ( ( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.47 = ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.47 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % aaa
% 5.13/5.47 thf(fact_629__092_060open_062z_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.13/5.47 ord_less_nat @ za @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>z < 2 ^ deg\<close>
% 5.13/5.47 thf(fact_630__C33_C,axiom,
% 5.13/5.47 ~ ? [U: nat] :
% 5.13/5.47 ( ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U )
% 5.13/5.47 & ( ord_less_nat @ U @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % "33"
% 5.13/5.47 thf(fact_631__092_060open_062invar__vebt_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_An_092_060close_062,axiom,
% 5.13/5.47 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ na ).
% 5.13/5.47
% 5.13/5.47 % \<open>invar_vebt (treeList ! high x (deg div 2)) n\<close>
% 5.13/5.47 thf(fact_632_mint__member,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = ( some_nat @ Maxi ) )
% 5.13/5.47 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mint_member
% 5.13/5.47 thf(fact_633_enat__ord__number_I1_J,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.13/5.47 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % enat_ord_number(1)
% 5.13/5.47 thf(fact_634_abh,axiom,
% 5.13/5.47 vEBT_vebt_member @ summary @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % abh
% 5.13/5.47 thf(fact_635__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 5.13/5.47 za != ma ).
% 5.13/5.47
% 5.13/5.47 % \<open>z \<noteq> ma\<close>
% 5.13/5.47 thf(fact_636__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 5.13/5.47 mi != ma ).
% 5.13/5.47
% 5.13/5.47 % \<open>mi \<noteq> ma\<close>
% 5.13/5.47 thf(fact_637_power__shift,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ( power_power_nat @ X @ Y4 )
% 5.13/5.47 = Z2 )
% 5.13/5.47 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y4 ) )
% 5.13/5.47 = ( some_nat @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_shift
% 5.13/5.47 thf(fact_638_set__vebt__set__vebt_H__valid,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( vEBT_set_vebt @ T )
% 5.13/5.47 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % set_vebt_set_vebt'_valid
% 5.13/5.47 thf(fact_639__C5_Ohyps_C_I10_J,axiom,
% 5.13/5.47 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(10)
% 5.13/5.47 thf(fact_640__092_060open_062x_A_092_060le_062_Ama_092_060close_062,axiom,
% 5.13/5.47 ord_less_eq_nat @ xa @ ma ).
% 5.13/5.47
% 5.13/5.47 % \<open>x \<le> ma\<close>
% 5.13/5.47 thf(fact_641__092_060open_062res_A_060_Ax_092_060close_062,axiom,
% 5.13/5.47 ord_less_nat @ res @ xa ).
% 5.13/5.47
% 5.13/5.47 % \<open>res < x\<close>
% 5.13/5.47 thf(fact_642__092_060open_062vebt__member_Asummary_Apr_092_060close_062,axiom,
% 5.13/5.47 vEBT_vebt_member @ summary @ pr ).
% 5.13/5.47
% 5.13/5.47 % \<open>vebt_member summary pr\<close>
% 5.13/5.47 thf(fact_643__092_060open_062res_A_060_Ama_092_060close_062,axiom,
% 5.13/5.47 ord_less_nat @ res @ ma ).
% 5.13/5.47
% 5.13/5.47 % \<open>res < ma\<close>
% 5.13/5.47 thf(fact_644__092_060open_062mi_A_060_Ares_092_060close_062,axiom,
% 5.13/5.47 ord_less_nat @ mi @ res ).
% 5.13/5.47
% 5.13/5.47 % \<open>mi < res\<close>
% 5.13/5.47 thf(fact_645_high__def,axiom,
% 5.13/5.47 ( vEBT_VEBT_high
% 5.13/5.47 = ( ^ [X2: nat,N2: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % high_def
% 5.13/5.47 thf(fact_646__C5_Ohyps_C_I2_J,axiom,
% 5.13/5.47 vEBT_invar_vebt @ summary @ m ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(2)
% 5.13/5.47 thf(fact_647_mint__sound,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.13/5.47 => ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = ( some_nat @ X ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mint_sound
% 5.13/5.47 thf(fact_648_mint__corr,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = ( some_nat @ X ) )
% 5.13/5.47 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mint_corr
% 5.13/5.47 thf(fact_649_member__bound,axiom,
% 5.13/5.47 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 5.13/5.47 ( ( vEBT_vebt_member @ Tree @ X )
% 5.13/5.47 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.13/5.47 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % member_bound
% 5.13/5.47 thf(fact_650_misiz,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( some_nat @ M )
% 5.13/5.47 = ( vEBT_vebt_mint @ T ) )
% 5.13/5.47 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % misiz
% 5.13/5.47 thf(fact_651_semiring__norm_I78_J,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.13/5.47 = ( ord_less_num @ M @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % semiring_norm(78)
% 5.13/5.47 thf(fact_652_semiring__norm_I75_J,axiom,
% 5.13/5.47 ! [M: num] :
% 5.13/5.47 ~ ( ord_less_num @ M @ one ) ).
% 5.13/5.47
% 5.13/5.47 % semiring_norm(75)
% 5.13/5.47 thf(fact_653_semiring__norm_I76_J,axiom,
% 5.13/5.47 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % semiring_norm(76)
% 5.13/5.47 thf(fact_654_enat__ord__number_I2_J,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.13/5.47 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % enat_ord_number(2)
% 5.13/5.47 thf(fact_655_pred__member,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,X: nat,Y4: nat] :
% 5.13/5.47 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y4 )
% 5.13/5.47 = ( ( vEBT_vebt_member @ T @ Y4 )
% 5.13/5.47 & ( ord_less_nat @ Y4 @ X )
% 5.13/5.47 & ! [Z4: nat] :
% 5.13/5.47 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.13/5.47 & ( ord_less_nat @ Z4 @ X ) )
% 5.13/5.47 => ( ord_less_eq_nat @ Z4 @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % pred_member
% 5.13/5.47 thf(fact_656__092_060open_062vebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_092_060close_062,axiom,
% 5.13/5.47 ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.47 = ( some_nat @ pr ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>vebt_pred summary (high x (deg div 2)) = Some pr\<close>
% 5.13/5.47 thf(fact_657__092_060open_062is__pred__in__set_A_Iset__vebt_H_Asummary_J_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_Apr_092_060close_062,axiom,
% 5.13/5.47 vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ pr ).
% 5.13/5.47
% 5.13/5.47 % \<open>is_pred_in_set (set_vebt' summary) (high x (deg div 2)) pr\<close>
% 5.13/5.47 thf(fact_658_post__member__pre__member,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat,Y4: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( ( ord_less_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y4 )
% 5.13/5.47 => ( ( vEBT_vebt_member @ T @ Y4 )
% 5.13/5.47 | ( X = Y4 ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % post_member_pre_member
% 5.13/5.47 thf(fact_659__C20_C,axiom,
% 5.13/5.47 ( ( za = mi )
% 5.13/5.47 | ( za = ma )
% 5.13/5.47 | ( ( ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.13/5.47 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % "20"
% 5.13/5.47 thf(fact_660__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,
% 5.13/5.47 ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.13/5.47 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>high x n < 2 ^ m \<and> low x n < 2 ^ n\<close>
% 5.13/5.47 thf(fact_661__092_060open_062high_Az_A_Ideg_Adiv_A2_J_A_060_A2_A_094_Am_092_060close_062,axiom,
% 5.13/5.47 ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>high z (deg div 2) < 2 ^ m\<close>
% 5.13/5.47 thf(fact_662_i1,axiom,
% 5.13/5.47 ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.47 = none_nat )
% 5.13/5.47 | ~ ( 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 ) ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % i1
% 5.13/5.47 thf(fact_663__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pr_O_Avebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.13/5.47 ~ ! [Pr: nat] :
% 5.13/5.47 ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.47 != ( some_nat @ Pr ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>\<And>thesis. (\<And>pr. vebt_pred summary (high x (deg div 2)) = Some pr \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.13/5.47 thf(fact_664__092_060open_062pr_A_060_A2_A_094_Am_092_060close_062,axiom,
% 5.13/5.47 ord_less_nat @ pr @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>pr < 2 ^ m\<close>
% 5.13/5.47 thf(fact_665__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ares_A_Ideg_Adiv_A2_J_J_A_Ilow_Ares_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,
% 5.13/5.47 vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ res @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ res @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>both_member_options (treeList ! high res (deg div 2)) (low res (deg div 2))\<close>
% 5.13/5.47 thf(fact_666__C5_Ohyps_C_I11_J,axiom,
% 5.13/5.47 ( ( mi != ma )
% 5.13/5.47 => ! [I: nat] :
% 5.13/5.47 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.13/5.47 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.13/5.47 = I )
% 5.13/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.13/5.47 & ! [X5: nat] :
% 5.13/5.47 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 5.13/5.47 = I )
% 5.13/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 5.13/5.47 => ( ( ord_less_nat @ mi @ X5 )
% 5.13/5.47 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(11)
% 5.13/5.47 thf(fact_667_fgh,axiom,
% 5.13/5.47 ( ( vEBT_VEBT_set_vebt @ ( nth_VEBT_VEBT @ treeList @ pr ) )
% 5.13/5.47 != bot_bot_set_nat ) ).
% 5.13/5.47
% 5.13/5.47 % fgh
% 5.13/5.47 thf(fact_668_self__le__ge2__pow,axiom,
% 5.13/5.47 ! [K: nat,M: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.13/5.47 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % self_le_ge2_pow
% 5.13/5.47 thf(fact_669_both__member__options__equiv__member,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.13/5.47 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % both_member_options_equiv_member
% 5.13/5.47 thf(fact_670_valid__member__both__member__options,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.13/5.47 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % valid_member_both_member_options
% 5.13/5.47 thf(fact_671_maxbmo,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,X: nat] :
% 5.13/5.47 ( ( ( vEBT_vebt_maxt @ T )
% 5.13/5.47 = ( some_nat @ X ) )
% 5.13/5.47 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % maxbmo
% 5.13/5.47 thf(fact_672__C5_Ohyps_C_I4_J,axiom,
% 5.13/5.47 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.13/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(4)
% 5.13/5.47 thf(fact_673__092_060open_062both__member__options_Asummary_Apr_092_060close_062,axiom,
% 5.13/5.47 vEBT_V8194947554948674370ptions @ summary @ pr ).
% 5.13/5.47
% 5.13/5.47 % \<open>both_member_options summary pr\<close>
% 5.13/5.47 thf(fact_674__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,axiom,
% 5.13/5.47 ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ pr ) @ X_1 ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>\<exists>maxy. both_member_options (treeList ! pr) maxy\<close>
% 5.13/5.47 thf(fact_675_mint__corr__help__empty,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = none_nat )
% 5.13/5.47 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.13/5.47 = bot_bot_set_nat ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mint_corr_help_empty
% 5.13/5.47 thf(fact_676_maxt__corr__help__empty,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ( vEBT_vebt_maxt @ T )
% 5.13/5.47 = none_nat )
% 5.13/5.47 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.13/5.47 = bot_bot_set_nat ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % maxt_corr_help_empty
% 5.13/5.47 thf(fact_677__C5_Ohyps_C_I3_J,axiom,
% 5.13/5.47 ! [X: nat,Px: nat] :
% 5.13/5.47 ( ( ( vEBT_vebt_pred @ summary @ X )
% 5.13/5.47 = ( some_nat @ Px ) )
% 5.13/5.47 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ X @ Px ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(3)
% 5.13/5.47 thf(fact_678_valid__insert__both__member__options__pres,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat,Y4: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( ( ord_less_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.13/5.47 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y4 ) @ X ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % valid_insert_both_member_options_pres
% 5.13/5.47 thf(fact_679_valid__insert__both__member__options__add,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.47 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % valid_insert_both_member_options_add
% 5.13/5.47 thf(fact_680__092_060open_062length_AtreeList_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_Am_092_060close_062,axiom,
% 5.13/5.47 ( ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.13/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.13/5.47 & ( vEBT_invar_vebt @ summary @ m ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>length treeList = 2 ^ m \<and> invar_vebt summary m\<close>
% 5.13/5.47 thf(fact_681__C5_Ohyps_C_I5_J,axiom,
% 5.13/5.47 ( m
% 5.13/5.47 = ( suc @ na ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(5)
% 5.13/5.47 thf(fact_682__C5_Ohyps_C_I6_J,axiom,
% 5.13/5.47 ( deg
% 5.13/5.47 = ( plus_plus_nat @ na @ m ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(6)
% 5.13/5.47 thf(fact_683_local_Opower__def,axiom,
% 5.13/5.47 ( vEBT_VEBT_power
% 5.13/5.47 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % local.power_def
% 5.13/5.47 thf(fact_684__C5_Ohyps_C_I1_J,axiom,
% 5.13/5.47 ! [X5: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.13/5.47 => ( ( vEBT_invar_vebt @ X5 @ na )
% 5.13/5.47 & ! [Xa: nat,Xb: nat] :
% 5.13/5.47 ( ( ( vEBT_vebt_pred @ X5 @ Xa )
% 5.13/5.47 = ( some_nat @ Xb ) )
% 5.13/5.47 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ X5 ) @ Xa @ Xb ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(1)
% 5.13/5.47 thf(fact_685__C5_Ohyps_C_I7_J,axiom,
% 5.13/5.47 ! [I: nat] :
% 5.13/5.47 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.13/5.47 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X6 ) )
% 5.13/5.47 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(7)
% 5.13/5.47 thf(fact_686_enat__less__induct,axiom,
% 5.13/5.47 ! [P: extended_enat > $o,N: extended_enat] :
% 5.13/5.47 ( ! [N3: extended_enat] :
% 5.13/5.47 ( ! [M3: extended_enat] :
% 5.13/5.47 ( ( ord_le72135733267957522d_enat @ M3 @ N3 )
% 5.13/5.47 => ( P @ M3 ) )
% 5.13/5.47 => ( P @ N3 ) )
% 5.13/5.47 => ( P @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % enat_less_induct
% 5.13/5.47 thf(fact_687_bot_Oextremum__uniqueI,axiom,
% 5.13/5.47 ! [A: extended_enat] :
% 5.13/5.47 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.13/5.47 => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_uniqueI
% 5.13/5.47 thf(fact_688_bot_Oextremum__uniqueI,axiom,
% 5.13/5.47 ! [A: set_int] :
% 5.13/5.47 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.13/5.47 => ( A = bot_bot_set_int ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_uniqueI
% 5.13/5.47 thf(fact_689_bot_Oextremum__uniqueI,axiom,
% 5.13/5.47 ! [A: set_real] :
% 5.13/5.47 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.13/5.47 => ( A = bot_bot_set_real ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_uniqueI
% 5.13/5.47 thf(fact_690_bot_Oextremum__uniqueI,axiom,
% 5.13/5.47 ! [A: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.13/5.47 => ( A = bot_bot_set_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_uniqueI
% 5.13/5.47 thf(fact_691_bot_Oextremum__uniqueI,axiom,
% 5.13/5.47 ! [A: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.13/5.47 => ( A = bot_bot_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_uniqueI
% 5.13/5.47 thf(fact_692_bot_Oextremum__unique,axiom,
% 5.13/5.47 ! [A: extended_enat] :
% 5.13/5.47 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.13/5.47 = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_unique
% 5.13/5.47 thf(fact_693_bot_Oextremum__unique,axiom,
% 5.13/5.47 ! [A: set_int] :
% 5.13/5.47 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.13/5.47 = ( A = bot_bot_set_int ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_unique
% 5.13/5.47 thf(fact_694_bot_Oextremum__unique,axiom,
% 5.13/5.47 ! [A: set_real] :
% 5.13/5.47 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.13/5.47 = ( A = bot_bot_set_real ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_unique
% 5.13/5.47 thf(fact_695_bot_Oextremum__unique,axiom,
% 5.13/5.47 ! [A: set_nat] :
% 5.13/5.47 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.13/5.47 = ( A = bot_bot_set_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_unique
% 5.13/5.47 thf(fact_696_bot_Oextremum__unique,axiom,
% 5.13/5.47 ! [A: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.13/5.47 = ( A = bot_bot_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_unique
% 5.13/5.47 thf(fact_697_bot_Oextremum,axiom,
% 5.13/5.47 ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum
% 5.13/5.47 thf(fact_698_bot_Oextremum,axiom,
% 5.13/5.47 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum
% 5.13/5.47 thf(fact_699_bot_Oextremum,axiom,
% 5.13/5.47 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum
% 5.13/5.47 thf(fact_700_bot_Oextremum,axiom,
% 5.13/5.47 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum
% 5.13/5.47 thf(fact_701_bot_Oextremum,axiom,
% 5.13/5.47 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum
% 5.13/5.47 thf(fact_702_bot_Oextremum__strict,axiom,
% 5.13/5.47 ! [A: set_nat] :
% 5.13/5.47 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_strict
% 5.13/5.47 thf(fact_703_bot_Oextremum__strict,axiom,
% 5.13/5.47 ! [A: extended_enat] :
% 5.13/5.47 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_strict
% 5.13/5.47 thf(fact_704_bot_Oextremum__strict,axiom,
% 5.13/5.47 ! [A: set_int] :
% 5.13/5.47 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_strict
% 5.13/5.47 thf(fact_705_bot_Oextremum__strict,axiom,
% 5.13/5.47 ! [A: set_real] :
% 5.13/5.47 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_strict
% 5.13/5.47 thf(fact_706_bot_Oextremum__strict,axiom,
% 5.13/5.47 ! [A: nat] :
% 5.13/5.47 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.13/5.47
% 5.13/5.47 % bot.extremum_strict
% 5.13/5.47 thf(fact_707_bot_Onot__eq__extremum,axiom,
% 5.13/5.47 ! [A: set_nat] :
% 5.13/5.47 ( ( A != bot_bot_set_nat )
% 5.13/5.47 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.not_eq_extremum
% 5.13/5.47 thf(fact_708_bot_Onot__eq__extremum,axiom,
% 5.13/5.47 ! [A: extended_enat] :
% 5.13/5.47 ( ( A != bot_bo4199563552545308370d_enat )
% 5.13/5.47 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.not_eq_extremum
% 5.13/5.47 thf(fact_709_bot_Onot__eq__extremum,axiom,
% 5.13/5.47 ! [A: set_int] :
% 5.13/5.47 ( ( A != bot_bot_set_int )
% 5.13/5.47 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.not_eq_extremum
% 5.13/5.47 thf(fact_710_bot_Onot__eq__extremum,axiom,
% 5.13/5.47 ! [A: set_real] :
% 5.13/5.47 ( ( A != bot_bot_set_real )
% 5.13/5.47 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.not_eq_extremum
% 5.13/5.47 thf(fact_711_bot_Onot__eq__extremum,axiom,
% 5.13/5.47 ! [A: nat] :
% 5.13/5.47 ( ( A != bot_bot_nat )
% 5.13/5.47 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.13/5.47
% 5.13/5.47 % bot.not_eq_extremum
% 5.13/5.47 thf(fact_712_is__pred__in__set__def,axiom,
% 5.13/5.47 ( vEBT_is_pred_in_set
% 5.13/5.47 = ( ^ [Xs: set_nat,X2: nat,Y: nat] :
% 5.13/5.47 ( ( member_nat @ Y @ Xs )
% 5.13/5.47 & ( ord_less_nat @ Y @ X2 )
% 5.13/5.47 & ! [Z4: nat] :
% 5.13/5.47 ( ( member_nat @ Z4 @ Xs )
% 5.13/5.47 => ( ( ord_less_nat @ Z4 @ X2 )
% 5.13/5.47 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % is_pred_in_set_def
% 5.13/5.47 thf(fact_713_power__divide,axiom,
% 5.13/5.47 ! [A: complex,B: complex,N: nat] :
% 5.13/5.47 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.13/5.47 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_divide
% 5.13/5.47 thf(fact_714_power__divide,axiom,
% 5.13/5.47 ! [A: real,B: real,N: nat] :
% 5.13/5.47 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.13/5.47 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_divide
% 5.13/5.47 thf(fact_715_power__divide,axiom,
% 5.13/5.47 ! [A: rat,B: rat,N: nat] :
% 5.13/5.47 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.13/5.47 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_divide
% 5.13/5.47 thf(fact_716_less__exp,axiom,
% 5.13/5.47 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_exp
% 5.13/5.47 thf(fact_717_power2__nat__le__imp__le,axiom,
% 5.13/5.47 ! [M: nat,N: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.13/5.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % power2_nat_le_imp_le
% 5.13/5.47 thf(fact_718_power2__nat__le__eq__le,axiom,
% 5.13/5.47 ! [M: nat,N: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.47 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % power2_nat_le_eq_le
% 5.13/5.47 thf(fact_719_in__children__def,axiom,
% 5.13/5.47 ( vEBT_V5917875025757280293ildren
% 5.13/5.47 = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N2 ) ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % in_children_def
% 5.13/5.47 thf(fact_720__092_060open_062max__in__set_A_Iset__vebt_H_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_J_Amaxy_092_060close_062,axiom,
% 5.13/5.47 vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ maxy ).
% 5.13/5.47
% 5.13/5.47 % \<open>max_in_set (set_vebt' (treeList ! the (vebt_pred summary (high x (deg div 2))))) maxy\<close>
% 5.13/5.47 thf(fact_721__092_060open_062Some_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_092_060close_062,axiom,
% 5.13/5.47 ( ( some_nat @ maxy )
% 5.13/5.47 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>Some maxy = vebt_maxt (treeList ! the (vebt_pred summary (high x (deg div 2))))\<close>
% 5.13/5.47 thf(fact_722_scmem,axiom,
% 5.13/5.47 vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ maxy ).
% 5.13/5.47
% 5.13/5.47 % scmem
% 5.13/5.47 thf(fact_723__092_060open_062invar__vebt_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_An_092_060close_062,axiom,
% 5.13/5.47 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ na ).
% 5.13/5.47
% 5.13/5.47 % \<open>invar_vebt (treeList ! the (vebt_pred summary (high x (deg div 2)))) n\<close>
% 5.13/5.47 thf(fact_724_both__member__options__ding,axiom,
% 5.13/5.47 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.13/5.47 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.13/5.47 => ( ( 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 ) ) ) ) )
% 5.13/5.47 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % both_member_options_ding
% 5.13/5.47 thf(fact_725_buildup__gives__empty,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.13/5.47 = bot_bot_set_nat ) ).
% 5.13/5.47
% 5.13/5.47 % buildup_gives_empty
% 5.13/5.47 thf(fact_726_minNullmin,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT] :
% 5.13/5.47 ( ( vEBT_VEBT_minNull @ T )
% 5.13/5.47 => ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = none_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % minNullmin
% 5.13/5.47 thf(fact_727_minminNull,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT] :
% 5.13/5.47 ( ( ( vEBT_vebt_mint @ T )
% 5.13/5.47 = none_nat )
% 5.13/5.47 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.13/5.47
% 5.13/5.47 % minminNull
% 5.13/5.47 thf(fact_728_not__None__eq,axiom,
% 5.13/5.47 ! [X: option_nat] :
% 5.13/5.47 ( ( X != none_nat )
% 5.13/5.47 = ( ? [Y: nat] :
% 5.13/5.47 ( X
% 5.13/5.47 = ( some_nat @ Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_None_eq
% 5.13/5.47 thf(fact_729_not__None__eq,axiom,
% 5.13/5.47 ! [X: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( X != none_P5556105721700978146at_nat )
% 5.13/5.47 = ( ? [Y: product_prod_nat_nat] :
% 5.13/5.47 ( X
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_None_eq
% 5.13/5.47 thf(fact_730_not__None__eq,axiom,
% 5.13/5.47 ! [X: option_num] :
% 5.13/5.47 ( ( X != none_num )
% 5.13/5.47 = ( ? [Y: num] :
% 5.13/5.47 ( X
% 5.13/5.47 = ( some_num @ Y ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_None_eq
% 5.13/5.47 thf(fact_731_not__Some__eq,axiom,
% 5.13/5.47 ! [X: option_nat] :
% 5.13/5.47 ( ( ! [Y: nat] :
% 5.13/5.47 ( X
% 5.13/5.47 != ( some_nat @ Y ) ) )
% 5.13/5.47 = ( X = none_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_Some_eq
% 5.13/5.47 thf(fact_732_not__Some__eq,axiom,
% 5.13/5.47 ! [X: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( ! [Y: product_prod_nat_nat] :
% 5.13/5.47 ( X
% 5.13/5.47 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.13/5.47 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_Some_eq
% 5.13/5.47 thf(fact_733_not__Some__eq,axiom,
% 5.13/5.47 ! [X: option_num] :
% 5.13/5.47 ( ( ! [Y: num] :
% 5.13/5.47 ( X
% 5.13/5.47 != ( some_num @ Y ) ) )
% 5.13/5.47 = ( X = none_num ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_Some_eq
% 5.13/5.47 thf(fact_734_even__odd__cases,axiom,
% 5.13/5.47 ! [X: nat] :
% 5.13/5.47 ( ! [N3: nat] :
% 5.13/5.47 ( X
% 5.13/5.47 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.13/5.47 => ~ ! [N3: nat] :
% 5.13/5.47 ( X
% 5.13/5.47 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % even_odd_cases
% 5.13/5.47 thf(fact_735_deg__deg__n,axiom,
% 5.13/5.47 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.13/5.47 => ( Deg = N ) ) ).
% 5.13/5.47
% 5.13/5.47 % deg_deg_n
% 5.13/5.47 thf(fact_736_not__min__Null__member,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT] :
% 5.13/5.47 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.13/5.47 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.13/5.47
% 5.13/5.47 % not_min_Null_member
% 5.13/5.47 thf(fact_737_min__Null__member,axiom,
% 5.13/5.47 ! [T: vEBT_VEBT,X: nat] :
% 5.13/5.47 ( ( vEBT_VEBT_minNull @ T )
% 5.13/5.47 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.13/5.47
% 5.13/5.47 % min_Null_member
% 5.13/5.47 thf(fact_738_deg__SUcn__Node,axiom,
% 5.13/5.47 ! [Tree: vEBT_VEBT,N: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.13/5.47 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.13/5.47 ( Tree
% 5.13/5.47 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % deg_SUcn_Node
% 5.13/5.47 thf(fact_739_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_real,P: real > $o,N: nat] :
% 5.13/5.47 ( ! [X3: real] :
% 5.13/5.47 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_740_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 5.13/5.47 ( ! [X3: complex] :
% 5.13/5.47 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_741_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 5.13/5.47 ( ! [X3: product_prod_nat_nat] :
% 5.13/5.47 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_742_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.13/5.47 ( ! [X3: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_743_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 5.13/5.47 ( ! [X3: $o] :
% 5.13/5.47 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_744_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 5.13/5.47 ( ! [X3: nat] :
% 5.13/5.47 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_745_inthall,axiom,
% 5.13/5.47 ! [Xs2: list_int,P: int > $o,N: nat] :
% 5.13/5.47 ( ! [X3: int] :
% 5.13/5.47 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.13/5.47 => ( P @ X3 ) )
% 5.13/5.47 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.47 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % inthall
% 5.13/5.47 thf(fact_746__C5_Ohyps_C_I8_J,axiom,
% 5.13/5.47 ( ( mi = ma )
% 5.13/5.47 => ! [X5: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.13/5.47 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % "5.hyps"(8)
% 5.13/5.47 thf(fact_747_option_Oinject,axiom,
% 5.13/5.47 ! [X22: nat,Y2: nat] :
% 5.13/5.47 ( ( ( some_nat @ X22 )
% 5.13/5.47 = ( some_nat @ Y2 ) )
% 5.13/5.47 = ( X22 = Y2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.inject
% 5.13/5.47 thf(fact_748_option_Oinject,axiom,
% 5.13/5.47 ! [X22: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.13/5.47 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 5.13/5.47 = ( X22 = Y2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.inject
% 5.13/5.47 thf(fact_749_option_Oinject,axiom,
% 5.13/5.47 ! [X22: num,Y2: num] :
% 5.13/5.47 ( ( ( some_num @ X22 )
% 5.13/5.47 = ( some_num @ Y2 ) )
% 5.13/5.47 = ( X22 = Y2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.inject
% 5.13/5.47 thf(fact_750_pow__sum,axiom,
% 5.13/5.47 ! [A: nat,B: nat] :
% 5.13/5.47 ( ( 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 ) )
% 5.13/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % pow_sum
% 5.13/5.47 thf(fact_751_high__bound__aux,axiom,
% 5.13/5.47 ! [Ma: nat,N: nat,M: nat] :
% 5.13/5.47 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.13/5.47 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % high_bound_aux
% 5.13/5.47 thf(fact_752_add__numeral__left,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: complex] :
% 5.13/5.47 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_numeral_left
% 5.13/5.47 thf(fact_753_add__numeral__left,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: real] :
% 5.13/5.47 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_numeral_left
% 5.13/5.47 thf(fact_754_add__numeral__left,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: rat] :
% 5.13/5.47 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_numeral_left
% 5.13/5.47 thf(fact_755_add__numeral__left,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: nat] :
% 5.13/5.47 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_numeral_left
% 5.13/5.47 thf(fact_756_add__numeral__left,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: int] :
% 5.13/5.47 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_numeral_left
% 5.13/5.47 thf(fact_757_numeral__plus__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.13/5.47 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_plus_numeral
% 5.13/5.47 thf(fact_758_numeral__plus__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.13/5.47 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_plus_numeral
% 5.13/5.47 thf(fact_759_numeral__plus__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.13/5.47 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_plus_numeral
% 5.13/5.47 thf(fact_760_numeral__plus__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.47 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_plus_numeral
% 5.13/5.47 thf(fact_761_numeral__plus__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.13/5.47 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_plus_numeral
% 5.13/5.47 thf(fact_762_option_Ocollapse,axiom,
% 5.13/5.47 ! [Option: option_nat] :
% 5.13/5.47 ( ( Option != none_nat )
% 5.13/5.47 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.13/5.47 = Option ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.collapse
% 5.13/5.47 thf(fact_763_option_Ocollapse,axiom,
% 5.13/5.47 ! [Option: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( Option != none_P5556105721700978146at_nat )
% 5.13/5.47 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.13/5.47 = Option ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.collapse
% 5.13/5.47 thf(fact_764_option_Ocollapse,axiom,
% 5.13/5.47 ! [Option: option_num] :
% 5.13/5.47 ( ( Option != none_num )
% 5.13/5.47 => ( ( some_num @ ( the_num @ Option ) )
% 5.13/5.47 = Option ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.collapse
% 5.13/5.47 thf(fact_765_add__2__eq__Suc,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.13/5.47 = ( suc @ ( suc @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_2_eq_Suc
% 5.13/5.47 thf(fact_766_add__2__eq__Suc_H,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.47 = ( suc @ ( suc @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_2_eq_Suc'
% 5.13/5.47 thf(fact_767_div2__Suc__Suc,axiom,
% 5.13/5.47 ! [M: nat] :
% 5.13/5.47 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.47 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % div2_Suc_Suc
% 5.13/5.47 thf(fact_768_add__self__div__2,axiom,
% 5.13/5.47 ! [M: nat] :
% 5.13/5.47 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.47 = M ) ).
% 5.13/5.47
% 5.13/5.47 % add_self_div_2
% 5.13/5.47 thf(fact_769__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,axiom,
% 5.13/5.47 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ za )
% 5.13/5.47 & ( ord_less_nat @ za @ xa ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>vebt_member (Node (Some (mi, ma)) deg treeList summary) z \<and> z < x\<close>
% 5.13/5.47 thf(fact_770_is__num__normalize_I1_J,axiom,
% 5.13/5.47 ! [A: real,B: real,C: real] :
% 5.13/5.47 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.47 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % is_num_normalize(1)
% 5.13/5.47 thf(fact_771_is__num__normalize_I1_J,axiom,
% 5.13/5.47 ! [A: rat,B: rat,C: rat] :
% 5.13/5.47 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.47 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % is_num_normalize(1)
% 5.13/5.47 thf(fact_772_is__num__normalize_I1_J,axiom,
% 5.13/5.47 ! [A: int,B: int,C: int] :
% 5.13/5.47 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.13/5.47 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % is_num_normalize(1)
% 5.13/5.47 thf(fact_773_option_Osel,axiom,
% 5.13/5.47 ! [X22: nat] :
% 5.13/5.47 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.13/5.47 = X22 ) ).
% 5.13/5.47
% 5.13/5.47 % option.sel
% 5.13/5.47 thf(fact_774_option_Osel,axiom,
% 5.13/5.47 ! [X22: product_prod_nat_nat] :
% 5.13/5.47 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.13/5.47 = X22 ) ).
% 5.13/5.47
% 5.13/5.47 % option.sel
% 5.13/5.47 thf(fact_775_option_Osel,axiom,
% 5.13/5.47 ! [X22: num] :
% 5.13/5.47 ( ( the_num @ ( some_num @ X22 ) )
% 5.13/5.47 = X22 ) ).
% 5.13/5.47
% 5.13/5.47 % option.sel
% 5.13/5.47 thf(fact_776_option_Oexpand,axiom,
% 5.13/5.47 ! [Option: option_nat,Option2: option_nat] :
% 5.13/5.47 ( ( ( Option = none_nat )
% 5.13/5.47 = ( Option2 = none_nat ) )
% 5.13/5.47 => ( ( ( Option != none_nat )
% 5.13/5.47 => ( ( Option2 != none_nat )
% 5.13/5.47 => ( ( the_nat @ Option )
% 5.13/5.47 = ( the_nat @ Option2 ) ) ) )
% 5.13/5.47 => ( Option = Option2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.expand
% 5.13/5.47 thf(fact_777_option_Oexpand,axiom,
% 5.13/5.47 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.13/5.47 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.13/5.47 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.13/5.47 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.13/5.47 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.13/5.47 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.13/5.47 => ( Option = Option2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.expand
% 5.13/5.47 thf(fact_778_option_Oexpand,axiom,
% 5.13/5.47 ! [Option: option_num,Option2: option_num] :
% 5.13/5.47 ( ( ( Option = none_num )
% 5.13/5.47 = ( Option2 = none_num ) )
% 5.13/5.47 => ( ( ( Option != none_num )
% 5.13/5.47 => ( ( Option2 != none_num )
% 5.13/5.47 => ( ( the_num @ Option )
% 5.13/5.47 = ( the_num @ Option2 ) ) ) )
% 5.13/5.47 => ( Option = Option2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.expand
% 5.13/5.47 thf(fact_779_vebt__pred_Osimps_I4_J,axiom,
% 5.13/5.47 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.13/5.47 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.13/5.47 = none_nat ) ).
% 5.13/5.47
% 5.13/5.47 % vebt_pred.simps(4)
% 5.13/5.47 thf(fact_780_option_Oexhaust__sel,axiom,
% 5.13/5.47 ! [Option: option_nat] :
% 5.13/5.47 ( ( Option != none_nat )
% 5.13/5.47 => ( Option
% 5.13/5.47 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.exhaust_sel
% 5.13/5.47 thf(fact_781_option_Oexhaust__sel,axiom,
% 5.13/5.47 ! [Option: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( Option != none_P5556105721700978146at_nat )
% 5.13/5.47 => ( Option
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.exhaust_sel
% 5.13/5.47 thf(fact_782_option_Oexhaust__sel,axiom,
% 5.13/5.47 ! [Option: option_num] :
% 5.13/5.47 ( ( Option != none_num )
% 5.13/5.47 => ( Option
% 5.13/5.47 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.exhaust_sel
% 5.13/5.47 thf(fact_783_numeral__Bit0,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.13/5.47 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_Bit0
% 5.13/5.47 thf(fact_784_numeral__Bit0,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.13/5.47 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_Bit0
% 5.13/5.47 thf(fact_785_numeral__Bit0,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.13/5.47 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_Bit0
% 5.13/5.47 thf(fact_786_numeral__Bit0,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.13/5.47 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_Bit0
% 5.13/5.47 thf(fact_787_numeral__Bit0,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.13/5.47 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_Bit0
% 5.13/5.47 thf(fact_788_Suc__div__le__mono,axiom,
% 5.13/5.47 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.13/5.47
% 5.13/5.47 % Suc_div_le_mono
% 5.13/5.47 thf(fact_789_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option_nat,P: option_nat > option_nat > $o,Y4: option_nat] :
% 5.13/5.47 ( ( ( X = none_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: nat,B2: nat] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_nat @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_nat @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_790_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y4: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( ( X = none_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_P5556105721700978146at_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: nat,B2: product_prod_nat_nat] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_nat @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_791_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option_nat,P: option_nat > option_num > $o,Y4: option_num] :
% 5.13/5.47 ( ( ( X = none_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_num )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: nat,B2: num] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_nat @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_num @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_792_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y4: option_nat] :
% 5.13/5.47 ( ( ( X = none_P5556105721700978146at_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: product_prod_nat_nat,B2: nat] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_nat @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_793_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y4: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( ( X = none_P5556105721700978146at_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_P5556105721700978146at_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_794_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y4: option_num] :
% 5.13/5.47 ( ( ( X = none_P5556105721700978146at_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_num )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: product_prod_nat_nat,B2: num] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_num @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_795_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option_num,P: option_num > option_nat > $o,Y4: option_nat] :
% 5.13/5.47 ( ( ( X = none_num )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: num,B2: nat] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_num @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_nat @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_796_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y4: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( ( X = none_num )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_P5556105721700978146at_nat )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: num,B2: product_prod_nat_nat] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_num @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_797_combine__options__cases,axiom,
% 5.13/5.47 ! [X: option_num,P: option_num > option_num > $o,Y4: option_num] :
% 5.13/5.47 ( ( ( X = none_num )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ( ( Y4 = none_num )
% 5.13/5.47 => ( P @ X @ Y4 ) )
% 5.13/5.47 => ( ! [A3: num,B2: num] :
% 5.13/5.47 ( ( X
% 5.13/5.47 = ( some_num @ A3 ) )
% 5.13/5.47 => ( ( Y4
% 5.13/5.47 = ( some_num @ B2 ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) )
% 5.13/5.47 => ( P @ X @ Y4 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % combine_options_cases
% 5.13/5.47 thf(fact_798_split__option__all,axiom,
% 5.13/5.47 ( ( ^ [P2: option_nat > $o] :
% 5.13/5.47 ! [X4: option_nat] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: option_nat > $o] :
% 5.13/5.47 ( ( P3 @ none_nat )
% 5.13/5.47 & ! [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % split_option_all
% 5.13/5.47 thf(fact_799_split__option__all,axiom,
% 5.13/5.47 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.13/5.47 ! [X4: option4927543243414619207at_nat] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.13/5.47 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.13/5.47 & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % split_option_all
% 5.13/5.47 thf(fact_800_split__option__all,axiom,
% 5.13/5.47 ( ( ^ [P2: option_num > $o] :
% 5.13/5.47 ! [X4: option_num] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: option_num > $o] :
% 5.13/5.47 ( ( P3 @ none_num )
% 5.13/5.47 & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % split_option_all
% 5.13/5.47 thf(fact_801_split__option__ex,axiom,
% 5.13/5.47 ( ( ^ [P2: option_nat > $o] :
% 5.13/5.47 ? [X4: option_nat] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: option_nat > $o] :
% 5.13/5.47 ( ( P3 @ none_nat )
% 5.13/5.47 | ? [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % split_option_ex
% 5.13/5.47 thf(fact_802_split__option__ex,axiom,
% 5.13/5.47 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.13/5.47 ? [X4: option4927543243414619207at_nat] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.13/5.47 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.13/5.47 | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % split_option_ex
% 5.13/5.47 thf(fact_803_split__option__ex,axiom,
% 5.13/5.47 ( ( ^ [P2: option_num > $o] :
% 5.13/5.47 ? [X4: option_num] : ( P2 @ X4 ) )
% 5.13/5.47 = ( ^ [P3: option_num > $o] :
% 5.13/5.47 ( ( P3 @ none_num )
% 5.13/5.47 | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % split_option_ex
% 5.13/5.47 thf(fact_804_option_Oexhaust,axiom,
% 5.13/5.47 ! [Y4: option_nat] :
% 5.13/5.47 ( ( Y4 != none_nat )
% 5.13/5.47 => ~ ! [X23: nat] :
% 5.13/5.47 ( Y4
% 5.13/5.47 != ( some_nat @ X23 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.exhaust
% 5.13/5.47 thf(fact_805_option_Oexhaust,axiom,
% 5.13/5.47 ! [Y4: option4927543243414619207at_nat] :
% 5.13/5.47 ( ( Y4 != none_P5556105721700978146at_nat )
% 5.13/5.47 => ~ ! [X23: product_prod_nat_nat] :
% 5.13/5.47 ( Y4
% 5.13/5.47 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.exhaust
% 5.13/5.47 thf(fact_806_option_Oexhaust,axiom,
% 5.13/5.47 ! [Y4: option_num] :
% 5.13/5.47 ( ( Y4 != none_num )
% 5.13/5.47 => ~ ! [X23: num] :
% 5.13/5.47 ( Y4
% 5.13/5.47 != ( some_num @ X23 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.exhaust
% 5.13/5.47 thf(fact_807_option_OdiscI,axiom,
% 5.13/5.47 ! [Option: option_nat,X22: nat] :
% 5.13/5.47 ( ( Option
% 5.13/5.47 = ( some_nat @ X22 ) )
% 5.13/5.47 => ( Option != none_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.discI
% 5.13/5.47 thf(fact_808_option_OdiscI,axiom,
% 5.13/5.47 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.13/5.47 ( ( Option
% 5.13/5.47 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.13/5.47 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.discI
% 5.13/5.47 thf(fact_809_option_OdiscI,axiom,
% 5.13/5.47 ! [Option: option_num,X22: num] :
% 5.13/5.47 ( ( Option
% 5.13/5.47 = ( some_num @ X22 ) )
% 5.13/5.47 => ( Option != none_num ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.discI
% 5.13/5.47 thf(fact_810_option_Odistinct_I1_J,axiom,
% 5.13/5.47 ! [X22: nat] :
% 5.13/5.47 ( none_nat
% 5.13/5.47 != ( some_nat @ X22 ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.distinct(1)
% 5.13/5.47 thf(fact_811_option_Odistinct_I1_J,axiom,
% 5.13/5.47 ! [X22: product_prod_nat_nat] :
% 5.13/5.47 ( none_P5556105721700978146at_nat
% 5.13/5.47 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.distinct(1)
% 5.13/5.47 thf(fact_812_option_Odistinct_I1_J,axiom,
% 5.13/5.47 ! [X22: num] :
% 5.13/5.47 ( none_num
% 5.13/5.47 != ( some_num @ X22 ) ) ).
% 5.13/5.47
% 5.13/5.47 % option.distinct(1)
% 5.13/5.47 thf(fact_813_snd,axiom,
% 5.13/5.47 ( res
% 5.13/5.47 = ( the_nat @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % snd
% 5.13/5.47 thf(fact_814_invar__vebt_Ointros_I3_J,axiom,
% 5.13/5.47 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.13/5.47 ( ! [X3: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.47 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.13/5.47 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.13/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.13/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.47 => ( ( M
% 5.13/5.47 = ( suc @ N ) )
% 5.13/5.47 => ( ( Deg
% 5.13/5.47 = ( plus_plus_nat @ N @ M ) )
% 5.13/5.47 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.13/5.47 => ( ! [X3: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.13/5.47 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % invar_vebt.intros(3)
% 5.13/5.47 thf(fact_815__092_060open_062res_A_061_A2_A_094_A_Ideg_Adiv_A2_J_A_K_Apr_A_L_Amaxy_092_060close_062,axiom,
% 5.13/5.47 ( res
% 5.13/5.47 = ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ pr ) @ maxy ) ) ).
% 5.13/5.47
% 5.13/5.47 % \<open>res = 2 ^ (deg div 2) * pr + maxy\<close>
% 5.13/5.47 thf(fact_816_invar__vebt_Ointros_I2_J,axiom,
% 5.13/5.47 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.13/5.47 ( ! [X3: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.47 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.13/5.47 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.13/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.13/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.47 => ( ( M = N )
% 5.13/5.47 => ( ( Deg
% 5.13/5.47 = ( plus_plus_nat @ N @ M ) )
% 5.13/5.47 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.13/5.47 => ( ! [X3: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.13/5.47 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % invar_vebt.intros(2)
% 5.13/5.47 thf(fact_817__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ares_092_060close_062,axiom,
% 5.13/5.47 vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ res ).
% 5.13/5.47
% 5.13/5.47 % \<open>vebt_member (Node (Some (mi, ma)) deg treeList summary) res\<close>
% 5.13/5.47 thf(fact_818__092_060open_062both__member__options_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ares_092_060close_062,axiom,
% 5.13/5.47 vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ res ).
% 5.13/5.47
% 5.13/5.47 % \<open>both_member_options (Node (Some (mi, ma)) deg treeList summary) res\<close>
% 5.13/5.47 thf(fact_819_member__inv,axiom,
% 5.13/5.47 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.13/5.47 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.47 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.13/5.47 & ( ( X = Mi )
% 5.13/5.47 | ( X = Ma )
% 5.13/5.47 | ( ( ord_less_nat @ X @ Ma )
% 5.13/5.47 & ( ord_less_nat @ Mi @ X )
% 5.13/5.47 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.47 & ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % member_inv
% 5.13/5.47 thf(fact_820_add__def,axiom,
% 5.13/5.47 ( vEBT_VEBT_add
% 5.13/5.47 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_def
% 5.13/5.47 thf(fact_821_thisvalid,axiom,
% 5.13/5.47 vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 5.13/5.47
% 5.13/5.47 % thisvalid
% 5.13/5.47 thf(fact_822_pred__list__to__short,axiom,
% 5.13/5.47 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.13/5.47 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.13/5.47 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.13/5.47 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.47 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.47 = none_nat ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % pred_list_to_short
% 5.13/5.47 thf(fact_823_set__n__deg__not__0,axiom,
% 5.13/5.47 ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 5.13/5.47 ( ! [X3: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.47 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.13/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.13/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.47 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % set_n_deg_not_0
% 5.13/5.47 thf(fact_824_add__shift,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ( plus_plus_nat @ X @ Y4 )
% 5.13/5.47 = Z2 )
% 5.13/5.47 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y4 ) )
% 5.13/5.47 = ( some_nat @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % add_shift
% 5.13/5.47 thf(fact_825_mul__shift,axiom,
% 5.13/5.47 ! [X: nat,Y4: nat,Z2: nat] :
% 5.13/5.47 ( ( ( times_times_nat @ X @ Y4 )
% 5.13/5.47 = Z2 )
% 5.13/5.47 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y4 ) )
% 5.13/5.47 = ( some_nat @ Z2 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mul_shift
% 5.13/5.47 thf(fact_826__092_060open_0621_A_092_060le_062_An_092_060close_062,axiom,
% 5.13/5.47 ord_less_eq_nat @ one_one_nat @ na ).
% 5.13/5.47
% 5.13/5.47 % \<open>1 \<le> n\<close>
% 5.13/5.47 thf(fact_827_mul__def,axiom,
% 5.13/5.47 ( vEBT_VEBT_mul
% 5.13/5.47 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.13/5.47
% 5.13/5.47 % mul_def
% 5.13/5.47 thf(fact_828_VEBT_Oinject_I1_J,axiom,
% 5.13/5.47 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.13/5.47 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.13/5.47 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.13/5.47 = ( ( X11 = Y11 )
% 5.13/5.47 & ( X12 = Y12 )
% 5.13/5.47 & ( X13 = Y13 )
% 5.13/5.47 & ( X14 = Y14 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % VEBT.inject(1)
% 5.13/5.47 thf(fact_829_mi__eq__ma__no__ch,axiom,
% 5.13/5.47 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.13/5.47 => ( ( Mi = Ma )
% 5.13/5.47 => ( ! [X5: vEBT_VEBT] :
% 5.13/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.47 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.13/5.47 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mi_eq_ma_no_ch
% 5.13/5.47 thf(fact_830_numeral__times__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.13/5.47 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_times_numeral
% 5.13/5.47 thf(fact_831_numeral__times__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.13/5.47 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_times_numeral
% 5.13/5.47 thf(fact_832_numeral__times__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.13/5.47 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_times_numeral
% 5.13/5.47 thf(fact_833_numeral__times__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.47 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_times_numeral
% 5.13/5.47 thf(fact_834_numeral__times__numeral,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.13/5.47 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_times_numeral
% 5.13/5.47 thf(fact_835_mult__numeral__left__semiring__numeral,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: complex] :
% 5.13/5.47 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % mult_numeral_left_semiring_numeral
% 5.13/5.47 thf(fact_836_mult__numeral__left__semiring__numeral,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: real] :
% 5.13/5.47 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % mult_numeral_left_semiring_numeral
% 5.13/5.47 thf(fact_837_mult__numeral__left__semiring__numeral,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: rat] :
% 5.13/5.47 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % mult_numeral_left_semiring_numeral
% 5.13/5.47 thf(fact_838_mult__numeral__left__semiring__numeral,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: nat] :
% 5.13/5.47 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % mult_numeral_left_semiring_numeral
% 5.13/5.47 thf(fact_839_mult__numeral__left__semiring__numeral,axiom,
% 5.13/5.47 ! [V: num,W2: num,Z2: int] :
% 5.13/5.47 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 5.13/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 5.13/5.47
% 5.13/5.47 % mult_numeral_left_semiring_numeral
% 5.13/5.47 thf(fact_840_high__inv,axiom,
% 5.13/5.47 ! [X: nat,N: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.13/5.47 = Y4 ) ) ).
% 5.13/5.47
% 5.13/5.47 % high_inv
% 5.13/5.47 thf(fact_841_low__inv,axiom,
% 5.13/5.47 ! [X: nat,N: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.47 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.13/5.47 = X ) ) ).
% 5.13/5.47
% 5.13/5.47 % low_inv
% 5.13/5.47 thf(fact_842_bit__concat__def,axiom,
% 5.13/5.47 ( vEBT_VEBT_bit_concat
% 5.13/5.47 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % bit_concat_def
% 5.13/5.47 thf(fact_843_power__one,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( power_power_rat @ one_one_rat @ N )
% 5.13/5.47 = one_one_rat ) ).
% 5.13/5.47
% 5.13/5.47 % power_one
% 5.13/5.47 thf(fact_844_power__one,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( power_power_nat @ one_one_nat @ N )
% 5.13/5.47 = one_one_nat ) ).
% 5.13/5.47
% 5.13/5.47 % power_one
% 5.13/5.47 thf(fact_845_power__one,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( power_power_real @ one_one_real @ N )
% 5.13/5.47 = one_one_real ) ).
% 5.13/5.47
% 5.13/5.47 % power_one
% 5.13/5.47 thf(fact_846_power__one,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( power_power_int @ one_one_int @ N )
% 5.13/5.47 = one_one_int ) ).
% 5.13/5.47
% 5.13/5.47 % power_one
% 5.13/5.47 thf(fact_847_power__one,axiom,
% 5.13/5.47 ! [N: nat] :
% 5.13/5.47 ( ( power_power_complex @ one_one_complex @ N )
% 5.13/5.47 = one_one_complex ) ).
% 5.13/5.47
% 5.13/5.47 % power_one
% 5.13/5.47 thf(fact_848_insert__simp__mima,axiom,
% 5.13/5.47 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.13/5.47 ( ( ( X = Mi )
% 5.13/5.47 | ( X = Ma ) )
% 5.13/5.47 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.13/5.47 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % insert_simp_mima
% 5.13/5.47 thf(fact_849_power__one__right,axiom,
% 5.13/5.47 ! [A: nat] :
% 5.13/5.47 ( ( power_power_nat @ A @ one_one_nat )
% 5.13/5.47 = A ) ).
% 5.13/5.47
% 5.13/5.47 % power_one_right
% 5.13/5.47 thf(fact_850_power__one__right,axiom,
% 5.13/5.47 ! [A: real] :
% 5.13/5.47 ( ( power_power_real @ A @ one_one_nat )
% 5.13/5.47 = A ) ).
% 5.13/5.47
% 5.13/5.47 % power_one_right
% 5.13/5.47 thf(fact_851_power__one__right,axiom,
% 5.13/5.47 ! [A: int] :
% 5.13/5.47 ( ( power_power_int @ A @ one_one_nat )
% 5.13/5.47 = A ) ).
% 5.13/5.47
% 5.13/5.47 % power_one_right
% 5.13/5.47 thf(fact_852_power__one__right,axiom,
% 5.13/5.47 ! [A: complex] :
% 5.13/5.47 ( ( power_power_complex @ A @ one_one_nat )
% 5.13/5.47 = A ) ).
% 5.13/5.47
% 5.13/5.47 % power_one_right
% 5.13/5.47 thf(fact_853_semiring__norm_I6_J,axiom,
% 5.13/5.47 ! [M: num,N: num] :
% 5.13/5.47 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.13/5.47 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % semiring_norm(6)
% 5.13/5.47 thf(fact_854_mi__ma__2__deg,axiom,
% 5.13/5.47 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.13/5.47 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.13/5.47 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % mi_ma_2_deg
% 5.13/5.47 thf(fact_855_pred__max,axiom,
% 5.13/5.47 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.13/5.47 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.13/5.47 => ( ( ord_less_nat @ Ma @ X )
% 5.13/5.47 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.47 = ( some_nat @ Ma ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % pred_max
% 5.13/5.47 thf(fact_856_distrib__left__numeral,axiom,
% 5.13/5.47 ! [V: num,B: complex,C: complex] :
% 5.13/5.47 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.13/5.47 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_left_numeral
% 5.13/5.47 thf(fact_857_distrib__left__numeral,axiom,
% 5.13/5.47 ! [V: num,B: real,C: real] :
% 5.13/5.47 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.13/5.47 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_left_numeral
% 5.13/5.47 thf(fact_858_distrib__left__numeral,axiom,
% 5.13/5.47 ! [V: num,B: rat,C: rat] :
% 5.13/5.47 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.47 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_left_numeral
% 5.13/5.47 thf(fact_859_distrib__left__numeral,axiom,
% 5.13/5.47 ! [V: num,B: nat,C: nat] :
% 5.13/5.47 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.47 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_left_numeral
% 5.13/5.47 thf(fact_860_distrib__left__numeral,axiom,
% 5.13/5.47 ! [V: num,B: int,C: int] :
% 5.13/5.47 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.13/5.47 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_left_numeral
% 5.13/5.47 thf(fact_861_distrib__right__numeral,axiom,
% 5.13/5.47 ! [A: complex,B: complex,V: num] :
% 5.13/5.47 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.13/5.47 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_right_numeral
% 5.13/5.47 thf(fact_862_distrib__right__numeral,axiom,
% 5.13/5.47 ! [A: real,B: real,V: num] :
% 5.13/5.47 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.13/5.47 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_right_numeral
% 5.13/5.47 thf(fact_863_distrib__right__numeral,axiom,
% 5.13/5.47 ! [A: rat,B: rat,V: num] :
% 5.13/5.47 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.13/5.47 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_right_numeral
% 5.13/5.47 thf(fact_864_distrib__right__numeral,axiom,
% 5.13/5.47 ! [A: nat,B: nat,V: num] :
% 5.13/5.47 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.13/5.47 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_right_numeral
% 5.13/5.47 thf(fact_865_distrib__right__numeral,axiom,
% 5.13/5.47 ! [A: int,B: int,V: num] :
% 5.13/5.47 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.13/5.47 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % distrib_right_numeral
% 5.13/5.47 thf(fact_866_one__eq__numeral__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( one_one_complex
% 5.13/5.47 = ( numera6690914467698888265omplex @ N ) )
% 5.13/5.47 = ( one = N ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_eq_numeral_iff
% 5.13/5.47 thf(fact_867_one__eq__numeral__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( one_one_real
% 5.13/5.47 = ( numeral_numeral_real @ N ) )
% 5.13/5.47 = ( one = N ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_eq_numeral_iff
% 5.13/5.47 thf(fact_868_one__eq__numeral__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( one_one_rat
% 5.13/5.47 = ( numeral_numeral_rat @ N ) )
% 5.13/5.47 = ( one = N ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_eq_numeral_iff
% 5.13/5.47 thf(fact_869_one__eq__numeral__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( one_one_nat
% 5.13/5.47 = ( numeral_numeral_nat @ N ) )
% 5.13/5.47 = ( one = N ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_eq_numeral_iff
% 5.13/5.47 thf(fact_870_one__eq__numeral__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( one_one_int
% 5.13/5.47 = ( numeral_numeral_int @ N ) )
% 5.13/5.47 = ( one = N ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_eq_numeral_iff
% 5.13/5.47 thf(fact_871_numeral__eq__one__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( ( numera6690914467698888265omplex @ N )
% 5.13/5.47 = one_one_complex )
% 5.13/5.47 = ( N = one ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_eq_one_iff
% 5.13/5.47 thf(fact_872_numeral__eq__one__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( ( numeral_numeral_real @ N )
% 5.13/5.47 = one_one_real )
% 5.13/5.47 = ( N = one ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_eq_one_iff
% 5.13/5.47 thf(fact_873_numeral__eq__one__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( ( numeral_numeral_rat @ N )
% 5.13/5.47 = one_one_rat )
% 5.13/5.47 = ( N = one ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_eq_one_iff
% 5.13/5.47 thf(fact_874_numeral__eq__one__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( ( numeral_numeral_nat @ N )
% 5.13/5.47 = one_one_nat )
% 5.13/5.47 = ( N = one ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_eq_one_iff
% 5.13/5.47 thf(fact_875_numeral__eq__one__iff,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( ( numeral_numeral_int @ N )
% 5.13/5.47 = one_one_int )
% 5.13/5.47 = ( N = one ) ) ).
% 5.13/5.47
% 5.13/5.47 % numeral_eq_one_iff
% 5.13/5.47 thf(fact_876_power__inject__exp,axiom,
% 5.13/5.47 ! [A: real,M: nat,N: nat] :
% 5.13/5.47 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.47 => ( ( ( power_power_real @ A @ M )
% 5.13/5.47 = ( power_power_real @ A @ N ) )
% 5.13/5.47 = ( M = N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_inject_exp
% 5.13/5.47 thf(fact_877_power__inject__exp,axiom,
% 5.13/5.47 ! [A: rat,M: nat,N: nat] :
% 5.13/5.47 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.47 => ( ( ( power_power_rat @ A @ M )
% 5.13/5.47 = ( power_power_rat @ A @ N ) )
% 5.13/5.47 = ( M = N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_inject_exp
% 5.13/5.47 thf(fact_878_power__inject__exp,axiom,
% 5.13/5.47 ! [A: nat,M: nat,N: nat] :
% 5.13/5.47 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.47 => ( ( ( power_power_nat @ A @ M )
% 5.13/5.47 = ( power_power_nat @ A @ N ) )
% 5.13/5.47 = ( M = N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_inject_exp
% 5.13/5.47 thf(fact_879_power__inject__exp,axiom,
% 5.13/5.47 ! [A: int,M: nat,N: nat] :
% 5.13/5.47 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.47 => ( ( ( power_power_int @ A @ M )
% 5.13/5.47 = ( power_power_int @ A @ N ) )
% 5.13/5.47 = ( M = N ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_inject_exp
% 5.13/5.47 thf(fact_880_summaxma,axiom,
% 5.13/5.47 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.13/5.47 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.13/5.47 => ( ( Mi != Ma )
% 5.13/5.47 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.13/5.47 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % summaxma
% 5.13/5.47 thf(fact_881_semiring__norm_I2_J,axiom,
% 5.13/5.47 ( ( plus_plus_num @ one @ one )
% 5.13/5.47 = ( bit0 @ one ) ) ).
% 5.13/5.47
% 5.13/5.47 % semiring_norm(2)
% 5.13/5.47 thf(fact_882_both__member__options__from__complete__tree__to__child,axiom,
% 5.13/5.47 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.13/5.47 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.13/5.47 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.47 => ( ( 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 ) ) ) ) )
% 5.13/5.47 | ( X = Mi )
% 5.13/5.47 | ( X = Ma ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % both_member_options_from_complete_tree_to_child
% 5.13/5.47 thf(fact_883_le__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [A: real,B: real,W2: num] :
% 5.13/5.47 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 5.13/5.47 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_divide_eq_numeral1(1)
% 5.13/5.47 thf(fact_884_le__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [A: rat,B: rat,W2: num] :
% 5.13/5.47 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.13/5.47 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % le_divide_eq_numeral1(1)
% 5.13/5.47 thf(fact_885_divide__le__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [B: real,W2: num,A: real] :
% 5.13/5.47 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 5.13/5.47 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % divide_le_eq_numeral1(1)
% 5.13/5.47 thf(fact_886_divide__le__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [B: rat,W2: num,A: rat] :
% 5.13/5.47 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 5.13/5.47 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % divide_le_eq_numeral1(1)
% 5.13/5.47 thf(fact_887_less__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [A: real,B: real,W2: num] :
% 5.13/5.47 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 5.13/5.47 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_divide_eq_numeral1(1)
% 5.13/5.47 thf(fact_888_less__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [A: rat,B: rat,W2: num] :
% 5.13/5.47 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.13/5.47 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % less_divide_eq_numeral1(1)
% 5.13/5.47 thf(fact_889_divide__less__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [B: real,W2: num,A: real] :
% 5.13/5.47 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 5.13/5.47 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % divide_less_eq_numeral1(1)
% 5.13/5.47 thf(fact_890_divide__less__eq__numeral1_I1_J,axiom,
% 5.13/5.47 ! [B: rat,W2: num,A: rat] :
% 5.13/5.47 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 5.13/5.47 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % divide_less_eq_numeral1(1)
% 5.13/5.47 thf(fact_891_power__strict__increasing__iff,axiom,
% 5.13/5.47 ! [B: real,X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_real @ one_one_real @ B )
% 5.13/5.47 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y4 ) )
% 5.13/5.47 = ( ord_less_nat @ X @ Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_strict_increasing_iff
% 5.13/5.47 thf(fact_892_power__strict__increasing__iff,axiom,
% 5.13/5.47 ! [B: rat,X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_rat @ one_one_rat @ B )
% 5.13/5.47 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y4 ) )
% 5.13/5.47 = ( ord_less_nat @ X @ Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_strict_increasing_iff
% 5.13/5.47 thf(fact_893_power__strict__increasing__iff,axiom,
% 5.13/5.47 ! [B: nat,X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_nat @ one_one_nat @ B )
% 5.13/5.47 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y4 ) )
% 5.13/5.47 = ( ord_less_nat @ X @ Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_strict_increasing_iff
% 5.13/5.47 thf(fact_894_power__strict__increasing__iff,axiom,
% 5.13/5.47 ! [B: int,X: nat,Y4: nat] :
% 5.13/5.47 ( ( ord_less_int @ one_one_int @ B )
% 5.13/5.47 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y4 ) )
% 5.13/5.47 = ( ord_less_nat @ X @ Y4 ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_strict_increasing_iff
% 5.13/5.47 thf(fact_895_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.13/5.47 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.13/5.47 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.47 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.13/5.47 => ( ( 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 ) ) ) ) )
% 5.13/5.47 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % both_member_options_from_chilf_to_complete_tree
% 5.13/5.47 thf(fact_896_power__add__numeral2,axiom,
% 5.13/5.47 ! [A: complex,M: num,N: num,B: complex] :
% 5.13/5.47 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.13/5.47 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral2
% 5.13/5.47 thf(fact_897_power__add__numeral2,axiom,
% 5.13/5.47 ! [A: real,M: num,N: num,B: real] :
% 5.13/5.47 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.13/5.47 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral2
% 5.13/5.47 thf(fact_898_power__add__numeral2,axiom,
% 5.13/5.47 ! [A: rat,M: num,N: num,B: rat] :
% 5.13/5.47 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.13/5.47 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral2
% 5.13/5.47 thf(fact_899_power__add__numeral2,axiom,
% 5.13/5.47 ! [A: nat,M: num,N: num,B: nat] :
% 5.13/5.47 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.13/5.47 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral2
% 5.13/5.47 thf(fact_900_power__add__numeral2,axiom,
% 5.13/5.47 ! [A: int,M: num,N: num,B: int] :
% 5.13/5.47 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.13/5.47 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral2
% 5.13/5.47 thf(fact_901_power__add__numeral,axiom,
% 5.13/5.47 ! [A: complex,M: num,N: num] :
% 5.13/5.47 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.13/5.47 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral
% 5.13/5.47 thf(fact_902_power__add__numeral,axiom,
% 5.13/5.47 ! [A: real,M: num,N: num] :
% 5.13/5.47 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.13/5.47 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral
% 5.13/5.47 thf(fact_903_power__add__numeral,axiom,
% 5.13/5.47 ! [A: rat,M: num,N: num] :
% 5.13/5.47 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.13/5.47 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral
% 5.13/5.47 thf(fact_904_power__add__numeral,axiom,
% 5.13/5.47 ! [A: nat,M: num,N: num] :
% 5.13/5.47 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.13/5.47 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral
% 5.13/5.47 thf(fact_905_power__add__numeral,axiom,
% 5.13/5.47 ! [A: int,M: num,N: num] :
% 5.13/5.47 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.13/5.47 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % power_add_numeral
% 5.13/5.47 thf(fact_906_Suc__numeral,axiom,
% 5.13/5.47 ! [N: num] :
% 5.13/5.47 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.13/5.47 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % Suc_numeral
% 5.13/5.47 thf(fact_907_one__add__one,axiom,
% 5.13/5.47 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.13/5.47 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_add_one
% 5.13/5.47 thf(fact_908_one__add__one,axiom,
% 5.13/5.47 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.13/5.47 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_add_one
% 5.13/5.47 thf(fact_909_one__add__one,axiom,
% 5.13/5.47 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.13/5.47 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.13/5.47
% 5.13/5.47 % one_add_one
% 5.13/5.47 thf(fact_910_one__add__one,axiom,
% 5.13/5.47 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.13/5.47 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_add_one
% 5.13/5.48 thf(fact_911_one__add__one,axiom,
% 5.13/5.48 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.13/5.48 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_add_one
% 5.13/5.48 thf(fact_912_power__increasing__iff,axiom,
% 5.13/5.48 ! [B: real,X: nat,Y4: nat] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.13/5.48 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y4 ) )
% 5.13/5.48 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing_iff
% 5.13/5.48 thf(fact_913_power__increasing__iff,axiom,
% 5.13/5.48 ! [B: rat,X: nat,Y4: nat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ B )
% 5.13/5.48 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y4 ) )
% 5.13/5.48 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing_iff
% 5.13/5.48 thf(fact_914_power__increasing__iff,axiom,
% 5.13/5.48 ! [B: nat,X: nat,Y4: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y4 ) )
% 5.13/5.48 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing_iff
% 5.13/5.48 thf(fact_915_power__increasing__iff,axiom,
% 5.13/5.48 ! [B: int,X: nat,Y4: nat] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ B )
% 5.13/5.48 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y4 ) )
% 5.13/5.48 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing_iff
% 5.13/5.48 thf(fact_916_nested__mint,axiom,
% 5.13/5.48 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.13/5.48 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.13/5.48 => ( ( N
% 5.13/5.48 = ( suc @ ( suc @ Va ) ) )
% 5.13/5.48 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.13/5.48 => ( ( Ma != Mi )
% 5.13/5.48 => ( 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 ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nested_mint
% 5.13/5.48 thf(fact_917_Suc__1,axiom,
% 5.13/5.48 ( ( suc @ one_one_nat )
% 5.13/5.48 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_1
% 5.13/5.48 thf(fact_918_one__plus__numeral,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.13/5.48 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral
% 5.13/5.48 thf(fact_919_one__plus__numeral,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.13/5.48 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral
% 5.13/5.48 thf(fact_920_one__plus__numeral,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.13/5.48 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral
% 5.13/5.48 thf(fact_921_one__plus__numeral,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.13/5.48 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral
% 5.13/5.48 thf(fact_922_one__plus__numeral,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.13/5.48 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral
% 5.13/5.48 thf(fact_923_numeral__plus__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.13/5.48 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_plus_one
% 5.13/5.48 thf(fact_924_numeral__plus__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.13/5.48 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_plus_one
% 5.13/5.48 thf(fact_925_numeral__plus__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.13/5.48 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_plus_one
% 5.13/5.48 thf(fact_926_numeral__plus__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.13/5.48 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_plus_one
% 5.13/5.48 thf(fact_927_numeral__plus__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.13/5.48 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_plus_one
% 5.13/5.48 thf(fact_928_numeral__le__one__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.13/5.48 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_le_one_iff
% 5.13/5.48 thf(fact_929_numeral__le__one__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.13/5.48 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_le_one_iff
% 5.13/5.48 thf(fact_930_numeral__le__one__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.13/5.48 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_le_one_iff
% 5.13/5.48 thf(fact_931_numeral__le__one__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.13/5.48 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_le_one_iff
% 5.13/5.48 thf(fact_932_one__less__numeral__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.13/5.48 = ( ord_less_num @ one @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_less_numeral_iff
% 5.13/5.48 thf(fact_933_one__less__numeral__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.13/5.48 = ( ord_less_num @ one @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_less_numeral_iff
% 5.13/5.48 thf(fact_934_one__less__numeral__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.13/5.48 = ( ord_less_num @ one @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_less_numeral_iff
% 5.13/5.48 thf(fact_935_one__less__numeral__iff,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.13/5.48 = ( ord_less_num @ one @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_less_numeral_iff
% 5.13/5.48 thf(fact_936_fst,axiom,
% 5.13/5.48 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.13/5.48 = ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % fst
% 5.13/5.48 thf(fact_937__C2_C,axiom,
% 5.13/5.48 ( ( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.48 = none_nat )
% 5.13/5.48 => ( ( ( ord_less_nat @ mi @ xa )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.13/5.48 = ( some_nat @ mi ) ) )
% 5.13/5.48 & ( ~ ( ord_less_nat @ mi @ xa )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.13/5.48 = none_nat ) ) ) )
% 5.13/5.48 & ( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.48 != none_nat )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.13/5.48 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % "2"
% 5.13/5.48 thf(fact_938_left__right__inverse__power,axiom,
% 5.13/5.48 ! [X: complex,Y4: complex,N: nat] :
% 5.13/5.48 ( ( ( times_times_complex @ X @ Y4 )
% 5.13/5.48 = one_one_complex )
% 5.13/5.48 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ N ) )
% 5.13/5.48 = one_one_complex ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_right_inverse_power
% 5.13/5.48 thf(fact_939_left__right__inverse__power,axiom,
% 5.13/5.48 ! [X: real,Y4: real,N: nat] :
% 5.13/5.48 ( ( ( times_times_real @ X @ Y4 )
% 5.13/5.48 = one_one_real )
% 5.13/5.48 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ N ) )
% 5.13/5.48 = one_one_real ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_right_inverse_power
% 5.13/5.48 thf(fact_940_left__right__inverse__power,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat,N: nat] :
% 5.13/5.48 ( ( ( times_times_rat @ X @ Y4 )
% 5.13/5.48 = one_one_rat )
% 5.13/5.48 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y4 @ N ) )
% 5.13/5.48 = one_one_rat ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_right_inverse_power
% 5.13/5.48 thf(fact_941_left__right__inverse__power,axiom,
% 5.13/5.48 ! [X: nat,Y4: nat,N: nat] :
% 5.13/5.48 ( ( ( times_times_nat @ X @ Y4 )
% 5.13/5.48 = one_one_nat )
% 5.13/5.48 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y4 @ N ) )
% 5.13/5.48 = one_one_nat ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_right_inverse_power
% 5.13/5.48 thf(fact_942_left__right__inverse__power,axiom,
% 5.13/5.48 ! [X: int,Y4: int,N: nat] :
% 5.13/5.48 ( ( ( times_times_int @ X @ Y4 )
% 5.13/5.48 = one_one_int )
% 5.13/5.48 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ N ) )
% 5.13/5.48 = one_one_int ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_right_inverse_power
% 5.13/5.48 thf(fact_943_power__less__power__Suc,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.48 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_power_Suc
% 5.13/5.48 thf(fact_944_power__less__power__Suc,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_power_Suc
% 5.13/5.48 thf(fact_945_power__less__power__Suc,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_power_Suc
% 5.13/5.48 thf(fact_946_power__less__power__Suc,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.48 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_power_Suc
% 5.13/5.48 thf(fact_947_power__gt1__lemma,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.48 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1_lemma
% 5.13/5.48 thf(fact_948_power__gt1__lemma,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1_lemma
% 5.13/5.48 thf(fact_949_power__gt1__lemma,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1_lemma
% 5.13/5.48 thf(fact_950_power__gt1__lemma,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.48 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1_lemma
% 5.13/5.48 thf(fact_951_add__One__commute,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( plus_plus_num @ one @ N )
% 5.13/5.48 = ( plus_plus_num @ N @ one ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_One_commute
% 5.13/5.48 thf(fact_952_power__commutes,axiom,
% 5.13/5.48 ! [A: complex,N: nat] :
% 5.13/5.48 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.13/5.48 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commutes
% 5.13/5.48 thf(fact_953_power__commutes,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.13/5.48 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commutes
% 5.13/5.48 thf(fact_954_power__commutes,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.13/5.48 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commutes
% 5.13/5.48 thf(fact_955_power__commutes,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.13/5.48 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commutes
% 5.13/5.48 thf(fact_956_power__commutes,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.13/5.48 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commutes
% 5.13/5.48 thf(fact_957_power__mult__distrib,axiom,
% 5.13/5.48 ! [A: complex,B: complex,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.13/5.48 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_distrib
% 5.13/5.48 thf(fact_958_power__mult__distrib,axiom,
% 5.13/5.48 ! [A: real,B: real,N: nat] :
% 5.13/5.48 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.13/5.48 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_distrib
% 5.13/5.48 thf(fact_959_power__mult__distrib,axiom,
% 5.13/5.48 ! [A: rat,B: rat,N: nat] :
% 5.13/5.48 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.13/5.48 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_distrib
% 5.13/5.48 thf(fact_960_power__mult__distrib,axiom,
% 5.13/5.48 ! [A: nat,B: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.13/5.48 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_distrib
% 5.13/5.48 thf(fact_961_power__mult__distrib,axiom,
% 5.13/5.48 ! [A: int,B: int,N: nat] :
% 5.13/5.48 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.13/5.48 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_distrib
% 5.13/5.48 thf(fact_962_power__commuting__commutes,axiom,
% 5.13/5.48 ! [X: complex,Y4: complex,N: nat] :
% 5.13/5.48 ( ( ( times_times_complex @ X @ Y4 )
% 5.13/5.48 = ( times_times_complex @ Y4 @ X ) )
% 5.13/5.48 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y4 )
% 5.13/5.48 = ( times_times_complex @ Y4 @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commuting_commutes
% 5.13/5.48 thf(fact_963_power__commuting__commutes,axiom,
% 5.13/5.48 ! [X: real,Y4: real,N: nat] :
% 5.13/5.48 ( ( ( times_times_real @ X @ Y4 )
% 5.13/5.48 = ( times_times_real @ Y4 @ X ) )
% 5.13/5.48 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y4 )
% 5.13/5.48 = ( times_times_real @ Y4 @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commuting_commutes
% 5.13/5.48 thf(fact_964_power__commuting__commutes,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat,N: nat] :
% 5.13/5.48 ( ( ( times_times_rat @ X @ Y4 )
% 5.13/5.48 = ( times_times_rat @ Y4 @ X ) )
% 5.13/5.48 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y4 )
% 5.13/5.48 = ( times_times_rat @ Y4 @ ( power_power_rat @ X @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commuting_commutes
% 5.13/5.48 thf(fact_965_power__commuting__commutes,axiom,
% 5.13/5.48 ! [X: nat,Y4: nat,N: nat] :
% 5.13/5.48 ( ( ( times_times_nat @ X @ Y4 )
% 5.13/5.48 = ( times_times_nat @ Y4 @ X ) )
% 5.13/5.48 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y4 )
% 5.13/5.48 = ( times_times_nat @ Y4 @ ( power_power_nat @ X @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commuting_commutes
% 5.13/5.48 thf(fact_966_power__commuting__commutes,axiom,
% 5.13/5.48 ! [X: int,Y4: int,N: nat] :
% 5.13/5.48 ( ( ( times_times_int @ X @ Y4 )
% 5.13/5.48 = ( times_times_int @ Y4 @ X ) )
% 5.13/5.48 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y4 )
% 5.13/5.48 = ( times_times_int @ Y4 @ ( power_power_int @ X @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_commuting_commutes
% 5.13/5.48 thf(fact_967_power__mult,axiom,
% 5.13/5.48 ! [A: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.13/5.48 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult
% 5.13/5.48 thf(fact_968_power__mult,axiom,
% 5.13/5.48 ! [A: real,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.13/5.48 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult
% 5.13/5.48 thf(fact_969_power__mult,axiom,
% 5.13/5.48 ! [A: int,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.13/5.48 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult
% 5.13/5.48 thf(fact_970_power__mult,axiom,
% 5.13/5.48 ! [A: complex,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.13/5.48 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult
% 5.13/5.48 thf(fact_971_le__numeral__extra_I4_J,axiom,
% 5.13/5.48 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.13/5.48
% 5.13/5.48 % le_numeral_extra(4)
% 5.13/5.48 thf(fact_972_le__numeral__extra_I4_J,axiom,
% 5.13/5.48 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.13/5.48
% 5.13/5.48 % le_numeral_extra(4)
% 5.13/5.48 thf(fact_973_le__numeral__extra_I4_J,axiom,
% 5.13/5.48 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.13/5.48
% 5.13/5.48 % le_numeral_extra(4)
% 5.13/5.48 thf(fact_974_le__numeral__extra_I4_J,axiom,
% 5.13/5.48 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.13/5.48
% 5.13/5.48 % le_numeral_extra(4)
% 5.13/5.48 thf(fact_975_less__numeral__extra_I4_J,axiom,
% 5.13/5.48 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.13/5.48
% 5.13/5.48 % less_numeral_extra(4)
% 5.13/5.48 thf(fact_976_less__numeral__extra_I4_J,axiom,
% 5.13/5.48 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.13/5.48
% 5.13/5.48 % less_numeral_extra(4)
% 5.13/5.48 thf(fact_977_less__numeral__extra_I4_J,axiom,
% 5.13/5.48 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.13/5.48
% 5.13/5.48 % less_numeral_extra(4)
% 5.13/5.48 thf(fact_978_less__numeral__extra_I4_J,axiom,
% 5.13/5.48 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.13/5.48
% 5.13/5.48 % less_numeral_extra(4)
% 5.13/5.48 thf(fact_979_left__add__mult__distrib,axiom,
% 5.13/5.48 ! [I2: nat,U2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ K ) )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U2 ) @ K ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_add_mult_distrib
% 5.13/5.48 thf(fact_980_div__mult2__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat,Q2: nat] :
% 5.13/5.48 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.13/5.48 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % div_mult2_eq
% 5.13/5.48 thf(fact_981_mult__numeral__1__right,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1_right
% 5.13/5.48 thf(fact_982_mult__numeral__1__right,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1_right
% 5.13/5.48 thf(fact_983_mult__numeral__1__right,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1_right
% 5.13/5.48 thf(fact_984_mult__numeral__1__right,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1_right
% 5.13/5.48 thf(fact_985_mult__numeral__1__right,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1_right
% 5.13/5.48 thf(fact_986_mult__numeral__1,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1
% 5.13/5.48 thf(fact_987_mult__numeral__1,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1
% 5.13/5.48 thf(fact_988_mult__numeral__1,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1
% 5.13/5.48 thf(fact_989_mult__numeral__1,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1
% 5.13/5.48 thf(fact_990_mult__numeral__1,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_numeral_1
% 5.13/5.48 thf(fact_991_power__Suc2,axiom,
% 5.13/5.48 ! [A: complex,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc2
% 5.13/5.48 thf(fact_992_power__Suc2,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc2
% 5.13/5.48 thf(fact_993_power__Suc2,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc2
% 5.13/5.48 thf(fact_994_power__Suc2,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc2
% 5.13/5.48 thf(fact_995_power__Suc2,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc2
% 5.13/5.48 thf(fact_996_power__Suc,axiom,
% 5.13/5.48 ! [A: complex,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc
% 5.13/5.48 thf(fact_997_power__Suc,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc
% 5.13/5.48 thf(fact_998_power__Suc,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc
% 5.13/5.48 thf(fact_999_power__Suc,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc
% 5.13/5.48 thf(fact_1000_power__Suc,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.13/5.48 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_Suc
% 5.13/5.48 thf(fact_1001_power__add,axiom,
% 5.13/5.48 ! [A: complex,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.48 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_add
% 5.13/5.48 thf(fact_1002_power__add,axiom,
% 5.13/5.48 ! [A: real,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.48 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_add
% 5.13/5.48 thf(fact_1003_power__add,axiom,
% 5.13/5.48 ! [A: rat,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.48 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_add
% 5.13/5.48 thf(fact_1004_power__add,axiom,
% 5.13/5.48 ! [A: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.48 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_add
% 5.13/5.48 thf(fact_1005_power__add,axiom,
% 5.13/5.48 ! [A: int,M: nat,N: nat] :
% 5.13/5.48 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.48 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_add
% 5.13/5.48 thf(fact_1006_one__le__numeral,axiom,
% 5.13/5.48 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_numeral
% 5.13/5.48 thf(fact_1007_one__le__numeral,axiom,
% 5.13/5.48 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_numeral
% 5.13/5.48 thf(fact_1008_one__le__numeral,axiom,
% 5.13/5.48 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_numeral
% 5.13/5.48 thf(fact_1009_one__le__numeral,axiom,
% 5.13/5.48 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_numeral
% 5.13/5.48 thf(fact_1010_not__numeral__less__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.13/5.48
% 5.13/5.48 % not_numeral_less_one
% 5.13/5.48 thf(fact_1011_not__numeral__less__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.13/5.48
% 5.13/5.48 % not_numeral_less_one
% 5.13/5.48 thf(fact_1012_not__numeral__less__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.13/5.48
% 5.13/5.48 % not_numeral_less_one
% 5.13/5.48 thf(fact_1013_not__numeral__less__one,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.13/5.48
% 5.13/5.48 % not_numeral_less_one
% 5.13/5.48 thf(fact_1014_one__plus__numeral__commute,axiom,
% 5.13/5.48 ! [X: num] :
% 5.13/5.48 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.13/5.48 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral_commute
% 5.13/5.48 thf(fact_1015_one__plus__numeral__commute,axiom,
% 5.13/5.48 ! [X: num] :
% 5.13/5.48 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.13/5.48 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral_commute
% 5.13/5.48 thf(fact_1016_one__plus__numeral__commute,axiom,
% 5.13/5.48 ! [X: num] :
% 5.13/5.48 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.13/5.48 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral_commute
% 5.13/5.48 thf(fact_1017_one__plus__numeral__commute,axiom,
% 5.13/5.48 ! [X: num] :
% 5.13/5.48 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.13/5.48 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral_commute
% 5.13/5.48 thf(fact_1018_one__plus__numeral__commute,axiom,
% 5.13/5.48 ! [X: num] :
% 5.13/5.48 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.13/5.48 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_plus_numeral_commute
% 5.13/5.48 thf(fact_1019_numeral__One,axiom,
% 5.13/5.48 ( ( numera6690914467698888265omplex @ one )
% 5.13/5.48 = one_one_complex ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_One
% 5.13/5.48 thf(fact_1020_numeral__One,axiom,
% 5.13/5.48 ( ( numeral_numeral_real @ one )
% 5.13/5.48 = one_one_real ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_One
% 5.13/5.48 thf(fact_1021_numeral__One,axiom,
% 5.13/5.48 ( ( numeral_numeral_rat @ one )
% 5.13/5.48 = one_one_rat ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_One
% 5.13/5.48 thf(fact_1022_numeral__One,axiom,
% 5.13/5.48 ( ( numeral_numeral_nat @ one )
% 5.13/5.48 = one_one_nat ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_One
% 5.13/5.48 thf(fact_1023_numeral__One,axiom,
% 5.13/5.48 ( ( numeral_numeral_int @ one )
% 5.13/5.48 = one_one_int ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_One
% 5.13/5.48 thf(fact_1024_one__le__power,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.13/5.48 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_power
% 5.13/5.48 thf(fact_1025_one__le__power,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_power
% 5.13/5.48 thf(fact_1026_one__le__power,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_power
% 5.13/5.48 thf(fact_1027_one__le__power,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.13/5.48 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_le_power
% 5.13/5.48 thf(fact_1028_less__mult__imp__div__less,axiom,
% 5.13/5.48 ! [M: nat,I2: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N ) )
% 5.13/5.48 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_mult_imp_div_less
% 5.13/5.48 thf(fact_1029_times__div__less__eq__dividend,axiom,
% 5.13/5.48 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.13/5.48
% 5.13/5.48 % times_div_less_eq_dividend
% 5.13/5.48 thf(fact_1030_div__times__less__eq__dividend,axiom,
% 5.13/5.48 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.13/5.48
% 5.13/5.48 % div_times_less_eq_dividend
% 5.13/5.48 thf(fact_1031_power__one__over,axiom,
% 5.13/5.48 ! [A: complex,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.13/5.48 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_one_over
% 5.13/5.48 thf(fact_1032_power__one__over,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.13/5.48 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_one_over
% 5.13/5.48 thf(fact_1033_power__one__over,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.13/5.48 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_one_over
% 5.13/5.48 thf(fact_1034_numerals_I1_J,axiom,
% 5.13/5.48 ( ( numeral_numeral_nat @ one )
% 5.13/5.48 = one_one_nat ) ).
% 5.13/5.48
% 5.13/5.48 % numerals(1)
% 5.13/5.48 thf(fact_1035_power__odd__eq,axiom,
% 5.13/5.48 ! [A: complex,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.13/5.48 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_odd_eq
% 5.13/5.48 thf(fact_1036_power__odd__eq,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.13/5.48 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_odd_eq
% 5.13/5.48 thf(fact_1037_power__odd__eq,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.13/5.48 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_odd_eq
% 5.13/5.48 thf(fact_1038_power__odd__eq,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.13/5.48 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_odd_eq
% 5.13/5.48 thf(fact_1039_power__odd__eq,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.13/5.48 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_odd_eq
% 5.13/5.48 thf(fact_1040_power__gt1,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.48 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1
% 5.13/5.48 thf(fact_1041_power__gt1,axiom,
% 5.13/5.48 ! [A: rat,N: nat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1
% 5.13/5.48 thf(fact_1042_power__gt1,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1
% 5.13/5.48 thf(fact_1043_power__gt1,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.48 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_gt1
% 5.13/5.48 thf(fact_1044_power__less__imp__less__exp,axiom,
% 5.13/5.48 ! [A: real,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.48 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_imp_less_exp
% 5.13/5.48 thf(fact_1045_power__less__imp__less__exp,axiom,
% 5.13/5.48 ! [A: rat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_imp_less_exp
% 5.13/5.48 thf(fact_1046_power__less__imp__less__exp,axiom,
% 5.13/5.48 ! [A: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_imp_less_exp
% 5.13/5.48 thf(fact_1047_power__less__imp__less__exp,axiom,
% 5.13/5.48 ! [A: int,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.48 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_less_imp_less_exp
% 5.13/5.48 thf(fact_1048_power__strict__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: real] :
% 5.13/5.48 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.48 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_strict_increasing
% 5.13/5.48 thf(fact_1049_power__strict__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: rat] :
% 5.13/5.48 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_strict_increasing
% 5.13/5.48 thf(fact_1050_power__strict__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: nat] :
% 5.13/5.48 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_strict_increasing
% 5.13/5.48 thf(fact_1051_power__strict__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: int] :
% 5.13/5.48 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.48 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_strict_increasing
% 5.13/5.48 thf(fact_1052_power__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: real] :
% 5.13/5.48 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.13/5.48 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing
% 5.13/5.48 thf(fact_1053_power__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: rat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing
% 5.13/5.48 thf(fact_1054_power__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing
% 5.13/5.48 thf(fact_1055_power__increasing,axiom,
% 5.13/5.48 ! [N: nat,N4: nat,A: int] :
% 5.13/5.48 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.48 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.13/5.48 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_increasing
% 5.13/5.48 thf(fact_1056_left__add__twice,axiom,
% 5.13/5.48 ! [A: complex,B: complex] :
% 5.13/5.48 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.13/5.48 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_add_twice
% 5.13/5.48 thf(fact_1057_left__add__twice,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_add_twice
% 5.13/5.48 thf(fact_1058_left__add__twice,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_add_twice
% 5.13/5.48 thf(fact_1059_left__add__twice,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_add_twice
% 5.13/5.48 thf(fact_1060_left__add__twice,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_add_twice
% 5.13/5.48 thf(fact_1061_mult__2__right,axiom,
% 5.13/5.48 ! [Z2: complex] :
% 5.13/5.48 ( ( times_times_complex @ Z2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_complex @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2_right
% 5.13/5.48 thf(fact_1062_mult__2__right,axiom,
% 5.13/5.48 ! [Z2: real] :
% 5.13/5.48 ( ( times_times_real @ Z2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2_right
% 5.13/5.48 thf(fact_1063_mult__2__right,axiom,
% 5.13/5.48 ! [Z2: rat] :
% 5.13/5.48 ( ( times_times_rat @ Z2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2_right
% 5.13/5.48 thf(fact_1064_mult__2__right,axiom,
% 5.13/5.48 ! [Z2: nat] :
% 5.13/5.48 ( ( times_times_nat @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2_right
% 5.13/5.48 thf(fact_1065_mult__2__right,axiom,
% 5.13/5.48 ! [Z2: int] :
% 5.13/5.48 ( ( times_times_int @ Z2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2_right
% 5.13/5.48 thf(fact_1066_mult__2,axiom,
% 5.13/5.48 ! [Z2: complex] :
% 5.13/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 )
% 5.13/5.48 = ( plus_plus_complex @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2
% 5.13/5.48 thf(fact_1067_mult__2,axiom,
% 5.13/5.48 ! [Z2: real] :
% 5.13/5.48 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 )
% 5.13/5.48 = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2
% 5.13/5.48 thf(fact_1068_mult__2,axiom,
% 5.13/5.48 ! [Z2: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 )
% 5.13/5.48 = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2
% 5.13/5.48 thf(fact_1069_mult__2,axiom,
% 5.13/5.48 ! [Z2: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z2 )
% 5.13/5.48 = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2
% 5.13/5.48 thf(fact_1070_mult__2,axiom,
% 5.13/5.48 ! [Z2: int] :
% 5.13/5.48 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z2 )
% 5.13/5.48 = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_2
% 5.13/5.48 thf(fact_1071_power2__eq__square,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( times_times_complex @ A @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_eq_square
% 5.13/5.48 thf(fact_1072_power2__eq__square,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( times_times_real @ A @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_eq_square
% 5.13/5.48 thf(fact_1073_power2__eq__square,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( times_times_rat @ A @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_eq_square
% 5.13/5.48 thf(fact_1074_power2__eq__square,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( times_times_nat @ A @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_eq_square
% 5.13/5.48 thf(fact_1075_power2__eq__square,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( times_times_int @ A @ A ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_eq_square
% 5.13/5.48 thf(fact_1076_power4__eq__xxxx,axiom,
% 5.13/5.48 ! [X: complex] :
% 5.13/5.48 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.13/5.48
% 5.13/5.48 % power4_eq_xxxx
% 5.13/5.48 thf(fact_1077_power4__eq__xxxx,axiom,
% 5.13/5.48 ! [X: real] :
% 5.13/5.48 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.13/5.48
% 5.13/5.48 % power4_eq_xxxx
% 5.13/5.48 thf(fact_1078_power4__eq__xxxx,axiom,
% 5.13/5.48 ! [X: rat] :
% 5.13/5.48 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.13/5.48
% 5.13/5.48 % power4_eq_xxxx
% 5.13/5.48 thf(fact_1079_power4__eq__xxxx,axiom,
% 5.13/5.48 ! [X: nat] :
% 5.13/5.48 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.13/5.48
% 5.13/5.48 % power4_eq_xxxx
% 5.13/5.48 thf(fact_1080_power4__eq__xxxx,axiom,
% 5.13/5.48 ! [X: int] :
% 5.13/5.48 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.13/5.48
% 5.13/5.48 % power4_eq_xxxx
% 5.13/5.48 thf(fact_1081_Suc__nat__number__of__add,axiom,
% 5.13/5.48 ! [V: num,N: nat] :
% 5.13/5.48 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.13/5.48 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_nat_number_of_add
% 5.13/5.48 thf(fact_1082_power__even__eq,axiom,
% 5.13/5.48 ! [A: nat,N: nat] :
% 5.13/5.48 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.48 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_even_eq
% 5.13/5.48 thf(fact_1083_power__even__eq,axiom,
% 5.13/5.48 ! [A: real,N: nat] :
% 5.13/5.48 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.48 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_even_eq
% 5.13/5.48 thf(fact_1084_power__even__eq,axiom,
% 5.13/5.48 ! [A: int,N: nat] :
% 5.13/5.48 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.48 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_even_eq
% 5.13/5.48 thf(fact_1085_power__even__eq,axiom,
% 5.13/5.48 ! [A: complex,N: nat] :
% 5.13/5.48 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.13/5.48 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_even_eq
% 5.13/5.48 thf(fact_1086_div__nat__eqI,axiom,
% 5.13/5.48 ! [N: nat,Q2: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.13/5.48 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.13/5.48 => ( ( divide_divide_nat @ M @ N )
% 5.13/5.48 = Q2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % div_nat_eqI
% 5.13/5.48 thf(fact_1087_power__le__imp__le__exp,axiom,
% 5.13/5.48 ! [A: real,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.48 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_le_imp_le_exp
% 5.13/5.48 thf(fact_1088_power__le__imp__le__exp,axiom,
% 5.13/5.48 ! [A: rat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.48 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_le_imp_le_exp
% 5.13/5.48 thf(fact_1089_power__le__imp__le__exp,axiom,
% 5.13/5.48 ! [A: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_le_imp_le_exp
% 5.13/5.48 thf(fact_1090_power__le__imp__le__exp,axiom,
% 5.13/5.48 ! [A: int,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.48 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_le_imp_le_exp
% 5.13/5.48 thf(fact_1091_one__power2,axiom,
% 5.13/5.48 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = one_one_rat ) ).
% 5.13/5.48
% 5.13/5.48 % one_power2
% 5.13/5.48 thf(fact_1092_one__power2,axiom,
% 5.13/5.48 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = one_one_nat ) ).
% 5.13/5.48
% 5.13/5.48 % one_power2
% 5.13/5.48 thf(fact_1093_one__power2,axiom,
% 5.13/5.48 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = one_one_real ) ).
% 5.13/5.48
% 5.13/5.48 % one_power2
% 5.13/5.48 thf(fact_1094_one__power2,axiom,
% 5.13/5.48 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = one_one_int ) ).
% 5.13/5.48
% 5.13/5.48 % one_power2
% 5.13/5.48 thf(fact_1095_one__power2,axiom,
% 5.13/5.48 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = one_one_complex ) ).
% 5.13/5.48
% 5.13/5.48 % one_power2
% 5.13/5.48 thf(fact_1096_nat__1__add__1,axiom,
% 5.13/5.48 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.13/5.48 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_1_add_1
% 5.13/5.48 thf(fact_1097_power2__sum,axiom,
% 5.13/5.48 ! [X: complex,Y4: complex] :
% 5.13/5.48 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_sum
% 5.13/5.48 thf(fact_1098_power2__sum,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( power_power_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_sum
% 5.13/5.48 thf(fact_1099_power2__sum,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] :
% 5.13/5.48 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_sum
% 5.13/5.48 thf(fact_1100_power2__sum,axiom,
% 5.13/5.48 ! [X: nat,Y4: nat] :
% 5.13/5.48 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_sum
% 5.13/5.48 thf(fact_1101_power2__sum,axiom,
% 5.13/5.48 ! [X: int,Y4: int] :
% 5.13/5.48 ( ( power_power_int @ ( plus_plus_int @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_sum
% 5.13/5.48 thf(fact_1102_ex__power__ivl2,axiom,
% 5.13/5.48 ! [B: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.13/5.48 => ? [N3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.13/5.48 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ex_power_ivl2
% 5.13/5.48 thf(fact_1103_ex__power__ivl1,axiom,
% 5.13/5.48 ! [B: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.13/5.48 => ? [N3: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.13/5.48 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ex_power_ivl1
% 5.13/5.48 thf(fact_1104_invar__vebt_Ointros_I4_J,axiom,
% 5.13/5.48 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.13/5.48 ( ! [X3: vEBT_VEBT] :
% 5.13/5.48 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.48 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.13/5.48 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.13/5.48 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.13/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 => ( ( M = N )
% 5.13/5.48 => ( ( Deg
% 5.13/5.48 = ( plus_plus_nat @ N @ M ) )
% 5.13/5.48 => ( ! [I3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 5.13/5.48 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.13/5.48 => ( ( ( Mi = Ma )
% 5.13/5.48 => ! [X3: vEBT_VEBT] :
% 5.13/5.48 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.48 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.13/5.48 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.13/5.48 => ( ( ( Mi != Ma )
% 5.13/5.48 => ! [I3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.13/5.48 = I3 )
% 5.13/5.48 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.13/5.48 & ! [X3: nat] :
% 5.13/5.48 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.13/5.48 = I3 )
% 5.13/5.48 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ Mi @ X3 )
% 5.13/5.48 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.13/5.48 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % invar_vebt.intros(4)
% 5.13/5.48 thf(fact_1105_invar__vebt_Ointros_I5_J,axiom,
% 5.13/5.48 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.13/5.48 ( ! [X3: vEBT_VEBT] :
% 5.13/5.48 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.48 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.13/5.48 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.13/5.48 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.13/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 => ( ( M
% 5.13/5.48 = ( suc @ N ) )
% 5.13/5.48 => ( ( Deg
% 5.13/5.48 = ( plus_plus_nat @ N @ M ) )
% 5.13/5.48 => ( ! [I3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 5.13/5.48 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.13/5.48 => ( ( ( Mi = Ma )
% 5.13/5.48 => ! [X3: vEBT_VEBT] :
% 5.13/5.48 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.13/5.48 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.13/5.48 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.13/5.48 => ( ( ( Mi != Ma )
% 5.13/5.48 => ! [I3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.13/5.48 = I3 )
% 5.13/5.48 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.13/5.48 & ! [X3: nat] :
% 5.13/5.48 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.13/5.48 = I3 )
% 5.13/5.48 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ Mi @ X3 )
% 5.13/5.48 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.13/5.48 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % invar_vebt.intros(5)
% 5.13/5.48 thf(fact_1106_mintlistlength,axiom,
% 5.13/5.48 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.13/5.48 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.13/5.48 => ( ( Mi != Ma )
% 5.13/5.48 => ( ( ord_less_nat @ Mi @ Ma )
% 5.13/5.48 & ? [M4: nat] :
% 5.13/5.48 ( ( ( some_nat @ M4 )
% 5.13/5.48 = ( vEBT_vebt_mint @ Summary ) )
% 5.13/5.48 & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mintlistlength
% 5.13/5.48 thf(fact_1107_sum__squares__bound,axiom,
% 5.13/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y4 ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % sum_squares_bound
% 5.13/5.48 thf(fact_1108_sum__squares__bound,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y4 ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % sum_squares_bound
% 5.13/5.48 thf(fact_1109_mult__Suc__right,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.13/5.48 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_Suc_right
% 5.13/5.48 thf(fact_1110_vebt__insert_Osimps_I4_J,axiom,
% 5.13/5.48 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.13/5.48 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 5.13/5.48 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_insert.simps(4)
% 5.13/5.48 thf(fact_1111__C1_C,axiom,
% 5.13/5.48 ( ( ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.48 != none_nat )
% 5.13/5.48 & ( 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 ) ) ) ) ) ) ) )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.13/5.48 = ( 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 ) ) ) ) ) ) ) )
% 5.13/5.48 & ( ~ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.48 != none_nat )
% 5.13/5.48 & ( 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 ) ) ) ) ) ) ) )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.13/5.48 = ( if_option_nat
% 5.13/5.48 @ ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.48 = none_nat )
% 5.13/5.48 @ ( if_option_nat @ ( ord_less_nat @ mi @ xa ) @ ( some_nat @ mi ) @ none_nat )
% 5.13/5.48 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % "1"
% 5.13/5.48 thf(fact_1112_div__exp__eq,axiom,
% 5.13/5.48 ! [A: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( 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 ) )
% 5.13/5.48 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % div_exp_eq
% 5.13/5.48 thf(fact_1113_div__exp__eq,axiom,
% 5.13/5.48 ! [A: int,M: nat,N: nat] :
% 5.13/5.48 ( ( 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 ) )
% 5.13/5.48 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % div_exp_eq
% 5.13/5.48 thf(fact_1114_field__less__half__sum,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( ord_less_real @ X @ Y4 )
% 5.13/5.48 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % field_less_half_sum
% 5.13/5.48 thf(fact_1115_field__less__half__sum,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] :
% 5.13/5.48 ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.48 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % field_less_half_sum
% 5.13/5.48 thf(fact_1116_vebt__maxt_Osimps_I3_J,axiom,
% 5.13/5.48 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.13/5.48 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.13/5.48 = ( some_nat @ Ma ) ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_maxt.simps(3)
% 5.13/5.48 thf(fact_1117_vebt__mint_Osimps_I3_J,axiom,
% 5.13/5.48 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.13/5.48 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.13/5.48 = ( some_nat @ Mi ) ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_mint.simps(3)
% 5.13/5.48 thf(fact_1118_nat__1__eq__mult__iff,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( one_one_nat
% 5.13/5.48 = ( times_times_nat @ M @ N ) )
% 5.13/5.48 = ( ( M = one_one_nat )
% 5.13/5.48 & ( N = one_one_nat ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_1_eq_mult_iff
% 5.13/5.48 thf(fact_1119_nat__mult__eq__1__iff,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ( times_times_nat @ M @ N )
% 5.13/5.48 = one_one_nat )
% 5.13/5.48 = ( ( M = one_one_nat )
% 5.13/5.48 & ( N = one_one_nat ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_mult_eq_1_iff
% 5.13/5.48 thf(fact_1120_set__vebt_H__def,axiom,
% 5.13/5.48 ( vEBT_VEBT_set_vebt
% 5.13/5.48 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_vebt'_def
% 5.13/5.48 thf(fact_1121_old_Onat_Oinject,axiom,
% 5.13/5.48 ! [Nat: nat,Nat2: nat] :
% 5.13/5.48 ( ( ( suc @ Nat )
% 5.13/5.48 = ( suc @ Nat2 ) )
% 5.13/5.48 = ( Nat = Nat2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % old.nat.inject
% 5.13/5.48 thf(fact_1122_nat_Oinject,axiom,
% 5.13/5.48 ! [X22: nat,Y2: nat] :
% 5.13/5.48 ( ( ( suc @ X22 )
% 5.13/5.48 = ( suc @ Y2 ) )
% 5.13/5.48 = ( X22 = Y2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat.inject
% 5.13/5.48 thf(fact_1123_power__minus__is__div,axiom,
% 5.13/5.48 ! [B: nat,A: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.48 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.13/5.48 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_minus_is_div
% 5.13/5.48 thf(fact_1124_bits__div__by__1,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % bits_div_by_1
% 5.13/5.48 thf(fact_1125_bits__div__by__1,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( divide_divide_int @ A @ one_one_int )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % bits_div_by_1
% 5.13/5.48 thf(fact_1126_Suc__less__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.13/5.48 = ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_less_eq
% 5.13/5.48 thf(fact_1127_Suc__mono,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_mono
% 5.13/5.48 thf(fact_1128_lessI,axiom,
% 5.13/5.48 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % lessI
% 5.13/5.48 thf(fact_1129_Suc__le__mono,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.13/5.48 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_le_mono
% 5.13/5.48 thf(fact_1130_add__Suc__right,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.13/5.48 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_Suc_right
% 5.13/5.48 thf(fact_1131_nat__add__left__cancel__less,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.13/5.48 = ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_add_left_cancel_less
% 5.13/5.48 thf(fact_1132_Suc__diff__diff,axiom,
% 5.13/5.48 ! [M: nat,N: nat,K: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.13/5.48 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_diff_diff
% 5.13/5.48 thf(fact_1133_diff__Suc__Suc,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.13/5.48 = ( minus_minus_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_Suc_Suc
% 5.13/5.48 thf(fact_1134_nat__add__left__cancel__le,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.13/5.48 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_add_left_cancel_le
% 5.13/5.48 thf(fact_1135_diff__diff__cancel,axiom,
% 5.13/5.48 ! [I2: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ N )
% 5.13/5.48 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 5.13/5.48 = I2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_cancel
% 5.13/5.48 thf(fact_1136_diff__diff__left,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.13/5.48 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_left
% 5.13/5.48 thf(fact_1137_semiring__norm_I13_J,axiom,
% 5.13/5.48 ! [M: num,N: num] :
% 5.13/5.48 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.13/5.48 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % semiring_norm(13)
% 5.13/5.48 thf(fact_1138_semiring__norm_I12_J,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( times_times_num @ one @ N )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % semiring_norm(12)
% 5.13/5.48 thf(fact_1139_semiring__norm_I11_J,axiom,
% 5.13/5.48 ! [M: num] :
% 5.13/5.48 ( ( times_times_num @ M @ one )
% 5.13/5.48 = M ) ).
% 5.13/5.48
% 5.13/5.48 % semiring_norm(11)
% 5.13/5.48 thf(fact_1140_right__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [V: num,B: complex,C: complex] :
% 5.13/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.13/5.48 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib_numeral
% 5.13/5.48 thf(fact_1141_right__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [V: num,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib_numeral
% 5.13/5.48 thf(fact_1142_right__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [V: num,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib_numeral
% 5.13/5.48 thf(fact_1143_right__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [V: num,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib_numeral
% 5.13/5.48 thf(fact_1144_left__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [A: complex,B: complex,V: num] :
% 5.13/5.48 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.13/5.48 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib_numeral
% 5.13/5.48 thf(fact_1145_left__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [A: real,B: real,V: num] :
% 5.13/5.48 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.13/5.48 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib_numeral
% 5.13/5.48 thf(fact_1146_left__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [A: rat,B: rat,V: num] :
% 5.13/5.48 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.13/5.48 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib_numeral
% 5.13/5.48 thf(fact_1147_left__diff__distrib__numeral,axiom,
% 5.13/5.48 ! [A: int,B: int,V: num] :
% 5.13/5.48 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.13/5.48 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib_numeral
% 5.13/5.48 thf(fact_1148_Nat_Odiff__diff__right,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.diff_diff_right
% 5.13/5.48 thf(fact_1149_Nat_Oadd__diff__assoc2,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.add_diff_assoc2
% 5.13/5.48 thf(fact_1150_Nat_Oadd__diff__assoc,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.add_diff_assoc
% 5.13/5.48 thf(fact_1151_diff__Suc__1,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % diff_Suc_1
% 5.13/5.48 thf(fact_1152_num__double,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.13/5.48 = ( bit0 @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % num_double
% 5.13/5.48 thf(fact_1153_power__mult__numeral,axiom,
% 5.13/5.48 ! [A: nat,M: num,N: num] :
% 5.13/5.48 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.48 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_numeral
% 5.13/5.48 thf(fact_1154_power__mult__numeral,axiom,
% 5.13/5.48 ! [A: real,M: num,N: num] :
% 5.13/5.48 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.48 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_numeral
% 5.13/5.48 thf(fact_1155_power__mult__numeral,axiom,
% 5.13/5.48 ! [A: int,M: num,N: num] :
% 5.13/5.48 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.48 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_numeral
% 5.13/5.48 thf(fact_1156_power__mult__numeral,axiom,
% 5.13/5.48 ! [A: complex,M: num,N: num] :
% 5.13/5.48 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.13/5.48 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_mult_numeral
% 5.13/5.48 thf(fact_1157_diff__Suc__diff__eq2,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 5.13/5.48 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_Suc_diff_eq2
% 5.13/5.48 thf(fact_1158_diff__Suc__diff__eq1,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_Suc_diff_eq1
% 5.13/5.48 thf(fact_1159_pred__lesseq__max,axiom,
% 5.13/5.48 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.13/5.48 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.48 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.48 @ ( if_option_nat
% 5.13/5.48 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.48 != none_nat )
% 5.13/5.48 & ( 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 ) ) ) ) ) ) ) )
% 5.13/5.48 @ ( 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 ) ) ) ) ) )
% 5.13/5.48 @ ( if_option_nat
% 5.13/5.48 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.48 = none_nat )
% 5.13/5.48 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.13/5.48 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.13/5.48 @ none_nat ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % pred_lesseq_max
% 5.13/5.48 thf(fact_1160_pred__less__length__list,axiom,
% 5.13/5.48 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.13/5.48 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.13/5.48 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.13/5.48 = ( if_option_nat
% 5.13/5.48 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.48 != none_nat )
% 5.13/5.48 & ( 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 ) ) ) ) ) ) ) )
% 5.13/5.48 @ ( 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 ) ) ) ) ) )
% 5.13/5.48 @ ( if_option_nat
% 5.13/5.48 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.48 = none_nat )
% 5.13/5.48 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.13/5.48 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % pred_less_length_list
% 5.13/5.48 thf(fact_1161_add__diff__add,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real,D: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.13/5.48 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_add
% 5.13/5.48 thf(fact_1162_add__diff__add,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.13/5.48 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_add
% 5.13/5.48 thf(fact_1163_add__diff__add,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int,D: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.13/5.48 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_add
% 5.13/5.48 thf(fact_1164_zero__induct__lemma,axiom,
% 5.13/5.48 ! [P: nat > $o,K: nat,I2: nat] :
% 5.13/5.48 ( ( P @ K )
% 5.13/5.48 => ( ! [N3: nat] :
% 5.13/5.48 ( ( P @ ( suc @ N3 ) )
% 5.13/5.48 => ( P @ N3 ) )
% 5.13/5.48 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % zero_induct_lemma
% 5.13/5.48 thf(fact_1165_less__imp__diff__less,axiom,
% 5.13/5.48 ! [J: nat,K: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ J @ K )
% 5.13/5.48 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_imp_diff_less
% 5.13/5.48 thf(fact_1166_diff__less__mono2,axiom,
% 5.13/5.48 ! [M: nat,N: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ( ord_less_nat @ M @ L2 )
% 5.13/5.48 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_less_mono2
% 5.13/5.48 thf(fact_1167_eq__diff__iff,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ M )
% 5.13/5.48 => ( ( ord_less_eq_nat @ K @ N )
% 5.13/5.48 => ( ( ( minus_minus_nat @ M @ K )
% 5.13/5.48 = ( minus_minus_nat @ N @ K ) )
% 5.13/5.48 = ( M = N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_diff_iff
% 5.13/5.48 thf(fact_1168_le__diff__iff,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ M )
% 5.13/5.48 => ( ( ord_less_eq_nat @ K @ N )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.13/5.48 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_diff_iff
% 5.13/5.48 thf(fact_1169_Nat_Odiff__diff__eq,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ M )
% 5.13/5.48 => ( ( ord_less_eq_nat @ K @ N )
% 5.13/5.48 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.13/5.48 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.diff_diff_eq
% 5.13/5.48 thf(fact_1170_diff__le__mono,axiom,
% 5.13/5.48 ! [M: nat,N: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_mono
% 5.13/5.48 thf(fact_1171_diff__le__self,axiom,
% 5.13/5.48 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_self
% 5.13/5.48 thf(fact_1172_le__diff__iff_H,axiom,
% 5.13/5.48 ! [A: nat,C: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ C )
% 5.13/5.48 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_diff_iff'
% 5.13/5.48 thf(fact_1173_diff__le__mono2,axiom,
% 5.13/5.48 ! [M: nat,N: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_mono2
% 5.13/5.48 thf(fact_1174_diff__add__inverse2,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.13/5.48 = M ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_inverse2
% 5.13/5.48 thf(fact_1175_diff__add__inverse,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.13/5.48 = M ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_inverse
% 5.13/5.48 thf(fact_1176_diff__cancel2,axiom,
% 5.13/5.48 ! [M: nat,K: nat,N: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.13/5.48 = ( minus_minus_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_cancel2
% 5.13/5.48 thf(fact_1177_Nat_Odiff__cancel,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.13/5.48 = ( minus_minus_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.diff_cancel
% 5.13/5.48 thf(fact_1178_diff__mult__distrib2,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.48 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_mult_distrib2
% 5.13/5.48 thf(fact_1179_diff__mult__distrib,axiom,
% 5.13/5.48 ! [M: nat,N: nat,K: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.13/5.48 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_mult_distrib
% 5.13/5.48 thf(fact_1180_numeral__code_I2_J,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.13/5.48 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_code(2)
% 5.13/5.48 thf(fact_1181_numeral__code_I2_J,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.13/5.48 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_code(2)
% 5.13/5.48 thf(fact_1182_numeral__code_I2_J,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.13/5.48 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_code(2)
% 5.13/5.48 thf(fact_1183_numeral__code_I2_J,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.13/5.48 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_code(2)
% 5.13/5.48 thf(fact_1184_numeral__code_I2_J,axiom,
% 5.13/5.48 ! [N: num] :
% 5.13/5.48 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.13/5.48 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % numeral_code(2)
% 5.13/5.48 thf(fact_1185_mult__diff__mult,axiom,
% 5.13/5.48 ! [X: real,Y4: real,A: real,B: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( times_times_real @ X @ Y4 ) @ ( times_times_real @ A @ B ) )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y4 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_diff_mult
% 5.13/5.48 thf(fact_1186_mult__diff__mult,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y4 ) @ ( times_times_rat @ A @ B ) )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y4 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_diff_mult
% 5.13/5.48 thf(fact_1187_mult__diff__mult,axiom,
% 5.13/5.48 ! [X: int,Y4: int,A: int,B: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( times_times_int @ X @ Y4 ) @ ( times_times_int @ A @ B ) )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y4 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_diff_mult
% 5.13/5.48 thf(fact_1188_set__vebt__def,axiom,
% 5.13/5.48 ( vEBT_set_vebt
% 5.13/5.48 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_vebt_def
% 5.13/5.48 thf(fact_1189_Suc__diff__Suc,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_nat @ N @ M )
% 5.13/5.48 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.13/5.48 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_diff_Suc
% 5.13/5.48 thf(fact_1190_diff__less__Suc,axiom,
% 5.13/5.48 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_less_Suc
% 5.13/5.48 thf(fact_1191_Suc__diff__le,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.48 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.13/5.48 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_diff_le
% 5.13/5.48 thf(fact_1192_diff__less__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ C @ A )
% 5.13/5.48 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_less_mono
% 5.13/5.48 thf(fact_1193_less__diff__iff,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ M )
% 5.13/5.48 => ( ( ord_less_eq_nat @ K @ N )
% 5.13/5.48 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.13/5.48 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_diff_iff
% 5.13/5.48 thf(fact_1194_less__diff__conv,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.13/5.48 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_diff_conv
% 5.13/5.48 thf(fact_1195_add__diff__inverse__nat,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ~ ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.48 = M ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_inverse_nat
% 5.13/5.48 thf(fact_1196_Nat_Ole__imp__diff__is__add,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ( minus_minus_nat @ J @ I2 )
% 5.13/5.48 = K )
% 5.13/5.48 = ( J
% 5.13/5.48 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.le_imp_diff_is_add
% 5.13/5.48 thf(fact_1197_Nat_Odiff__add__assoc2,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 5.13/5.48 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.diff_add_assoc2
% 5.13/5.48 thf(fact_1198_Nat_Odiff__add__assoc,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.13/5.48 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.diff_add_assoc
% 5.13/5.48 thf(fact_1199_Nat_Ole__diff__conv2,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.13/5.48 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.le_diff_conv2
% 5.13/5.48 thf(fact_1200_le__diff__conv,axiom,
% 5.13/5.48 ! [J: nat,K: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.13/5.48 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_diff_conv
% 5.13/5.48 thf(fact_1201_diff__Suc__eq__diff__pred,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.13/5.48 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_Suc_eq_diff_pred
% 5.13/5.48 thf(fact_1202_two__realpow__ge__one,axiom,
% 5.13/5.48 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % two_realpow_ge_one
% 5.13/5.48 thf(fact_1203_power__numeral__even,axiom,
% 5.13/5.48 ! [Z2: complex,W2: num] :
% 5.13/5.48 ( ( power_power_complex @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.13/5.48 = ( times_times_complex @ ( power_power_complex @ Z2 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_complex @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_numeral_even
% 5.13/5.48 thf(fact_1204_power__numeral__even,axiom,
% 5.13/5.48 ! [Z2: real,W2: num] :
% 5.13/5.48 ( ( power_power_real @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.13/5.48 = ( times_times_real @ ( power_power_real @ Z2 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_real @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_numeral_even
% 5.13/5.48 thf(fact_1205_power__numeral__even,axiom,
% 5.13/5.48 ! [Z2: rat,W2: num] :
% 5.13/5.48 ( ( power_power_rat @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.13/5.48 = ( times_times_rat @ ( power_power_rat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_rat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_numeral_even
% 5.13/5.48 thf(fact_1206_power__numeral__even,axiom,
% 5.13/5.48 ! [Z2: nat,W2: num] :
% 5.13/5.48 ( ( power_power_nat @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.13/5.48 = ( times_times_nat @ ( power_power_nat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_nat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_numeral_even
% 5.13/5.48 thf(fact_1207_power__numeral__even,axiom,
% 5.13/5.48 ! [Z2: int,W2: num] :
% 5.13/5.48 ( ( power_power_int @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.13/5.48 = ( times_times_int @ ( power_power_int @ Z2 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_int @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power_numeral_even
% 5.13/5.48 thf(fact_1208_four__x__squared,axiom,
% 5.13/5.48 ! [X: real] :
% 5.13/5.48 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % four_x_squared
% 5.13/5.48 thf(fact_1209_L2__set__mult__ineq__lemma,axiom,
% 5.13/5.48 ! [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 ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % L2_set_mult_ineq_lemma
% 5.13/5.48 thf(fact_1210_div__mult2__numeral__eq,axiom,
% 5.13/5.48 ! [A: nat,K: num,L2: num] :
% 5.13/5.48 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.13/5.48 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % div_mult2_numeral_eq
% 5.13/5.48 thf(fact_1211_div__mult2__numeral__eq,axiom,
% 5.13/5.48 ! [A: int,K: num,L2: num] :
% 5.13/5.48 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.13/5.48 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % div_mult2_numeral_eq
% 5.13/5.48 thf(fact_1212_less__diff__conv2,axiom,
% 5.13/5.48 ! [K: nat,J: nat,I2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ J )
% 5.13/5.48 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.13/5.48 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_diff_conv2
% 5.13/5.48 thf(fact_1213_nat__diff__add__eq2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U2 ) @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_diff_add_eq2
% 5.13/5.48 thf(fact_1214_nat__diff__add__eq1,axiom,
% 5.13/5.48 ! [J: nat,I2: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ J @ I2 )
% 5.13/5.48 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U2 ) @ M ) @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_diff_add_eq1
% 5.13/5.48 thf(fact_1215_nat__le__add__iff2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U2 ) @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_le_add_iff2
% 5.13/5.48 thf(fact_1216_nat__le__add__iff1,axiom,
% 5.13/5.48 ! [J: nat,I2: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ J @ I2 )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U2 ) @ M ) @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_le_add_iff1
% 5.13/5.48 thf(fact_1217_nat__eq__add__iff2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( M
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U2 ) @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_eq_add_iff2
% 5.13/5.48 thf(fact_1218_nat__eq__add__iff1,axiom,
% 5.13/5.48 ! [J: nat,I2: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ J @ I2 )
% 5.13/5.48 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U2 ) @ M )
% 5.13/5.48 = N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_eq_add_iff1
% 5.13/5.48 thf(fact_1219_n__not__Suc__n,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ( N
% 5.13/5.48 != ( suc @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % n_not_Suc_n
% 5.13/5.48 thf(fact_1220_Suc__inject,axiom,
% 5.13/5.48 ! [X: nat,Y4: nat] :
% 5.13/5.48 ( ( ( suc @ X )
% 5.13/5.48 = ( suc @ Y4 ) )
% 5.13/5.48 => ( X = Y4 ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_inject
% 5.13/5.48 thf(fact_1221_linorder__neqE__nat,axiom,
% 5.13/5.48 ! [X: nat,Y4: nat] :
% 5.13/5.48 ( ( X != Y4 )
% 5.13/5.48 => ( ~ ( ord_less_nat @ X @ Y4 )
% 5.13/5.48 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % linorder_neqE_nat
% 5.13/5.48 thf(fact_1222_infinite__descent,axiom,
% 5.13/5.48 ! [P: nat > $o,N: nat] :
% 5.13/5.48 ( ! [N3: nat] :
% 5.13/5.48 ( ~ ( P @ N3 )
% 5.13/5.48 => ? [M3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M3 @ N3 )
% 5.13/5.48 & ~ ( P @ M3 ) ) )
% 5.13/5.48 => ( P @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % infinite_descent
% 5.13/5.48 thf(fact_1223_nat__less__induct,axiom,
% 5.13/5.48 ! [P: nat > $o,N: nat] :
% 5.13/5.48 ( ! [N3: nat] :
% 5.13/5.48 ( ! [M3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M3 @ N3 )
% 5.13/5.48 => ( P @ M3 ) )
% 5.13/5.48 => ( P @ N3 ) )
% 5.13/5.48 => ( P @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_less_induct
% 5.13/5.48 thf(fact_1224_less__irrefl__nat,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ~ ( ord_less_nat @ N @ N ) ).
% 5.13/5.48
% 5.13/5.48 % less_irrefl_nat
% 5.13/5.48 thf(fact_1225_less__not__refl3,axiom,
% 5.13/5.48 ! [S2: nat,T: nat] :
% 5.13/5.48 ( ( ord_less_nat @ S2 @ T )
% 5.13/5.48 => ( S2 != T ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_not_refl3
% 5.13/5.48 thf(fact_1226_less__not__refl2,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_nat @ N @ M )
% 5.13/5.48 => ( M != N ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_not_refl2
% 5.13/5.48 thf(fact_1227_less__not__refl,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ~ ( ord_less_nat @ N @ N ) ).
% 5.13/5.48
% 5.13/5.48 % less_not_refl
% 5.13/5.48 thf(fact_1228_nat__neq__iff,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( M != N )
% 5.13/5.48 = ( ( ord_less_nat @ M @ N )
% 5.13/5.48 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_neq_iff
% 5.13/5.48 thf(fact_1229_le__refl,axiom,
% 5.13/5.48 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.13/5.48
% 5.13/5.48 % le_refl
% 5.13/5.48 thf(fact_1230_le__trans,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_eq_nat @ J @ K )
% 5.13/5.48 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_trans
% 5.13/5.48 thf(fact_1231_eq__imp__le,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( M = N )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_imp_le
% 5.13/5.48 thf(fact_1232_le__antisym,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.48 => ( M = N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_antisym
% 5.13/5.48 thf(fact_1233_nat__le__linear,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_le_linear
% 5.13/5.48 thf(fact_1234_Nat_Oex__has__greatest__nat,axiom,
% 5.13/5.48 ! [P: nat > $o,K: nat,B: nat] :
% 5.13/5.48 ( ( P @ K )
% 5.13/5.48 => ( ! [Y3: nat] :
% 5.13/5.48 ( ( P @ Y3 )
% 5.13/5.48 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.13/5.48 => ? [X3: nat] :
% 5.13/5.48 ( ( P @ X3 )
% 5.13/5.48 & ! [Y5: nat] :
% 5.13/5.48 ( ( P @ Y5 )
% 5.13/5.48 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.ex_has_greatest_nat
% 5.13/5.48 thf(fact_1235_size__neq__size__imp__neq,axiom,
% 5.13/5.48 ! [X: list_VEBT_VEBT,Y4: list_VEBT_VEBT] :
% 5.13/5.48 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.13/5.48 != ( size_s6755466524823107622T_VEBT @ Y4 ) )
% 5.13/5.48 => ( X != Y4 ) ) ).
% 5.13/5.48
% 5.13/5.48 % size_neq_size_imp_neq
% 5.13/5.48 thf(fact_1236_size__neq__size__imp__neq,axiom,
% 5.13/5.48 ! [X: list_o,Y4: list_o] :
% 5.13/5.48 ( ( ( size_size_list_o @ X )
% 5.13/5.48 != ( size_size_list_o @ Y4 ) )
% 5.13/5.48 => ( X != Y4 ) ) ).
% 5.13/5.48
% 5.13/5.48 % size_neq_size_imp_neq
% 5.13/5.48 thf(fact_1237_size__neq__size__imp__neq,axiom,
% 5.13/5.48 ! [X: list_nat,Y4: list_nat] :
% 5.13/5.48 ( ( ( size_size_list_nat @ X )
% 5.13/5.48 != ( size_size_list_nat @ Y4 ) )
% 5.13/5.48 => ( X != Y4 ) ) ).
% 5.13/5.48
% 5.13/5.48 % size_neq_size_imp_neq
% 5.13/5.48 thf(fact_1238_size__neq__size__imp__neq,axiom,
% 5.13/5.48 ! [X: list_int,Y4: list_int] :
% 5.13/5.48 ( ( ( size_size_list_int @ X )
% 5.13/5.48 != ( size_size_list_int @ Y4 ) )
% 5.13/5.48 => ( X != Y4 ) ) ).
% 5.13/5.48
% 5.13/5.48 % size_neq_size_imp_neq
% 5.13/5.48 thf(fact_1239_size__neq__size__imp__neq,axiom,
% 5.13/5.48 ! [X: num,Y4: num] :
% 5.13/5.48 ( ( ( size_size_num @ X )
% 5.13/5.48 != ( size_size_num @ Y4 ) )
% 5.13/5.48 => ( X != Y4 ) ) ).
% 5.13/5.48
% 5.13/5.48 % size_neq_size_imp_neq
% 5.13/5.48 thf(fact_1240_power2__commute,axiom,
% 5.13/5.48 ! [X: complex,Y4: complex] :
% 5.13/5.48 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( power_power_complex @ ( minus_minus_complex @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_commute
% 5.13/5.48 thf(fact_1241_power2__commute,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( power_power_real @ ( minus_minus_real @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( power_power_real @ ( minus_minus_real @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_commute
% 5.13/5.48 thf(fact_1242_power2__commute,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] :
% 5.13/5.48 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( power_power_rat @ ( minus_minus_rat @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_commute
% 5.13/5.48 thf(fact_1243_power2__commute,axiom,
% 5.13/5.48 ! [X: int,Y4: int] :
% 5.13/5.48 ( ( power_power_int @ ( minus_minus_int @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( power_power_int @ ( minus_minus_int @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_commute
% 5.13/5.48 thf(fact_1244_nat__less__add__iff2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U2 ) @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_less_add_iff2
% 5.13/5.48 thf(fact_1245_nat__less__add__iff1,axiom,
% 5.13/5.48 ! [J: nat,I2: nat,U2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ J @ I2 )
% 5.13/5.48 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U2 ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U2 ) @ N ) )
% 5.13/5.48 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U2 ) @ M ) @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_less_add_iff1
% 5.13/5.48 thf(fact_1246_diff__le__diff__pow,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.13/5.48 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_diff_pow
% 5.13/5.48 thf(fact_1247_not__less__less__Suc__eq,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ~ ( ord_less_nat @ N @ M )
% 5.13/5.48 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.13/5.48 = ( N = M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % not_less_less_Suc_eq
% 5.13/5.48 thf(fact_1248_strict__inc__induct,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,P: nat > $o] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ! [I3: nat] :
% 5.13/5.48 ( ( J
% 5.13/5.48 = ( suc @ I3 ) )
% 5.13/5.48 => ( P @ I3 ) )
% 5.13/5.48 => ( ! [I3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ J )
% 5.13/5.48 => ( ( P @ ( suc @ I3 ) )
% 5.13/5.48 => ( P @ I3 ) ) )
% 5.13/5.48 => ( P @ I2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % strict_inc_induct
% 5.13/5.48 thf(fact_1249_less__Suc__induct,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.13/5.48 => ( ! [I3: nat,J2: nat,K2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ J2 )
% 5.13/5.48 => ( ( ord_less_nat @ J2 @ K2 )
% 5.13/5.48 => ( ( P @ I3 @ J2 )
% 5.13/5.48 => ( ( P @ J2 @ K2 )
% 5.13/5.48 => ( P @ I3 @ K2 ) ) ) ) )
% 5.13/5.48 => ( P @ I2 @ J ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_Suc_induct
% 5.13/5.48 thf(fact_1250_less__trans__Suc,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_nat @ J @ K )
% 5.13/5.48 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_trans_Suc
% 5.13/5.48 thf(fact_1251_Suc__less__SucD,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_less_SucD
% 5.13/5.48 thf(fact_1252_less__antisym,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ~ ( ord_less_nat @ N @ M )
% 5.13/5.48 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.13/5.48 => ( M = N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_antisym
% 5.13/5.48 thf(fact_1253_Suc__less__eq2,axiom,
% 5.13/5.48 ! [N: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.13/5.48 = ( ? [M5: nat] :
% 5.13/5.48 ( ( M
% 5.13/5.48 = ( suc @ M5 ) )
% 5.13/5.48 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_less_eq2
% 5.13/5.48 thf(fact_1254_All__less__Suc,axiom,
% 5.13/5.48 ! [N: nat,P: nat > $o] :
% 5.13/5.48 ( ( ! [I4: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.13/5.48 => ( P @ I4 ) ) )
% 5.13/5.48 = ( ( P @ N )
% 5.13/5.48 & ! [I4: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I4 @ N )
% 5.13/5.48 => ( P @ I4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % All_less_Suc
% 5.13/5.48 thf(fact_1255_not__less__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.13/5.48 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % not_less_eq
% 5.13/5.48 thf(fact_1256_less__Suc__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.13/5.48 = ( ( ord_less_nat @ M @ N )
% 5.13/5.48 | ( M = N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_Suc_eq
% 5.13/5.48 thf(fact_1257_Ex__less__Suc,axiom,
% 5.13/5.48 ! [N: nat,P: nat > $o] :
% 5.13/5.48 ( ( ? [I4: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.13/5.48 & ( P @ I4 ) ) )
% 5.13/5.48 = ( ( P @ N )
% 5.13/5.48 | ? [I4: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I4 @ N )
% 5.13/5.48 & ( P @ I4 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Ex_less_Suc
% 5.13/5.48 thf(fact_1258_less__SucI,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_SucI
% 5.13/5.48 thf(fact_1259_less__SucE,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.13/5.48 => ( ~ ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( M = N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_SucE
% 5.13/5.48 thf(fact_1260_Suc__lessI,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ( ( suc @ M )
% 5.13/5.48 != N )
% 5.13/5.48 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_lessI
% 5.13/5.48 thf(fact_1261_Suc__lessE,axiom,
% 5.13/5.48 ! [I2: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.13/5.48 => ~ ! [J2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J2 )
% 5.13/5.48 => ( K
% 5.13/5.48 != ( suc @ J2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_lessE
% 5.13/5.48 thf(fact_1262_Suc__lessD,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_lessD
% 5.13/5.48 thf(fact_1263_Nat_OlessE,axiom,
% 5.13/5.48 ! [I2: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ K )
% 5.13/5.48 => ( ( K
% 5.13/5.48 != ( suc @ I2 ) )
% 5.13/5.48 => ~ ! [J2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J2 )
% 5.13/5.48 => ( K
% 5.13/5.48 != ( suc @ J2 ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Nat.lessE
% 5.13/5.48 thf(fact_1264_power2__diff,axiom,
% 5.13/5.48 ! [X: complex,Y4: complex] :
% 5.13/5.48 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_diff
% 5.13/5.48 thf(fact_1265_power2__diff,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( power_power_real @ ( minus_minus_real @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_diff
% 5.13/5.48 thf(fact_1266_power2__diff,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] :
% 5.13/5.48 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_diff
% 5.13/5.48 thf(fact_1267_power2__diff,axiom,
% 5.13/5.48 ! [X: int,Y4: int] :
% 5.13/5.48 ( ( power_power_int @ ( minus_minus_int @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.48 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % power2_diff
% 5.13/5.48 thf(fact_1268_Suc__leD,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_leD
% 5.13/5.48 thf(fact_1269_le__SucE,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.13/5.48 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( M
% 5.13/5.48 = ( suc @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_SucE
% 5.13/5.48 thf(fact_1270_le__SucI,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_SucI
% 5.13/5.48 thf(fact_1271_Suc__le__D,axiom,
% 5.13/5.48 ! [N: nat,M6: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 5.13/5.48 => ? [M4: nat] :
% 5.13/5.48 ( M6
% 5.13/5.48 = ( suc @ M4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_le_D
% 5.13/5.48 thf(fact_1272_le__Suc__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.13/5.48 = ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 | ( M
% 5.13/5.48 = ( suc @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_Suc_eq
% 5.13/5.48 thf(fact_1273_Suc__n__not__le__n,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_n_not_le_n
% 5.13/5.48 thf(fact_1274_not__less__eq__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.13/5.48 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.13/5.48
% 5.13/5.48 % not_less_eq_eq
% 5.13/5.48 thf(fact_1275_full__nat__induct,axiom,
% 5.13/5.48 ! [P: nat > $o,N: nat] :
% 5.13/5.48 ( ! [N3: nat] :
% 5.13/5.48 ( ! [M3: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 5.13/5.48 => ( P @ M3 ) )
% 5.13/5.48 => ( P @ N3 ) )
% 5.13/5.48 => ( P @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % full_nat_induct
% 5.13/5.48 thf(fact_1276_nat__induct__at__least,axiom,
% 5.13/5.48 ! [M: nat,N: nat,P: nat > $o] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ( P @ M )
% 5.13/5.48 => ( ! [N3: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N3 )
% 5.13/5.48 => ( ( P @ N3 )
% 5.13/5.48 => ( P @ ( suc @ N3 ) ) ) )
% 5.13/5.48 => ( P @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_induct_at_least
% 5.13/5.48 thf(fact_1277_transitive__stepwise__le,axiom,
% 5.13/5.48 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 5.13/5.48 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 5.13/5.48 ( ( R @ X3 @ Y3 )
% 5.13/5.48 => ( ( R @ Y3 @ Z )
% 5.13/5.48 => ( R @ X3 @ Z ) ) )
% 5.13/5.48 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.13/5.48 => ( R @ M @ N ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % transitive_stepwise_le
% 5.13/5.48 thf(fact_1278_add__Suc__shift,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.13/5.48 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_Suc_shift
% 5.13/5.48 thf(fact_1279_add__Suc,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.13/5.48 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_Suc
% 5.13/5.48 thf(fact_1280_nat__arith_Osuc1,axiom,
% 5.13/5.48 ! [A2: nat,K: nat,A: nat] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_nat @ K @ A ) )
% 5.13/5.48 => ( ( suc @ A2 )
% 5.13/5.48 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_arith.suc1
% 5.13/5.48 thf(fact_1281_nat__less__le,axiom,
% 5.13/5.48 ( ord_less_nat
% 5.13/5.48 = ( ^ [M2: nat,N2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.13/5.48 & ( M2 != N2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_less_le
% 5.13/5.48 thf(fact_1282_less__imp__le__nat,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_imp_le_nat
% 5.13/5.48 thf(fact_1283_le__eq__less__or__eq,axiom,
% 5.13/5.48 ( ord_less_eq_nat
% 5.13/5.48 = ( ^ [M2: nat,N2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M2 @ N2 )
% 5.13/5.48 | ( M2 = N2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_eq_less_or_eq
% 5.13/5.48 thf(fact_1284_less__or__eq__imp__le,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ( ord_less_nat @ M @ N )
% 5.13/5.48 | ( M = N ) )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_or_eq_imp_le
% 5.13/5.48 thf(fact_1285_le__neq__implies__less,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ( M != N )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_neq_implies_less
% 5.13/5.48 thf(fact_1286_less__mono__imp__le__mono,axiom,
% 5.13/5.48 ! [F: nat > nat,I2: nat,J: nat] :
% 5.13/5.48 ( ! [I3: nat,J2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I3 @ J2 )
% 5.13/5.48 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_mono_imp_le_mono
% 5.13/5.48 thf(fact_1287_less__add__eq__less,axiom,
% 5.13/5.48 ! [K: nat,L2: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ K @ L2 )
% 5.13/5.48 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.13/5.48 = ( plus_plus_nat @ K @ N ) )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_eq_less
% 5.13/5.48 thf(fact_1288_trans__less__add2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % trans_less_add2
% 5.13/5.48 thf(fact_1289_trans__less__add1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % trans_less_add1
% 5.13/5.48 thf(fact_1290_add__less__mono1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_mono1
% 5.13/5.48 thf(fact_1291_not__add__less2,axiom,
% 5.13/5.48 ! [J: nat,I2: nat] :
% 5.13/5.48 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 5.13/5.48
% 5.13/5.48 % not_add_less2
% 5.13/5.48 thf(fact_1292_not__add__less1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat] :
% 5.13/5.48 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 5.13/5.48
% 5.13/5.48 % not_add_less1
% 5.13/5.48 thf(fact_1293_add__less__mono,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_nat @ K @ L2 )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_mono
% 5.13/5.48 thf(fact_1294_add__lessD1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.13/5.48 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_lessD1
% 5.13/5.48 thf(fact_1295_Suc__mult__cancel1,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.13/5.48 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.13/5.48 = ( M = N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_mult_cancel1
% 5.13/5.48 thf(fact_1296_add__leE,axiom,
% 5.13/5.48 ! [M: nat,K: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.13/5.48 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_leE
% 5.13/5.48 thf(fact_1297_le__add1,axiom,
% 5.13/5.48 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add1
% 5.13/5.48 thf(fact_1298_le__add2,axiom,
% 5.13/5.48 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add2
% 5.13/5.48 thf(fact_1299_add__leD1,axiom,
% 5.13/5.48 ! [M: nat,K: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_leD1
% 5.13/5.48 thf(fact_1300_add__leD2,axiom,
% 5.13/5.48 ! [M: nat,K: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_leD2
% 5.13/5.48 thf(fact_1301_le__Suc__ex,axiom,
% 5.13/5.48 ! [K: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ K @ L2 )
% 5.13/5.48 => ? [N3: nat] :
% 5.13/5.48 ( L2
% 5.13/5.48 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_Suc_ex
% 5.13/5.48 thf(fact_1302_add__le__mono,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_mono
% 5.13/5.48 thf(fact_1303_add__le__mono1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_mono1
% 5.13/5.48 thf(fact_1304_trans__le__add1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % trans_le_add1
% 5.13/5.48 thf(fact_1305_trans__le__add2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,M: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % trans_le_add2
% 5.13/5.48 thf(fact_1306_nat__le__iff__add,axiom,
% 5.13/5.48 ( ord_less_eq_nat
% 5.13/5.48 = ( ^ [M2: nat,N2: nat] :
% 5.13/5.48 ? [K3: nat] :
% 5.13/5.48 ( N2
% 5.13/5.48 = ( plus_plus_nat @ M2 @ K3 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % nat_le_iff_add
% 5.13/5.48 thf(fact_1307_le__cube,axiom,
% 5.13/5.48 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_cube
% 5.13/5.48 thf(fact_1308_le__square,axiom,
% 5.13/5.48 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_square
% 5.13/5.48 thf(fact_1309_mult__le__mono,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.13/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_le_mono
% 5.13/5.48 thf(fact_1310_mult__le__mono1,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_le_mono1
% 5.13/5.48 thf(fact_1311_mult__le__mono2,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_le_mono2
% 5.13/5.48 thf(fact_1312_add__mult__distrib2,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mult_distrib2
% 5.13/5.48 thf(fact_1313_add__mult__distrib,axiom,
% 5.13/5.48 ! [M: nat,N: nat,K: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mult_distrib
% 5.13/5.48 thf(fact_1314_nat__mult__1__right,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ( ( times_times_nat @ N @ one_one_nat )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % nat_mult_1_right
% 5.13/5.48 thf(fact_1315_nat__mult__1,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ( ( times_times_nat @ one_one_nat @ N )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % nat_mult_1
% 5.13/5.48 thf(fact_1316_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.13/5.48 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.13/5.48 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.13/5.48 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(3)
% 5.13/5.48 thf(fact_1317_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.13/5.48 ! [F: num > num > num,A: num,B: num] :
% 5.13/5.48 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.13/5.48 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(3)
% 5.13/5.48 thf(fact_1318_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.13/5.48 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.13/5.48 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.13/5.48 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(3)
% 5.13/5.48 thf(fact_1319_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.13/5.48 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.13/5.48 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.13/5.48 = none_P5556105721700978146at_nat ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(1)
% 5.13/5.48 thf(fact_1320_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.13/5.48 ! [Uu: num > num > num,Uv: option_num] :
% 5.13/5.48 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.13/5.48 = none_num ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(1)
% 5.13/5.48 thf(fact_1321_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.13/5.48 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.13/5.48 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.13/5.48 = none_nat ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(1)
% 5.13/5.48 thf(fact_1322_lift__Suc__mono__less__iff,axiom,
% 5.13/5.48 ! [F: nat > real,N: nat,M: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.13/5.48 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less_iff
% 5.13/5.48 thf(fact_1323_lift__Suc__mono__less__iff,axiom,
% 5.13/5.48 ! [F: nat > rat,N: nat,M: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.13/5.48 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less_iff
% 5.13/5.48 thf(fact_1324_lift__Suc__mono__less__iff,axiom,
% 5.13/5.48 ! [F: nat > num,N: nat,M: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.13/5.48 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less_iff
% 5.13/5.48 thf(fact_1325_lift__Suc__mono__less__iff,axiom,
% 5.13/5.48 ! [F: nat > nat,N: nat,M: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.13/5.48 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less_iff
% 5.13/5.48 thf(fact_1326_lift__Suc__mono__less__iff,axiom,
% 5.13/5.48 ! [F: nat > int,N: nat,M: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.13/5.48 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less_iff
% 5.13/5.48 thf(fact_1327_lift__Suc__mono__less,axiom,
% 5.13/5.48 ! [F: nat > real,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less
% 5.13/5.48 thf(fact_1328_lift__Suc__mono__less,axiom,
% 5.13/5.48 ! [F: nat > rat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less
% 5.13/5.48 thf(fact_1329_lift__Suc__mono__less,axiom,
% 5.13/5.48 ! [F: nat > num,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less
% 5.13/5.48 thf(fact_1330_lift__Suc__mono__less,axiom,
% 5.13/5.48 ! [F: nat > nat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less
% 5.13/5.48 thf(fact_1331_lift__Suc__mono__less,axiom,
% 5.13/5.48 ! [F: nat > int,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_less
% 5.13/5.48 thf(fact_1332_lift__Suc__mono__le,axiom,
% 5.13/5.48 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_le
% 5.13/5.48 thf(fact_1333_lift__Suc__mono__le,axiom,
% 5.13/5.48 ! [F: nat > rat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_le
% 5.13/5.48 thf(fact_1334_lift__Suc__mono__le,axiom,
% 5.13/5.48 ! [F: nat > num,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_le
% 5.13/5.48 thf(fact_1335_lift__Suc__mono__le,axiom,
% 5.13/5.48 ! [F: nat > nat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_le
% 5.13/5.48 thf(fact_1336_lift__Suc__mono__le,axiom,
% 5.13/5.48 ! [F: nat > int,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_mono_le
% 5.13/5.48 thf(fact_1337_lift__Suc__antimono__le,axiom,
% 5.13/5.48 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_antimono_le
% 5.13/5.48 thf(fact_1338_lift__Suc__antimono__le,axiom,
% 5.13/5.48 ! [F: nat > rat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_antimono_le
% 5.13/5.48 thf(fact_1339_lift__Suc__antimono__le,axiom,
% 5.13/5.48 ! [F: nat > num,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_antimono_le
% 5.13/5.48 thf(fact_1340_lift__Suc__antimono__le,axiom,
% 5.13/5.48 ! [F: nat > nat,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_antimono_le
% 5.13/5.48 thf(fact_1341_lift__Suc__antimono__le,axiom,
% 5.13/5.48 ! [F: nat > int,N: nat,N5: nat] :
% 5.13/5.48 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.13/5.48 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % lift_Suc_antimono_le
% 5.13/5.48 thf(fact_1342_le__imp__less__Suc,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_imp_less_Suc
% 5.13/5.48 thf(fact_1343_less__eq__Suc__le,axiom,
% 5.13/5.48 ( ord_less_nat
% 5.13/5.48 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_eq_Suc_le
% 5.13/5.48 thf(fact_1344_less__Suc__eq__le,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.13/5.48 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_Suc_eq_le
% 5.13/5.48 thf(fact_1345_le__less__Suc__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.48 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.13/5.48 = ( N = M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_less_Suc_eq
% 5.13/5.48 thf(fact_1346_Suc__le__lessD,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.13/5.48 => ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_le_lessD
% 5.13/5.48 thf(fact_1347_inc__induct,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,P: nat > $o] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( P @ J )
% 5.13/5.48 => ( ! [N3: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.13/5.48 => ( ( ord_less_nat @ N3 @ J )
% 5.13/5.48 => ( ( P @ ( suc @ N3 ) )
% 5.13/5.48 => ( P @ N3 ) ) ) )
% 5.13/5.48 => ( P @ I2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % inc_induct
% 5.13/5.48 thf(fact_1348_dec__induct,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,P: nat > $o] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 => ( ( P @ I2 )
% 5.13/5.48 => ( ! [N3: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.13/5.48 => ( ( ord_less_nat @ N3 @ J )
% 5.13/5.48 => ( ( P @ N3 )
% 5.13/5.48 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.13/5.48 => ( P @ J ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % dec_induct
% 5.13/5.48 thf(fact_1349_Suc__le__eq,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.13/5.48 = ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_le_eq
% 5.13/5.48 thf(fact_1350_Suc__leI,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_leI
% 5.13/5.48 thf(fact_1351_less__natE,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ~ ! [Q3: nat] :
% 5.13/5.48 ( N
% 5.13/5.48 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_natE
% 5.13/5.48 thf(fact_1352_less__add__Suc1,axiom,
% 5.13/5.48 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_Suc1
% 5.13/5.48 thf(fact_1353_less__add__Suc2,axiom,
% 5.13/5.48 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_Suc2
% 5.13/5.48 thf(fact_1354_less__iff__Suc__add,axiom,
% 5.13/5.48 ( ord_less_nat
% 5.13/5.48 = ( ^ [M2: nat,N2: nat] :
% 5.13/5.48 ? [K3: nat] :
% 5.13/5.48 ( N2
% 5.13/5.48 = ( suc @ ( plus_plus_nat @ M2 @ K3 ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_iff_Suc_add
% 5.13/5.48 thf(fact_1355_less__imp__Suc__add,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M @ N )
% 5.13/5.48 => ? [K2: nat] :
% 5.13/5.48 ( N
% 5.13/5.48 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_imp_Suc_add
% 5.13/5.48 thf(fact_1356_Suc__mult__less__cancel1,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.13/5.48 = ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_mult_less_cancel1
% 5.13/5.48 thf(fact_1357_mono__nat__linear__lb,axiom,
% 5.13/5.48 ! [F: nat > nat,M: nat,K: nat] :
% 5.13/5.48 ( ! [M4: nat,N3: nat] :
% 5.13/5.48 ( ( ord_less_nat @ M4 @ N3 )
% 5.13/5.48 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mono_nat_linear_lb
% 5.13/5.48 thf(fact_1358_Suc__mult__le__cancel1,axiom,
% 5.13/5.48 ! [K: nat,M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.13/5.48 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_mult_le_cancel1
% 5.13/5.48 thf(fact_1359_mult__Suc,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.13/5.48 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult_Suc
% 5.13/5.48 thf(fact_1360_Suc__eq__plus1__left,axiom,
% 5.13/5.48 ( suc
% 5.13/5.48 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_eq_plus1_left
% 5.13/5.48 thf(fact_1361_plus__1__eq__Suc,axiom,
% 5.13/5.48 ( ( plus_plus_nat @ one_one_nat )
% 5.13/5.48 = suc ) ).
% 5.13/5.48
% 5.13/5.48 % plus_1_eq_Suc
% 5.13/5.48 thf(fact_1362_Suc__eq__plus1,axiom,
% 5.13/5.48 ( suc
% 5.13/5.48 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_eq_plus1
% 5.13/5.48 thf(fact_1363_vebt__pred_Osimps_I7_J,axiom,
% 5.13/5.48 ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.13/5.48 ( ( ( ord_less_nat @ Ma @ X )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.13/5.48 = ( some_nat @ Ma ) ) )
% 5.13/5.48 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.13/5.48 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.13/5.48 = ( 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 ) )
% 5.13/5.48 @ ( if_option_nat
% 5.13/5.48 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.48 != none_nat )
% 5.13/5.48 & ( 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 ) ) ) ) ) ) ) )
% 5.13/5.48 @ ( 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 ) ) ) ) ) )
% 5.13/5.48 @ ( if_option_nat
% 5.13/5.48 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.48 = none_nat )
% 5.13/5.48 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.13/5.48 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.13/5.48 @ none_nat ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_pred.simps(7)
% 5.13/5.48 thf(fact_1364_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.13/5.48 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.13/5.48 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.13/5.48 = none_P5556105721700978146at_nat ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(2)
% 5.13/5.48 thf(fact_1365_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.13/5.48 ! [Uw: num > num > num,V: num] :
% 5.13/5.48 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.13/5.48 = none_num ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(2)
% 5.13/5.48 thf(fact_1366_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.13/5.48 ! [Uw: nat > nat > nat,V: nat] :
% 5.13/5.48 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.13/5.48 = none_nat ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.simps(2)
% 5.13/5.48 thf(fact_1367_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.13/5.48 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb2: option4927543243414619207at_nat,Y4: option4927543243414619207at_nat] :
% 5.13/5.48 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb2 )
% 5.13/5.48 = Y4 )
% 5.13/5.48 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.13/5.48 => ( Y4 != none_P5556105721700978146at_nat ) )
% 5.13/5.48 => ( ( ? [V2: product_prod_nat_nat] :
% 5.13/5.48 ( Xa2
% 5.13/5.48 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.13/5.48 => ( ( Xb2 = none_P5556105721700978146at_nat )
% 5.13/5.48 => ( Y4 != none_P5556105721700978146at_nat ) ) )
% 5.13/5.48 => ~ ! [A3: product_prod_nat_nat] :
% 5.13/5.48 ( ( Xa2
% 5.13/5.48 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.13/5.48 => ! [B2: product_prod_nat_nat] :
% 5.13/5.48 ( ( Xb2
% 5.13/5.48 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.13/5.48 => ( Y4
% 5.13/5.48 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.elims
% 5.13/5.48 thf(fact_1368_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.13/5.48 ! [X: num > num > num,Xa2: option_num,Xb2: option_num,Y4: option_num] :
% 5.13/5.48 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb2 )
% 5.13/5.48 = Y4 )
% 5.13/5.48 => ( ( ( Xa2 = none_num )
% 5.13/5.48 => ( Y4 != none_num ) )
% 5.13/5.48 => ( ( ? [V2: num] :
% 5.13/5.48 ( Xa2
% 5.13/5.48 = ( some_num @ V2 ) )
% 5.13/5.48 => ( ( Xb2 = none_num )
% 5.13/5.48 => ( Y4 != none_num ) ) )
% 5.13/5.48 => ~ ! [A3: num] :
% 5.13/5.48 ( ( Xa2
% 5.13/5.48 = ( some_num @ A3 ) )
% 5.13/5.48 => ! [B2: num] :
% 5.13/5.48 ( ( Xb2
% 5.13/5.48 = ( some_num @ B2 ) )
% 5.13/5.48 => ( Y4
% 5.13/5.48 != ( some_num @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.elims
% 5.13/5.48 thf(fact_1369_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.13/5.48 ! [X: nat > nat > nat,Xa2: option_nat,Xb2: option_nat,Y4: option_nat] :
% 5.13/5.48 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb2 )
% 5.13/5.48 = Y4 )
% 5.13/5.48 => ( ( ( Xa2 = none_nat )
% 5.13/5.48 => ( Y4 != none_nat ) )
% 5.13/5.48 => ( ( ? [V2: nat] :
% 5.13/5.48 ( Xa2
% 5.13/5.48 = ( some_nat @ V2 ) )
% 5.13/5.48 => ( ( Xb2 = none_nat )
% 5.13/5.48 => ( Y4 != none_nat ) ) )
% 5.13/5.48 => ~ ! [A3: nat] :
% 5.13/5.48 ( ( Xa2
% 5.13/5.48 = ( some_nat @ A3 ) )
% 5.13/5.48 => ! [B2: nat] :
% 5.13/5.48 ( ( Xb2
% 5.13/5.48 = ( some_nat @ B2 ) )
% 5.13/5.48 => ( Y4
% 5.13/5.48 != ( some_nat @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.option_shift.elims
% 5.13/5.48 thf(fact_1370_vebt__mint_Osimps_I2_J,axiom,
% 5.13/5.48 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.13/5.48 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.13/5.48 = none_nat ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_mint.simps(2)
% 5.13/5.48 thf(fact_1371_vebt__maxt_Osimps_I2_J,axiom,
% 5.13/5.48 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.13/5.48 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.13/5.48 = none_nat ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_maxt.simps(2)
% 5.13/5.48 thf(fact_1372_field__sum__of__halves,axiom,
% 5.13/5.48 ! [X: real] :
% 5.13/5.48 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = X ) ).
% 5.13/5.48
% 5.13/5.48 % field_sum_of_halves
% 5.13/5.48 thf(fact_1373_field__sum__of__halves,axiom,
% 5.13/5.48 ! [X: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.13/5.48 = X ) ).
% 5.13/5.48
% 5.13/5.48 % field_sum_of_halves
% 5.13/5.48 thf(fact_1374_vebt__member_Osimps_I5_J,axiom,
% 5.13/5.48 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.13/5.48 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.13/5.48 = ( ( X != Mi )
% 5.13/5.48 => ( ( X != Ma )
% 5.13/5.48 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.13/5.48 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.13/5.48 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.13/5.48 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.13/5.48 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.48 => ( 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 ) ) ) ) ) )
% 5.13/5.48 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % vebt_member.simps(5)
% 5.13/5.48 thf(fact_1375_le__add__diff__inverse2,axiom,
% 5.13/5.48 ! [B: real,A: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.48 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse2
% 5.13/5.48 thf(fact_1376_le__add__diff__inverse2,axiom,
% 5.13/5.48 ! [B: rat,A: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.48 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse2
% 5.13/5.48 thf(fact_1377_le__add__diff__inverse2,axiom,
% 5.13/5.48 ! [B: nat,A: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.48 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse2
% 5.13/5.48 thf(fact_1378_le__add__diff__inverse2,axiom,
% 5.13/5.48 ! [B: int,A: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.48 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse2
% 5.13/5.48 thf(fact_1379_le__add__diff__inverse,axiom,
% 5.13/5.48 ! [B: real,A: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.48 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse
% 5.13/5.48 thf(fact_1380_le__add__diff__inverse,axiom,
% 5.13/5.48 ! [B: rat,A: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.48 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse
% 5.13/5.48 thf(fact_1381_le__add__diff__inverse,axiom,
% 5.13/5.48 ! [B: nat,A: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.48 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse
% 5.13/5.48 thf(fact_1382_le__add__diff__inverse,axiom,
% 5.13/5.48 ! [B: int,A: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.48 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff_inverse
% 5.13/5.48 thf(fact_1383_set__conv__nth,axiom,
% 5.13/5.48 ( set_complex2
% 5.13/5.48 = ( ^ [Xs: list_complex] :
% 5.13/5.48 ( collect_complex
% 5.13/5.48 @ ^ [Uu2: complex] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_complex @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1384_set__conv__nth,axiom,
% 5.13/5.48 ( set_real2
% 5.13/5.48 = ( ^ [Xs: list_real] :
% 5.13/5.48 ( collect_real
% 5.13/5.48 @ ^ [Uu2: real] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_real @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1385_set__conv__nth,axiom,
% 5.13/5.48 ( set_Pr5648618587558075414at_nat
% 5.13/5.48 = ( ^ [Xs: list_P6011104703257516679at_nat] :
% 5.13/5.48 ( collec3392354462482085612at_nat
% 5.13/5.48 @ ^ [Uu2: product_prod_nat_nat] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1386_set__conv__nth,axiom,
% 5.13/5.48 ( set_list_nat2
% 5.13/5.48 = ( ^ [Xs: list_list_nat] :
% 5.13/5.48 ( collect_list_nat
% 5.13/5.48 @ ^ [Uu2: list_nat] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_list_nat @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_s3023201423986296836st_nat @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1387_set__conv__nth,axiom,
% 5.13/5.48 ( set_VEBT_VEBT2
% 5.13/5.48 = ( ^ [Xs: list_VEBT_VEBT] :
% 5.13/5.48 ( collect_VEBT_VEBT
% 5.13/5.48 @ ^ [Uu2: vEBT_VEBT] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1388_set__conv__nth,axiom,
% 5.13/5.48 ( set_o2
% 5.13/5.48 = ( ^ [Xs: list_o] :
% 5.13/5.48 ( collect_o
% 5.13/5.48 @ ^ [Uu2: $o] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_o @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1389_set__conv__nth,axiom,
% 5.13/5.48 ( set_nat2
% 5.13/5.48 = ( ^ [Xs: list_nat] :
% 5.13/5.48 ( collect_nat
% 5.13/5.48 @ ^ [Uu2: nat] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_nat @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1390_set__conv__nth,axiom,
% 5.13/5.48 ( set_int2
% 5.13/5.48 = ( ^ [Xs: list_int] :
% 5.13/5.48 ( collect_int
% 5.13/5.48 @ ^ [Uu2: int] :
% 5.13/5.48 ? [I4: nat] :
% 5.13/5.48 ( ( Uu2
% 5.13/5.48 = ( nth_int @ Xs @ I4 ) )
% 5.13/5.48 & ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % set_conv_nth
% 5.13/5.48 thf(fact_1391_Suc__double__not__eq__double,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.13/5.48 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.13/5.48
% 5.13/5.48 % Suc_double_not_eq_double
% 5.13/5.48 thf(fact_1392_double__not__eq__Suc__double,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.13/5.48 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % double_not_eq_Suc_double
% 5.13/5.48 thf(fact_1393_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.13/5.48 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.13/5.48 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 5.13/5.48 = ( ( X = Mi )
% 5.13/5.48 | ( X = Ma )
% 5.13/5.48 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.48 => ( 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 ) ) ) ) ) )
% 5.13/5.48 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % VEBT_internal.membermima.simps(4)
% 5.13/5.48 thf(fact_1394_div__by__1,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % div_by_1
% 5.13/5.48 thf(fact_1395_div__by__1,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( divide_divide_real @ A @ one_one_real )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % div_by_1
% 5.13/5.48 thf(fact_1396_div__by__1,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % div_by_1
% 5.13/5.48 thf(fact_1397_div__by__1,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % div_by_1
% 5.13/5.48 thf(fact_1398_div__by__1,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( divide_divide_int @ A @ one_one_int )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % div_by_1
% 5.13/5.48 thf(fact_1399_add__diff__cancel__right_H,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right'
% 5.13/5.48 thf(fact_1400_add__diff__cancel__right_H,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right'
% 5.13/5.48 thf(fact_1401_add__diff__cancel__right_H,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right'
% 5.13/5.48 thf(fact_1402_add__diff__cancel__right_H,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right'
% 5.13/5.48 thf(fact_1403_add__diff__cancel__right,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right
% 5.13/5.48 thf(fact_1404_add__diff__cancel__right,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right
% 5.13/5.48 thf(fact_1405_add__diff__cancel__right,axiom,
% 5.13/5.48 ! [A: nat,C: nat,B: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right
% 5.13/5.48 thf(fact_1406_add__diff__cancel__right,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_right
% 5.13/5.48 thf(fact_1407_add__diff__cancel__left_H,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.13/5.48 = B ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left'
% 5.13/5.48 thf(fact_1408_add__diff__cancel__left_H,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.13/5.48 = B ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left'
% 5.13/5.48 thf(fact_1409_add__diff__cancel__left_H,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.13/5.48 = B ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left'
% 5.13/5.48 thf(fact_1410_add__diff__cancel__left_H,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.13/5.48 = B ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left'
% 5.13/5.48 thf(fact_1411_buildup__nothing__in__min__max,axiom,
% 5.13/5.48 ! [N: nat,X: nat] :
% 5.13/5.48 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.13/5.48
% 5.13/5.48 % buildup_nothing_in_min_max
% 5.13/5.48 thf(fact_1412_add__left__cancel,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ A @ B )
% 5.13/5.48 = ( plus_plus_real @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_cancel
% 5.13/5.48 thf(fact_1413_add__left__cancel,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ A @ B )
% 5.13/5.48 = ( plus_plus_rat @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_cancel
% 5.13/5.48 thf(fact_1414_add__left__cancel,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ( plus_plus_nat @ A @ B )
% 5.13/5.48 = ( plus_plus_nat @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_cancel
% 5.13/5.48 thf(fact_1415_add__left__cancel,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ A @ B )
% 5.13/5.48 = ( plus_plus_int @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_cancel
% 5.13/5.48 thf(fact_1416_add__right__cancel,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ B @ A )
% 5.13/5.48 = ( plus_plus_real @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_cancel
% 5.13/5.48 thf(fact_1417_add__right__cancel,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ B @ A )
% 5.13/5.48 = ( plus_plus_rat @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_cancel
% 5.13/5.48 thf(fact_1418_add__right__cancel,axiom,
% 5.13/5.48 ! [B: nat,A: nat,C: nat] :
% 5.13/5.48 ( ( ( plus_plus_nat @ B @ A )
% 5.13/5.48 = ( plus_plus_nat @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_cancel
% 5.13/5.48 thf(fact_1419_add__right__cancel,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ B @ A )
% 5.13/5.48 = ( plus_plus_int @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_cancel
% 5.13/5.48 thf(fact_1420_real__divide__square__eq,axiom,
% 5.13/5.48 ! [R2: real,A: real] :
% 5.13/5.48 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.13/5.48 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % real_divide_square_eq
% 5.13/5.48 thf(fact_1421_add__le__cancel__right,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_right
% 5.13/5.48 thf(fact_1422_add__le__cancel__right,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_right
% 5.13/5.48 thf(fact_1423_add__le__cancel__right,axiom,
% 5.13/5.48 ! [A: nat,C: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.48 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_right
% 5.13/5.48 thf(fact_1424_add__le__cancel__right,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_right
% 5.13/5.48 thf(fact_1425_add__le__cancel__left,axiom,
% 5.13/5.48 ! [C: real,A: real,B: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_left
% 5.13/5.48 thf(fact_1426_add__le__cancel__left,axiom,
% 5.13/5.48 ! [C: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_left
% 5.13/5.48 thf(fact_1427_add__le__cancel__left,axiom,
% 5.13/5.48 ! [C: nat,A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_left
% 5.13/5.48 thf(fact_1428_add__le__cancel__left,axiom,
% 5.13/5.48 ! [C: int,A: int,B: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_cancel_left
% 5.13/5.48 thf(fact_1429_add__less__cancel__left,axiom,
% 5.13/5.48 ! [C: real,A: real,B: real] :
% 5.13/5.48 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.13/5.48 = ( ord_less_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_left
% 5.13/5.48 thf(fact_1430_add__less__cancel__left,axiom,
% 5.13/5.48 ! [C: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.13/5.48 = ( ord_less_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_left
% 5.13/5.48 thf(fact_1431_add__less__cancel__left,axiom,
% 5.13/5.48 ! [C: nat,A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.13/5.48 = ( ord_less_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_left
% 5.13/5.48 thf(fact_1432_add__less__cancel__left,axiom,
% 5.13/5.48 ! [C: int,A: int,B: int] :
% 5.13/5.48 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.13/5.48 = ( ord_less_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_left
% 5.13/5.48 thf(fact_1433_add__less__cancel__right,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 = ( ord_less_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_right
% 5.13/5.48 thf(fact_1434_add__less__cancel__right,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 = ( ord_less_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_right
% 5.13/5.48 thf(fact_1435_add__less__cancel__right,axiom,
% 5.13/5.48 ! [A: nat,C: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.48 = ( ord_less_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_right
% 5.13/5.48 thf(fact_1436_add__less__cancel__right,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 = ( ord_less_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_cancel_right
% 5.13/5.48 thf(fact_1437_mult_Oright__neutral,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( times_times_complex @ A @ one_one_complex )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.right_neutral
% 5.13/5.48 thf(fact_1438_mult_Oright__neutral,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( times_times_real @ A @ one_one_real )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.right_neutral
% 5.13/5.48 thf(fact_1439_mult_Oright__neutral,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ one_one_rat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.right_neutral
% 5.13/5.48 thf(fact_1440_mult_Oright__neutral,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( times_times_nat @ A @ one_one_nat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.right_neutral
% 5.13/5.48 thf(fact_1441_mult_Oright__neutral,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( times_times_int @ A @ one_one_int )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.right_neutral
% 5.13/5.48 thf(fact_1442_mult__1,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( times_times_complex @ one_one_complex @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_1
% 5.13/5.48 thf(fact_1443_mult__1,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( times_times_real @ one_one_real @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_1
% 5.13/5.48 thf(fact_1444_mult__1,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( times_times_rat @ one_one_rat @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_1
% 5.13/5.48 thf(fact_1445_mult__1,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( times_times_nat @ one_one_nat @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_1
% 5.13/5.48 thf(fact_1446_mult__1,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( times_times_int @ one_one_int @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult_1
% 5.13/5.48 thf(fact_1447_add__diff__cancel,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel
% 5.13/5.48 thf(fact_1448_add__diff__cancel,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel
% 5.13/5.48 thf(fact_1449_add__diff__cancel,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel
% 5.13/5.48 thf(fact_1450_diff__add__cancel,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_cancel
% 5.13/5.48 thf(fact_1451_diff__add__cancel,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_cancel
% 5.13/5.48 thf(fact_1452_diff__add__cancel,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_cancel
% 5.13/5.48 thf(fact_1453_add__diff__cancel__left,axiom,
% 5.13/5.48 ! [C: real,A: real,B: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.13/5.48 = ( minus_minus_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left
% 5.13/5.48 thf(fact_1454_add__diff__cancel__left,axiom,
% 5.13/5.48 ! [C: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.13/5.48 = ( minus_minus_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left
% 5.13/5.48 thf(fact_1455_add__diff__cancel__left,axiom,
% 5.13/5.48 ! [C: nat,A: nat,B: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.13/5.48 = ( minus_minus_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left
% 5.13/5.48 thf(fact_1456_add__diff__cancel__left,axiom,
% 5.13/5.48 ! [C: int,A: int,B: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.13/5.48 = ( minus_minus_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_cancel_left
% 5.13/5.48 thf(fact_1457_real__arch__pow,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ X )
% 5.13/5.48 => ? [N3: nat] : ( ord_less_real @ Y4 @ ( power_power_real @ X @ N3 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % real_arch_pow
% 5.13/5.48 thf(fact_1458_add__diff__assoc__enat,axiom,
% 5.13/5.48 ! [Z2: extended_enat,Y4: extended_enat,X: extended_enat] :
% 5.13/5.48 ( ( ord_le2932123472753598470d_enat @ Z2 @ Y4 )
% 5.13/5.48 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y4 @ Z2 ) )
% 5.13/5.48 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_assoc_enat
% 5.13/5.48 thf(fact_1459_linorder__neqE__linordered__idom,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( X != Y4 )
% 5.13/5.48 => ( ~ ( ord_less_real @ X @ Y4 )
% 5.13/5.48 => ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % linorder_neqE_linordered_idom
% 5.13/5.48 thf(fact_1460_linorder__neqE__linordered__idom,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] :
% 5.13/5.48 ( ( X != Y4 )
% 5.13/5.48 => ( ~ ( ord_less_rat @ X @ Y4 )
% 5.13/5.48 => ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % linorder_neqE_linordered_idom
% 5.13/5.48 thf(fact_1461_linorder__neqE__linordered__idom,axiom,
% 5.13/5.48 ! [X: int,Y4: int] :
% 5.13/5.48 ( ( X != Y4 )
% 5.13/5.48 => ( ~ ( ord_less_int @ X @ Y4 )
% 5.13/5.48 => ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % linorder_neqE_linordered_idom
% 5.13/5.48 thf(fact_1462_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.13/5.48 thf(fact_1463_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.13/5.48 thf(fact_1464_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.13/5.48 thf(fact_1465_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.13/5.48 thf(fact_1466_mult_Oassoc,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.assoc
% 5.13/5.48 thf(fact_1467_mult_Oassoc,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.assoc
% 5.13/5.48 thf(fact_1468_mult_Oassoc,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.assoc
% 5.13/5.48 thf(fact_1469_mult_Oassoc,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.13/5.48 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.assoc
% 5.13/5.48 thf(fact_1470_mult_Ocommute,axiom,
% 5.13/5.48 ( times_times_real
% 5.13/5.48 = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.commute
% 5.13/5.48 thf(fact_1471_mult_Ocommute,axiom,
% 5.13/5.48 ( times_times_rat
% 5.13/5.48 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.commute
% 5.13/5.48 thf(fact_1472_mult_Ocommute,axiom,
% 5.13/5.48 ( times_times_nat
% 5.13/5.48 = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.commute
% 5.13/5.48 thf(fact_1473_mult_Ocommute,axiom,
% 5.13/5.48 ( times_times_int
% 5.13/5.48 = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.commute
% 5.13/5.48 thf(fact_1474_mult_Oleft__commute,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.13/5.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.left_commute
% 5.13/5.48 thf(fact_1475_mult_Oleft__commute,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.13/5.48 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.left_commute
% 5.13/5.48 thf(fact_1476_mult_Oleft__commute,axiom,
% 5.13/5.48 ! [B: nat,A: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.13/5.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.left_commute
% 5.13/5.48 thf(fact_1477_mult_Oleft__commute,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.13/5.48 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % mult.left_commute
% 5.13/5.48 thf(fact_1478_one__reorient,axiom,
% 5.13/5.48 ! [X: complex] :
% 5.13/5.48 ( ( one_one_complex = X )
% 5.13/5.48 = ( X = one_one_complex ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_reorient
% 5.13/5.48 thf(fact_1479_one__reorient,axiom,
% 5.13/5.48 ! [X: real] :
% 5.13/5.48 ( ( one_one_real = X )
% 5.13/5.48 = ( X = one_one_real ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_reorient
% 5.13/5.48 thf(fact_1480_one__reorient,axiom,
% 5.13/5.48 ! [X: rat] :
% 5.13/5.48 ( ( one_one_rat = X )
% 5.13/5.48 = ( X = one_one_rat ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_reorient
% 5.13/5.48 thf(fact_1481_one__reorient,axiom,
% 5.13/5.48 ! [X: nat] :
% 5.13/5.48 ( ( one_one_nat = X )
% 5.13/5.48 = ( X = one_one_nat ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_reorient
% 5.13/5.48 thf(fact_1482_one__reorient,axiom,
% 5.13/5.48 ! [X: int] :
% 5.13/5.48 ( ( one_one_int = X )
% 5.13/5.48 = ( X = one_one_int ) ) ).
% 5.13/5.48
% 5.13/5.48 % one_reorient
% 5.13/5.48 thf(fact_1483_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_add_class.add_ac(1)
% 5.13/5.48 thf(fact_1484_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_add_class.add_ac(1)
% 5.13/5.48 thf(fact_1485_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_add_class.add_ac(1)
% 5.13/5.48 thf(fact_1486_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ab_semigroup_add_class.add_ac(1)
% 5.13/5.48 thf(fact_1487_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ( plus_plus_real @ I2 @ K )
% 5.13/5.48 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(4)
% 5.13/5.48 thf(fact_1488_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ( plus_plus_rat @ I2 @ K )
% 5.13/5.48 = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(4)
% 5.13/5.48 thf(fact_1489_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ( plus_plus_nat @ I2 @ K )
% 5.13/5.48 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(4)
% 5.13/5.48 thf(fact_1490_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ( plus_plus_int @ I2 @ K )
% 5.13/5.48 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(4)
% 5.13/5.48 thf(fact_1491_group__cancel_Oadd1,axiom,
% 5.13/5.48 ! [A2: real,K: real,A: real,B: real] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_real @ K @ A ) )
% 5.13/5.48 => ( ( plus_plus_real @ A2 @ B )
% 5.13/5.48 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add1
% 5.13/5.48 thf(fact_1492_group__cancel_Oadd1,axiom,
% 5.13/5.48 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_rat @ K @ A ) )
% 5.13/5.48 => ( ( plus_plus_rat @ A2 @ B )
% 5.13/5.48 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add1
% 5.13/5.48 thf(fact_1493_group__cancel_Oadd1,axiom,
% 5.13/5.48 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_nat @ K @ A ) )
% 5.13/5.48 => ( ( plus_plus_nat @ A2 @ B )
% 5.13/5.48 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add1
% 5.13/5.48 thf(fact_1494_group__cancel_Oadd1,axiom,
% 5.13/5.48 ! [A2: int,K: int,A: int,B: int] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_int @ K @ A ) )
% 5.13/5.48 => ( ( plus_plus_int @ A2 @ B )
% 5.13/5.48 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add1
% 5.13/5.48 thf(fact_1495_group__cancel_Oadd2,axiom,
% 5.13/5.48 ! [B5: real,K: real,B: real,A: real] :
% 5.13/5.48 ( ( B5
% 5.13/5.48 = ( plus_plus_real @ K @ B ) )
% 5.13/5.48 => ( ( plus_plus_real @ A @ B5 )
% 5.13/5.48 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add2
% 5.13/5.48 thf(fact_1496_group__cancel_Oadd2,axiom,
% 5.13/5.48 ! [B5: rat,K: rat,B: rat,A: rat] :
% 5.13/5.48 ( ( B5
% 5.13/5.48 = ( plus_plus_rat @ K @ B ) )
% 5.13/5.48 => ( ( plus_plus_rat @ A @ B5 )
% 5.13/5.48 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add2
% 5.13/5.48 thf(fact_1497_group__cancel_Oadd2,axiom,
% 5.13/5.48 ! [B5: nat,K: nat,B: nat,A: nat] :
% 5.13/5.48 ( ( B5
% 5.13/5.48 = ( plus_plus_nat @ K @ B ) )
% 5.13/5.48 => ( ( plus_plus_nat @ A @ B5 )
% 5.13/5.48 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add2
% 5.13/5.48 thf(fact_1498_group__cancel_Oadd2,axiom,
% 5.13/5.48 ! [B5: int,K: int,B: int,A: int] :
% 5.13/5.48 ( ( B5
% 5.13/5.48 = ( plus_plus_int @ K @ B ) )
% 5.13/5.48 => ( ( plus_plus_int @ A @ B5 )
% 5.13/5.48 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.add2
% 5.13/5.48 thf(fact_1499_add_Oassoc,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.assoc
% 5.13/5.48 thf(fact_1500_add_Oassoc,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.assoc
% 5.13/5.48 thf(fact_1501_add_Oassoc,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.assoc
% 5.13/5.48 thf(fact_1502_add_Oassoc,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.assoc
% 5.13/5.48 thf(fact_1503_add_Oleft__cancel,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ A @ B )
% 5.13/5.48 = ( plus_plus_real @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_cancel
% 5.13/5.48 thf(fact_1504_add_Oleft__cancel,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ A @ B )
% 5.13/5.48 = ( plus_plus_rat @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_cancel
% 5.13/5.48 thf(fact_1505_add_Oleft__cancel,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ A @ B )
% 5.13/5.48 = ( plus_plus_int @ A @ C ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_cancel
% 5.13/5.48 thf(fact_1506_add_Oright__cancel,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ B @ A )
% 5.13/5.48 = ( plus_plus_real @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.right_cancel
% 5.13/5.48 thf(fact_1507_add_Oright__cancel,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ B @ A )
% 5.13/5.48 = ( plus_plus_rat @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.right_cancel
% 5.13/5.48 thf(fact_1508_add_Oright__cancel,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ B @ A )
% 5.13/5.48 = ( plus_plus_int @ C @ A ) )
% 5.13/5.48 = ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.right_cancel
% 5.13/5.48 thf(fact_1509_add_Ocommute,axiom,
% 5.13/5.48 ( plus_plus_real
% 5.13/5.48 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.commute
% 5.13/5.48 thf(fact_1510_add_Ocommute,axiom,
% 5.13/5.48 ( plus_plus_rat
% 5.13/5.48 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.commute
% 5.13/5.48 thf(fact_1511_add_Ocommute,axiom,
% 5.13/5.48 ( plus_plus_nat
% 5.13/5.48 = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.commute
% 5.13/5.48 thf(fact_1512_add_Ocommute,axiom,
% 5.13/5.48 ( plus_plus_int
% 5.13/5.48 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.commute
% 5.13/5.48 thf(fact_1513_add_Oleft__commute,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.13/5.48 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_commute
% 5.13/5.48 thf(fact_1514_add_Oleft__commute,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.13/5.48 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_commute
% 5.13/5.48 thf(fact_1515_add_Oleft__commute,axiom,
% 5.13/5.48 ! [B: nat,A: nat,C: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.13/5.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_commute
% 5.13/5.48 thf(fact_1516_add_Oleft__commute,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.13/5.48 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add.left_commute
% 5.13/5.48 thf(fact_1517_add__left__imp__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ A @ B )
% 5.13/5.48 = ( plus_plus_real @ A @ C ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_imp_eq
% 5.13/5.48 thf(fact_1518_add__left__imp__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ A @ B )
% 5.13/5.48 = ( plus_plus_rat @ A @ C ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_imp_eq
% 5.13/5.48 thf(fact_1519_add__left__imp__eq,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ( plus_plus_nat @ A @ B )
% 5.13/5.48 = ( plus_plus_nat @ A @ C ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_imp_eq
% 5.13/5.48 thf(fact_1520_add__left__imp__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ A @ B )
% 5.13/5.48 = ( plus_plus_int @ A @ C ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_imp_eq
% 5.13/5.48 thf(fact_1521_add__right__imp__eq,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ B @ A )
% 5.13/5.48 = ( plus_plus_real @ C @ A ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_imp_eq
% 5.13/5.48 thf(fact_1522_add__right__imp__eq,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ B @ A )
% 5.13/5.48 = ( plus_plus_rat @ C @ A ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_imp_eq
% 5.13/5.48 thf(fact_1523_add__right__imp__eq,axiom,
% 5.13/5.48 ! [B: nat,A: nat,C: nat] :
% 5.13/5.48 ( ( ( plus_plus_nat @ B @ A )
% 5.13/5.48 = ( plus_plus_nat @ C @ A ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_imp_eq
% 5.13/5.48 thf(fact_1524_add__right__imp__eq,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ B @ A )
% 5.13/5.48 = ( plus_plus_int @ C @ A ) )
% 5.13/5.48 => ( B = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_imp_eq
% 5.13/5.48 thf(fact_1525_subset__code_I1_J,axiom,
% 5.13/5.48 ! [Xs2: list_real,B5: set_real] :
% 5.13/5.48 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B5 )
% 5.13/5.48 = ( ! [X2: real] :
% 5.13/5.48 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.13/5.48 => ( member_real @ X2 @ B5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % subset_code(1)
% 5.13/5.48 thf(fact_1526_subset__code_I1_J,axiom,
% 5.13/5.48 ! [Xs2: list_complex,B5: set_complex] :
% 5.13/5.48 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B5 )
% 5.13/5.48 = ( ! [X2: complex] :
% 5.13/5.48 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.13/5.48 => ( member_complex @ X2 @ B5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % subset_code(1)
% 5.13/5.48 thf(fact_1527_subset__code_I1_J,axiom,
% 5.13/5.48 ! [Xs2: list_P6011104703257516679at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.13/5.48 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B5 )
% 5.13/5.48 = ( ! [X2: product_prod_nat_nat] :
% 5.13/5.48 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.13/5.48 => ( member8440522571783428010at_nat @ X2 @ B5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % subset_code(1)
% 5.13/5.48 thf(fact_1528_subset__code_I1_J,axiom,
% 5.13/5.48 ! [Xs2: list_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.13/5.48 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B5 )
% 5.13/5.48 = ( ! [X2: vEBT_VEBT] :
% 5.13/5.48 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.48 => ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % subset_code(1)
% 5.13/5.48 thf(fact_1529_subset__code_I1_J,axiom,
% 5.13/5.48 ! [Xs2: list_int,B5: set_int] :
% 5.13/5.48 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B5 )
% 5.13/5.48 = ( ! [X2: int] :
% 5.13/5.48 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.13/5.48 => ( member_int @ X2 @ B5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % subset_code(1)
% 5.13/5.48 thf(fact_1530_subset__code_I1_J,axiom,
% 5.13/5.48 ! [Xs2: list_nat,B5: set_nat] :
% 5.13/5.48 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B5 )
% 5.13/5.48 = ( ! [X2: nat] :
% 5.13/5.48 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.13/5.48 => ( member_nat @ X2 @ B5 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % subset_code(1)
% 5.13/5.48 thf(fact_1531_Ex__list__of__length,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ? [Xs3: list_VEBT_VEBT] :
% 5.13/5.48 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % Ex_list_of_length
% 5.13/5.48 thf(fact_1532_Ex__list__of__length,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ? [Xs3: list_o] :
% 5.13/5.48 ( ( size_size_list_o @ Xs3 )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % Ex_list_of_length
% 5.13/5.48 thf(fact_1533_Ex__list__of__length,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ? [Xs3: list_nat] :
% 5.13/5.48 ( ( size_size_list_nat @ Xs3 )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % Ex_list_of_length
% 5.13/5.48 thf(fact_1534_Ex__list__of__length,axiom,
% 5.13/5.48 ! [N: nat] :
% 5.13/5.48 ? [Xs3: list_int] :
% 5.13/5.48 ( ( size_size_list_int @ Xs3 )
% 5.13/5.48 = N ) ).
% 5.13/5.48
% 5.13/5.48 % Ex_list_of_length
% 5.13/5.48 thf(fact_1535_neq__if__length__neq,axiom,
% 5.13/5.48 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.13/5.48 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.13/5.48 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.13/5.48 => ( Xs2 != Ys ) ) ).
% 5.13/5.48
% 5.13/5.48 % neq_if_length_neq
% 5.13/5.48 thf(fact_1536_neq__if__length__neq,axiom,
% 5.13/5.48 ! [Xs2: list_o,Ys: list_o] :
% 5.13/5.48 ( ( ( size_size_list_o @ Xs2 )
% 5.13/5.48 != ( size_size_list_o @ Ys ) )
% 5.13/5.48 => ( Xs2 != Ys ) ) ).
% 5.13/5.48
% 5.13/5.48 % neq_if_length_neq
% 5.13/5.48 thf(fact_1537_neq__if__length__neq,axiom,
% 5.13/5.48 ! [Xs2: list_nat,Ys: list_nat] :
% 5.13/5.48 ( ( ( size_size_list_nat @ Xs2 )
% 5.13/5.48 != ( size_size_list_nat @ Ys ) )
% 5.13/5.48 => ( Xs2 != Ys ) ) ).
% 5.13/5.48
% 5.13/5.48 % neq_if_length_neq
% 5.13/5.48 thf(fact_1538_neq__if__length__neq,axiom,
% 5.13/5.48 ! [Xs2: list_int,Ys: list_int] :
% 5.13/5.48 ( ( ( size_size_list_int @ Xs2 )
% 5.13/5.48 != ( size_size_list_int @ Ys ) )
% 5.13/5.48 => ( Xs2 != Ys ) ) ).
% 5.13/5.48
% 5.13/5.48 % neq_if_length_neq
% 5.13/5.48 thf(fact_1539_add__le__imp__le__right,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_right
% 5.13/5.48 thf(fact_1540_add__le__imp__le__right,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_right
% 5.13/5.48 thf(fact_1541_add__le__imp__le__right,axiom,
% 5.13/5.48 ! [A: nat,C: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.48 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_right
% 5.13/5.48 thf(fact_1542_add__le__imp__le__right,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_right
% 5.13/5.48 thf(fact_1543_add__le__imp__le__left,axiom,
% 5.13/5.48 ! [C: real,A: real,B: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.13/5.48 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_left
% 5.13/5.48 thf(fact_1544_add__le__imp__le__left,axiom,
% 5.13/5.48 ! [C: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.13/5.48 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_left
% 5.13/5.48 thf(fact_1545_add__le__imp__le__left,axiom,
% 5.13/5.48 ! [C: nat,A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.13/5.48 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_left
% 5.13/5.48 thf(fact_1546_add__le__imp__le__left,axiom,
% 5.13/5.48 ! [C: int,A: int,B: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.13/5.48 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_left
% 5.13/5.48 thf(fact_1547_le__iff__add,axiom,
% 5.13/5.48 ( ord_less_eq_nat
% 5.13/5.48 = ( ^ [A4: nat,B3: nat] :
% 5.13/5.48 ? [C2: nat] :
% 5.13/5.48 ( B3
% 5.13/5.48 = ( plus_plus_nat @ A4 @ C2 ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_iff_add
% 5.13/5.48 thf(fact_1548_add__right__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_mono
% 5.13/5.48 thf(fact_1549_add__right__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_mono
% 5.13/5.48 thf(fact_1550_add__right__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_mono
% 5.13/5.48 thf(fact_1551_add__right__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_right_mono
% 5.13/5.48 thf(fact_1552_less__eqE,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ~ ! [C3: nat] :
% 5.13/5.48 ( B
% 5.13/5.48 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_eqE
% 5.13/5.48 thf(fact_1553_add__left__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_mono
% 5.13/5.48 thf(fact_1554_add__left__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_mono
% 5.13/5.48 thf(fact_1555_add__left__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_mono
% 5.13/5.48 thf(fact_1556_add__left__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_left_mono
% 5.13/5.48 thf(fact_1557_add__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_real @ C @ D )
% 5.13/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono
% 5.13/5.48 thf(fact_1558_add__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_rat @ C @ D )
% 5.13/5.48 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono
% 5.13/5.48 thf(fact_1559_add__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ C @ D )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono
% 5.13/5.48 thf(fact_1560_add__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_int @ C @ D )
% 5.13/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono
% 5.13/5.48 thf(fact_1561_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_real @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(1)
% 5.13/5.48 thf(fact_1562_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(1)
% 5.13/5.48 thf(fact_1563_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(1)
% 5.13/5.48 thf(fact_1564_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_int @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(1)
% 5.13/5.48 thf(fact_1565_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_eq_real @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(2)
% 5.13/5.48 thf(fact_1566_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(2)
% 5.13/5.48 thf(fact_1567_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(2)
% 5.13/5.48 thf(fact_1568_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_eq_int @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(2)
% 5.13/5.48 thf(fact_1569_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(3)
% 5.13/5.48 thf(fact_1570_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(3)
% 5.13/5.48 thf(fact_1571_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(3)
% 5.13/5.48 thf(fact_1572_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_semiring(3)
% 5.13/5.48 thf(fact_1573_diff__eq__diff__less__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.48 ( ( ( minus_minus_real @ A @ B )
% 5.13/5.48 = ( minus_minus_real @ C @ D ) )
% 5.13/5.48 => ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_diff_less_eq
% 5.13/5.48 thf(fact_1574_diff__eq__diff__less__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.48 ( ( ( minus_minus_rat @ A @ B )
% 5.13/5.48 = ( minus_minus_rat @ C @ D ) )
% 5.13/5.48 => ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_diff_less_eq
% 5.13/5.48 thf(fact_1575_diff__eq__diff__less__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.48 ( ( ( minus_minus_int @ A @ B )
% 5.13/5.48 = ( minus_minus_int @ C @ D ) )
% 5.13/5.48 => ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_diff_less_eq
% 5.13/5.48 thf(fact_1576_diff__right__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_right_mono
% 5.13/5.48 thf(fact_1577_diff__right__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_right_mono
% 5.13/5.48 thf(fact_1578_diff__right__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_right_mono
% 5.13/5.48 thf(fact_1579_diff__left__mono,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_left_mono
% 5.13/5.48 thf(fact_1580_diff__left__mono,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_left_mono
% 5.13/5.48 thf(fact_1581_diff__left__mono,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_left_mono
% 5.13/5.48 thf(fact_1582_diff__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,D: real,C: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_real @ D @ C )
% 5.13/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_mono
% 5.13/5.48 thf(fact_1583_diff__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_rat @ D @ C )
% 5.13/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_mono
% 5.13/5.48 thf(fact_1584_diff__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,D: int,C: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_int @ D @ C )
% 5.13/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_mono
% 5.13/5.48 thf(fact_1585_add__mono__thms__linordered__field_I5_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( ord_less_real @ I2 @ J )
% 5.13/5.48 & ( ord_less_real @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(5)
% 5.13/5.48 thf(fact_1586_add__mono__thms__linordered__field_I5_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( ord_less_rat @ I2 @ J )
% 5.13/5.48 & ( ord_less_rat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(5)
% 5.13/5.48 thf(fact_1587_add__mono__thms__linordered__field_I5_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 & ( ord_less_nat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(5)
% 5.13/5.48 thf(fact_1588_add__mono__thms__linordered__field_I5_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( ord_less_int @ I2 @ J )
% 5.13/5.48 & ( ord_less_int @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(5)
% 5.13/5.48 thf(fact_1589_add__mono__thms__linordered__field_I2_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_real @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(2)
% 5.13/5.48 thf(fact_1590_add__mono__thms__linordered__field_I2_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_rat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(2)
% 5.13/5.48 thf(fact_1591_add__mono__thms__linordered__field_I2_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_nat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(2)
% 5.13/5.48 thf(fact_1592_add__mono__thms__linordered__field_I2_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( I2 = J )
% 5.13/5.48 & ( ord_less_int @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(2)
% 5.13/5.48 thf(fact_1593_add__mono__thms__linordered__field_I1_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( ord_less_real @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(1)
% 5.13/5.48 thf(fact_1594_add__mono__thms__linordered__field_I1_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( ord_less_rat @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(1)
% 5.13/5.48 thf(fact_1595_add__mono__thms__linordered__field_I1_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(1)
% 5.13/5.48 thf(fact_1596_add__mono__thms__linordered__field_I1_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( ord_less_int @ I2 @ J )
% 5.13/5.48 & ( K = L2 ) )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(1)
% 5.13/5.48 thf(fact_1597_add__strict__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ( ord_less_real @ C @ D )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_mono
% 5.13/5.48 thf(fact_1598_add__strict__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ( ord_less_rat @ C @ D )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_mono
% 5.13/5.48 thf(fact_1599_add__strict__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.48 ( ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_nat @ C @ D )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_mono
% 5.13/5.48 thf(fact_1600_add__strict__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ( ord_less_int @ C @ D )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_mono
% 5.13/5.48 thf(fact_1601_add__strict__left__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_left_mono
% 5.13/5.48 thf(fact_1602_add__strict__left__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_left_mono
% 5.13/5.48 thf(fact_1603_add__strict__left__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_left_mono
% 5.13/5.48 thf(fact_1604_add__strict__left__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_left_mono
% 5.13/5.48 thf(fact_1605_add__strict__right__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_right_mono
% 5.13/5.48 thf(fact_1606_add__strict__right__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_right_mono
% 5.13/5.48 thf(fact_1607_add__strict__right__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_right_mono
% 5.13/5.48 thf(fact_1608_add__strict__right__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_strict_right_mono
% 5.13/5.48 thf(fact_1609_add__less__imp__less__left,axiom,
% 5.13/5.48 ! [C: real,A: real,B: real] :
% 5.13/5.48 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.13/5.48 => ( ord_less_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_left
% 5.13/5.48 thf(fact_1610_add__less__imp__less__left,axiom,
% 5.13/5.48 ! [C: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.13/5.48 => ( ord_less_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_left
% 5.13/5.48 thf(fact_1611_add__less__imp__less__left,axiom,
% 5.13/5.48 ! [C: nat,A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.13/5.48 => ( ord_less_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_left
% 5.13/5.48 thf(fact_1612_add__less__imp__less__left,axiom,
% 5.13/5.48 ! [C: int,A: int,B: int] :
% 5.13/5.48 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.13/5.48 => ( ord_less_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_left
% 5.13/5.48 thf(fact_1613_add__less__imp__less__right,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 => ( ord_less_real @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_right
% 5.13/5.48 thf(fact_1614_add__less__imp__less__right,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 => ( ord_less_rat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_right
% 5.13/5.48 thf(fact_1615_add__less__imp__less__right,axiom,
% 5.13/5.48 ! [A: nat,C: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.48 => ( ord_less_nat @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_right
% 5.13/5.48 thf(fact_1616_add__less__imp__less__right,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 => ( ord_less_int @ A @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_imp_less_right
% 5.13/5.48 thf(fact_1617_diff__strict__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,D: real,C: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ( ord_less_real @ D @ C )
% 5.13/5.48 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_mono
% 5.13/5.48 thf(fact_1618_diff__strict__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ( ord_less_rat @ D @ C )
% 5.13/5.48 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_mono
% 5.13/5.48 thf(fact_1619_diff__strict__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,D: int,C: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ( ord_less_int @ D @ C )
% 5.13/5.48 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_mono
% 5.13/5.48 thf(fact_1620_diff__eq__diff__less,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.48 ( ( ( minus_minus_real @ A @ B )
% 5.13/5.48 = ( minus_minus_real @ C @ D ) )
% 5.13/5.48 => ( ( ord_less_real @ A @ B )
% 5.13/5.48 = ( ord_less_real @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_diff_less
% 5.13/5.48 thf(fact_1621_diff__eq__diff__less,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.48 ( ( ( minus_minus_rat @ A @ B )
% 5.13/5.48 = ( minus_minus_rat @ C @ D ) )
% 5.13/5.48 => ( ( ord_less_rat @ A @ B )
% 5.13/5.48 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_diff_less
% 5.13/5.48 thf(fact_1622_diff__eq__diff__less,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.48 ( ( ( minus_minus_int @ A @ B )
% 5.13/5.48 = ( minus_minus_int @ C @ D ) )
% 5.13/5.48 => ( ( ord_less_int @ A @ B )
% 5.13/5.48 = ( ord_less_int @ C @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_diff_less
% 5.13/5.48 thf(fact_1623_diff__strict__left__mono,axiom,
% 5.13/5.48 ! [B: real,A: real,C: real] :
% 5.13/5.48 ( ( ord_less_real @ B @ A )
% 5.13/5.48 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_left_mono
% 5.13/5.48 thf(fact_1624_diff__strict__left__mono,axiom,
% 5.13/5.48 ! [B: rat,A: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_rat @ B @ A )
% 5.13/5.48 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_left_mono
% 5.13/5.48 thf(fact_1625_diff__strict__left__mono,axiom,
% 5.13/5.48 ! [B: int,A: int,C: int] :
% 5.13/5.48 ( ( ord_less_int @ B @ A )
% 5.13/5.48 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_left_mono
% 5.13/5.48 thf(fact_1626_diff__strict__right__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_right_mono
% 5.13/5.48 thf(fact_1627_diff__strict__right__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_right_mono
% 5.13/5.48 thf(fact_1628_diff__strict__right__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_strict_right_mono
% 5.13/5.48 thf(fact_1629_comm__monoid__mult__class_Omult__1,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( times_times_complex @ one_one_complex @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % comm_monoid_mult_class.mult_1
% 5.13/5.48 thf(fact_1630_comm__monoid__mult__class_Omult__1,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( times_times_real @ one_one_real @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % comm_monoid_mult_class.mult_1
% 5.13/5.48 thf(fact_1631_comm__monoid__mult__class_Omult__1,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( times_times_rat @ one_one_rat @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % comm_monoid_mult_class.mult_1
% 5.13/5.48 thf(fact_1632_comm__monoid__mult__class_Omult__1,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( times_times_nat @ one_one_nat @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % comm_monoid_mult_class.mult_1
% 5.13/5.48 thf(fact_1633_comm__monoid__mult__class_Omult__1,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( times_times_int @ one_one_int @ A )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % comm_monoid_mult_class.mult_1
% 5.13/5.48 thf(fact_1634_mult_Ocomm__neutral,axiom,
% 5.13/5.48 ! [A: complex] :
% 5.13/5.48 ( ( times_times_complex @ A @ one_one_complex )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.comm_neutral
% 5.13/5.48 thf(fact_1635_mult_Ocomm__neutral,axiom,
% 5.13/5.48 ! [A: real] :
% 5.13/5.48 ( ( times_times_real @ A @ one_one_real )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.comm_neutral
% 5.13/5.48 thf(fact_1636_mult_Ocomm__neutral,axiom,
% 5.13/5.48 ! [A: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ one_one_rat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.comm_neutral
% 5.13/5.48 thf(fact_1637_mult_Ocomm__neutral,axiom,
% 5.13/5.48 ! [A: nat] :
% 5.13/5.48 ( ( times_times_nat @ A @ one_one_nat )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.comm_neutral
% 5.13/5.48 thf(fact_1638_mult_Ocomm__neutral,axiom,
% 5.13/5.48 ! [A: int] :
% 5.13/5.48 ( ( times_times_int @ A @ one_one_int )
% 5.13/5.48 = A ) ).
% 5.13/5.48
% 5.13/5.48 % mult.comm_neutral
% 5.13/5.48 thf(fact_1639_ring__class_Oring__distribs_I2_J,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ring_class.ring_distribs(2)
% 5.13/5.48 thf(fact_1640_ring__class_Oring__distribs_I2_J,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ring_class.ring_distribs(2)
% 5.13/5.48 thf(fact_1641_ring__class_Oring__distribs_I2_J,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ring_class.ring_distribs(2)
% 5.13/5.48 thf(fact_1642_ring__class_Oring__distribs_I1_J,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ring_class.ring_distribs(1)
% 5.13/5.48 thf(fact_1643_ring__class_Oring__distribs_I1_J,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ring_class.ring_distribs(1)
% 5.13/5.48 thf(fact_1644_ring__class_Oring__distribs_I1_J,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ring_class.ring_distribs(1)
% 5.13/5.48 thf(fact_1645_comm__semiring__class_Odistrib,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % comm_semiring_class.distrib
% 5.13/5.48 thf(fact_1646_comm__semiring__class_Odistrib,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % comm_semiring_class.distrib
% 5.13/5.48 thf(fact_1647_comm__semiring__class_Odistrib,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % comm_semiring_class.distrib
% 5.13/5.48 thf(fact_1648_comm__semiring__class_Odistrib,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % comm_semiring_class.distrib
% 5.13/5.48 thf(fact_1649_distrib__left,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_left
% 5.13/5.48 thf(fact_1650_distrib__left,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_left
% 5.13/5.48 thf(fact_1651_distrib__left,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_left
% 5.13/5.48 thf(fact_1652_distrib__left,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_left
% 5.13/5.48 thf(fact_1653_distrib__right,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_right
% 5.13/5.48 thf(fact_1654_distrib__right,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_right
% 5.13/5.48 thf(fact_1655_distrib__right,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_right
% 5.13/5.48 thf(fact_1656_distrib__right,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % distrib_right
% 5.13/5.48 thf(fact_1657_combine__common__factor,axiom,
% 5.13/5.48 ! [A: real,E: real,B: real,C: real] :
% 5.13/5.48 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % combine_common_factor
% 5.13/5.48 thf(fact_1658_combine__common__factor,axiom,
% 5.13/5.48 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % combine_common_factor
% 5.13/5.48 thf(fact_1659_combine__common__factor,axiom,
% 5.13/5.48 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.13/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % combine_common_factor
% 5.13/5.48 thf(fact_1660_combine__common__factor,axiom,
% 5.13/5.48 ! [A: int,E: int,B: int,C: int] :
% 5.13/5.48 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.13/5.48 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % combine_common_factor
% 5.13/5.48 thf(fact_1661_left__diff__distrib,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib
% 5.13/5.48 thf(fact_1662_left__diff__distrib,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib
% 5.13/5.48 thf(fact_1663_left__diff__distrib,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib
% 5.13/5.48 thf(fact_1664_right__diff__distrib,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib
% 5.13/5.48 thf(fact_1665_right__diff__distrib,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib
% 5.13/5.48 thf(fact_1666_right__diff__distrib,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib
% 5.13/5.48 thf(fact_1667_left__diff__distrib_H,axiom,
% 5.13/5.48 ! [B: real,C: real,A: real] :
% 5.13/5.48 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.13/5.48 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib'
% 5.13/5.48 thf(fact_1668_left__diff__distrib_H,axiom,
% 5.13/5.48 ! [B: rat,C: rat,A: rat] :
% 5.13/5.48 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.13/5.48 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib'
% 5.13/5.48 thf(fact_1669_left__diff__distrib_H,axiom,
% 5.13/5.48 ! [B: nat,C: nat,A: nat] :
% 5.13/5.48 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.13/5.48 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib'
% 5.13/5.48 thf(fact_1670_left__diff__distrib_H,axiom,
% 5.13/5.48 ! [B: int,C: int,A: int] :
% 5.13/5.48 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.13/5.48 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % left_diff_distrib'
% 5.13/5.48 thf(fact_1671_right__diff__distrib_H,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib'
% 5.13/5.48 thf(fact_1672_right__diff__distrib_H,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib'
% 5.13/5.48 thf(fact_1673_right__diff__distrib_H,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib'
% 5.13/5.48 thf(fact_1674_right__diff__distrib_H,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % right_diff_distrib'
% 5.13/5.48 thf(fact_1675_group__cancel_Osub1,axiom,
% 5.13/5.48 ! [A2: real,K: real,A: real,B: real] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_real @ K @ A ) )
% 5.13/5.48 => ( ( minus_minus_real @ A2 @ B )
% 5.13/5.48 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.sub1
% 5.13/5.48 thf(fact_1676_group__cancel_Osub1,axiom,
% 5.13/5.48 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_rat @ K @ A ) )
% 5.13/5.48 => ( ( minus_minus_rat @ A2 @ B )
% 5.13/5.48 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.sub1
% 5.13/5.48 thf(fact_1677_group__cancel_Osub1,axiom,
% 5.13/5.48 ! [A2: int,K: int,A: int,B: int] :
% 5.13/5.48 ( ( A2
% 5.13/5.48 = ( plus_plus_int @ K @ A ) )
% 5.13/5.48 => ( ( minus_minus_int @ A2 @ B )
% 5.13/5.48 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % group_cancel.sub1
% 5.13/5.48 thf(fact_1678_diff__eq__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ( minus_minus_real @ A @ B )
% 5.13/5.48 = C )
% 5.13/5.48 = ( A
% 5.13/5.48 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_eq
% 5.13/5.48 thf(fact_1679_diff__eq__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ( minus_minus_rat @ A @ B )
% 5.13/5.48 = C )
% 5.13/5.48 = ( A
% 5.13/5.48 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_eq
% 5.13/5.48 thf(fact_1680_diff__eq__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ( minus_minus_int @ A @ B )
% 5.13/5.48 = C )
% 5.13/5.48 = ( A
% 5.13/5.48 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_eq_eq
% 5.13/5.48 thf(fact_1681_eq__diff__eq,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( A
% 5.13/5.48 = ( minus_minus_real @ C @ B ) )
% 5.13/5.48 = ( ( plus_plus_real @ A @ B )
% 5.13/5.48 = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_diff_eq
% 5.13/5.48 thf(fact_1682_eq__diff__eq,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( A
% 5.13/5.48 = ( minus_minus_rat @ C @ B ) )
% 5.13/5.48 = ( ( plus_plus_rat @ A @ B )
% 5.13/5.48 = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_diff_eq
% 5.13/5.48 thf(fact_1683_eq__diff__eq,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( A
% 5.13/5.48 = ( minus_minus_int @ C @ B ) )
% 5.13/5.48 = ( ( plus_plus_int @ A @ B )
% 5.13/5.48 = C ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_diff_eq
% 5.13/5.48 thf(fact_1684_add__diff__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_eq
% 5.13/5.48 thf(fact_1685_add__diff__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_eq
% 5.13/5.48 thf(fact_1686_add__diff__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_diff_eq
% 5.13/5.48 thf(fact_1687_diff__diff__eq2,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq2
% 5.13/5.48 thf(fact_1688_diff__diff__eq2,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq2
% 5.13/5.48 thf(fact_1689_diff__diff__eq2,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq2
% 5.13/5.48 thf(fact_1690_diff__add__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_eq
% 5.13/5.48 thf(fact_1691_diff__add__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_eq
% 5.13/5.48 thf(fact_1692_diff__add__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_eq
% 5.13/5.48 thf(fact_1693_diff__add__eq__diff__diff__swap,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.13/5.48 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_eq_diff_diff_swap
% 5.13/5.48 thf(fact_1694_diff__add__eq__diff__diff__swap,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.13/5.48 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_eq_diff_diff_swap
% 5.13/5.48 thf(fact_1695_diff__add__eq__diff__diff__swap,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.13/5.48 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add_eq_diff_diff_swap
% 5.13/5.48 thf(fact_1696_add__implies__diff,axiom,
% 5.13/5.48 ! [C: real,B: real,A: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ C @ B )
% 5.13/5.48 = A )
% 5.13/5.48 => ( C
% 5.13/5.48 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_implies_diff
% 5.13/5.48 thf(fact_1697_add__implies__diff,axiom,
% 5.13/5.48 ! [C: rat,B: rat,A: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ C @ B )
% 5.13/5.48 = A )
% 5.13/5.48 => ( C
% 5.13/5.48 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_implies_diff
% 5.13/5.48 thf(fact_1698_add__implies__diff,axiom,
% 5.13/5.48 ! [C: nat,B: nat,A: nat] :
% 5.13/5.48 ( ( ( plus_plus_nat @ C @ B )
% 5.13/5.48 = A )
% 5.13/5.48 => ( C
% 5.13/5.48 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_implies_diff
% 5.13/5.48 thf(fact_1699_add__implies__diff,axiom,
% 5.13/5.48 ! [C: int,B: int,A: int] :
% 5.13/5.48 ( ( ( plus_plus_int @ C @ B )
% 5.13/5.48 = A )
% 5.13/5.48 => ( C
% 5.13/5.48 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_implies_diff
% 5.13/5.48 thf(fact_1700_diff__diff__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq
% 5.13/5.48 thf(fact_1701_diff__diff__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq
% 5.13/5.48 thf(fact_1702_diff__diff__eq,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq
% 5.13/5.48 thf(fact_1703_diff__diff__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.13/5.48 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_diff_eq
% 5.13/5.48 thf(fact_1704_length__induct,axiom,
% 5.13/5.48 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.13/5.48 ( ! [Xs3: list_VEBT_VEBT] :
% 5.13/5.48 ( ! [Ys2: list_VEBT_VEBT] :
% 5.13/5.48 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.13/5.48 => ( P @ Ys2 ) )
% 5.13/5.48 => ( P @ Xs3 ) )
% 5.13/5.48 => ( P @ Xs2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % length_induct
% 5.13/5.48 thf(fact_1705_length__induct,axiom,
% 5.13/5.48 ! [P: list_o > $o,Xs2: list_o] :
% 5.13/5.48 ( ! [Xs3: list_o] :
% 5.13/5.48 ( ! [Ys2: list_o] :
% 5.13/5.48 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.13/5.48 => ( P @ Ys2 ) )
% 5.13/5.48 => ( P @ Xs3 ) )
% 5.13/5.48 => ( P @ Xs2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % length_induct
% 5.13/5.48 thf(fact_1706_length__induct,axiom,
% 5.13/5.48 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.13/5.48 ( ! [Xs3: list_nat] :
% 5.13/5.48 ( ! [Ys2: list_nat] :
% 5.13/5.48 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.13/5.48 => ( P @ Ys2 ) )
% 5.13/5.48 => ( P @ Xs3 ) )
% 5.13/5.48 => ( P @ Xs2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % length_induct
% 5.13/5.48 thf(fact_1707_length__induct,axiom,
% 5.13/5.48 ! [P: list_int > $o,Xs2: list_int] :
% 5.13/5.48 ( ! [Xs3: list_int] :
% 5.13/5.48 ( ! [Ys2: list_int] :
% 5.13/5.48 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.13/5.48 => ( P @ Ys2 ) )
% 5.13/5.48 => ( P @ Xs3 ) )
% 5.13/5.48 => ( P @ Xs2 ) ) ).
% 5.13/5.48
% 5.13/5.48 % length_induct
% 5.13/5.48 thf(fact_1708_lambda__one,axiom,
% 5.13/5.48 ( ( ^ [X2: complex] : X2 )
% 5.13/5.48 = ( times_times_complex @ one_one_complex ) ) ).
% 5.13/5.48
% 5.13/5.48 % lambda_one
% 5.13/5.48 thf(fact_1709_lambda__one,axiom,
% 5.13/5.48 ( ( ^ [X2: real] : X2 )
% 5.13/5.48 = ( times_times_real @ one_one_real ) ) ).
% 5.13/5.48
% 5.13/5.48 % lambda_one
% 5.13/5.48 thf(fact_1710_lambda__one,axiom,
% 5.13/5.48 ( ( ^ [X2: rat] : X2 )
% 5.13/5.48 = ( times_times_rat @ one_one_rat ) ) ).
% 5.13/5.48
% 5.13/5.48 % lambda_one
% 5.13/5.48 thf(fact_1711_lambda__one,axiom,
% 5.13/5.48 ( ( ^ [X2: nat] : X2 )
% 5.13/5.48 = ( times_times_nat @ one_one_nat ) ) ).
% 5.13/5.48
% 5.13/5.48 % lambda_one
% 5.13/5.48 thf(fact_1712_lambda__one,axiom,
% 5.13/5.48 ( ( ^ [X2: int] : X2 )
% 5.13/5.48 = ( times_times_int @ one_one_int ) ) ).
% 5.13/5.48
% 5.13/5.48 % lambda_one
% 5.13/5.48 thf(fact_1713_add__mono__thms__linordered__field_I4_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.13/5.48 & ( ord_less_real @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(4)
% 5.13/5.48 thf(fact_1714_add__mono__thms__linordered__field_I4_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.13/5.48 & ( ord_less_rat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(4)
% 5.13/5.48 thf(fact_1715_add__mono__thms__linordered__field_I4_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.13/5.48 & ( ord_less_nat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(4)
% 5.13/5.48 thf(fact_1716_add__mono__thms__linordered__field_I4_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.13/5.48 & ( ord_less_int @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(4)
% 5.13/5.48 thf(fact_1717_add__mono__thms__linordered__field_I3_J,axiom,
% 5.13/5.48 ! [I2: real,J: real,K: real,L2: real] :
% 5.13/5.48 ( ( ( ord_less_real @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_real @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(3)
% 5.13/5.48 thf(fact_1718_add__mono__thms__linordered__field_I3_J,axiom,
% 5.13/5.48 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.13/5.48 ( ( ( ord_less_rat @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(3)
% 5.13/5.48 thf(fact_1719_add__mono__thms__linordered__field_I3_J,axiom,
% 5.13/5.48 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.13/5.48 ( ( ( ord_less_nat @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(3)
% 5.13/5.48 thf(fact_1720_add__mono__thms__linordered__field_I3_J,axiom,
% 5.13/5.48 ! [I2: int,J: int,K: int,L2: int] :
% 5.13/5.48 ( ( ( ord_less_int @ I2 @ J )
% 5.13/5.48 & ( ord_less_eq_int @ K @ L2 ) )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono_thms_linordered_field(3)
% 5.13/5.48 thf(fact_1721_add__le__less__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.48 => ( ( ord_less_real @ C @ D )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_less_mono
% 5.13/5.48 thf(fact_1722_add__le__less__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.48 => ( ( ord_less_rat @ C @ D )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_less_mono
% 5.13/5.48 thf(fact_1723_add__le__less__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_nat @ C @ D )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_less_mono
% 5.13/5.48 thf(fact_1724_add__le__less__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.48 => ( ( ord_less_int @ C @ D )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_less_mono
% 5.13/5.48 thf(fact_1725_add__less__le__mono,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_real @ C @ D )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_le_mono
% 5.13/5.48 thf(fact_1726_add__less__le__mono,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_rat @ C @ D )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_le_mono
% 5.13/5.48 thf(fact_1727_add__less__le__mono,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.48 ( ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ C @ D )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_le_mono
% 5.13/5.48 thf(fact_1728_add__less__le__mono,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_int @ C @ D )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_less_le_mono
% 5.13/5.48 thf(fact_1729_less__1__mult,axiom,
% 5.13/5.48 ! [M: real,N: real] :
% 5.13/5.48 ( ( ord_less_real @ one_one_real @ M )
% 5.13/5.48 => ( ( ord_less_real @ one_one_real @ N )
% 5.13/5.48 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_1_mult
% 5.13/5.48 thf(fact_1730_less__1__mult,axiom,
% 5.13/5.48 ! [M: rat,N: rat] :
% 5.13/5.48 ( ( ord_less_rat @ one_one_rat @ M )
% 5.13/5.48 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.13/5.48 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_1_mult
% 5.13/5.48 thf(fact_1731_less__1__mult,axiom,
% 5.13/5.48 ! [M: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_nat @ one_one_nat @ M )
% 5.13/5.48 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.13/5.48 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_1_mult
% 5.13/5.48 thf(fact_1732_less__1__mult,axiom,
% 5.13/5.48 ! [M: int,N: int] :
% 5.13/5.48 ( ( ord_less_int @ one_one_int @ M )
% 5.13/5.48 => ( ( ord_less_int @ one_one_int @ N )
% 5.13/5.48 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_1_mult
% 5.13/5.48 thf(fact_1733_diff__le__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.13/5.48 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_eq
% 5.13/5.48 thf(fact_1734_diff__le__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_eq
% 5.13/5.48 thf(fact_1735_diff__le__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.13/5.48 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_le_eq
% 5.13/5.48 thf(fact_1736_le__diff__eq,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_diff_eq
% 5.13/5.48 thf(fact_1737_le__diff__eq,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_diff_eq
% 5.13/5.48 thf(fact_1738_le__diff__eq,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.13/5.48 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_diff_eq
% 5.13/5.48 thf(fact_1739_add__le__imp__le__diff,axiom,
% 5.13/5.48 ! [I2: real,K: real,N: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.13/5.48 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_diff
% 5.13/5.48 thf(fact_1740_add__le__imp__le__diff,axiom,
% 5.13/5.48 ! [I2: rat,K: rat,N: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.13/5.48 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_diff
% 5.13/5.48 thf(fact_1741_add__le__imp__le__diff,axiom,
% 5.13/5.48 ! [I2: nat,K: nat,N: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.13/5.48 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_diff
% 5.13/5.48 thf(fact_1742_add__le__imp__le__diff,axiom,
% 5.13/5.48 ! [I2: int,K: int,N: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.13/5.48 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_imp_le_diff
% 5.13/5.48 thf(fact_1743_diff__add,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.13/5.48 = B ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_add
% 5.13/5.48 thf(fact_1744_add__le__add__imp__diff__le,axiom,
% 5.13/5.48 ! [I2: real,K: real,N: real,J: real] :
% 5.13/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.13/5.48 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.13/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_add_imp_diff_le
% 5.13/5.48 thf(fact_1745_add__le__add__imp__diff__le,axiom,
% 5.13/5.48 ! [I2: rat,K: rat,N: rat,J: rat] :
% 5.13/5.48 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.13/5.48 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.13/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_add_imp_diff_le
% 5.13/5.48 thf(fact_1746_add__le__add__imp__diff__le,axiom,
% 5.13/5.48 ! [I2: nat,K: nat,N: nat,J: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.13/5.48 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.13/5.48 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_add_imp_diff_le
% 5.13/5.48 thf(fact_1747_add__le__add__imp__diff__le,axiom,
% 5.13/5.48 ! [I2: int,K: int,N: int,J: int] :
% 5.13/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.13/5.48 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.13/5.48 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.13/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_le_add_imp_diff_le
% 5.13/5.48 thf(fact_1748_le__add__diff,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % le_add_diff
% 5.13/5.48 thf(fact_1749_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.13/5.48 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.13/5.48 thf(fact_1750_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.13/5.48 thf(fact_1751_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.13/5.48 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.13/5.48 thf(fact_1752_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.13/5.48 thf(fact_1753_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.13/5.48 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.13/5.48 thf(fact_1754_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.13/5.48 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.13/5.48 thf(fact_1755_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.13/5.48 = B ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.13/5.48 thf(fact_1756_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.13/5.48 ! [A: nat,B: nat,C: nat] :
% 5.13/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.48 => ( ( ( minus_minus_nat @ B @ A )
% 5.13/5.48 = C )
% 5.13/5.48 = ( B
% 5.13/5.48 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.13/5.48 thf(fact_1757_add__mono1,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono1
% 5.13/5.48 thf(fact_1758_add__mono1,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono1
% 5.13/5.48 thf(fact_1759_add__mono1,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono1
% 5.13/5.48 thf(fact_1760_add__mono1,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % add_mono1
% 5.13/5.48 thf(fact_1761_less__add__one,axiom,
% 5.13/5.48 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_one
% 5.13/5.48 thf(fact_1762_less__add__one,axiom,
% 5.13/5.48 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_one
% 5.13/5.48 thf(fact_1763_less__add__one,axiom,
% 5.13/5.48 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_one
% 5.13/5.48 thf(fact_1764_less__add__one,axiom,
% 5.13/5.48 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_add_one
% 5.13/5.48 thf(fact_1765_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.13/5.48 ! [A: real,B: real] :
% 5.13/5.48 ( ~ ( ord_less_real @ A @ B )
% 5.13/5.48 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % linordered_semidom_class.add_diff_inverse
% 5.13/5.48 thf(fact_1766_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.13/5.48 ! [A: rat,B: rat] :
% 5.13/5.48 ( ~ ( ord_less_rat @ A @ B )
% 5.13/5.48 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % linordered_semidom_class.add_diff_inverse
% 5.13/5.48 thf(fact_1767_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.13/5.48 ! [A: nat,B: nat] :
% 5.13/5.48 ( ~ ( ord_less_nat @ A @ B )
% 5.13/5.48 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % linordered_semidom_class.add_diff_inverse
% 5.13/5.48 thf(fact_1768_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.13/5.48 ! [A: int,B: int] :
% 5.13/5.48 ( ~ ( ord_less_int @ A @ B )
% 5.13/5.48 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.13/5.48 = A ) ) ).
% 5.13/5.48
% 5.13/5.48 % linordered_semidom_class.add_diff_inverse
% 5.13/5.48 thf(fact_1769_less__diff__eq,axiom,
% 5.13/5.48 ! [A: real,C: real,B: real] :
% 5.13/5.48 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.13/5.48 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_diff_eq
% 5.13/5.48 thf(fact_1770_less__diff__eq,axiom,
% 5.13/5.48 ! [A: rat,C: rat,B: rat] :
% 5.13/5.48 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.13/5.48 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_diff_eq
% 5.13/5.48 thf(fact_1771_less__diff__eq,axiom,
% 5.13/5.48 ! [A: int,C: int,B: int] :
% 5.13/5.48 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.13/5.48 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.13/5.48
% 5.13/5.48 % less_diff_eq
% 5.13/5.48 thf(fact_1772_diff__less__eq,axiom,
% 5.13/5.48 ! [A: real,B: real,C: real] :
% 5.13/5.48 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.13/5.48 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_less_eq
% 5.13/5.48 thf(fact_1773_diff__less__eq,axiom,
% 5.13/5.48 ! [A: rat,B: rat,C: rat] :
% 5.13/5.48 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.13/5.48 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_less_eq
% 5.13/5.48 thf(fact_1774_diff__less__eq,axiom,
% 5.13/5.48 ! [A: int,B: int,C: int] :
% 5.13/5.48 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.13/5.48 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % diff_less_eq
% 5.13/5.48 thf(fact_1775_square__diff__square__factored,axiom,
% 5.13/5.48 ! [X: real,Y4: real] :
% 5.13/5.48 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) )
% 5.13/5.48 = ( times_times_real @ ( plus_plus_real @ X @ Y4 ) @ ( minus_minus_real @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % square_diff_square_factored
% 5.13/5.48 thf(fact_1776_square__diff__square__factored,axiom,
% 5.13/5.48 ! [X: rat,Y4: rat] :
% 5.13/5.48 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) )
% 5.13/5.48 = ( times_times_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( minus_minus_rat @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % square_diff_square_factored
% 5.13/5.48 thf(fact_1777_square__diff__square__factored,axiom,
% 5.13/5.48 ! [X: int,Y4: int] :
% 5.13/5.48 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) )
% 5.13/5.48 = ( times_times_int @ ( plus_plus_int @ X @ Y4 ) @ ( minus_minus_int @ X @ Y4 ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % square_diff_square_factored
% 5.13/5.48 thf(fact_1778_eq__add__iff2,axiom,
% 5.13/5.48 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.13/5.48 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.13/5.48 = ( C
% 5.13/5.48 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_add_iff2
% 5.13/5.48 thf(fact_1779_eq__add__iff2,axiom,
% 5.13/5.48 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.13/5.48 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.13/5.48 = ( C
% 5.13/5.48 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.48
% 5.13/5.48 % eq_add_iff2
% 5.13/5.49 thf(fact_1780_eq__add__iff2,axiom,
% 5.13/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.13/5.49 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.13/5.49 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.13/5.49 = ( C
% 5.13/5.49 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_add_iff2
% 5.13/5.49 thf(fact_1781_eq__add__iff1,axiom,
% 5.13/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.13/5.49 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.13/5.49 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.13/5.49 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.13/5.49 = D ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_add_iff1
% 5.13/5.49 thf(fact_1782_eq__add__iff1,axiom,
% 5.13/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.13/5.49 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.13/5.49 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.13/5.49 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.13/5.49 = D ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_add_iff1
% 5.13/5.49 thf(fact_1783_eq__add__iff1,axiom,
% 5.13/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.13/5.49 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.13/5.49 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.13/5.49 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.13/5.49 = D ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_add_iff1
% 5.13/5.49 thf(fact_1784_nth__equalityI,axiom,
% 5.13/5.49 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.13/5.49 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.13/5.49 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.13/5.49 => ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.49 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.13/5.49 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 5.13/5.49 => ( Xs2 = Ys ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_equalityI
% 5.13/5.49 thf(fact_1785_nth__equalityI,axiom,
% 5.13/5.49 ! [Xs2: list_o,Ys: list_o] :
% 5.13/5.49 ( ( ( size_size_list_o @ Xs2 )
% 5.13/5.49 = ( size_size_list_o @ Ys ) )
% 5.13/5.49 => ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.49 => ( ( nth_o @ Xs2 @ I3 )
% 5.13/5.49 = ( nth_o @ Ys @ I3 ) ) )
% 5.13/5.49 => ( Xs2 = Ys ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_equalityI
% 5.13/5.49 thf(fact_1786_nth__equalityI,axiom,
% 5.13/5.49 ! [Xs2: list_nat,Ys: list_nat] :
% 5.13/5.49 ( ( ( size_size_list_nat @ Xs2 )
% 5.13/5.49 = ( size_size_list_nat @ Ys ) )
% 5.13/5.49 => ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.49 => ( ( nth_nat @ Xs2 @ I3 )
% 5.13/5.49 = ( nth_nat @ Ys @ I3 ) ) )
% 5.13/5.49 => ( Xs2 = Ys ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_equalityI
% 5.13/5.49 thf(fact_1787_nth__equalityI,axiom,
% 5.13/5.49 ! [Xs2: list_int,Ys: list_int] :
% 5.13/5.49 ( ( ( size_size_list_int @ Xs2 )
% 5.13/5.49 = ( size_size_list_int @ Ys ) )
% 5.13/5.49 => ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.49 => ( ( nth_int @ Xs2 @ I3 )
% 5.13/5.49 = ( nth_int @ Ys @ I3 ) ) )
% 5.13/5.49 => ( Xs2 = Ys ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_equalityI
% 5.13/5.49 thf(fact_1788_Skolem__list__nth,axiom,
% 5.13/5.49 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.13/5.49 ( ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ? [X6: vEBT_VEBT] : ( P @ I4 @ X6 ) ) )
% 5.13/5.49 = ( ? [Xs: list_VEBT_VEBT] :
% 5.13/5.49 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.13/5.49 = K )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % Skolem_list_nth
% 5.13/5.49 thf(fact_1789_Skolem__list__nth,axiom,
% 5.13/5.49 ! [K: nat,P: nat > $o > $o] :
% 5.13/5.49 ( ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ? [X6: $o] : ( P @ I4 @ X6 ) ) )
% 5.13/5.49 = ( ? [Xs: list_o] :
% 5.13/5.49 ( ( ( size_size_list_o @ Xs )
% 5.13/5.49 = K )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ( P @ I4 @ ( nth_o @ Xs @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % Skolem_list_nth
% 5.13/5.49 thf(fact_1790_Skolem__list__nth,axiom,
% 5.13/5.49 ! [K: nat,P: nat > nat > $o] :
% 5.13/5.49 ( ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ? [X6: nat] : ( P @ I4 @ X6 ) ) )
% 5.13/5.49 = ( ? [Xs: list_nat] :
% 5.13/5.49 ( ( ( size_size_list_nat @ Xs )
% 5.13/5.49 = K )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ( P @ I4 @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % Skolem_list_nth
% 5.13/5.49 thf(fact_1791_Skolem__list__nth,axiom,
% 5.13/5.49 ! [K: nat,P: nat > int > $o] :
% 5.13/5.49 ( ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ? [X6: int] : ( P @ I4 @ X6 ) ) )
% 5.13/5.49 = ( ? [Xs: list_int] :
% 5.13/5.49 ( ( ( size_size_list_int @ Xs )
% 5.13/5.49 = K )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.13/5.49 => ( P @ I4 @ ( nth_int @ Xs @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % Skolem_list_nth
% 5.13/5.49 thf(fact_1792_list__eq__iff__nth__eq,axiom,
% 5.13/5.49 ( ( ^ [Y6: list_VEBT_VEBT,Z3: list_VEBT_VEBT] : ( Y6 = Z3 ) )
% 5.13/5.49 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.13/5.49 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.13/5.49 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.13/5.49 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.13/5.49 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_eq_iff_nth_eq
% 5.13/5.49 thf(fact_1793_list__eq__iff__nth__eq,axiom,
% 5.13/5.49 ( ( ^ [Y6: list_o,Z3: list_o] : ( Y6 = Z3 ) )
% 5.13/5.49 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.13/5.49 ( ( ( size_size_list_o @ Xs )
% 5.13/5.49 = ( size_size_list_o @ Ys3 ) )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.13/5.49 => ( ( nth_o @ Xs @ I4 )
% 5.13/5.49 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_eq_iff_nth_eq
% 5.13/5.49 thf(fact_1794_list__eq__iff__nth__eq,axiom,
% 5.13/5.49 ( ( ^ [Y6: list_nat,Z3: list_nat] : ( Y6 = Z3 ) )
% 5.13/5.49 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.13/5.49 ( ( ( size_size_list_nat @ Xs )
% 5.13/5.49 = ( size_size_list_nat @ Ys3 ) )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.13/5.49 => ( ( nth_nat @ Xs @ I4 )
% 5.13/5.49 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_eq_iff_nth_eq
% 5.13/5.49 thf(fact_1795_list__eq__iff__nth__eq,axiom,
% 5.13/5.49 ( ( ^ [Y6: list_int,Z3: list_int] : ( Y6 = Z3 ) )
% 5.13/5.49 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.13/5.49 ( ( ( size_size_list_int @ Xs )
% 5.13/5.49 = ( size_size_list_int @ Ys3 ) )
% 5.13/5.49 & ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.13/5.49 => ( ( nth_int @ Xs @ I4 )
% 5.13/5.49 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_eq_iff_nth_eq
% 5.13/5.49 thf(fact_1796_vebt__member_Osimps_I2_J,axiom,
% 5.13/5.49 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.13/5.49 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.13/5.49
% 5.13/5.49 % vebt_member.simps(2)
% 5.13/5.49 thf(fact_1797_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.13/5.49 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.13/5.49 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.13/5.49
% 5.13/5.49 % VEBT_internal.minNull.simps(5)
% 5.13/5.49 thf(fact_1798_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.13/5.49 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.13/5.49
% 5.13/5.49 % VEBT_internal.minNull.simps(4)
% 5.13/5.49 thf(fact_1799_ordered__ring__class_Ole__add__iff1,axiom,
% 5.13/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_ring_class.le_add_iff1
% 5.13/5.49 thf(fact_1800_ordered__ring__class_Ole__add__iff1,axiom,
% 5.13/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_ring_class.le_add_iff1
% 5.13/5.49 thf(fact_1801_ordered__ring__class_Ole__add__iff1,axiom,
% 5.13/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_ring_class.le_add_iff1
% 5.13/5.49 thf(fact_1802_ordered__ring__class_Ole__add__iff2,axiom,
% 5.13/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_ring_class.le_add_iff2
% 5.13/5.49 thf(fact_1803_ordered__ring__class_Ole__add__iff2,axiom,
% 5.13/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_ring_class.le_add_iff2
% 5.13/5.49 thf(fact_1804_ordered__ring__class_Ole__add__iff2,axiom,
% 5.13/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_ring_class.le_add_iff2
% 5.13/5.49 thf(fact_1805_less__add__iff2,axiom,
% 5.13/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.13/5.49 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_iff2
% 5.13/5.49 thf(fact_1806_less__add__iff2,axiom,
% 5.13/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_iff2
% 5.13/5.49 thf(fact_1807_less__add__iff2,axiom,
% 5.13/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.13/5.49 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_iff2
% 5.13/5.49 thf(fact_1808_less__add__iff1,axiom,
% 5.13/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.13/5.49 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_iff1
% 5.13/5.49 thf(fact_1809_less__add__iff1,axiom,
% 5.13/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_iff1
% 5.13/5.49 thf(fact_1810_less__add__iff1,axiom,
% 5.13/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.13/5.49 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.13/5.49 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_iff1
% 5.13/5.49 thf(fact_1811_square__diff__one__factored,axiom,
% 5.13/5.49 ! [X: complex] :
% 5.13/5.49 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.13/5.49 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % square_diff_one_factored
% 5.13/5.49 thf(fact_1812_square__diff__one__factored,axiom,
% 5.13/5.49 ! [X: real] :
% 5.13/5.49 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.13/5.49 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % square_diff_one_factored
% 5.13/5.49 thf(fact_1813_square__diff__one__factored,axiom,
% 5.13/5.49 ! [X: rat] :
% 5.13/5.49 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.13/5.49 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % square_diff_one_factored
% 5.13/5.49 thf(fact_1814_square__diff__one__factored,axiom,
% 5.13/5.49 ! [X: int] :
% 5.13/5.49 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.13/5.49 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % square_diff_one_factored
% 5.13/5.49 thf(fact_1815_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_real] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.13/5.49 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1816_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_complex] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.13/5.49 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1817_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_P6011104703257516679at_nat] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.13/5.49 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1818_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.49 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1819_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_o] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.49 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1820_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_nat] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.49 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1821_nth__mem,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_int] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.49 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nth_mem
% 5.13/5.49 thf(fact_1822_list__ball__nth,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.49 => ( ! [X3: vEBT_VEBT] :
% 5.13/5.49 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X3 ) )
% 5.13/5.49 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_ball_nth
% 5.13/5.49 thf(fact_1823_list__ball__nth,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.49 => ( ! [X3: $o] :
% 5.13/5.49 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X3 ) )
% 5.13/5.49 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_ball_nth
% 5.13/5.49 thf(fact_1824_list__ball__nth,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.49 => ( ! [X3: nat] :
% 5.13/5.49 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X3 ) )
% 5.13/5.49 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_ball_nth
% 5.13/5.49 thf(fact_1825_list__ball__nth,axiom,
% 5.13/5.49 ! [N: nat,Xs2: list_int,P: int > $o] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.49 => ( ! [X3: int] :
% 5.13/5.49 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X3 ) )
% 5.13/5.49 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % list_ball_nth
% 5.13/5.49 thf(fact_1826_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: real,Xs2: list_real] :
% 5.13/5.49 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.13/5.49 & ( ( nth_real @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1827_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: complex,Xs2: list_complex] :
% 5.13/5.49 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.13/5.49 & ( ( nth_complex @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1828_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.13/5.49 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.13/5.49 & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1829_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.13/5.49 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.49 & ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1830_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: $o,Xs2: list_o] :
% 5.13/5.49 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.49 & ( ( nth_o @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1831_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: nat,Xs2: list_nat] :
% 5.13/5.49 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.49 & ( ( nth_nat @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1832_in__set__conv__nth,axiom,
% 5.13/5.49 ! [X: int,Xs2: list_int] :
% 5.13/5.49 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.13/5.49 = ( ? [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.49 & ( ( nth_int @ Xs2 @ I4 )
% 5.13/5.49 = X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % in_set_conv_nth
% 5.13/5.49 thf(fact_1833_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_real,P: real > $o,X: real] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1834_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_complex @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1835_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1836_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1837_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_o,P: $o > $o,X: $o] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1838_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1839_all__nth__imp__all__set,axiom,
% 5.13/5.49 ! [Xs2: list_int,P: int > $o,X: int] :
% 5.13/5.49 ( ! [I3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 5.13/5.49 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_nth_imp_all_set
% 5.13/5.49 thf(fact_1840_all__set__conv__all__nth,axiom,
% 5.13/5.49 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.13/5.49 ( ( ! [X2: vEBT_VEBT] :
% 5.13/5.49 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X2 ) ) )
% 5.13/5.49 = ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_set_conv_all_nth
% 5.13/5.49 thf(fact_1841_all__set__conv__all__nth,axiom,
% 5.13/5.49 ! [Xs2: list_o,P: $o > $o] :
% 5.13/5.49 ( ( ! [X2: $o] :
% 5.13/5.49 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X2 ) ) )
% 5.13/5.49 = ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_set_conv_all_nth
% 5.13/5.49 thf(fact_1842_all__set__conv__all__nth,axiom,
% 5.13/5.49 ! [Xs2: list_nat,P: nat > $o] :
% 5.13/5.49 ( ( ! [X2: nat] :
% 5.13/5.49 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X2 ) ) )
% 5.13/5.49 = ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_set_conv_all_nth
% 5.13/5.49 thf(fact_1843_all__set__conv__all__nth,axiom,
% 5.13/5.49 ! [Xs2: list_int,P: int > $o] :
% 5.13/5.49 ( ( ! [X2: int] :
% 5.13/5.49 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.13/5.49 => ( P @ X2 ) ) )
% 5.13/5.49 = ( ! [I4: nat] :
% 5.13/5.49 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.13/5.49 => ( P @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % all_set_conv_all_nth
% 5.13/5.49 thf(fact_1844_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.13/5.49 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 5.13/5.49 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X )
% 5.13/5.49 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.49 => ( 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 ) ) ) ) ) )
% 5.13/5.49 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % VEBT_internal.membermima.simps(5)
% 5.13/5.49 thf(fact_1845_real__average__minus__first,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.13/5.49 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % real_average_minus_first
% 5.13/5.49 thf(fact_1846_real__average__minus__second,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.13/5.49 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % real_average_minus_second
% 5.13/5.49 thf(fact_1847_member__valid__both__member__options,axiom,
% 5.13/5.49 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 5.13/5.49 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.13/5.49 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.13/5.49 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.13/5.49 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % member_valid_both_member_options
% 5.13/5.49 thf(fact_1848_both__member__options__def,axiom,
% 5.13/5.49 ( vEBT_V8194947554948674370ptions
% 5.13/5.49 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.13/5.49 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.13/5.49 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % both_member_options_def
% 5.13/5.49 thf(fact_1849_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.13/5.49 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.13/5.49 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.13/5.49 => ( ! [Mi2: nat,Ma2: nat] :
% 5.13/5.49 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.13/5.49 ( X
% 5.13/5.49 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.13/5.49 => ~ ( ( Xa2 = Mi2 )
% 5.13/5.49 | ( Xa2 = Ma2 ) ) )
% 5.13/5.49 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.13/5.49 ( ? [Vc2: vEBT_VEBT] :
% 5.13/5.49 ( X
% 5.13/5.49 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.13/5.49 => ~ ( ( Xa2 = Mi2 )
% 5.13/5.49 | ( Xa2 = Ma2 )
% 5.13/5.49 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.13/5.49 => ( 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 ) ) ) ) ) )
% 5.13/5.49 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.13/5.49 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.13/5.49 ( ? [Vd2: vEBT_VEBT] :
% 5.13/5.49 ( X
% 5.13/5.49 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.13/5.49 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.13/5.49 => ( 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 ) ) ) ) ) )
% 5.13/5.49 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % VEBT_internal.membermima.elims(2)
% 5.13/5.49 thf(fact_1850_times__divide__eq__right,axiom,
% 5.13/5.49 ! [A: complex,B: complex,C: complex] :
% 5.13/5.49 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.13/5.49
% 5.13/5.49 % times_divide_eq_right
% 5.13/5.49 thf(fact_1851_times__divide__eq__right,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.13/5.49
% 5.13/5.49 % times_divide_eq_right
% 5.13/5.49 thf(fact_1852_times__divide__eq__right,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.13/5.49
% 5.13/5.49 % times_divide_eq_right
% 5.13/5.49 thf(fact_1853_divide__divide__eq__right,axiom,
% 5.13/5.49 ! [A: complex,B: complex,C: complex] :
% 5.13/5.49 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_divide_eq_right
% 5.13/5.49 thf(fact_1854_divide__divide__eq__right,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_divide_eq_right
% 5.13/5.49 thf(fact_1855_divide__divide__eq__right,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_divide_eq_right
% 5.13/5.49 thf(fact_1856_divide__divide__eq__left,axiom,
% 5.13/5.49 ! [A: complex,B: complex,C: complex] :
% 5.13/5.49 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_divide_eq_left
% 5.13/5.49 thf(fact_1857_divide__divide__eq__left,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.13/5.49 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_divide_eq_left
% 5.13/5.49 thf(fact_1858_divide__divide__eq__left,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.13/5.49 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_divide_eq_left
% 5.13/5.49 thf(fact_1859_times__divide__eq__left,axiom,
% 5.13/5.49 ! [B: complex,C: complex,A: complex] :
% 5.13/5.49 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.13/5.49
% 5.13/5.49 % times_divide_eq_left
% 5.13/5.49 thf(fact_1860_times__divide__eq__left,axiom,
% 5.13/5.49 ! [B: real,C: real,A: real] :
% 5.13/5.49 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.49 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.13/5.49
% 5.13/5.49 % times_divide_eq_left
% 5.13/5.49 thf(fact_1861_times__divide__eq__left,axiom,
% 5.13/5.49 ! [B: rat,C: rat,A: rat] :
% 5.13/5.49 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.49 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.13/5.49
% 5.13/5.49 % times_divide_eq_left
% 5.13/5.49 thf(fact_1862_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.13/5.49 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.13/5.49 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S2 ) @ X )
% 5.13/5.49 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.13/5.49 => ( 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 ) ) ) ) ) )
% 5.13/5.49 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % VEBT_internal.naive_member.simps(3)
% 5.13/5.49 thf(fact_1863_valid__0__not,axiom,
% 5.13/5.49 ! [T: vEBT_VEBT] :
% 5.13/5.49 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % valid_0_not
% 5.13/5.49 thf(fact_1864_valid__tree__deg__neq__0,axiom,
% 5.13/5.49 ! [T: vEBT_VEBT] :
% 5.13/5.49 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % valid_tree_deg_neq_0
% 5.13/5.49 thf(fact_1865_buildup__nothing__in__leaf,axiom,
% 5.13/5.49 ! [N: nat,X: nat] :
% 5.13/5.49 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.13/5.49
% 5.13/5.49 % buildup_nothing_in_leaf
% 5.13/5.49 thf(fact_1866_deg__not__0,axiom,
% 5.13/5.49 ! [T: vEBT_VEBT,N: nat] :
% 5.13/5.49 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % deg_not_0
% 5.13/5.49 thf(fact_1867_buildup__gives__valid,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % buildup_gives_valid
% 5.13/5.49 thf(fact_1868_le__zero__eq,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.13/5.49 = ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_zero_eq
% 5.13/5.49 thf(fact_1869_not__gr__zero,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.13/5.49 = ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % not_gr_zero
% 5.13/5.49 thf(fact_1870_mult__cancel__right,axiom,
% 5.13/5.49 ! [A: complex,C: complex,B: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ A @ C )
% 5.13/5.49 = ( times_times_complex @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right
% 5.13/5.49 thf(fact_1871_mult__cancel__right,axiom,
% 5.13/5.49 ! [A: real,C: real,B: real] :
% 5.13/5.49 ( ( ( times_times_real @ A @ C )
% 5.13/5.49 = ( times_times_real @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right
% 5.13/5.49 thf(fact_1872_mult__cancel__right,axiom,
% 5.13/5.49 ! [A: rat,C: rat,B: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ A @ C )
% 5.13/5.49 = ( times_times_rat @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right
% 5.13/5.49 thf(fact_1873_mult__cancel__right,axiom,
% 5.13/5.49 ! [A: nat,C: nat,B: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ A @ C )
% 5.13/5.49 = ( times_times_nat @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_nat )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right
% 5.13/5.49 thf(fact_1874_mult__cancel__right,axiom,
% 5.13/5.49 ! [A: int,C: int,B: int] :
% 5.13/5.49 ( ( ( times_times_int @ A @ C )
% 5.13/5.49 = ( times_times_int @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_int )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right
% 5.13/5.49 thf(fact_1875_mult__cancel__left,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ C @ A )
% 5.13/5.49 = ( times_times_complex @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left
% 5.13/5.49 thf(fact_1876_mult__cancel__left,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( ( times_times_real @ C @ A )
% 5.13/5.49 = ( times_times_real @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left
% 5.13/5.49 thf(fact_1877_mult__cancel__left,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ C @ A )
% 5.13/5.49 = ( times_times_rat @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left
% 5.13/5.49 thf(fact_1878_mult__cancel__left,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ C @ A )
% 5.13/5.49 = ( times_times_nat @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_nat )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left
% 5.13/5.49 thf(fact_1879_mult__cancel__left,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( ( times_times_int @ C @ A )
% 5.13/5.49 = ( times_times_int @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_int )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left
% 5.13/5.49 thf(fact_1880_mult__eq__0__iff,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ A @ B )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 = ( ( A = zero_zero_complex )
% 5.13/5.49 | ( B = zero_zero_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_eq_0_iff
% 5.13/5.49 thf(fact_1881_mult__eq__0__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( times_times_real @ A @ B )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( A = zero_zero_real )
% 5.13/5.49 | ( B = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_eq_0_iff
% 5.13/5.49 thf(fact_1882_mult__eq__0__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ A @ B )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( A = zero_zero_rat )
% 5.13/5.49 | ( B = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_eq_0_iff
% 5.13/5.49 thf(fact_1883_mult__eq__0__iff,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ A @ B )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( A = zero_zero_nat )
% 5.13/5.49 | ( B = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_eq_0_iff
% 5.13/5.49 thf(fact_1884_mult__eq__0__iff,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ( times_times_int @ A @ B )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( ( A = zero_zero_int )
% 5.13/5.49 | ( B = zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_eq_0_iff
% 5.13/5.49 thf(fact_1885_mult__zero__right,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_right
% 5.13/5.49 thf(fact_1886_mult__zero__right,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( times_times_real @ A @ zero_zero_real )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_right
% 5.13/5.49 thf(fact_1887_mult__zero__right,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_right
% 5.13/5.49 thf(fact_1888_mult__zero__right,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_right
% 5.13/5.49 thf(fact_1889_mult__zero__right,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( times_times_int @ A @ zero_zero_int )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_right
% 5.13/5.49 thf(fact_1890_mult__zero__left,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_left
% 5.13/5.49 thf(fact_1891_mult__zero__left,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( times_times_real @ zero_zero_real @ A )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_left
% 5.13/5.49 thf(fact_1892_mult__zero__left,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_left
% 5.13/5.49 thf(fact_1893_mult__zero__left,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_left
% 5.13/5.49 thf(fact_1894_mult__zero__left,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( times_times_int @ zero_zero_int @ A )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % mult_zero_left
% 5.13/5.49 thf(fact_1895_add__0,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add_0
% 5.13/5.49 thf(fact_1896_add__0,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add_0
% 5.13/5.49 thf(fact_1897_add__0,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add_0
% 5.13/5.49 thf(fact_1898_add__0,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add_0
% 5.13/5.49 thf(fact_1899_add__0,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add_0
% 5.13/5.49 thf(fact_1900_zero__eq__add__iff__both__eq__0,axiom,
% 5.13/5.49 ! [X: nat,Y4: nat] :
% 5.13/5.49 ( ( zero_zero_nat
% 5.13/5.49 = ( plus_plus_nat @ X @ Y4 ) )
% 5.13/5.49 = ( ( X = zero_zero_nat )
% 5.13/5.49 & ( Y4 = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_add_iff_both_eq_0
% 5.13/5.49 thf(fact_1901_add__eq__0__iff__both__eq__0,axiom,
% 5.13/5.49 ! [X: nat,Y4: nat] :
% 5.13/5.49 ( ( ( plus_plus_nat @ X @ Y4 )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( X = zero_zero_nat )
% 5.13/5.49 & ( Y4 = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_eq_0_iff_both_eq_0
% 5.13/5.49 thf(fact_1902_add__cancel__right__right,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_complex @ A @ B ) )
% 5.13/5.49 = ( B = zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_right
% 5.13/5.49 thf(fact_1903_add__cancel__right__right,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_real @ A @ B ) )
% 5.13/5.49 = ( B = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_right
% 5.13/5.49 thf(fact_1904_add__cancel__right__right,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_rat @ A @ B ) )
% 5.13/5.49 = ( B = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_right
% 5.13/5.49 thf(fact_1905_add__cancel__right__right,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_nat @ A @ B ) )
% 5.13/5.49 = ( B = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_right
% 5.13/5.49 thf(fact_1906_add__cancel__right__right,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_int @ A @ B ) )
% 5.13/5.49 = ( B = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_right
% 5.13/5.49 thf(fact_1907_add__cancel__right__left,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_complex @ B @ A ) )
% 5.13/5.49 = ( B = zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_left
% 5.13/5.49 thf(fact_1908_add__cancel__right__left,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_real @ B @ A ) )
% 5.13/5.49 = ( B = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_left
% 5.13/5.49 thf(fact_1909_add__cancel__right__left,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_rat @ B @ A ) )
% 5.13/5.49 = ( B = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_left
% 5.13/5.49 thf(fact_1910_add__cancel__right__left,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_nat @ B @ A ) )
% 5.13/5.49 = ( B = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_left
% 5.13/5.49 thf(fact_1911_add__cancel__right__left,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( plus_plus_int @ B @ A ) )
% 5.13/5.49 = ( B = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_right_left
% 5.13/5.49 thf(fact_1912_add__cancel__left__right,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( ( plus_plus_complex @ A @ B )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_right
% 5.13/5.49 thf(fact_1913_add__cancel__left__right,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( plus_plus_real @ A @ B )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_right
% 5.13/5.49 thf(fact_1914_add__cancel__left__right,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( plus_plus_rat @ A @ B )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_right
% 5.13/5.49 thf(fact_1915_add__cancel__left__right,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ( plus_plus_nat @ A @ B )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_right
% 5.13/5.49 thf(fact_1916_add__cancel__left__right,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ( plus_plus_int @ A @ B )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_right
% 5.13/5.49 thf(fact_1917_add__cancel__left__left,axiom,
% 5.13/5.49 ! [B: complex,A: complex] :
% 5.13/5.49 ( ( ( plus_plus_complex @ B @ A )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_left
% 5.13/5.49 thf(fact_1918_add__cancel__left__left,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( ( plus_plus_real @ B @ A )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_left
% 5.13/5.49 thf(fact_1919_add__cancel__left__left,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( ( plus_plus_rat @ B @ A )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_left
% 5.13/5.49 thf(fact_1920_add__cancel__left__left,axiom,
% 5.13/5.49 ! [B: nat,A: nat] :
% 5.13/5.49 ( ( ( plus_plus_nat @ B @ A )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_left
% 5.13/5.49 thf(fact_1921_add__cancel__left__left,axiom,
% 5.13/5.49 ! [B: int,A: int] :
% 5.13/5.49 ( ( ( plus_plus_int @ B @ A )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_cancel_left_left
% 5.13/5.49 thf(fact_1922_double__zero__sym,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( zero_zero_real
% 5.13/5.49 = ( plus_plus_real @ A @ A ) )
% 5.13/5.49 = ( A = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_zero_sym
% 5.13/5.49 thf(fact_1923_double__zero__sym,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( zero_zero_rat
% 5.13/5.49 = ( plus_plus_rat @ A @ A ) )
% 5.13/5.49 = ( A = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_zero_sym
% 5.13/5.49 thf(fact_1924_double__zero__sym,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( zero_zero_int
% 5.13/5.49 = ( plus_plus_int @ A @ A ) )
% 5.13/5.49 = ( A = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_zero_sym
% 5.13/5.49 thf(fact_1925_add_Oright__neutral,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.right_neutral
% 5.13/5.49 thf(fact_1926_add_Oright__neutral,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.right_neutral
% 5.13/5.49 thf(fact_1927_add_Oright__neutral,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.right_neutral
% 5.13/5.49 thf(fact_1928_add_Oright__neutral,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.right_neutral
% 5.13/5.49 thf(fact_1929_add_Oright__neutral,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.right_neutral
% 5.13/5.49 thf(fact_1930_divide__eq__0__iff,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 = ( ( A = zero_zero_complex )
% 5.13/5.49 | ( B = zero_zero_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_0_iff
% 5.13/5.49 thf(fact_1931_divide__eq__0__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ A @ B )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( A = zero_zero_real )
% 5.13/5.49 | ( B = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_0_iff
% 5.13/5.49 thf(fact_1932_divide__eq__0__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ A @ B )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( A = zero_zero_rat )
% 5.13/5.49 | ( B = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_0_iff
% 5.13/5.49 thf(fact_1933_divide__cancel__left,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.13/5.49 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_cancel_left
% 5.13/5.49 thf(fact_1934_divide__cancel__left,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ C @ A )
% 5.13/5.49 = ( divide_divide_real @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_cancel_left
% 5.13/5.49 thf(fact_1935_divide__cancel__left,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ C @ A )
% 5.13/5.49 = ( divide_divide_rat @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_cancel_left
% 5.13/5.49 thf(fact_1936_divide__cancel__right,axiom,
% 5.13/5.49 ! [A: complex,C: complex,B: complex] :
% 5.13/5.49 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.13/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_cancel_right
% 5.13/5.49 thf(fact_1937_divide__cancel__right,axiom,
% 5.13/5.49 ! [A: real,C: real,B: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ A @ C )
% 5.13/5.49 = ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_cancel_right
% 5.13/5.49 thf(fact_1938_divide__cancel__right,axiom,
% 5.13/5.49 ! [A: rat,C: rat,B: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ A @ C )
% 5.13/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_cancel_right
% 5.13/5.49 thf(fact_1939_division__ring__divide__zero,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % division_ring_divide_zero
% 5.13/5.49 thf(fact_1940_division__ring__divide__zero,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % division_ring_divide_zero
% 5.13/5.49 thf(fact_1941_division__ring__divide__zero,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % division_ring_divide_zero
% 5.13/5.49 thf(fact_1942_bits__div__0,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % bits_div_0
% 5.13/5.49 thf(fact_1943_bits__div__0,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % bits_div_0
% 5.13/5.49 thf(fact_1944_bits__div__by__0,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % bits_div_by_0
% 5.13/5.49 thf(fact_1945_bits__div__by__0,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % bits_div_by_0
% 5.13/5.49 thf(fact_1946_div__0,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % div_0
% 5.13/5.49 thf(fact_1947_div__0,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % div_0
% 5.13/5.49 thf(fact_1948_div__0,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % div_0
% 5.13/5.49 thf(fact_1949_div__0,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % div_0
% 5.13/5.49 thf(fact_1950_div__0,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % div_0
% 5.13/5.49 thf(fact_1951_div__by__0,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % div_by_0
% 5.13/5.49 thf(fact_1952_div__by__0,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % div_by_0
% 5.13/5.49 thf(fact_1953_div__by__0,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % div_by_0
% 5.13/5.49 thf(fact_1954_div__by__0,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % div_by_0
% 5.13/5.49 thf(fact_1955_div__by__0,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % div_by_0
% 5.13/5.49 thf(fact_1956_less__nat__zero__code,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % less_nat_zero_code
% 5.13/5.49 thf(fact_1957_neq0__conv,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( N != zero_zero_nat )
% 5.13/5.49 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % neq0_conv
% 5.13/5.49 thf(fact_1958_bot__nat__0_Onot__eq__extremum,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( A != zero_zero_nat )
% 5.13/5.49 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % bot_nat_0.not_eq_extremum
% 5.13/5.49 thf(fact_1959_bot__nat__0_Oextremum,axiom,
% 5.13/5.49 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.13/5.49
% 5.13/5.49 % bot_nat_0.extremum
% 5.13/5.49 thf(fact_1960_le0,axiom,
% 5.13/5.49 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.13/5.49
% 5.13/5.49 % le0
% 5.13/5.49 thf(fact_1961_Nat_Oadd__0__right,axiom,
% 5.13/5.49 ! [M: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.13/5.49 = M ) ).
% 5.13/5.49
% 5.13/5.49 % Nat.add_0_right
% 5.13/5.49 thf(fact_1962_add__is__0,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ( plus_plus_nat @ M @ N )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( M = zero_zero_nat )
% 5.13/5.49 & ( N = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_is_0
% 5.13/5.49 thf(fact_1963_mult__cancel2,axiom,
% 5.13/5.49 ! [M: nat,K: nat,N: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ M @ K )
% 5.13/5.49 = ( times_times_nat @ N @ K ) )
% 5.13/5.49 = ( ( M = N )
% 5.13/5.49 | ( K = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel2
% 5.13/5.49 thf(fact_1964_mult__cancel1,axiom,
% 5.13/5.49 ! [K: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ K @ M )
% 5.13/5.49 = ( times_times_nat @ K @ N ) )
% 5.13/5.49 = ( ( M = N )
% 5.13/5.49 | ( K = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel1
% 5.13/5.49 thf(fact_1965_mult__0__right,axiom,
% 5.13/5.49 ! [M: nat] :
% 5.13/5.49 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % mult_0_right
% 5.13/5.49 thf(fact_1966_mult__is__0,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ M @ N )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( M = zero_zero_nat )
% 5.13/5.49 | ( N = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_is_0
% 5.13/5.49 thf(fact_1967_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.13/5.49 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_double_add_iff_zero_le_single_add
% 5.13/5.49 thf(fact_1968_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.13/5.49 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_double_add_iff_zero_le_single_add
% 5.13/5.49 thf(fact_1969_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.13/5.49 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_double_add_iff_zero_le_single_add
% 5.13/5.49 thf(fact_1970_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.13/5.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_add_le_zero_iff_single_add_le_zero
% 5.13/5.49 thf(fact_1971_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_add_le_zero_iff_single_add_le_zero
% 5.13/5.49 thf(fact_1972_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.13/5.49 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_add_le_zero_iff_single_add_le_zero
% 5.13/5.49 thf(fact_1973_le__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel2
% 5.13/5.49 thf(fact_1974_le__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel2
% 5.13/5.49 thf(fact_1975_le__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel2
% 5.13/5.49 thf(fact_1976_le__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel2
% 5.13/5.49 thf(fact_1977_le__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel1
% 5.13/5.49 thf(fact_1978_le__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel1
% 5.13/5.49 thf(fact_1979_le__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel1
% 5.13/5.49 thf(fact_1980_le__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_add_same_cancel1
% 5.13/5.49 thf(fact_1981_add__le__same__cancel2,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel2
% 5.13/5.49 thf(fact_1982_add__le__same__cancel2,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel2
% 5.13/5.49 thf(fact_1983_add__le__same__cancel2,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel2
% 5.13/5.49 thf(fact_1984_add__le__same__cancel2,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel2
% 5.13/5.49 thf(fact_1985_add__le__same__cancel1,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel1
% 5.13/5.49 thf(fact_1986_add__le__same__cancel1,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel1
% 5.13/5.49 thf(fact_1987_add__le__same__cancel1,axiom,
% 5.13/5.49 ! [B: nat,A: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel1
% 5.13/5.49 thf(fact_1988_add__le__same__cancel1,axiom,
% 5.13/5.49 ! [B: int,A: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_le_same_cancel1
% 5.13/5.49 thf(fact_1989_diff__ge__0__iff__ge,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_ge_0_iff_ge
% 5.13/5.49 thf(fact_1990_diff__ge__0__iff__ge,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_ge_0_iff_ge
% 5.13/5.49 thf(fact_1991_diff__ge__0__iff__ge,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.13/5.49 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_ge_0_iff_ge
% 5.13/5.49 thf(fact_1992_add__less__same__cancel1,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel1
% 5.13/5.49 thf(fact_1993_add__less__same__cancel1,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel1
% 5.13/5.49 thf(fact_1994_add__less__same__cancel1,axiom,
% 5.13/5.49 ! [B: nat,A: nat] :
% 5.13/5.49 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel1
% 5.13/5.49 thf(fact_1995_add__less__same__cancel1,axiom,
% 5.13/5.49 ! [B: int,A: int] :
% 5.13/5.49 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.13/5.49 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel1
% 5.13/5.49 thf(fact_1996_add__less__same__cancel2,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel2
% 5.13/5.49 thf(fact_1997_add__less__same__cancel2,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel2
% 5.13/5.49 thf(fact_1998_add__less__same__cancel2,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel2
% 5.13/5.49 thf(fact_1999_add__less__same__cancel2,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.13/5.49 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_less_same_cancel2
% 5.13/5.49 thf(fact_2000_less__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.13/5.49 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel1
% 5.13/5.49 thf(fact_2001_less__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.13/5.49 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel1
% 5.13/5.49 thf(fact_2002_less__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.13/5.49 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel1
% 5.13/5.49 thf(fact_2003_less__add__same__cancel1,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.13/5.49 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel1
% 5.13/5.49 thf(fact_2004_less__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.13/5.49 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel2
% 5.13/5.49 thf(fact_2005_less__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.13/5.49 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel2
% 5.13/5.49 thf(fact_2006_less__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.13/5.49 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel2
% 5.13/5.49 thf(fact_2007_less__add__same__cancel2,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.13/5.49 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_add_same_cancel2
% 5.13/5.49 thf(fact_2008_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.13/5.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_add_less_zero_iff_single_add_less_zero
% 5.13/5.49 thf(fact_2009_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.13/5.49 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_add_less_zero_iff_single_add_less_zero
% 5.13/5.49 thf(fact_2010_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.13/5.49 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % double_add_less_zero_iff_single_add_less_zero
% 5.13/5.49 thf(fact_2011_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.13/5.49 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_double_add_iff_zero_less_single_add
% 5.13/5.49 thf(fact_2012_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.13/5.49 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_double_add_iff_zero_less_single_add
% 5.13/5.49 thf(fact_2013_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.13/5.49 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_double_add_iff_zero_less_single_add
% 5.13/5.49 thf(fact_2014_diff__gt__0__iff__gt,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.13/5.49 = ( ord_less_real @ B @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_gt_0_iff_gt
% 5.13/5.49 thf(fact_2015_diff__gt__0__iff__gt,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.13/5.49 = ( ord_less_rat @ B @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_gt_0_iff_gt
% 5.13/5.49 thf(fact_2016_diff__gt__0__iff__gt,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.13/5.49 = ( ord_less_int @ B @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_gt_0_iff_gt
% 5.13/5.49 thf(fact_2017_mult__cancel__right2,axiom,
% 5.13/5.49 ! [A: complex,C: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ A @ C )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( A = one_one_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right2
% 5.13/5.49 thf(fact_2018_mult__cancel__right2,axiom,
% 5.13/5.49 ! [A: real,C: real] :
% 5.13/5.49 ( ( ( times_times_real @ A @ C )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( A = one_one_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right2
% 5.13/5.49 thf(fact_2019_mult__cancel__right2,axiom,
% 5.13/5.49 ! [A: rat,C: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ A @ C )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( A = one_one_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right2
% 5.13/5.49 thf(fact_2020_mult__cancel__right2,axiom,
% 5.13/5.49 ! [A: int,C: int] :
% 5.13/5.49 ( ( ( times_times_int @ A @ C )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_int )
% 5.13/5.49 | ( A = one_one_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right2
% 5.13/5.49 thf(fact_2021_mult__cancel__right1,axiom,
% 5.13/5.49 ! [C: complex,B: complex] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_complex @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( B = one_one_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right1
% 5.13/5.49 thf(fact_2022_mult__cancel__right1,axiom,
% 5.13/5.49 ! [C: real,B: real] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_real @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( B = one_one_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right1
% 5.13/5.49 thf(fact_2023_mult__cancel__right1,axiom,
% 5.13/5.49 ! [C: rat,B: rat] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_rat @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( B = one_one_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right1
% 5.13/5.49 thf(fact_2024_mult__cancel__right1,axiom,
% 5.13/5.49 ! [C: int,B: int] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_int @ B @ C ) )
% 5.13/5.49 = ( ( C = zero_zero_int )
% 5.13/5.49 | ( B = one_one_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_right1
% 5.13/5.49 thf(fact_2025_mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: complex,A: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ C @ A )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( A = one_one_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left2
% 5.13/5.49 thf(fact_2026_mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: real,A: real] :
% 5.13/5.49 ( ( ( times_times_real @ C @ A )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( A = one_one_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left2
% 5.13/5.49 thf(fact_2027_mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: rat,A: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ C @ A )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( A = one_one_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left2
% 5.13/5.49 thf(fact_2028_mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: int,A: int] :
% 5.13/5.49 ( ( ( times_times_int @ C @ A )
% 5.13/5.49 = C )
% 5.13/5.49 = ( ( C = zero_zero_int )
% 5.13/5.49 | ( A = one_one_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left2
% 5.13/5.49 thf(fact_2029_mult__cancel__left1,axiom,
% 5.13/5.49 ! [C: complex,B: complex] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_complex @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_complex )
% 5.13/5.49 | ( B = one_one_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left1
% 5.13/5.49 thf(fact_2030_mult__cancel__left1,axiom,
% 5.13/5.49 ! [C: real,B: real] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_real @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_real )
% 5.13/5.49 | ( B = one_one_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left1
% 5.13/5.49 thf(fact_2031_mult__cancel__left1,axiom,
% 5.13/5.49 ! [C: rat,B: rat] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_rat @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_rat )
% 5.13/5.49 | ( B = one_one_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left1
% 5.13/5.49 thf(fact_2032_mult__cancel__left1,axiom,
% 5.13/5.49 ! [C: int,B: int] :
% 5.13/5.49 ( ( C
% 5.13/5.49 = ( times_times_int @ C @ B ) )
% 5.13/5.49 = ( ( C = zero_zero_int )
% 5.13/5.49 | ( B = one_one_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_cancel_left1
% 5.13/5.49 thf(fact_2033_sum__squares__eq__zero__iff,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( X = zero_zero_real )
% 5.13/5.49 & ( Y4 = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % sum_squares_eq_zero_iff
% 5.13/5.49 thf(fact_2034_sum__squares__eq__zero__iff,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( X = zero_zero_rat )
% 5.13/5.49 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % sum_squares_eq_zero_iff
% 5.13/5.49 thf(fact_2035_sum__squares__eq__zero__iff,axiom,
% 5.13/5.49 ! [X: int,Y4: int] :
% 5.13/5.49 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( ( X = zero_zero_int )
% 5.13/5.49 & ( Y4 = zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % sum_squares_eq_zero_iff
% 5.13/5.49 thf(fact_2036_mult__divide__mult__cancel__left__if,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( ( C = zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.13/5.49 = zero_zero_complex ) )
% 5.13/5.49 & ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_divide_mult_cancel_left_if
% 5.13/5.49 thf(fact_2037_mult__divide__mult__cancel__left__if,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( ( C = zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.49 = zero_zero_real ) )
% 5.13/5.49 & ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.49 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_divide_mult_cancel_left_if
% 5.13/5.49 thf(fact_2038_mult__divide__mult__cancel__left__if,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ( C = zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.49 = zero_zero_rat ) )
% 5.13/5.49 & ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.49 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_divide_mult_cancel_left_if
% 5.13/5.49 thf(fact_2039_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_left
% 5.13/5.49 thf(fact_2040_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.49 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_left
% 5.13/5.49 thf(fact_2041_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.49 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_left
% 5.13/5.49 thf(fact_2042_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_left2
% 5.13/5.49 thf(fact_2043_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.13/5.49 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_left2
% 5.13/5.49 thf(fact_2044_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.49 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_left2
% 5.13/5.49 thf(fact_2045_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_right
% 5.13/5.49 thf(fact_2046_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.13/5.49 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_right
% 5.13/5.49 thf(fact_2047_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.49 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_right
% 5.13/5.49 thf(fact_2048_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_right2
% 5.13/5.49 thf(fact_2049_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.13/5.49 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_right2
% 5.13/5.49 thf(fact_2050_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.49 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_divide_mult_cancel_right2
% 5.13/5.49 thf(fact_2051_div__mult__mult1__if,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( ( C = zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.13/5.49 = zero_zero_nat ) )
% 5.13/5.49 & ( ( C != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.13/5.49 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_mult1_if
% 5.13/5.49 thf(fact_2052_div__mult__mult1__if,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( ( C = zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.49 = zero_zero_int ) )
% 5.13/5.49 & ( ( C != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.49 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_mult1_if
% 5.13/5.49 thf(fact_2053_div__mult__mult2,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( C != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.13/5.49 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_mult2
% 5.13/5.49 thf(fact_2054_div__mult__mult2,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( C != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.13/5.49 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_mult2
% 5.13/5.49 thf(fact_2055_div__mult__mult1,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( C != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.13/5.49 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_mult1
% 5.13/5.49 thf(fact_2056_div__mult__mult1,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( C != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.49 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_mult1
% 5.13/5.49 thf(fact_2057_nonzero__mult__div__cancel__left,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.13/5.49 = B ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_left
% 5.13/5.49 thf(fact_2058_nonzero__mult__div__cancel__left,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.13/5.49 = B ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_left
% 5.13/5.49 thf(fact_2059_nonzero__mult__div__cancel__left,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.13/5.49 = B ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_left
% 5.13/5.49 thf(fact_2060_nonzero__mult__div__cancel__left,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( A != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.13/5.49 = B ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_left
% 5.13/5.49 thf(fact_2061_nonzero__mult__div__cancel__left,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( A != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.13/5.49 = B ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_left
% 5.13/5.49 thf(fact_2062_nonzero__mult__div__cancel__right,axiom,
% 5.13/5.49 ! [B: complex,A: complex] :
% 5.13/5.49 ( ( B != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.13/5.49 = A ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_right
% 5.13/5.49 thf(fact_2063_nonzero__mult__div__cancel__right,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( B != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.13/5.49 = A ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_right
% 5.13/5.49 thf(fact_2064_nonzero__mult__div__cancel__right,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( B != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.13/5.49 = A ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_right
% 5.13/5.49 thf(fact_2065_nonzero__mult__div__cancel__right,axiom,
% 5.13/5.49 ! [B: nat,A: nat] :
% 5.13/5.49 ( ( B != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.13/5.49 = A ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_right
% 5.13/5.49 thf(fact_2066_nonzero__mult__div__cancel__right,axiom,
% 5.13/5.49 ! [B: int,A: int] :
% 5.13/5.49 ( ( B != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.13/5.49 = A ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_mult_div_cancel_right
% 5.13/5.49 thf(fact_2067_diff__numeral__special_I9_J,axiom,
% 5.13/5.49 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % diff_numeral_special(9)
% 5.13/5.49 thf(fact_2068_diff__numeral__special_I9_J,axiom,
% 5.13/5.49 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % diff_numeral_special(9)
% 5.13/5.49 thf(fact_2069_diff__numeral__special_I9_J,axiom,
% 5.13/5.49 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % diff_numeral_special(9)
% 5.13/5.49 thf(fact_2070_diff__numeral__special_I9_J,axiom,
% 5.13/5.49 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % diff_numeral_special(9)
% 5.13/5.49 thf(fact_2071_diff__add__zero,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % diff_add_zero
% 5.13/5.49 thf(fact_2072_divide__eq__1__iff,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.13/5.49 = one_one_complex )
% 5.13/5.49 = ( ( B != zero_zero_complex )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_1_iff
% 5.13/5.49 thf(fact_2073_divide__eq__1__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ A @ B )
% 5.13/5.49 = one_one_real )
% 5.13/5.49 = ( ( B != zero_zero_real )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_1_iff
% 5.13/5.49 thf(fact_2074_divide__eq__1__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ A @ B )
% 5.13/5.49 = one_one_rat )
% 5.13/5.49 = ( ( B != zero_zero_rat )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_1_iff
% 5.13/5.49 thf(fact_2075_one__eq__divide__iff,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( one_one_complex
% 5.13/5.49 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.13/5.49 = ( ( B != zero_zero_complex )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_eq_divide_iff
% 5.13/5.49 thf(fact_2076_one__eq__divide__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( one_one_real
% 5.13/5.49 = ( divide_divide_real @ A @ B ) )
% 5.13/5.49 = ( ( B != zero_zero_real )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_eq_divide_iff
% 5.13/5.49 thf(fact_2077_one__eq__divide__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( one_one_rat
% 5.13/5.49 = ( divide_divide_rat @ A @ B ) )
% 5.13/5.49 = ( ( B != zero_zero_rat )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_eq_divide_iff
% 5.13/5.49 thf(fact_2078_divide__self,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.13/5.49 = one_one_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_self
% 5.13/5.49 thf(fact_2079_divide__self,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ A @ A )
% 5.13/5.49 = one_one_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_self
% 5.13/5.49 thf(fact_2080_divide__self,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ A @ A )
% 5.13/5.49 = one_one_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_self
% 5.13/5.49 thf(fact_2081_divide__self__if,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( ( A = zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.13/5.49 = zero_zero_complex ) )
% 5.13/5.49 & ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.13/5.49 = one_one_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_self_if
% 5.13/5.49 thf(fact_2082_divide__self__if,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ( A = zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ A @ A )
% 5.13/5.49 = zero_zero_real ) )
% 5.13/5.49 & ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ A @ A )
% 5.13/5.49 = one_one_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_self_if
% 5.13/5.49 thf(fact_2083_divide__self__if,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ( A = zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ A @ A )
% 5.13/5.49 = zero_zero_rat ) )
% 5.13/5.49 & ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ A @ A )
% 5.13/5.49 = one_one_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_self_if
% 5.13/5.49 thf(fact_2084_divide__eq__eq__1,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ B @ A )
% 5.13/5.49 = one_one_real )
% 5.13/5.49 = ( ( A != zero_zero_real )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq_1
% 5.13/5.49 thf(fact_2085_divide__eq__eq__1,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ B @ A )
% 5.13/5.49 = one_one_rat )
% 5.13/5.49 = ( ( A != zero_zero_rat )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq_1
% 5.13/5.49 thf(fact_2086_eq__divide__eq__1,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( one_one_real
% 5.13/5.49 = ( divide_divide_real @ B @ A ) )
% 5.13/5.49 = ( ( A != zero_zero_real )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq_1
% 5.13/5.49 thf(fact_2087_eq__divide__eq__1,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( one_one_rat
% 5.13/5.49 = ( divide_divide_rat @ B @ A ) )
% 5.13/5.49 = ( ( A != zero_zero_rat )
% 5.13/5.49 & ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq_1
% 5.13/5.49 thf(fact_2088_one__divide__eq__0__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( A = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_divide_eq_0_iff
% 5.13/5.49 thf(fact_2089_one__divide__eq__0__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( A = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_divide_eq_0_iff
% 5.13/5.49 thf(fact_2090_zero__eq__1__divide__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( zero_zero_real
% 5.13/5.49 = ( divide_divide_real @ one_one_real @ A ) )
% 5.13/5.49 = ( A = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_1_divide_iff
% 5.13/5.49 thf(fact_2091_zero__eq__1__divide__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( zero_zero_rat
% 5.13/5.49 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.13/5.49 = ( A = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_1_divide_iff
% 5.13/5.49 thf(fact_2092_div__self,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.13/5.49 = one_one_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_self
% 5.13/5.49 thf(fact_2093_div__self,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ A @ A )
% 5.13/5.49 = one_one_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_self
% 5.13/5.49 thf(fact_2094_div__self,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ A @ A )
% 5.13/5.49 = one_one_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_self
% 5.13/5.49 thf(fact_2095_div__self,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( A != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ A @ A )
% 5.13/5.49 = one_one_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_self
% 5.13/5.49 thf(fact_2096_div__self,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( A != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ A @ A )
% 5.13/5.49 = one_one_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_self
% 5.13/5.49 thf(fact_2097_power__0__Suc,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_Suc
% 5.13/5.49 thf(fact_2098_power__0__Suc,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_Suc
% 5.13/5.49 thf(fact_2099_power__0__Suc,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_Suc
% 5.13/5.49 thf(fact_2100_power__0__Suc,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_Suc
% 5.13/5.49 thf(fact_2101_power__0__Suc,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_Suc
% 5.13/5.49 thf(fact_2102_power__zero__numeral,axiom,
% 5.13/5.49 ! [K: num] :
% 5.13/5.49 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.13/5.49 = zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % power_zero_numeral
% 5.13/5.49 thf(fact_2103_power__zero__numeral,axiom,
% 5.13/5.49 ! [K: num] :
% 5.13/5.49 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % power_zero_numeral
% 5.13/5.49 thf(fact_2104_power__zero__numeral,axiom,
% 5.13/5.49 ! [K: num] :
% 5.13/5.49 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.13/5.49 = zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % power_zero_numeral
% 5.13/5.49 thf(fact_2105_power__zero__numeral,axiom,
% 5.13/5.49 ! [K: num] :
% 5.13/5.49 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % power_zero_numeral
% 5.13/5.49 thf(fact_2106_power__zero__numeral,axiom,
% 5.13/5.49 ! [K: num] :
% 5.13/5.49 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.13/5.49 = zero_zero_complex ) ).
% 5.13/5.49
% 5.13/5.49 % power_zero_numeral
% 5.13/5.49 thf(fact_2107_power__Suc0__right,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % power_Suc0_right
% 5.13/5.49 thf(fact_2108_power__Suc0__right,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % power_Suc0_right
% 5.13/5.49 thf(fact_2109_power__Suc0__right,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % power_Suc0_right
% 5.13/5.49 thf(fact_2110_power__Suc0__right,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % power_Suc0_right
% 5.13/5.49 thf(fact_2111_less__Suc0,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.13/5.49 = ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_Suc0
% 5.13/5.49 thf(fact_2112_zero__less__Suc,axiom,
% 5.13/5.49 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_Suc
% 5.13/5.49 thf(fact_2113_add__gr__0,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.49 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_gr_0
% 5.13/5.49 thf(fact_2114_mult__eq__1__iff,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ M @ N )
% 5.13/5.49 = ( suc @ zero_zero_nat ) )
% 5.13/5.49 = ( ( M
% 5.13/5.49 = ( suc @ zero_zero_nat ) )
% 5.13/5.49 & ( N
% 5.13/5.49 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_eq_1_iff
% 5.13/5.49 thf(fact_2115_one__eq__mult__iff,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ( suc @ zero_zero_nat )
% 5.13/5.49 = ( times_times_nat @ M @ N ) )
% 5.13/5.49 = ( ( M
% 5.13/5.49 = ( suc @ zero_zero_nat ) )
% 5.13/5.49 & ( N
% 5.13/5.49 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_eq_mult_iff
% 5.13/5.49 thf(fact_2116_div__by__Suc__0,axiom,
% 5.13/5.49 ! [M: nat] :
% 5.13/5.49 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.13/5.49 = M ) ).
% 5.13/5.49
% 5.13/5.49 % div_by_Suc_0
% 5.13/5.49 thf(fact_2117_zero__less__diff,axiom,
% 5.13/5.49 ! [N: nat,M: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.13/5.49 = ( ord_less_nat @ M @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_diff
% 5.13/5.49 thf(fact_2118_mult__less__cancel2,axiom,
% 5.13/5.49 ! [M: nat,K: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.49 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_less_cancel2
% 5.13/5.49 thf(fact_2119_nat__0__less__mult__iff,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.49 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_0_less_mult_iff
% 5.13/5.49 thf(fact_2120_nat__mult__less__cancel__disj,axiom,
% 5.13/5.49 ! [K: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.49 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_mult_less_cancel_disj
% 5.13/5.49 thf(fact_2121_div__less,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ M @ N )
% 5.13/5.49 => ( ( divide_divide_nat @ M @ N )
% 5.13/5.49 = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_less
% 5.13/5.49 thf(fact_2122_diff__is__0__eq_H,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.49 => ( ( minus_minus_nat @ M @ N )
% 5.13/5.49 = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_is_0_eq'
% 5.13/5.49 thf(fact_2123_diff__is__0__eq,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ( minus_minus_nat @ M @ N )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_is_0_eq
% 5.13/5.49 thf(fact_2124_less__one,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ N @ one_one_nat )
% 5.13/5.49 = ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_one
% 5.13/5.49 thf(fact_2125_power__Suc__0,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.13/5.49 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_Suc_0
% 5.13/5.49 thf(fact_2126_nat__power__eq__Suc__0__iff,axiom,
% 5.13/5.49 ! [X: nat,M: nat] :
% 5.13/5.49 ( ( ( power_power_nat @ X @ M )
% 5.13/5.49 = ( suc @ zero_zero_nat ) )
% 5.13/5.49 = ( ( M = zero_zero_nat )
% 5.13/5.49 | ( X
% 5.13/5.49 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_power_eq_Suc_0_iff
% 5.13/5.49 thf(fact_2127_nat__zero__less__power__iff,axiom,
% 5.13/5.49 ! [X: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.13/5.49 | ( N = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_zero_less_power_iff
% 5.13/5.49 thf(fact_2128_nat__mult__div__cancel__disj,axiom,
% 5.13/5.49 ! [K: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ( K = zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.49 = zero_zero_nat ) )
% 5.13/5.49 & ( ( K != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.49 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_mult_div_cancel_disj
% 5.13/5.49 thf(fact_2129_divide__le__0__1__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.13/5.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_0_1_iff
% 5.13/5.49 thf(fact_2130_divide__le__0__1__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_0_1_iff
% 5.13/5.49 thf(fact_2131_zero__le__divide__1__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.13/5.49 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_divide_1_iff
% 5.13/5.49 thf(fact_2132_zero__le__divide__1__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.13/5.49 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_divide_1_iff
% 5.13/5.49 thf(fact_2133_zero__less__divide__1__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.13/5.49 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_divide_1_iff
% 5.13/5.49 thf(fact_2134_zero__less__divide__1__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.13/5.49 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_divide_1_iff
% 5.13/5.49 thf(fact_2135_less__divide__eq__1__pos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.13/5.49 = ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq_1_pos
% 5.13/5.49 thf(fact_2136_less__divide__eq__1__pos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.13/5.49 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq_1_pos
% 5.13/5.49 thf(fact_2137_less__divide__eq__1__neg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.13/5.49 = ( ord_less_real @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq_1_neg
% 5.13/5.49 thf(fact_2138_less__divide__eq__1__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.13/5.49 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq_1_neg
% 5.13/5.49 thf(fact_2139_divide__less__eq__1__pos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.13/5.49 = ( ord_less_real @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq_1_pos
% 5.13/5.49 thf(fact_2140_divide__less__eq__1__pos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.13/5.49 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq_1_pos
% 5.13/5.49 thf(fact_2141_divide__less__eq__1__neg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.13/5.49 = ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq_1_neg
% 5.13/5.49 thf(fact_2142_divide__less__eq__1__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.13/5.49 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq_1_neg
% 5.13/5.49 thf(fact_2143_divide__less__0__1__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.13/5.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_0_1_iff
% 5.13/5.49 thf(fact_2144_divide__less__0__1__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.13/5.49 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_0_1_iff
% 5.13/5.49 thf(fact_2145_divide__eq__eq__numeral1_I1_J,axiom,
% 5.13/5.49 ! [B: complex,W2: num,A: complex] :
% 5.13/5.49 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) )
% 5.13/5.49 = A )
% 5.13/5.49 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.49 != zero_zero_complex )
% 5.13/5.49 => ( B
% 5.13/5.49 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 5.13/5.49 & ( ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 => ( A = zero_zero_complex ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq_numeral1(1)
% 5.13/5.49 thf(fact_2146_divide__eq__eq__numeral1_I1_J,axiom,
% 5.13/5.49 ! [B: real,W2: num,A: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 5.13/5.49 = A )
% 5.13/5.49 = ( ( ( ( numeral_numeral_real @ W2 )
% 5.13/5.49 != zero_zero_real )
% 5.13/5.49 => ( B
% 5.13/5.49 = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.13/5.49 & ( ( ( numeral_numeral_real @ W2 )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 => ( A = zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq_numeral1(1)
% 5.13/5.49 thf(fact_2147_divide__eq__eq__numeral1_I1_J,axiom,
% 5.13/5.49 ! [B: rat,W2: num,A: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 5.13/5.49 = A )
% 5.13/5.49 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.13/5.49 != zero_zero_rat )
% 5.13/5.49 => ( B
% 5.13/5.49 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.13/5.49 & ( ( ( numeral_numeral_rat @ W2 )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 => ( A = zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq_numeral1(1)
% 5.13/5.49 thf(fact_2148_eq__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.49 ! [A: complex,B: complex,W2: num] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.13/5.49 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.49 != zero_zero_complex )
% 5.13/5.49 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 => ( A = zero_zero_complex ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq_numeral1(1)
% 5.13/5.49 thf(fact_2149_eq__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.49 ! [A: real,B: real,W2: num] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 5.13/5.49 = ( ( ( ( numeral_numeral_real @ W2 )
% 5.13/5.49 != zero_zero_real )
% 5.13/5.49 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( ( numeral_numeral_real @ W2 )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 => ( A = zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq_numeral1(1)
% 5.13/5.49 thf(fact_2150_eq__divide__eq__numeral1_I1_J,axiom,
% 5.13/5.49 ! [A: rat,B: rat,W2: num] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.13/5.49 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.13/5.49 != zero_zero_rat )
% 5.13/5.49 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( ( numeral_numeral_rat @ W2 )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 => ( A = zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq_numeral1(1)
% 5.13/5.49 thf(fact_2151_nonzero__divide__mult__cancel__left,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_mult_cancel_left
% 5.13/5.49 thf(fact_2152_nonzero__divide__mult__cancel__left,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.13/5.49 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_mult_cancel_left
% 5.13/5.49 thf(fact_2153_nonzero__divide__mult__cancel__left,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.13/5.49 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_mult_cancel_left
% 5.13/5.49 thf(fact_2154_nonzero__divide__mult__cancel__right,axiom,
% 5.13/5.49 ! [B: complex,A: complex] :
% 5.13/5.49 ( ( B != zero_zero_complex )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_mult_cancel_right
% 5.13/5.49 thf(fact_2155_nonzero__divide__mult__cancel__right,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( B != zero_zero_real )
% 5.13/5.49 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.13/5.49 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_mult_cancel_right
% 5.13/5.49 thf(fact_2156_nonzero__divide__mult__cancel__right,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( B != zero_zero_rat )
% 5.13/5.49 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.13/5.49 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_mult_cancel_right
% 5.13/5.49 thf(fact_2157_div__mult__self1,axiom,
% 5.13/5.49 ! [B: nat,A: nat,C: nat] :
% 5.13/5.49 ( ( B != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.13/5.49 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self1
% 5.13/5.49 thf(fact_2158_div__mult__self1,axiom,
% 5.13/5.49 ! [B: int,A: int,C: int] :
% 5.13/5.49 ( ( B != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.13/5.49 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self1
% 5.13/5.49 thf(fact_2159_div__mult__self2,axiom,
% 5.13/5.49 ! [B: nat,A: nat,C: nat] :
% 5.13/5.49 ( ( B != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.13/5.49 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self2
% 5.13/5.49 thf(fact_2160_div__mult__self2,axiom,
% 5.13/5.49 ! [B: int,A: int,C: int] :
% 5.13/5.49 ( ( B != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.13/5.49 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self2
% 5.13/5.49 thf(fact_2161_div__mult__self3,axiom,
% 5.13/5.49 ! [B: nat,C: nat,A: nat] :
% 5.13/5.49 ( ( B != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.13/5.49 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self3
% 5.13/5.49 thf(fact_2162_div__mult__self3,axiom,
% 5.13/5.49 ! [B: int,C: int,A: int] :
% 5.13/5.49 ( ( B != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.13/5.49 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self3
% 5.13/5.49 thf(fact_2163_div__mult__self4,axiom,
% 5.13/5.49 ! [B: nat,C: nat,A: nat] :
% 5.13/5.49 ( ( B != zero_zero_nat )
% 5.13/5.49 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.13/5.49 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self4
% 5.13/5.49 thf(fact_2164_div__mult__self4,axiom,
% 5.13/5.49 ! [B: int,C: int,A: int] :
% 5.13/5.49 ( ( B != zero_zero_int )
% 5.13/5.49 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.13/5.49 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self4
% 5.13/5.49 thf(fact_2165_power__eq__0__iff,axiom,
% 5.13/5.49 ! [A: rat,N: nat] :
% 5.13/5.49 ( ( ( power_power_rat @ A @ N )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( A = zero_zero_rat )
% 5.13/5.49 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_0_iff
% 5.13/5.49 thf(fact_2166_power__eq__0__iff,axiom,
% 5.13/5.49 ! [A: nat,N: nat] :
% 5.13/5.49 ( ( ( power_power_nat @ A @ N )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( A = zero_zero_nat )
% 5.13/5.49 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_0_iff
% 5.13/5.49 thf(fact_2167_power__eq__0__iff,axiom,
% 5.13/5.49 ! [A: real,N: nat] :
% 5.13/5.49 ( ( ( power_power_real @ A @ N )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( A = zero_zero_real )
% 5.13/5.49 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_0_iff
% 5.13/5.49 thf(fact_2168_power__eq__0__iff,axiom,
% 5.13/5.49 ! [A: int,N: nat] :
% 5.13/5.49 ( ( ( power_power_int @ A @ N )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( ( A = zero_zero_int )
% 5.13/5.49 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_0_iff
% 5.13/5.49 thf(fact_2169_power__eq__0__iff,axiom,
% 5.13/5.49 ! [A: complex,N: nat] :
% 5.13/5.49 ( ( ( power_power_complex @ A @ N )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 = ( ( A = zero_zero_complex )
% 5.13/5.49 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_0_iff
% 5.13/5.49 thf(fact_2170_Suc__pred,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.13/5.49 = N ) ) ).
% 5.13/5.49
% 5.13/5.49 % Suc_pred
% 5.13/5.49 thf(fact_2171_one__le__mult__iff,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.13/5.49 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.13/5.49 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % one_le_mult_iff
% 5.13/5.49 thf(fact_2172_mult__le__cancel2,axiom,
% 5.13/5.49 ! [M: nat,K: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.49 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_le_cancel2
% 5.13/5.49 thf(fact_2173_nat__mult__le__cancel__disj,axiom,
% 5.13/5.49 ! [K: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.49 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.49 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_mult_le_cancel_disj
% 5.13/5.49 thf(fact_2174_div__mult__self1__is__m,axiom,
% 5.13/5.49 ! [N: nat,M: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.13/5.49 = M ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self1_is_m
% 5.13/5.49 thf(fact_2175_div__mult__self__is__m,axiom,
% 5.13/5.49 ! [N: nat,M: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.13/5.49 = M ) ) ).
% 5.13/5.49
% 5.13/5.49 % div_mult_self_is_m
% 5.13/5.49 thf(fact_2176_divide__le__eq__1__neg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.13/5.49 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_eq_1_neg
% 5.13/5.49 thf(fact_2177_divide__le__eq__1__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_eq_1_neg
% 5.13/5.49 thf(fact_2178_divide__le__eq__1__pos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.13/5.49 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_eq_1_pos
% 5.13/5.49 thf(fact_2179_divide__le__eq__1__pos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.13/5.49 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_eq_1_pos
% 5.13/5.49 thf(fact_2180_le__divide__eq__1__neg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_divide_eq_1_neg
% 5.13/5.49 thf(fact_2181_le__divide__eq__1__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_divide_eq_1_neg
% 5.13/5.49 thf(fact_2182_le__divide__eq__1__pos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_divide_eq_1_pos
% 5.13/5.49 thf(fact_2183_le__divide__eq__1__pos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_divide_eq_1_pos
% 5.13/5.49 thf(fact_2184_power__strict__decreasing__iff,axiom,
% 5.13/5.49 ! [B: real,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ( ord_less_real @ B @ one_one_real )
% 5.13/5.49 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.13/5.49 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_decreasing_iff
% 5.13/5.49 thf(fact_2185_power__strict__decreasing__iff,axiom,
% 5.13/5.49 ! [B: rat,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.13/5.49 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.13/5.49 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_decreasing_iff
% 5.13/5.49 thf(fact_2186_power__strict__decreasing__iff,axiom,
% 5.13/5.49 ! [B: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.13/5.49 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.13/5.49 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_decreasing_iff
% 5.13/5.49 thf(fact_2187_power__strict__decreasing__iff,axiom,
% 5.13/5.49 ! [B: int,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ( ord_less_int @ B @ one_one_int )
% 5.13/5.49 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.13/5.49 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_decreasing_iff
% 5.13/5.49 thf(fact_2188_zero__eq__power2,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( A = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_power2
% 5.13/5.49 thf(fact_2189_zero__eq__power2,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( A = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_power2
% 5.13/5.49 thf(fact_2190_zero__eq__power2,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( A = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_power2
% 5.13/5.49 thf(fact_2191_zero__eq__power2,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( A = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_power2
% 5.13/5.49 thf(fact_2192_zero__eq__power2,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 = ( A = zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_eq_power2
% 5.13/5.49 thf(fact_2193_power__mono__iff,axiom,
% 5.13/5.49 ! [A: real,B: real,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_mono_iff
% 5.13/5.49 thf(fact_2194_power__mono__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_mono_iff
% 5.13/5.49 thf(fact_2195_power__mono__iff,axiom,
% 5.13/5.49 ! [A: nat,B: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_mono_iff
% 5.13/5.49 thf(fact_2196_power__mono__iff,axiom,
% 5.13/5.49 ! [A: int,B: int,N: nat] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_mono_iff
% 5.13/5.49 thf(fact_2197_Suc__diff__1,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.13/5.49 = N ) ) ).
% 5.13/5.49
% 5.13/5.49 % Suc_diff_1
% 5.13/5.49 thf(fact_2198_bits__1__div__2,axiom,
% 5.13/5.49 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % bits_1_div_2
% 5.13/5.49 thf(fact_2199_bits__1__div__2,axiom,
% 5.13/5.49 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % bits_1_div_2
% 5.13/5.49 thf(fact_2200_one__div__two__eq__zero,axiom,
% 5.13/5.49 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % one_div_two_eq_zero
% 5.13/5.49 thf(fact_2201_one__div__two__eq__zero,axiom,
% 5.13/5.49 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.13/5.49 = zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % one_div_two_eq_zero
% 5.13/5.49 thf(fact_2202_power__decreasing__iff,axiom,
% 5.13/5.49 ! [B: real,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ( ord_less_real @ B @ one_one_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_decreasing_iff
% 5.13/5.49 thf(fact_2203_power__decreasing__iff,axiom,
% 5.13/5.49 ! [B: rat,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_decreasing_iff
% 5.13/5.49 thf(fact_2204_power__decreasing__iff,axiom,
% 5.13/5.49 ! [B: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.13/5.49 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_decreasing_iff
% 5.13/5.49 thf(fact_2205_power__decreasing__iff,axiom,
% 5.13/5.49 ! [B: int,M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ( ord_less_int @ B @ one_one_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.13/5.49 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_decreasing_iff
% 5.13/5.49 thf(fact_2206_power2__less__eq__zero__iff,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.13/5.49 = ( A = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_less_eq_zero_iff
% 5.13/5.49 thf(fact_2207_power2__less__eq__zero__iff,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.13/5.49 = ( A = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_less_eq_zero_iff
% 5.13/5.49 thf(fact_2208_power2__less__eq__zero__iff,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.13/5.49 = ( A = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_less_eq_zero_iff
% 5.13/5.49 thf(fact_2209_power2__eq__iff__nonneg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( X = Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_eq_iff_nonneg
% 5.13/5.49 thf(fact_2210_power2__eq__iff__nonneg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( X = Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_eq_iff_nonneg
% 5.13/5.49 thf(fact_2211_power2__eq__iff__nonneg,axiom,
% 5.13/5.49 ! [X: nat,Y4: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.13/5.49 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( X = Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_eq_iff_nonneg
% 5.13/5.49 thf(fact_2212_power2__eq__iff__nonneg,axiom,
% 5.13/5.49 ! [X: int,Y4: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.49 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.49 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( X = Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power2_eq_iff_nonneg
% 5.13/5.49 thf(fact_2213_zero__less__power2,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( A != zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_power2
% 5.13/5.49 thf(fact_2214_zero__less__power2,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( A != zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_power2
% 5.13/5.49 thf(fact_2215_zero__less__power2,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = ( A != zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_power2
% 5.13/5.49 thf(fact_2216_sum__power2__eq__zero__iff,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( X = zero_zero_rat )
% 5.13/5.49 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % sum_power2_eq_zero_iff
% 5.13/5.49 thf(fact_2217_sum__power2__eq__zero__iff,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( X = zero_zero_real )
% 5.13/5.49 & ( Y4 = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % sum_power2_eq_zero_iff
% 5.13/5.49 thf(fact_2218_sum__power2__eq__zero__iff,axiom,
% 5.13/5.49 ! [X: int,Y4: int] :
% 5.13/5.49 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( ( X = zero_zero_int )
% 5.13/5.49 & ( Y4 = zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % sum_power2_eq_zero_iff
% 5.13/5.49 thf(fact_2219_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.13/5.49 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.13/5.49 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.13/5.49
% 5.13/5.49 % VEBT_internal.naive_member.simps(2)
% 5.13/5.49 thf(fact_2220_power__0__left,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ( N = zero_zero_nat )
% 5.13/5.49 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.13/5.49 = one_one_rat ) )
% 5.13/5.49 & ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.13/5.49 = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_left
% 5.13/5.49 thf(fact_2221_power__0__left,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ( N = zero_zero_nat )
% 5.13/5.49 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.13/5.49 = one_one_nat ) )
% 5.13/5.49 & ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.13/5.49 = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_left
% 5.13/5.49 thf(fact_2222_power__0__left,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ( N = zero_zero_nat )
% 5.13/5.49 => ( ( power_power_real @ zero_zero_real @ N )
% 5.13/5.49 = one_one_real ) )
% 5.13/5.49 & ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ( power_power_real @ zero_zero_real @ N )
% 5.13/5.49 = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_left
% 5.13/5.49 thf(fact_2223_power__0__left,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ( N = zero_zero_nat )
% 5.13/5.49 => ( ( power_power_int @ zero_zero_int @ N )
% 5.13/5.49 = one_one_int ) )
% 5.13/5.49 & ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ( power_power_int @ zero_zero_int @ N )
% 5.13/5.49 = zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_left
% 5.13/5.49 thf(fact_2224_power__0__left,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ( N = zero_zero_nat )
% 5.13/5.49 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.13/5.49 = one_one_complex ) )
% 5.13/5.49 & ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.13/5.49 = zero_zero_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_0_left
% 5.13/5.49 thf(fact_2225_zero__power,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.13/5.49 = zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_power
% 5.13/5.49 thf(fact_2226_zero__power,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.13/5.49 = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_power
% 5.13/5.49 thf(fact_2227_zero__power,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( power_power_real @ zero_zero_real @ N )
% 5.13/5.49 = zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_power
% 5.13/5.49 thf(fact_2228_zero__power,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( power_power_int @ zero_zero_int @ N )
% 5.13/5.49 = zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_power
% 5.13/5.49 thf(fact_2229_zero__power,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.13/5.49 = zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_power
% 5.13/5.49 thf(fact_2230_le__numeral__extra_I3_J,axiom,
% 5.13/5.49 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.13/5.49
% 5.13/5.49 % le_numeral_extra(3)
% 5.13/5.49 thf(fact_2231_le__numeral__extra_I3_J,axiom,
% 5.13/5.49 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.13/5.49
% 5.13/5.49 % le_numeral_extra(3)
% 5.13/5.49 thf(fact_2232_le__numeral__extra_I3_J,axiom,
% 5.13/5.49 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.13/5.49
% 5.13/5.49 % le_numeral_extra(3)
% 5.13/5.49 thf(fact_2233_le__numeral__extra_I3_J,axiom,
% 5.13/5.49 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.13/5.49
% 5.13/5.49 % le_numeral_extra(3)
% 5.13/5.49 thf(fact_2234_zero__le,axiom,
% 5.13/5.49 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le
% 5.13/5.49 thf(fact_2235_field__lbound__gt__zero,axiom,
% 5.13/5.49 ! [D1: real,D22: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.13/5.49 => ? [E2: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.13/5.49 & ( ord_less_real @ E2 @ D1 )
% 5.13/5.49 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % field_lbound_gt_zero
% 5.13/5.49 thf(fact_2236_field__lbound__gt__zero,axiom,
% 5.13/5.49 ! [D1: rat,D22: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.13/5.49 => ? [E2: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.13/5.49 & ( ord_less_rat @ E2 @ D1 )
% 5.13/5.49 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % field_lbound_gt_zero
% 5.13/5.49 thf(fact_2237_less__numeral__extra_I3_J,axiom,
% 5.13/5.49 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % less_numeral_extra(3)
% 5.13/5.49 thf(fact_2238_less__numeral__extra_I3_J,axiom,
% 5.13/5.49 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % less_numeral_extra(3)
% 5.13/5.49 thf(fact_2239_less__numeral__extra_I3_J,axiom,
% 5.13/5.49 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % less_numeral_extra(3)
% 5.13/5.49 thf(fact_2240_less__numeral__extra_I3_J,axiom,
% 5.13/5.49 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % less_numeral_extra(3)
% 5.13/5.49 thf(fact_2241_zero__less__iff__neq__zero,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 = ( N != zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_iff_neq_zero
% 5.13/5.49 thf(fact_2242_gr__implies__not__zero,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ M @ N )
% 5.13/5.49 => ( N != zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % gr_implies_not_zero
% 5.13/5.49 thf(fact_2243_not__less__zero,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % not_less_zero
% 5.13/5.49 thf(fact_2244_gr__zeroI,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % gr_zeroI
% 5.13/5.49 thf(fact_2245_zero__neq__numeral,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ( zero_zero_complex
% 5.13/5.49 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_numeral
% 5.13/5.49 thf(fact_2246_zero__neq__numeral,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ( zero_zero_real
% 5.13/5.49 != ( numeral_numeral_real @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_numeral
% 5.13/5.49 thf(fact_2247_zero__neq__numeral,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ( zero_zero_rat
% 5.13/5.49 != ( numeral_numeral_rat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_numeral
% 5.13/5.49 thf(fact_2248_zero__neq__numeral,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ( zero_zero_nat
% 5.13/5.49 != ( numeral_numeral_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_numeral
% 5.13/5.49 thf(fact_2249_zero__neq__numeral,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ( zero_zero_int
% 5.13/5.49 != ( numeral_numeral_int @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_numeral
% 5.13/5.49 thf(fact_2250_mult__right__cancel,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( ( times_times_complex @ A @ C )
% 5.13/5.49 = ( times_times_complex @ B @ C ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_cancel
% 5.13/5.49 thf(fact_2251_mult__right__cancel,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( ( times_times_real @ A @ C )
% 5.13/5.49 = ( times_times_real @ B @ C ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_cancel
% 5.13/5.49 thf(fact_2252_mult__right__cancel,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( ( times_times_rat @ A @ C )
% 5.13/5.49 = ( times_times_rat @ B @ C ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_cancel
% 5.13/5.49 thf(fact_2253_mult__right__cancel,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( C != zero_zero_nat )
% 5.13/5.49 => ( ( ( times_times_nat @ A @ C )
% 5.13/5.49 = ( times_times_nat @ B @ C ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_cancel
% 5.13/5.49 thf(fact_2254_mult__right__cancel,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( C != zero_zero_int )
% 5.13/5.49 => ( ( ( times_times_int @ A @ C )
% 5.13/5.49 = ( times_times_int @ B @ C ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_cancel
% 5.13/5.49 thf(fact_2255_mult__left__cancel,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( ( times_times_complex @ C @ A )
% 5.13/5.49 = ( times_times_complex @ C @ B ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_cancel
% 5.13/5.49 thf(fact_2256_mult__left__cancel,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( ( times_times_real @ C @ A )
% 5.13/5.49 = ( times_times_real @ C @ B ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_cancel
% 5.13/5.49 thf(fact_2257_mult__left__cancel,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( ( times_times_rat @ C @ A )
% 5.13/5.49 = ( times_times_rat @ C @ B ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_cancel
% 5.13/5.49 thf(fact_2258_mult__left__cancel,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( C != zero_zero_nat )
% 5.13/5.49 => ( ( ( times_times_nat @ C @ A )
% 5.13/5.49 = ( times_times_nat @ C @ B ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_cancel
% 5.13/5.49 thf(fact_2259_mult__left__cancel,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( C != zero_zero_int )
% 5.13/5.49 => ( ( ( times_times_int @ C @ A )
% 5.13/5.49 = ( times_times_int @ C @ B ) )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_cancel
% 5.13/5.49 thf(fact_2260_no__zero__divisors,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( B != zero_zero_complex )
% 5.13/5.49 => ( ( times_times_complex @ A @ B )
% 5.13/5.49 != zero_zero_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % no_zero_divisors
% 5.13/5.49 thf(fact_2261_no__zero__divisors,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( B != zero_zero_real )
% 5.13/5.49 => ( ( times_times_real @ A @ B )
% 5.13/5.49 != zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % no_zero_divisors
% 5.13/5.49 thf(fact_2262_no__zero__divisors,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( B != zero_zero_rat )
% 5.13/5.49 => ( ( times_times_rat @ A @ B )
% 5.13/5.49 != zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % no_zero_divisors
% 5.13/5.49 thf(fact_2263_no__zero__divisors,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( A != zero_zero_nat )
% 5.13/5.49 => ( ( B != zero_zero_nat )
% 5.13/5.49 => ( ( times_times_nat @ A @ B )
% 5.13/5.49 != zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % no_zero_divisors
% 5.13/5.49 thf(fact_2264_no__zero__divisors,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( A != zero_zero_int )
% 5.13/5.49 => ( ( B != zero_zero_int )
% 5.13/5.49 => ( ( times_times_int @ A @ B )
% 5.13/5.49 != zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % no_zero_divisors
% 5.13/5.49 thf(fact_2265_divisors__zero,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ A @ B )
% 5.13/5.49 = zero_zero_complex )
% 5.13/5.49 => ( ( A = zero_zero_complex )
% 5.13/5.49 | ( B = zero_zero_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divisors_zero
% 5.13/5.49 thf(fact_2266_divisors__zero,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( times_times_real @ A @ B )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 => ( ( A = zero_zero_real )
% 5.13/5.49 | ( B = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divisors_zero
% 5.13/5.49 thf(fact_2267_divisors__zero,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ A @ B )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 => ( ( A = zero_zero_rat )
% 5.13/5.49 | ( B = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divisors_zero
% 5.13/5.49 thf(fact_2268_divisors__zero,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ A @ B )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 => ( ( A = zero_zero_nat )
% 5.13/5.49 | ( B = zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divisors_zero
% 5.13/5.49 thf(fact_2269_divisors__zero,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ( times_times_int @ A @ B )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 => ( ( A = zero_zero_int )
% 5.13/5.49 | ( B = zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divisors_zero
% 5.13/5.49 thf(fact_2270_mult__not__zero,axiom,
% 5.13/5.49 ! [A: complex,B: complex] :
% 5.13/5.49 ( ( ( times_times_complex @ A @ B )
% 5.13/5.49 != zero_zero_complex )
% 5.13/5.49 => ( ( A != zero_zero_complex )
% 5.13/5.49 & ( B != zero_zero_complex ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_not_zero
% 5.13/5.49 thf(fact_2271_mult__not__zero,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( times_times_real @ A @ B )
% 5.13/5.49 != zero_zero_real )
% 5.13/5.49 => ( ( A != zero_zero_real )
% 5.13/5.49 & ( B != zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_not_zero
% 5.13/5.49 thf(fact_2272_mult__not__zero,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( times_times_rat @ A @ B )
% 5.13/5.49 != zero_zero_rat )
% 5.13/5.49 => ( ( A != zero_zero_rat )
% 5.13/5.49 & ( B != zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_not_zero
% 5.13/5.49 thf(fact_2273_mult__not__zero,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ A @ B )
% 5.13/5.49 != zero_zero_nat )
% 5.13/5.49 => ( ( A != zero_zero_nat )
% 5.13/5.49 & ( B != zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_not_zero
% 5.13/5.49 thf(fact_2274_mult__not__zero,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ( times_times_int @ A @ B )
% 5.13/5.49 != zero_zero_int )
% 5.13/5.49 => ( ( A != zero_zero_int )
% 5.13/5.49 & ( B != zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_not_zero
% 5.13/5.49 thf(fact_2275_zero__neq__one,axiom,
% 5.13/5.49 zero_zero_complex != one_one_complex ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_one
% 5.13/5.49 thf(fact_2276_zero__neq__one,axiom,
% 5.13/5.49 zero_zero_real != one_one_real ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_one
% 5.13/5.49 thf(fact_2277_zero__neq__one,axiom,
% 5.13/5.49 zero_zero_rat != one_one_rat ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_one
% 5.13/5.49 thf(fact_2278_zero__neq__one,axiom,
% 5.13/5.49 zero_zero_nat != one_one_nat ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_one
% 5.13/5.49 thf(fact_2279_zero__neq__one,axiom,
% 5.13/5.49 zero_zero_int != one_one_int ).
% 5.13/5.49
% 5.13/5.49 % zero_neq_one
% 5.13/5.49 thf(fact_2280_verit__sum__simplify,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % verit_sum_simplify
% 5.13/5.49 thf(fact_2281_verit__sum__simplify,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % verit_sum_simplify
% 5.13/5.49 thf(fact_2282_verit__sum__simplify,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % verit_sum_simplify
% 5.13/5.49 thf(fact_2283_verit__sum__simplify,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % verit_sum_simplify
% 5.13/5.49 thf(fact_2284_verit__sum__simplify,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % verit_sum_simplify
% 5.13/5.49 thf(fact_2285_add_Ogroup__left__neutral,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.group_left_neutral
% 5.13/5.49 thf(fact_2286_add_Ogroup__left__neutral,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.group_left_neutral
% 5.13/5.49 thf(fact_2287_add_Ogroup__left__neutral,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.group_left_neutral
% 5.13/5.49 thf(fact_2288_add_Ogroup__left__neutral,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.group_left_neutral
% 5.13/5.49 thf(fact_2289_add_Ocomm__neutral,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.comm_neutral
% 5.13/5.49 thf(fact_2290_add_Ocomm__neutral,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.comm_neutral
% 5.13/5.49 thf(fact_2291_add_Ocomm__neutral,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.comm_neutral
% 5.13/5.49 thf(fact_2292_add_Ocomm__neutral,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.comm_neutral
% 5.13/5.49 thf(fact_2293_add_Ocomm__neutral,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % add.comm_neutral
% 5.13/5.49 thf(fact_2294_comm__monoid__add__class_Oadd__0,axiom,
% 5.13/5.49 ! [A: complex] :
% 5.13/5.49 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % comm_monoid_add_class.add_0
% 5.13/5.49 thf(fact_2295_comm__monoid__add__class_Oadd__0,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % comm_monoid_add_class.add_0
% 5.13/5.49 thf(fact_2296_comm__monoid__add__class_Oadd__0,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % comm_monoid_add_class.add_0
% 5.13/5.49 thf(fact_2297_comm__monoid__add__class_Oadd__0,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % comm_monoid_add_class.add_0
% 5.13/5.49 thf(fact_2298_comm__monoid__add__class_Oadd__0,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.13/5.49 = A ) ).
% 5.13/5.49
% 5.13/5.49 % comm_monoid_add_class.add_0
% 5.13/5.49 thf(fact_2299_power__not__zero,axiom,
% 5.13/5.49 ! [A: rat,N: nat] :
% 5.13/5.49 ( ( A != zero_zero_rat )
% 5.13/5.49 => ( ( power_power_rat @ A @ N )
% 5.13/5.49 != zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_not_zero
% 5.13/5.49 thf(fact_2300_power__not__zero,axiom,
% 5.13/5.49 ! [A: nat,N: nat] :
% 5.13/5.49 ( ( A != zero_zero_nat )
% 5.13/5.49 => ( ( power_power_nat @ A @ N )
% 5.13/5.49 != zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_not_zero
% 5.13/5.49 thf(fact_2301_power__not__zero,axiom,
% 5.13/5.49 ! [A: real,N: nat] :
% 5.13/5.49 ( ( A != zero_zero_real )
% 5.13/5.49 => ( ( power_power_real @ A @ N )
% 5.13/5.49 != zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_not_zero
% 5.13/5.49 thf(fact_2302_power__not__zero,axiom,
% 5.13/5.49 ! [A: int,N: nat] :
% 5.13/5.49 ( ( A != zero_zero_int )
% 5.13/5.49 => ( ( power_power_int @ A @ N )
% 5.13/5.49 != zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_not_zero
% 5.13/5.49 thf(fact_2303_power__not__zero,axiom,
% 5.13/5.49 ! [A: complex,N: nat] :
% 5.13/5.49 ( ( A != zero_zero_complex )
% 5.13/5.49 => ( ( power_power_complex @ A @ N )
% 5.13/5.49 != zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_not_zero
% 5.13/5.49 thf(fact_2304_num_Osize_I4_J,axiom,
% 5.13/5.49 ( ( size_size_num @ one )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % num.size(4)
% 5.13/5.49 thf(fact_2305_not0__implies__Suc,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( N != zero_zero_nat )
% 5.13/5.49 => ? [M4: nat] :
% 5.13/5.49 ( N
% 5.13/5.49 = ( suc @ M4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % not0_implies_Suc
% 5.13/5.49 thf(fact_2306_Zero__not__Suc,axiom,
% 5.13/5.49 ! [M: nat] :
% 5.13/5.49 ( zero_zero_nat
% 5.13/5.49 != ( suc @ M ) ) ).
% 5.13/5.49
% 5.13/5.49 % Zero_not_Suc
% 5.13/5.49 thf(fact_2307_Zero__neq__Suc,axiom,
% 5.13/5.49 ! [M: nat] :
% 5.13/5.49 ( zero_zero_nat
% 5.13/5.49 != ( suc @ M ) ) ).
% 5.13/5.49
% 5.13/5.49 % Zero_neq_Suc
% 5.13/5.49 thf(fact_2308_Suc__neq__Zero,axiom,
% 5.13/5.49 ! [M: nat] :
% 5.13/5.49 ( ( suc @ M )
% 5.13/5.49 != zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % Suc_neq_Zero
% 5.13/5.49 thf(fact_2309_zero__induct,axiom,
% 5.13/5.49 ! [P: nat > $o,K: nat] :
% 5.13/5.49 ( ( P @ K )
% 5.13/5.49 => ( ! [N3: nat] :
% 5.13/5.49 ( ( P @ ( suc @ N3 ) )
% 5.13/5.49 => ( P @ N3 ) )
% 5.13/5.49 => ( P @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_induct
% 5.13/5.49 thf(fact_2310_diff__induct,axiom,
% 5.13/5.49 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.13/5.49 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.13/5.49 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.13/5.49 => ( ! [X3: nat,Y3: nat] :
% 5.13/5.49 ( ( P @ X3 @ Y3 )
% 5.13/5.49 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.13/5.49 => ( P @ M @ N ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_induct
% 5.13/5.49 thf(fact_2311_nat__induct,axiom,
% 5.13/5.49 ! [P: nat > $o,N: nat] :
% 5.13/5.49 ( ( P @ zero_zero_nat )
% 5.13/5.49 => ( ! [N3: nat] :
% 5.13/5.49 ( ( P @ N3 )
% 5.13/5.49 => ( P @ ( suc @ N3 ) ) )
% 5.13/5.49 => ( P @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_induct
% 5.13/5.49 thf(fact_2312_old_Onat_Oexhaust,axiom,
% 5.13/5.49 ! [Y4: nat] :
% 5.13/5.49 ( ( Y4 != zero_zero_nat )
% 5.13/5.49 => ~ ! [Nat3: nat] :
% 5.13/5.49 ( Y4
% 5.13/5.49 != ( suc @ Nat3 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % old.nat.exhaust
% 5.13/5.49 thf(fact_2313_nat_OdiscI,axiom,
% 5.13/5.49 ! [Nat: nat,X22: nat] :
% 5.13/5.49 ( ( Nat
% 5.13/5.49 = ( suc @ X22 ) )
% 5.13/5.49 => ( Nat != zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat.discI
% 5.13/5.49 thf(fact_2314_old_Onat_Odistinct_I1_J,axiom,
% 5.13/5.49 ! [Nat2: nat] :
% 5.13/5.49 ( zero_zero_nat
% 5.13/5.49 != ( suc @ Nat2 ) ) ).
% 5.13/5.49
% 5.13/5.49 % old.nat.distinct(1)
% 5.13/5.49 thf(fact_2315_old_Onat_Odistinct_I2_J,axiom,
% 5.13/5.49 ! [Nat2: nat] :
% 5.13/5.49 ( ( suc @ Nat2 )
% 5.13/5.49 != zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % old.nat.distinct(2)
% 5.13/5.49 thf(fact_2316_nat_Odistinct_I1_J,axiom,
% 5.13/5.49 ! [X22: nat] :
% 5.13/5.49 ( zero_zero_nat
% 5.13/5.49 != ( suc @ X22 ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat.distinct(1)
% 5.13/5.49 thf(fact_2317_vebt__buildup_Ocases,axiom,
% 5.13/5.49 ! [X: nat] :
% 5.13/5.49 ( ( X != zero_zero_nat )
% 5.13/5.49 => ( ( X
% 5.13/5.49 != ( suc @ zero_zero_nat ) )
% 5.13/5.49 => ~ ! [Va3: nat] :
% 5.13/5.49 ( X
% 5.13/5.49 != ( suc @ ( suc @ Va3 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % vebt_buildup.cases
% 5.13/5.49 thf(fact_2318_infinite__descent0,axiom,
% 5.13/5.49 ! [P: nat > $o,N: nat] :
% 5.13/5.49 ( ( P @ zero_zero_nat )
% 5.13/5.49 => ( ! [N3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.13/5.49 => ( ~ ( P @ N3 )
% 5.13/5.49 => ? [M3: nat] :
% 5.13/5.49 ( ( ord_less_nat @ M3 @ N3 )
% 5.13/5.49 & ~ ( P @ M3 ) ) ) )
% 5.13/5.49 => ( P @ N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % infinite_descent0
% 5.13/5.49 thf(fact_2319_gr__implies__not0,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ M @ N )
% 5.13/5.49 => ( N != zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % gr_implies_not0
% 5.13/5.49 thf(fact_2320_less__zeroE,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % less_zeroE
% 5.13/5.49 thf(fact_2321_not__less0,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % not_less0
% 5.13/5.49 thf(fact_2322_not__gr0,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.13/5.49 = ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % not_gr0
% 5.13/5.49 thf(fact_2323_gr0I,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( N != zero_zero_nat )
% 5.13/5.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % gr0I
% 5.13/5.49 thf(fact_2324_bot__nat__0_Oextremum__strict,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % bot_nat_0.extremum_strict
% 5.13/5.49 thf(fact_2325_less__eq__nat_Osimps_I1_J,axiom,
% 5.13/5.49 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.13/5.49
% 5.13/5.49 % less_eq_nat.simps(1)
% 5.13/5.49 thf(fact_2326_bot__nat__0_Oextremum__unique,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.49 = ( A = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % bot_nat_0.extremum_unique
% 5.13/5.49 thf(fact_2327_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.13/5.49 ! [A: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.49 => ( A = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % bot_nat_0.extremum_uniqueI
% 5.13/5.49 thf(fact_2328_le__0__eq,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.13/5.49 = ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % le_0_eq
% 5.13/5.49 thf(fact_2329_add__eq__self__zero,axiom,
% 5.13/5.49 ! [M: nat,N: nat] :
% 5.13/5.49 ( ( ( plus_plus_nat @ M @ N )
% 5.13/5.49 = M )
% 5.13/5.49 => ( N = zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_eq_self_zero
% 5.13/5.49 thf(fact_2330_plus__nat_Oadd__0,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.13/5.49 = N ) ).
% 5.13/5.49
% 5.13/5.49 % plus_nat.add_0
% 5.13/5.49 thf(fact_2331_mult__0,axiom,
% 5.13/5.49 ! [N: nat] :
% 5.13/5.49 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.13/5.49 = zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % mult_0
% 5.13/5.49 thf(fact_2332_nat__mult__eq__cancel__disj,axiom,
% 5.13/5.49 ! [K: nat,M: nat,N: nat] :
% 5.13/5.49 ( ( ( times_times_nat @ K @ M )
% 5.13/5.49 = ( times_times_nat @ K @ N ) )
% 5.13/5.49 = ( ( K = zero_zero_nat )
% 5.13/5.49 | ( M = N ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nat_mult_eq_cancel_disj
% 5.13/5.49 thf(fact_2333_divide__le__0__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.13/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.13/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_0_iff
% 5.13/5.49 thf(fact_2334_divide__le__0__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.13/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.13/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_0_iff
% 5.13/5.49 thf(fact_2335_divide__right__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_right_mono
% 5.13/5.49 thf(fact_2336_divide__right__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_right_mono
% 5.13/5.49 thf(fact_2337_zero__le__divide__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_divide_iff
% 5.13/5.49 thf(fact_2338_zero__le__divide__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_divide_iff
% 5.13/5.49 thf(fact_2339_divide__nonneg__nonneg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_nonneg
% 5.13/5.49 thf(fact_2340_divide__nonneg__nonneg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_nonneg
% 5.13/5.49 thf(fact_2341_divide__nonneg__nonpos,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_nonpos
% 5.13/5.49 thf(fact_2342_divide__nonneg__nonpos,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_nonpos
% 5.13/5.49 thf(fact_2343_divide__nonpos__nonneg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_nonneg
% 5.13/5.49 thf(fact_2344_divide__nonpos__nonneg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_nonneg
% 5.13/5.49 thf(fact_2345_divide__nonpos__nonpos,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_nonpos
% 5.13/5.49 thf(fact_2346_divide__nonpos__nonpos,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_nonpos
% 5.13/5.49 thf(fact_2347_divide__right__mono__neg,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_right_mono_neg
% 5.13/5.49 thf(fact_2348_divide__right__mono__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_right_mono_neg
% 5.13/5.49 thf(fact_2349_divide__strict__right__mono__neg,axiom,
% 5.13/5.49 ! [B: real,A: real,C: real] :
% 5.13/5.49 ( ( ord_less_real @ B @ A )
% 5.13/5.49 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_right_mono_neg
% 5.13/5.49 thf(fact_2350_divide__strict__right__mono__neg,axiom,
% 5.13/5.49 ! [B: rat,A: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_rat @ B @ A )
% 5.13/5.49 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_right_mono_neg
% 5.13/5.49 thf(fact_2351_divide__strict__right__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_right_mono
% 5.13/5.49 thf(fact_2352_divide__strict__right__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_right_mono
% 5.13/5.49 thf(fact_2353_zero__less__divide__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.13/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_divide_iff
% 5.13/5.49 thf(fact_2354_zero__less__divide__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.13/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_divide_iff
% 5.13/5.49 thf(fact_2355_divide__less__cancel,axiom,
% 5.13/5.49 ! [A: real,C: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_real @ A @ B ) )
% 5.13/5.49 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ B @ A ) )
% 5.13/5.49 & ( C != zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_cancel
% 5.13/5.49 thf(fact_2356_divide__less__cancel,axiom,
% 5.13/5.49 ! [A: rat,C: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_rat @ A @ B ) )
% 5.13/5.49 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ B @ A ) )
% 5.13/5.49 & ( C != zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_cancel
% 5.13/5.49 thf(fact_2357_divide__less__0__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.13/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_0_iff
% 5.13/5.49 thf(fact_2358_divide__less__0__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.13/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_0_iff
% 5.13/5.49 thf(fact_2359_divide__pos__pos,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_pos_pos
% 5.13/5.49 thf(fact_2360_divide__pos__pos,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_pos_pos
% 5.13/5.49 thf(fact_2361_divide__pos__neg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_pos_neg
% 5.13/5.49 thf(fact_2362_divide__pos__neg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_pos_neg
% 5.13/5.49 thf(fact_2363_divide__neg__pos,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_neg_pos
% 5.13/5.49 thf(fact_2364_divide__neg__pos,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_neg_pos
% 5.13/5.49 thf(fact_2365_divide__neg__neg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_neg_neg
% 5.13/5.49 thf(fact_2366_divide__neg__neg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_neg_neg
% 5.13/5.49 thf(fact_2367_frac__eq__eq,axiom,
% 5.13/5.49 ! [Y4: complex,Z2: complex,X: complex,W2: complex] :
% 5.13/5.49 ( ( Y4 != zero_zero_complex )
% 5.13/5.49 => ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( ( divide1717551699836669952omplex @ X @ Y4 )
% 5.13/5.49 = ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 5.13/5.49 = ( ( times_times_complex @ X @ Z2 )
% 5.13/5.49 = ( times_times_complex @ W2 @ Y4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_eq_eq
% 5.13/5.49 thf(fact_2368_frac__eq__eq,axiom,
% 5.13/5.49 ! [Y4: real,Z2: real,X: real,W2: real] :
% 5.13/5.49 ( ( Y4 != zero_zero_real )
% 5.13/5.49 => ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( ( divide_divide_real @ X @ Y4 )
% 5.13/5.49 = ( divide_divide_real @ W2 @ Z2 ) )
% 5.13/5.49 = ( ( times_times_real @ X @ Z2 )
% 5.13/5.49 = ( times_times_real @ W2 @ Y4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_eq_eq
% 5.13/5.49 thf(fact_2369_frac__eq__eq,axiom,
% 5.13/5.49 ! [Y4: rat,Z2: rat,X: rat,W2: rat] :
% 5.13/5.49 ( ( Y4 != zero_zero_rat )
% 5.13/5.49 => ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( ( divide_divide_rat @ X @ Y4 )
% 5.13/5.49 = ( divide_divide_rat @ W2 @ Z2 ) )
% 5.13/5.49 = ( ( times_times_rat @ X @ Z2 )
% 5.13/5.49 = ( times_times_rat @ W2 @ Y4 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_eq_eq
% 5.13/5.49 thf(fact_2370_divide__eq__eq,axiom,
% 5.13/5.49 ! [B: complex,C: complex,A: complex] :
% 5.13/5.49 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.13/5.49 = A )
% 5.13/5.49 = ( ( ( C != zero_zero_complex )
% 5.13/5.49 => ( B
% 5.13/5.49 = ( times_times_complex @ A @ C ) ) )
% 5.13/5.49 & ( ( C = zero_zero_complex )
% 5.13/5.49 => ( A = zero_zero_complex ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq
% 5.13/5.49 thf(fact_2371_divide__eq__eq,axiom,
% 5.13/5.49 ! [B: real,C: real,A: real] :
% 5.13/5.49 ( ( ( divide_divide_real @ B @ C )
% 5.13/5.49 = A )
% 5.13/5.49 = ( ( ( C != zero_zero_real )
% 5.13/5.49 => ( B
% 5.13/5.49 = ( times_times_real @ A @ C ) ) )
% 5.13/5.49 & ( ( C = zero_zero_real )
% 5.13/5.49 => ( A = zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq
% 5.13/5.49 thf(fact_2372_divide__eq__eq,axiom,
% 5.13/5.49 ! [B: rat,C: rat,A: rat] :
% 5.13/5.49 ( ( ( divide_divide_rat @ B @ C )
% 5.13/5.49 = A )
% 5.13/5.49 = ( ( ( C != zero_zero_rat )
% 5.13/5.49 => ( B
% 5.13/5.49 = ( times_times_rat @ A @ C ) ) )
% 5.13/5.49 & ( ( C = zero_zero_rat )
% 5.13/5.49 => ( A = zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_eq
% 5.13/5.49 thf(fact_2373_eq__divide__eq,axiom,
% 5.13/5.49 ! [A: complex,B: complex,C: complex] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.13/5.49 = ( ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( times_times_complex @ A @ C )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( C = zero_zero_complex )
% 5.13/5.49 => ( A = zero_zero_complex ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq
% 5.13/5.49 thf(fact_2374_eq__divide__eq,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( times_times_real @ A @ C )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( C = zero_zero_real )
% 5.13/5.49 => ( A = zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq
% 5.13/5.49 thf(fact_2375_eq__divide__eq,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( A
% 5.13/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( times_times_rat @ A @ C )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( C = zero_zero_rat )
% 5.13/5.49 => ( A = zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_eq
% 5.13/5.49 thf(fact_2376_divide__eq__imp,axiom,
% 5.13/5.49 ! [C: complex,B: complex,A: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( B
% 5.13/5.49 = ( times_times_complex @ A @ C ) )
% 5.13/5.49 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.13/5.49 = A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_imp
% 5.13/5.49 thf(fact_2377_divide__eq__imp,axiom,
% 5.13/5.49 ! [C: real,B: real,A: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( B
% 5.13/5.49 = ( times_times_real @ A @ C ) )
% 5.13/5.49 => ( ( divide_divide_real @ B @ C )
% 5.13/5.49 = A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_imp
% 5.13/5.49 thf(fact_2378_divide__eq__imp,axiom,
% 5.13/5.49 ! [C: rat,B: rat,A: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( B
% 5.13/5.49 = ( times_times_rat @ A @ C ) )
% 5.13/5.49 => ( ( divide_divide_rat @ B @ C )
% 5.13/5.49 = A ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_eq_imp
% 5.13/5.49 thf(fact_2379_eq__divide__imp,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( ( times_times_complex @ A @ C )
% 5.13/5.49 = B )
% 5.13/5.49 => ( A
% 5.13/5.49 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_imp
% 5.13/5.49 thf(fact_2380_eq__divide__imp,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( ( times_times_real @ A @ C )
% 5.13/5.49 = B )
% 5.13/5.49 => ( A
% 5.13/5.49 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_imp
% 5.13/5.49 thf(fact_2381_eq__divide__imp,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( ( times_times_rat @ A @ C )
% 5.13/5.49 = B )
% 5.13/5.49 => ( A
% 5.13/5.49 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % eq_divide_imp
% 5.13/5.49 thf(fact_2382_nonzero__divide__eq__eq,axiom,
% 5.13/5.49 ! [C: complex,B: complex,A: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B
% 5.13/5.49 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_eq_eq
% 5.13/5.49 thf(fact_2383_nonzero__divide__eq__eq,axiom,
% 5.13/5.49 ! [C: real,B: real,A: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( ( divide_divide_real @ B @ C )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B
% 5.13/5.49 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_eq_eq
% 5.13/5.49 thf(fact_2384_nonzero__divide__eq__eq,axiom,
% 5.13/5.49 ! [C: rat,B: rat,A: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( ( divide_divide_rat @ B @ C )
% 5.13/5.49 = A )
% 5.13/5.49 = ( B
% 5.13/5.49 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_divide_eq_eq
% 5.13/5.49 thf(fact_2385_nonzero__eq__divide__eq,axiom,
% 5.13/5.49 ! [C: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( C != zero_zero_complex )
% 5.13/5.49 => ( ( A
% 5.13/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.13/5.49 = ( ( times_times_complex @ A @ C )
% 5.13/5.49 = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_eq_divide_eq
% 5.13/5.49 thf(fact_2386_nonzero__eq__divide__eq,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( C != zero_zero_real )
% 5.13/5.49 => ( ( A
% 5.13/5.49 = ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ( times_times_real @ A @ C )
% 5.13/5.49 = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_eq_divide_eq
% 5.13/5.49 thf(fact_2387_nonzero__eq__divide__eq,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( C != zero_zero_rat )
% 5.13/5.49 => ( ( A
% 5.13/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ( times_times_rat @ A @ C )
% 5.13/5.49 = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % nonzero_eq_divide_eq
% 5.13/5.49 thf(fact_2388_right__inverse__eq,axiom,
% 5.13/5.49 ! [B: complex,A: complex] :
% 5.13/5.49 ( ( B != zero_zero_complex )
% 5.13/5.49 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.13/5.49 = one_one_complex )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % right_inverse_eq
% 5.13/5.49 thf(fact_2389_right__inverse__eq,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( B != zero_zero_real )
% 5.13/5.49 => ( ( ( divide_divide_real @ A @ B )
% 5.13/5.49 = one_one_real )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % right_inverse_eq
% 5.13/5.49 thf(fact_2390_right__inverse__eq,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( B != zero_zero_rat )
% 5.13/5.49 => ( ( ( divide_divide_rat @ A @ B )
% 5.13/5.49 = one_one_rat )
% 5.13/5.49 = ( A = B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % right_inverse_eq
% 5.13/5.49 thf(fact_2391_power__eq__imp__eq__base,axiom,
% 5.13/5.49 ! [A: real,N: nat,B: real] :
% 5.13/5.49 ( ( ( power_power_real @ A @ N )
% 5.13/5.49 = ( power_power_real @ B @ N ) )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_imp_eq_base
% 5.13/5.49 thf(fact_2392_power__eq__imp__eq__base,axiom,
% 5.13/5.49 ! [A: rat,N: nat,B: rat] :
% 5.13/5.49 ( ( ( power_power_rat @ A @ N )
% 5.13/5.49 = ( power_power_rat @ B @ N ) )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_imp_eq_base
% 5.13/5.49 thf(fact_2393_power__eq__imp__eq__base,axiom,
% 5.13/5.49 ! [A: nat,N: nat,B: nat] :
% 5.13/5.49 ( ( ( power_power_nat @ A @ N )
% 5.13/5.49 = ( power_power_nat @ B @ N ) )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_imp_eq_base
% 5.13/5.49 thf(fact_2394_power__eq__imp__eq__base,axiom,
% 5.13/5.49 ! [A: int,N: nat,B: int] :
% 5.13/5.49 ( ( ( power_power_int @ A @ N )
% 5.13/5.49 = ( power_power_int @ B @ N ) )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_imp_eq_base
% 5.13/5.49 thf(fact_2395_power__eq__iff__eq__base,axiom,
% 5.13/5.49 ! [N: nat,A: real,B: real] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ( ( power_power_real @ A @ N )
% 5.13/5.49 = ( power_power_real @ B @ N ) )
% 5.13/5.49 = ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_iff_eq_base
% 5.13/5.49 thf(fact_2396_power__eq__iff__eq__base,axiom,
% 5.13/5.49 ! [N: nat,A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ( ( power_power_rat @ A @ N )
% 5.13/5.49 = ( power_power_rat @ B @ N ) )
% 5.13/5.49 = ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_iff_eq_base
% 5.13/5.49 thf(fact_2397_power__eq__iff__eq__base,axiom,
% 5.13/5.49 ! [N: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ( ( power_power_nat @ A @ N )
% 5.13/5.49 = ( power_power_nat @ B @ N ) )
% 5.13/5.49 = ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_iff_eq_base
% 5.13/5.49 thf(fact_2398_power__eq__iff__eq__base,axiom,
% 5.13/5.49 ! [N: nat,A: int,B: int] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ( ( power_power_int @ A @ N )
% 5.13/5.49 = ( power_power_int @ B @ N ) )
% 5.13/5.49 = ( A = B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_eq_iff_eq_base
% 5.13/5.49 thf(fact_2399_lambda__zero,axiom,
% 5.13/5.49 ( ( ^ [H: complex] : zero_zero_complex )
% 5.13/5.49 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.13/5.49
% 5.13/5.49 % lambda_zero
% 5.13/5.49 thf(fact_2400_lambda__zero,axiom,
% 5.13/5.49 ( ( ^ [H: real] : zero_zero_real )
% 5.13/5.49 = ( times_times_real @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % lambda_zero
% 5.13/5.49 thf(fact_2401_lambda__zero,axiom,
% 5.13/5.49 ( ( ^ [H: rat] : zero_zero_rat )
% 5.13/5.49 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % lambda_zero
% 5.13/5.49 thf(fact_2402_lambda__zero,axiom,
% 5.13/5.49 ( ( ^ [H: nat] : zero_zero_nat )
% 5.13/5.49 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % lambda_zero
% 5.13/5.49 thf(fact_2403_lambda__zero,axiom,
% 5.13/5.49 ( ( ^ [H: int] : zero_zero_int )
% 5.13/5.49 = ( times_times_int @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % lambda_zero
% 5.13/5.49 thf(fact_2404_power__strict__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,N: nat] :
% 5.13/5.49 ( ( ord_less_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_mono
% 5.13/5.49 thf(fact_2405_power__strict__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,N: nat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_mono
% 5.13/5.49 thf(fact_2406_power__strict__mono,axiom,
% 5.13/5.49 ! [A: nat,B: nat,N: nat] :
% 5.13/5.49 ( ( ord_less_nat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_mono
% 5.13/5.49 thf(fact_2407_power__strict__mono,axiom,
% 5.13/5.49 ! [A: int,B: int,N: nat] :
% 5.13/5.49 ( ( ord_less_int @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.49 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % power_strict_mono
% 5.13/5.49 thf(fact_2408_field__le__epsilon,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ! [E2: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.13/5.49 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y4 @ E2 ) ) )
% 5.13/5.49 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.13/5.49
% 5.13/5.49 % field_le_epsilon
% 5.13/5.49 thf(fact_2409_field__le__epsilon,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ! [E2: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.13/5.49 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y4 @ E2 ) ) )
% 5.13/5.49 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.13/5.49
% 5.13/5.49 % field_le_epsilon
% 5.13/5.49 thf(fact_2410_frac__le,axiom,
% 5.13/5.49 ! [Y4: real,X: real,W2: real,Z2: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.13/5.49 => ( ( ord_less_eq_real @ W2 @ Z2 )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z2 ) @ ( divide_divide_real @ Y4 @ W2 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_le
% 5.13/5.49 thf(fact_2411_frac__le,axiom,
% 5.13/5.49 ! [Y4: rat,X: rat,W2: rat,Z2: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.13/5.49 => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z2 ) @ ( divide_divide_rat @ Y4 @ W2 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_le
% 5.13/5.49 thf(fact_2412_frac__less,axiom,
% 5.13/5.49 ! [X: real,Y4: real,W2: real,Z2: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_real @ X @ Y4 )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.13/5.49 => ( ( ord_less_eq_real @ W2 @ Z2 )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ X @ Z2 ) @ ( divide_divide_real @ Y4 @ W2 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_less
% 5.13/5.49 thf(fact_2413_frac__less,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat,W2: rat,Z2: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_rat @ X @ Y4 )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.13/5.49 => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z2 ) @ ( divide_divide_rat @ Y4 @ W2 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_less
% 5.13/5.49 thf(fact_2414_frac__less2,axiom,
% 5.13/5.49 ! [X: real,Y4: real,W2: real,Z2: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.13/5.49 => ( ( ord_less_real @ W2 @ Z2 )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ X @ Z2 ) @ ( divide_divide_real @ Y4 @ W2 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_less2
% 5.13/5.49 thf(fact_2415_frac__less2,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat,W2: rat,Z2: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.13/5.49 => ( ( ord_less_rat @ W2 @ Z2 )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z2 ) @ ( divide_divide_rat @ Y4 @ W2 ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % frac_less2
% 5.13/5.49 thf(fact_2416_divide__le__cancel,axiom,
% 5.13/5.49 ! [A: real,C: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ A @ B ) )
% 5.13/5.49 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_cancel
% 5.13/5.49 thf(fact_2417_divide__le__cancel,axiom,
% 5.13/5.49 ! [A: rat,C: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ A @ B ) )
% 5.13/5.49 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_le_cancel
% 5.13/5.49 thf(fact_2418_divide__nonneg__neg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_neg
% 5.13/5.49 thf(fact_2419_divide__nonneg__neg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_neg
% 5.13/5.49 thf(fact_2420_divide__nonneg__pos,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_pos
% 5.13/5.49 thf(fact_2421_divide__nonneg__pos,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonneg_pos
% 5.13/5.49 thf(fact_2422_divide__nonpos__neg,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_neg
% 5.13/5.49 thf(fact_2423_divide__nonpos__neg,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_neg
% 5.13/5.49 thf(fact_2424_divide__nonpos__pos,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_pos
% 5.13/5.49 thf(fact_2425_divide__nonpos__pos,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_nonpos_pos
% 5.13/5.49 thf(fact_2426_divide__strict__left__mono__neg,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_left_mono_neg
% 5.13/5.49 thf(fact_2427_divide__strict__left__mono__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_left_mono_neg
% 5.13/5.49 thf(fact_2428_divide__strict__left__mono,axiom,
% 5.13/5.49 ! [B: real,A: real,C: real] :
% 5.13/5.49 ( ( ord_less_real @ B @ A )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_left_mono
% 5.13/5.49 thf(fact_2429_divide__strict__left__mono,axiom,
% 5.13/5.49 ! [B: rat,A: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_rat @ B @ A )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_strict_left_mono
% 5.13/5.49 thf(fact_2430_mult__imp__less__div__pos,axiom,
% 5.13/5.49 ! [Y4: real,Z2: real,X: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ( ord_less_real @ ( times_times_real @ Z2 @ Y4 ) @ X )
% 5.13/5.49 => ( ord_less_real @ Z2 @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_imp_less_div_pos
% 5.13/5.49 thf(fact_2431_mult__imp__less__div__pos,axiom,
% 5.13/5.49 ! [Y4: rat,Z2: rat,X: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ( ord_less_rat @ ( times_times_rat @ Z2 @ Y4 ) @ X )
% 5.13/5.49 => ( ord_less_rat @ Z2 @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_imp_less_div_pos
% 5.13/5.49 thf(fact_2432_mult__imp__div__pos__less,axiom,
% 5.13/5.49 ! [Y4: real,X: real,Z2: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ( ord_less_real @ X @ ( times_times_real @ Z2 @ Y4 ) )
% 5.13/5.49 => ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_imp_div_pos_less
% 5.13/5.49 thf(fact_2433_mult__imp__div__pos__less,axiom,
% 5.13/5.49 ! [Y4: rat,X: rat,Z2: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z2 @ Y4 ) )
% 5.13/5.49 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_imp_div_pos_less
% 5.13/5.49 thf(fact_2434_pos__less__divide__eq,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % pos_less_divide_eq
% 5.13/5.49 thf(fact_2435_pos__less__divide__eq,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % pos_less_divide_eq
% 5.13/5.49 thf(fact_2436_pos__divide__less__eq,axiom,
% 5.13/5.49 ! [C: real,B: real,A: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.49 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % pos_divide_less_eq
% 5.13/5.49 thf(fact_2437_pos__divide__less__eq,axiom,
% 5.13/5.49 ! [C: rat,B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.49 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % pos_divide_less_eq
% 5.13/5.49 thf(fact_2438_neg__less__divide__eq,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % neg_less_divide_eq
% 5.13/5.49 thf(fact_2439_neg__less__divide__eq,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % neg_less_divide_eq
% 5.13/5.49 thf(fact_2440_neg__divide__less__eq,axiom,
% 5.13/5.49 ! [C: real,B: real,A: real] :
% 5.13/5.49 ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.49 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % neg_divide_less_eq
% 5.13/5.49 thf(fact_2441_neg__divide__less__eq,axiom,
% 5.13/5.49 ! [C: rat,B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.49 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % neg_divide_less_eq
% 5.13/5.49 thf(fact_2442_less__divide__eq,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.13/5.49 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.13/5.49 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq
% 5.13/5.49 thf(fact_2443_less__divide__eq,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.13/5.49 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.13/5.49 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq
% 5.13/5.49 thf(fact_2444_divide__less__eq,axiom,
% 5.13/5.49 ! [B: real,C: real,A: real] :
% 5.13/5.49 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.13/5.49 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.13/5.49 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq
% 5.13/5.49 thf(fact_2445_divide__less__eq,axiom,
% 5.13/5.49 ! [B: rat,C: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.13/5.49 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.13/5.49 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq
% 5.13/5.49 thf(fact_2446_less__divide__eq__1,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_real @ A @ B ) )
% 5.13/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq_1
% 5.13/5.49 thf(fact_2447_less__divide__eq__1,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_rat @ A @ B ) )
% 5.13/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % less_divide_eq_1
% 5.13/5.49 thf(fact_2448_divide__less__eq__1,axiom,
% 5.13/5.49 ! [B: real,A: real] :
% 5.13/5.49 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_real @ B @ A ) )
% 5.13/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_real @ A @ B ) )
% 5.13/5.49 | ( A = zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq_1
% 5.13/5.49 thf(fact_2449_divide__less__eq__1,axiom,
% 5.13/5.49 ! [B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_rat @ B @ A ) )
% 5.13/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_rat @ A @ B ) )
% 5.13/5.49 | ( A = zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_less_eq_1
% 5.13/5.49 thf(fact_2450_add__divide__eq__if__simps_I2_J,axiom,
% 5.13/5.49 ! [Z2: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(2)
% 5.13/5.49 thf(fact_2451_add__divide__eq__if__simps_I2_J,axiom,
% 5.13/5.49 ! [Z2: real,A: real,B: real] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(2)
% 5.13/5.49 thf(fact_2452_add__divide__eq__if__simps_I2_J,axiom,
% 5.13/5.49 ! [Z2: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.13/5.49 = B ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(2)
% 5.13/5.49 thf(fact_2453_add__divide__eq__if__simps_I1_J,axiom,
% 5.13/5.49 ! [Z2: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.13/5.49 = A ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(1)
% 5.13/5.49 thf(fact_2454_add__divide__eq__if__simps_I1_J,axiom,
% 5.13/5.49 ! [Z2: real,A: real,B: real] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.13/5.49 = A ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(1)
% 5.13/5.49 thf(fact_2455_add__divide__eq__if__simps_I1_J,axiom,
% 5.13/5.49 ! [Z2: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.13/5.49 = A ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(1)
% 5.13/5.49 thf(fact_2456_add__frac__eq,axiom,
% 5.13/5.49 ! [Y4: complex,Z2: complex,X: complex,W2: complex] :
% 5.13/5.49 ( ( Y4 != zero_zero_complex )
% 5.13/5.49 => ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z2 ) @ ( times_times_complex @ W2 @ Y4 ) ) @ ( times_times_complex @ Y4 @ Z2 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_frac_eq
% 5.13/5.49 thf(fact_2457_add__frac__eq,axiom,
% 5.13/5.49 ! [Y4: real,Z2: real,X: real,W2: real] :
% 5.13/5.49 ( ( Y4 != zero_zero_real )
% 5.13/5.49 => ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W2 @ Y4 ) ) @ ( times_times_real @ Y4 @ Z2 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_frac_eq
% 5.13/5.49 thf(fact_2458_add__frac__eq,axiom,
% 5.13/5.49 ! [Y4: rat,Z2: rat,X: rat,W2: rat] :
% 5.13/5.49 ( ( Y4 != zero_zero_rat )
% 5.13/5.49 => ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W2 @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z2 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_frac_eq
% 5.13/5.49 thf(fact_2459_add__frac__num,axiom,
% 5.13/5.49 ! [Y4: complex,X: complex,Z2: complex] :
% 5.13/5.49 ( ( Y4 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ Z2 )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z2 @ Y4 ) ) @ Y4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_frac_num
% 5.13/5.49 thf(fact_2460_add__frac__num,axiom,
% 5.13/5.49 ! [Y4: real,X: real,Z2: real] :
% 5.13/5.49 ( ( Y4 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y4 ) @ Z2 )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z2 @ Y4 ) ) @ Y4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_frac_num
% 5.13/5.49 thf(fact_2461_add__frac__num,axiom,
% 5.13/5.49 ! [Y4: rat,X: rat,Z2: rat] :
% 5.13/5.49 ( ( Y4 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y4 ) @ Z2 )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z2 @ Y4 ) ) @ Y4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_frac_num
% 5.13/5.49 thf(fact_2462_add__num__frac,axiom,
% 5.13/5.49 ! [Y4: complex,Z2: complex,X: complex] :
% 5.13/5.49 ( ( Y4 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ X @ Y4 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z2 @ Y4 ) ) @ Y4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_num_frac
% 5.13/5.49 thf(fact_2463_add__num__frac,axiom,
% 5.13/5.49 ! [Y4: real,Z2: real,X: real] :
% 5.13/5.49 ( ( Y4 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ Z2 @ ( divide_divide_real @ X @ Y4 ) )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z2 @ Y4 ) ) @ Y4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_num_frac
% 5.13/5.49 thf(fact_2464_add__num__frac,axiom,
% 5.13/5.49 ! [Y4: rat,Z2: rat,X: rat] :
% 5.13/5.49 ( ( Y4 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ X @ Y4 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z2 @ Y4 ) ) @ Y4 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_num_frac
% 5.13/5.49 thf(fact_2465_add__divide__eq__iff,axiom,
% 5.13/5.49 ! [Z2: complex,X: complex,Y4: complex] :
% 5.13/5.49 ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y4 @ Z2 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z2 ) @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_iff
% 5.13/5.49 thf(fact_2466_add__divide__eq__iff,axiom,
% 5.13/5.49 ! [Z2: real,X: real,Y4: real] :
% 5.13/5.49 ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y4 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z2 ) @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_iff
% 5.13/5.49 thf(fact_2467_add__divide__eq__iff,axiom,
% 5.13/5.49 ! [Z2: rat,X: rat,Y4: rat] :
% 5.13/5.49 ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y4 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z2 ) @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_iff
% 5.13/5.49 thf(fact_2468_divide__add__eq__iff,axiom,
% 5.13/5.49 ! [Z2: complex,X: complex,Y4: complex] :
% 5.13/5.49 ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z2 ) @ Y4 )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_add_eq_iff
% 5.13/5.49 thf(fact_2469_divide__add__eq__iff,axiom,
% 5.13/5.49 ! [Z2: real,X: real,Y4: real] :
% 5.13/5.49 ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z2 ) @ Y4 )
% 5.13/5.49 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_add_eq_iff
% 5.13/5.49 thf(fact_2470_divide__add__eq__iff,axiom,
% 5.13/5.49 ! [Z2: rat,X: rat,Y4: rat] :
% 5.13/5.49 ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z2 ) @ Y4 )
% 5.13/5.49 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_add_eq_iff
% 5.13/5.49 thf(fact_2471_add__divide__eq__if__simps_I4_J,axiom,
% 5.13/5.49 ! [Z2: complex,A: complex,B: complex] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_complex )
% 5.13/5.49 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.13/5.49 = A ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(4)
% 5.13/5.49 thf(fact_2472_add__divide__eq__if__simps_I4_J,axiom,
% 5.13/5.49 ! [Z2: real,A: real,B: real] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_real )
% 5.13/5.49 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.13/5.49 = A ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.13/5.49 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(4)
% 5.13/5.49 thf(fact_2473_add__divide__eq__if__simps_I4_J,axiom,
% 5.13/5.49 ! [Z2: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ( Z2 = zero_zero_rat )
% 5.13/5.49 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.13/5.49 = A ) )
% 5.13/5.49 & ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_divide_eq_if_simps(4)
% 5.13/5.49 thf(fact_2474_diff__frac__eq,axiom,
% 5.13/5.49 ! [Y4: complex,Z2: complex,X: complex,W2: complex] :
% 5.13/5.49 ( ( Y4 != zero_zero_complex )
% 5.13/5.49 => ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ W2 @ Z2 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z2 ) @ ( times_times_complex @ W2 @ Y4 ) ) @ ( times_times_complex @ Y4 @ Z2 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_frac_eq
% 5.13/5.49 thf(fact_2475_diff__frac__eq,axiom,
% 5.13/5.49 ! [Y4: real,Z2: real,X: real,W2: real] :
% 5.13/5.49 ( ( Y4 != zero_zero_real )
% 5.13/5.49 => ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W2 @ Y4 ) ) @ ( times_times_real @ Y4 @ Z2 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_frac_eq
% 5.13/5.49 thf(fact_2476_diff__frac__eq,axiom,
% 5.13/5.49 ! [Y4: rat,Z2: rat,X: rat,W2: rat] :
% 5.13/5.49 ( ( Y4 != zero_zero_rat )
% 5.13/5.49 => ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W2 @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z2 ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_frac_eq
% 5.13/5.49 thf(fact_2477_diff__divide__eq__iff,axiom,
% 5.13/5.49 ! [Z2: complex,X: complex,Y4: complex] :
% 5.13/5.49 ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y4 @ Z2 ) )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z2 ) @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_divide_eq_iff
% 5.13/5.49 thf(fact_2478_diff__divide__eq__iff,axiom,
% 5.13/5.49 ! [Z2: real,X: real,Y4: real] :
% 5.13/5.49 ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y4 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_divide_eq_iff
% 5.13/5.49 thf(fact_2479_diff__divide__eq__iff,axiom,
% 5.13/5.49 ! [Z2: rat,X: rat,Y4: rat] :
% 5.13/5.49 ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y4 @ Z2 ) )
% 5.13/5.49 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % diff_divide_eq_iff
% 5.13/5.49 thf(fact_2480_divide__diff__eq__iff,axiom,
% 5.13/5.49 ! [Z2: complex,X: complex,Y4: complex] :
% 5.13/5.49 ( ( Z2 != zero_zero_complex )
% 5.13/5.49 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z2 ) @ Y4 )
% 5.13/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_diff_eq_iff
% 5.13/5.49 thf(fact_2481_divide__diff__eq__iff,axiom,
% 5.13/5.49 ! [Z2: real,X: real,Y4: real] :
% 5.13/5.49 ( ( Z2 != zero_zero_real )
% 5.13/5.49 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z2 ) @ Y4 )
% 5.13/5.49 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_diff_eq_iff
% 5.13/5.49 thf(fact_2482_divide__diff__eq__iff,axiom,
% 5.13/5.49 ! [Z2: rat,X: rat,Y4: rat] :
% 5.13/5.49 ( ( Z2 != zero_zero_rat )
% 5.13/5.49 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z2 ) @ Y4 )
% 5.13/5.49 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % divide_diff_eq_iff
% 5.13/5.49 thf(fact_2483_zero__le__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_numeral
% 5.13/5.49 thf(fact_2484_zero__le__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_numeral
% 5.13/5.49 thf(fact_2485_zero__le__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_numeral
% 5.13/5.49 thf(fact_2486_zero__le__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_numeral
% 5.13/5.49 thf(fact_2487_not__numeral__le__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_le_zero
% 5.13/5.49 thf(fact_2488_not__numeral__le__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_le_zero
% 5.13/5.49 thf(fact_2489_not__numeral__le__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_le_zero
% 5.13/5.49 thf(fact_2490_not__numeral__le__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_le_zero
% 5.13/5.49 thf(fact_2491_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.13/5.49 thf(fact_2492_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.13/5.49 thf(fact_2493_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.13/5.49 ! [A: nat,B: nat,C: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.13/5.49 thf(fact_2494_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.13/5.49 ! [A: int,B: int,C: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.13/5.49 thf(fact_2495_zero__le__mult__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_mult_iff
% 5.13/5.49 thf(fact_2496_zero__le__mult__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_mult_iff
% 5.13/5.49 thf(fact_2497_zero__le__mult__iff,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.13/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_mult_iff
% 5.13/5.49 thf(fact_2498_mult__nonneg__nonpos2,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos2
% 5.13/5.49 thf(fact_2499_mult__nonneg__nonpos2,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos2
% 5.13/5.49 thf(fact_2500_mult__nonneg__nonpos2,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos2
% 5.13/5.49 thf(fact_2501_mult__nonneg__nonpos2,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos2
% 5.13/5.49 thf(fact_2502_mult__nonpos__nonneg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonneg
% 5.13/5.49 thf(fact_2503_mult__nonpos__nonneg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonneg
% 5.13/5.49 thf(fact_2504_mult__nonpos__nonneg,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonneg
% 5.13/5.49 thf(fact_2505_mult__nonpos__nonneg,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonneg
% 5.13/5.49 thf(fact_2506_mult__nonneg__nonpos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos
% 5.13/5.49 thf(fact_2507_mult__nonneg__nonpos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos
% 5.13/5.49 thf(fact_2508_mult__nonneg__nonpos,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos
% 5.13/5.49 thf(fact_2509_mult__nonneg__nonpos,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonpos
% 5.13/5.49 thf(fact_2510_mult__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonneg
% 5.13/5.49 thf(fact_2511_mult__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonneg
% 5.13/5.49 thf(fact_2512_mult__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonneg
% 5.13/5.49 thf(fact_2513_mult__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonneg_nonneg
% 5.13/5.49 thf(fact_2514_split__mult__neg__le,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.13/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_neg_le
% 5.13/5.49 thf(fact_2515_split__mult__neg__le,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.13/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_neg_le
% 5.13/5.49 thf(fact_2516_split__mult__neg__le,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.13/5.49 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.49 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_neg_le
% 5.13/5.49 thf(fact_2517_split__mult__neg__le,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.13/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_neg_le
% 5.13/5.49 thf(fact_2518_mult__le__0__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.13/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.13/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_le_0_iff
% 5.13/5.49 thf(fact_2519_mult__le__0__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.13/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.13/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_le_0_iff
% 5.13/5.49 thf(fact_2520_mult__le__0__iff,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.13/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.13/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_le_0_iff
% 5.13/5.49 thf(fact_2521_mult__right__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono
% 5.13/5.49 thf(fact_2522_mult__right__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono
% 5.13/5.49 thf(fact_2523_mult__right__mono,axiom,
% 5.13/5.49 ! [A: nat,B: nat,C: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono
% 5.13/5.49 thf(fact_2524_mult__right__mono,axiom,
% 5.13/5.49 ! [A: int,B: int,C: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono
% 5.13/5.49 thf(fact_2525_mult__right__mono__neg,axiom,
% 5.13/5.49 ! [B: real,A: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono_neg
% 5.13/5.49 thf(fact_2526_mult__right__mono__neg,axiom,
% 5.13/5.49 ! [B: rat,A: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono_neg
% 5.13/5.49 thf(fact_2527_mult__right__mono__neg,axiom,
% 5.13/5.49 ! [B: int,A: int,C: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_right_mono_neg
% 5.13/5.49 thf(fact_2528_mult__left__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono
% 5.13/5.49 thf(fact_2529_mult__left__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono
% 5.13/5.49 thf(fact_2530_mult__left__mono,axiom,
% 5.13/5.49 ! [A: nat,B: nat,C: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono
% 5.13/5.49 thf(fact_2531_mult__left__mono,axiom,
% 5.13/5.49 ! [A: int,B: int,C: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono
% 5.13/5.49 thf(fact_2532_mult__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonpos
% 5.13/5.49 thf(fact_2533_mult__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonpos
% 5.13/5.49 thf(fact_2534_mult__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.13/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_nonpos_nonpos
% 5.13/5.49 thf(fact_2535_mult__left__mono__neg,axiom,
% 5.13/5.49 ! [B: real,A: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono_neg
% 5.13/5.49 thf(fact_2536_mult__left__mono__neg,axiom,
% 5.13/5.49 ! [B: rat,A: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono_neg
% 5.13/5.49 thf(fact_2537_mult__left__mono__neg,axiom,
% 5.13/5.49 ! [B: int,A: int,C: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ B @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_left_mono_neg
% 5.13/5.49 thf(fact_2538_split__mult__pos__le,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_pos_le
% 5.13/5.49 thf(fact_2539_split__mult__pos__le,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_pos_le
% 5.13/5.49 thf(fact_2540_split__mult__pos__le,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.13/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.13/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % split_mult_pos_le
% 5.13/5.49 thf(fact_2541_zero__le__square,axiom,
% 5.13/5.49 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_square
% 5.13/5.49 thf(fact_2542_zero__le__square,axiom,
% 5.13/5.49 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_square
% 5.13/5.49 thf(fact_2543_zero__le__square,axiom,
% 5.13/5.49 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_le_square
% 5.13/5.49 thf(fact_2544_mult__mono_H,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono'
% 5.13/5.49 thf(fact_2545_mult__mono_H,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono'
% 5.13/5.49 thf(fact_2546_mult__mono_H,axiom,
% 5.13/5.49 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono'
% 5.13/5.49 thf(fact_2547_mult__mono_H,axiom,
% 5.13/5.49 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono'
% 5.13/5.49 thf(fact_2548_mult__mono,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono
% 5.13/5.49 thf(fact_2549_mult__mono,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono
% 5.13/5.49 thf(fact_2550_mult__mono,axiom,
% 5.13/5.49 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono
% 5.13/5.49 thf(fact_2551_mult__mono,axiom,
% 5.13/5.49 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ C @ D )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_mono
% 5.13/5.49 thf(fact_2552_not__numeral__less__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_less_zero
% 5.13/5.49 thf(fact_2553_not__numeral__less__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_less_zero
% 5.13/5.49 thf(fact_2554_not__numeral__less__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_less_zero
% 5.13/5.49 thf(fact_2555_not__numeral__less__zero,axiom,
% 5.13/5.49 ! [N: num] :
% 5.13/5.49 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % not_numeral_less_zero
% 5.13/5.49 thf(fact_2556_zero__less__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_numeral
% 5.13/5.49 thf(fact_2557_zero__less__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_numeral
% 5.13/5.49 thf(fact_2558_zero__less__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_numeral
% 5.13/5.49 thf(fact_2559_zero__less__numeral,axiom,
% 5.13/5.49 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.13/5.49
% 5.13/5.49 % zero_less_numeral
% 5.13/5.49 thf(fact_2560_not__one__le__zero,axiom,
% 5.13/5.49 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % not_one_le_zero
% 5.13/5.49 thf(fact_2561_not__one__le__zero,axiom,
% 5.13/5.49 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % not_one_le_zero
% 5.13/5.49 thf(fact_2562_not__one__le__zero,axiom,
% 5.13/5.49 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.13/5.49
% 5.13/5.49 % not_one_le_zero
% 5.13/5.49 thf(fact_2563_not__one__le__zero,axiom,
% 5.13/5.49 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % not_one_le_zero
% 5.13/5.49 thf(fact_2564_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.13/5.49
% 5.13/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.13/5.49 thf(fact_2565_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.13/5.49
% 5.13/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.13/5.49 thf(fact_2566_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.13/5.49
% 5.13/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.13/5.49 thf(fact_2567_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.13/5.49
% 5.13/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.13/5.49 thf(fact_2568_zero__less__one__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.13/5.49
% 5.13/5.49 % zero_less_one_class.zero_le_one
% 5.13/5.49 thf(fact_2569_zero__less__one__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.13/5.49
% 5.13/5.49 % zero_less_one_class.zero_le_one
% 5.13/5.49 thf(fact_2570_zero__less__one__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.13/5.49
% 5.13/5.49 % zero_less_one_class.zero_le_one
% 5.13/5.49 thf(fact_2571_zero__less__one__class_Ozero__le__one,axiom,
% 5.13/5.49 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.13/5.49
% 5.13/5.49 % zero_less_one_class.zero_le_one
% 5.13/5.49 thf(fact_2572_add__nonpos__eq__0__iff,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.13/5.49 => ( ( ( plus_plus_real @ X @ Y4 )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( X = zero_zero_real )
% 5.13/5.49 & ( Y4 = zero_zero_real ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_eq_0_iff
% 5.13/5.49 thf(fact_2573_add__nonpos__eq__0__iff,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.13/5.49 => ( ( ( plus_plus_rat @ X @ Y4 )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( X = zero_zero_rat )
% 5.13/5.49 & ( Y4 = zero_zero_rat ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_eq_0_iff
% 5.13/5.49 thf(fact_2574_add__nonpos__eq__0__iff,axiom,
% 5.13/5.49 ! [X: nat,Y4: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.13/5.49 => ( ( ord_less_eq_nat @ Y4 @ zero_zero_nat )
% 5.13/5.49 => ( ( ( plus_plus_nat @ X @ Y4 )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( X = zero_zero_nat )
% 5.13/5.49 & ( Y4 = zero_zero_nat ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_eq_0_iff
% 5.13/5.49 thf(fact_2575_add__nonpos__eq__0__iff,axiom,
% 5.13/5.49 ! [X: int,Y4: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ Y4 @ zero_zero_int )
% 5.13/5.49 => ( ( ( plus_plus_int @ X @ Y4 )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( ( X = zero_zero_int )
% 5.13/5.49 & ( Y4 = zero_zero_int ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_eq_0_iff
% 5.13/5.49 thf(fact_2576_add__nonneg__eq__0__iff,axiom,
% 5.13/5.49 ! [X: real,Y4: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.49 => ( ( ( plus_plus_real @ X @ Y4 )
% 5.13/5.49 = zero_zero_real )
% 5.13/5.49 = ( ( X = zero_zero_real )
% 5.13/5.49 & ( Y4 = zero_zero_real ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_eq_0_iff
% 5.13/5.49 thf(fact_2577_add__nonneg__eq__0__iff,axiom,
% 5.13/5.49 ! [X: rat,Y4: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.49 => ( ( ( plus_plus_rat @ X @ Y4 )
% 5.13/5.49 = zero_zero_rat )
% 5.13/5.49 = ( ( X = zero_zero_rat )
% 5.13/5.49 & ( Y4 = zero_zero_rat ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_eq_0_iff
% 5.13/5.49 thf(fact_2578_add__nonneg__eq__0__iff,axiom,
% 5.13/5.49 ! [X: nat,Y4: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.13/5.49 => ( ( ( plus_plus_nat @ X @ Y4 )
% 5.13/5.49 = zero_zero_nat )
% 5.13/5.49 = ( ( X = zero_zero_nat )
% 5.13/5.49 & ( Y4 = zero_zero_nat ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_eq_0_iff
% 5.13/5.49 thf(fact_2579_add__nonneg__eq__0__iff,axiom,
% 5.13/5.49 ! [X: int,Y4: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.49 => ( ( ( plus_plus_int @ X @ Y4 )
% 5.13/5.49 = zero_zero_int )
% 5.13/5.49 = ( ( X = zero_zero_int )
% 5.13/5.49 & ( Y4 = zero_zero_int ) ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_eq_0_iff
% 5.13/5.49 thf(fact_2580_add__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_nonpos
% 5.13/5.49 thf(fact_2581_add__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_nonpos
% 5.13/5.49 thf(fact_2582_add__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.49 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.13/5.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_nonpos
% 5.13/5.49 thf(fact_2583_add__nonpos__nonpos,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.13/5.49 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonpos_nonpos
% 5.13/5.49 thf(fact_2584_add__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_nonneg
% 5.13/5.49 thf(fact_2585_add__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_nonneg
% 5.13/5.49 thf(fact_2586_add__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_nonneg
% 5.13/5.49 thf(fact_2587_add__nonneg__nonneg,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_nonneg_nonneg
% 5.13/5.49 thf(fact_2588_add__increasing2,axiom,
% 5.13/5.49 ! [C: real,B: real,A: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.49 => ( ( ord_less_eq_real @ B @ A )
% 5.13/5.49 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing2
% 5.13/5.49 thf(fact_2589_add__increasing2,axiom,
% 5.13/5.49 ! [C: rat,B: rat,A: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.49 => ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.49 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing2
% 5.13/5.49 thf(fact_2590_add__increasing2,axiom,
% 5.13/5.49 ! [C: nat,B: nat,A: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.49 => ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.49 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing2
% 5.13/5.49 thf(fact_2591_add__increasing2,axiom,
% 5.13/5.49 ! [C: int,B: int,A: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.49 => ( ( ord_less_eq_int @ B @ A )
% 5.13/5.49 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing2
% 5.13/5.49 thf(fact_2592_add__decreasing2,axiom,
% 5.13/5.49 ! [C: real,A: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ A @ B )
% 5.13/5.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing2
% 5.13/5.49 thf(fact_2593_add__decreasing2,axiom,
% 5.13/5.49 ! [C: rat,A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.49 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing2
% 5.13/5.49 thf(fact_2594_add__decreasing2,axiom,
% 5.13/5.49 ! [C: nat,A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.13/5.49 => ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing2
% 5.13/5.49 thf(fact_2595_add__decreasing2,axiom,
% 5.13/5.49 ! [C: int,A: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ A @ B )
% 5.13/5.49 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing2
% 5.13/5.49 thf(fact_2596_add__increasing,axiom,
% 5.13/5.49 ! [A: real,B: real,C: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_eq_real @ B @ C )
% 5.13/5.49 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing
% 5.13/5.49 thf(fact_2597_add__increasing,axiom,
% 5.13/5.49 ! [A: rat,B: rat,C: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.49 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing
% 5.13/5.49 thf(fact_2598_add__increasing,axiom,
% 5.13/5.49 ! [A: nat,B: nat,C: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.49 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing
% 5.13/5.49 thf(fact_2599_add__increasing,axiom,
% 5.13/5.49 ! [A: int,B: int,C: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.49 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_increasing
% 5.13/5.49 thf(fact_2600_add__decreasing,axiom,
% 5.13/5.49 ! [A: real,C: real,B: real] :
% 5.13/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_eq_real @ C @ B )
% 5.13/5.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing
% 5.13/5.49 thf(fact_2601_add__decreasing,axiom,
% 5.13/5.49 ! [A: rat,C: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_eq_rat @ C @ B )
% 5.13/5.49 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing
% 5.13/5.49 thf(fact_2602_add__decreasing,axiom,
% 5.13/5.49 ! [A: nat,C: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.49 => ( ( ord_less_eq_nat @ C @ B )
% 5.13/5.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing
% 5.13/5.49 thf(fact_2603_add__decreasing,axiom,
% 5.13/5.49 ! [A: int,C: int,B: int] :
% 5.13/5.49 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_eq_int @ C @ B )
% 5.13/5.49 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % add_decreasing
% 5.13/5.49 thf(fact_2604_mult__neg__neg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_neg
% 5.13/5.49 thf(fact_2605_mult__neg__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_neg
% 5.13/5.49 thf(fact_2606_mult__neg__neg,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.13/5.49 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_neg
% 5.13/5.49 thf(fact_2607_not__square__less__zero,axiom,
% 5.13/5.49 ! [A: real] :
% 5.13/5.49 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.13/5.49
% 5.13/5.49 % not_square_less_zero
% 5.13/5.49 thf(fact_2608_not__square__less__zero,axiom,
% 5.13/5.49 ! [A: rat] :
% 5.13/5.49 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.13/5.49
% 5.13/5.49 % not_square_less_zero
% 5.13/5.49 thf(fact_2609_not__square__less__zero,axiom,
% 5.13/5.49 ! [A: int] :
% 5.13/5.49 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.13/5.49
% 5.13/5.49 % not_square_less_zero
% 5.13/5.49 thf(fact_2610_mult__less__0__iff,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.13/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.13/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_less_0_iff
% 5.13/5.49 thf(fact_2611_mult__less__0__iff,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.13/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.13/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_less_0_iff
% 5.13/5.49 thf(fact_2612_mult__less__0__iff,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.13/5.49 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.49 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.13/5.49 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.49 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_less_0_iff
% 5.13/5.49 thf(fact_2613_mult__neg__pos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_pos
% 5.13/5.49 thf(fact_2614_mult__neg__pos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_pos
% 5.13/5.49 thf(fact_2615_mult__neg__pos,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_pos
% 5.13/5.49 thf(fact_2616_mult__neg__pos,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_neg_pos
% 5.13/5.49 thf(fact_2617_mult__pos__neg,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg
% 5.13/5.49 thf(fact_2618_mult__pos__neg,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg
% 5.13/5.49 thf(fact_2619_mult__pos__neg,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.13/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg
% 5.13/5.49 thf(fact_2620_mult__pos__neg,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.13/5.49 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg
% 5.13/5.49 thf(fact_2621_mult__pos__pos,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.49 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_pos
% 5.13/5.49 thf(fact_2622_mult__pos__pos,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.49 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_pos
% 5.13/5.49 thf(fact_2623_mult__pos__pos,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.49 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_pos
% 5.13/5.49 thf(fact_2624_mult__pos__pos,axiom,
% 5.13/5.49 ! [A: int,B: int] :
% 5.13/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.49 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_pos
% 5.13/5.49 thf(fact_2625_mult__pos__neg2,axiom,
% 5.13/5.49 ! [A: real,B: real] :
% 5.13/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.13/5.49 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg2
% 5.13/5.49 thf(fact_2626_mult__pos__neg2,axiom,
% 5.13/5.49 ! [A: rat,B: rat] :
% 5.13/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.13/5.49 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg2
% 5.13/5.49 thf(fact_2627_mult__pos__neg2,axiom,
% 5.13/5.49 ! [A: nat,B: nat] :
% 5.13/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.49 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.13/5.49 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.13/5.49
% 5.13/5.49 % mult_pos_neg2
% 5.13/5.50 thf(fact_2628_mult__pos__neg2,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_pos_neg2
% 5.13/5.50 thf(fact_2629_zero__less__mult__iff,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.13/5.50 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.50 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_iff
% 5.13/5.50 thf(fact_2630_zero__less__mult__iff,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.13/5.50 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.50 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_iff
% 5.13/5.50 thf(fact_2631_zero__less__mult__iff,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.13/5.50 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.50 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_iff
% 5.13/5.50 thf(fact_2632_zero__less__mult__pos,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos
% 5.13/5.50 thf(fact_2633_zero__less__mult__pos,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos
% 5.13/5.50 thf(fact_2634_zero__less__mult__pos,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos
% 5.13/5.50 thf(fact_2635_zero__less__mult__pos,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos
% 5.13/5.50 thf(fact_2636_zero__less__mult__pos2,axiom,
% 5.13/5.50 ! [B: real,A: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos2
% 5.13/5.50 thf(fact_2637_zero__less__mult__pos2,axiom,
% 5.13/5.50 ! [B: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos2
% 5.13/5.50 thf(fact_2638_zero__less__mult__pos2,axiom,
% 5.13/5.50 ! [B: nat,A: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos2
% 5.13/5.50 thf(fact_2639_zero__less__mult__pos2,axiom,
% 5.13/5.50 ! [B: int,A: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_mult_pos2
% 5.13/5.50 thf(fact_2640_mult__less__cancel__left__neg,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ord_less_real @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_neg
% 5.13/5.50 thf(fact_2641_mult__less__cancel__left__neg,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_neg
% 5.13/5.50 thf(fact_2642_mult__less__cancel__left__neg,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ord_less_int @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_neg
% 5.13/5.50 thf(fact_2643_mult__less__cancel__left__pos,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_pos
% 5.13/5.50 thf(fact_2644_mult__less__cancel__left__pos,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_pos
% 5.13/5.50 thf(fact_2645_mult__less__cancel__left__pos,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ord_less_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_pos
% 5.13/5.50 thf(fact_2646_mult__strict__left__mono__neg,axiom,
% 5.13/5.50 ! [B: real,A: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ B @ A )
% 5.13/5.50 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono_neg
% 5.13/5.50 thf(fact_2647_mult__strict__left__mono__neg,axiom,
% 5.13/5.50 ! [B: rat,A: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ B @ A )
% 5.13/5.50 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono_neg
% 5.13/5.50 thf(fact_2648_mult__strict__left__mono__neg,axiom,
% 5.13/5.50 ! [B: int,A: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ B @ A )
% 5.13/5.50 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono_neg
% 5.13/5.50 thf(fact_2649_mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono
% 5.13/5.50 thf(fact_2650_mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono
% 5.13/5.50 thf(fact_2651_mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono
% 5.13/5.50 thf(fact_2652_mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_left_mono
% 5.13/5.50 thf(fact_2653_mult__less__cancel__left__disj,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 & ( ord_less_real @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_disj
% 5.13/5.50 thf(fact_2654_mult__less__cancel__left__disj,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 & ( ord_less_rat @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_disj
% 5.13/5.50 thf(fact_2655_mult__less__cancel__left__disj,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 & ( ord_less_int @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left_disj
% 5.13/5.50 thf(fact_2656_mult__strict__right__mono__neg,axiom,
% 5.13/5.50 ! [B: real,A: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ B @ A )
% 5.13/5.50 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono_neg
% 5.13/5.50 thf(fact_2657_mult__strict__right__mono__neg,axiom,
% 5.13/5.50 ! [B: rat,A: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ B @ A )
% 5.13/5.50 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono_neg
% 5.13/5.50 thf(fact_2658_mult__strict__right__mono__neg,axiom,
% 5.13/5.50 ! [B: int,A: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ B @ A )
% 5.13/5.50 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono_neg
% 5.13/5.50 thf(fact_2659_mult__strict__right__mono,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono
% 5.13/5.50 thf(fact_2660_mult__strict__right__mono,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono
% 5.13/5.50 thf(fact_2661_mult__strict__right__mono,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono
% 5.13/5.50 thf(fact_2662_mult__strict__right__mono,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_right_mono
% 5.13/5.50 thf(fact_2663_mult__less__cancel__right__disj,axiom,
% 5.13/5.50 ! [A: real,C: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 & ( ord_less_real @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right_disj
% 5.13/5.50 thf(fact_2664_mult__less__cancel__right__disj,axiom,
% 5.13/5.50 ! [A: rat,C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 & ( ord_less_rat @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right_disj
% 5.13/5.50 thf(fact_2665_mult__less__cancel__right__disj,axiom,
% 5.13/5.50 ! [A: int,C: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 & ( ord_less_int @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right_disj
% 5.13/5.50 thf(fact_2666_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.13/5.50 thf(fact_2667_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.13/5.50 thf(fact_2668_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.13/5.50 thf(fact_2669_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.13/5.50 thf(fact_2670_le__iff__diff__le__0,axiom,
% 5.13/5.50 ( ord_less_eq_real
% 5.13/5.50 = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_iff_diff_le_0
% 5.13/5.50 thf(fact_2671_le__iff__diff__le__0,axiom,
% 5.13/5.50 ( ord_less_eq_rat
% 5.13/5.50 = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_iff_diff_le_0
% 5.13/5.50 thf(fact_2672_le__iff__diff__le__0,axiom,
% 5.13/5.50 ( ord_less_eq_int
% 5.13/5.50 = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_iff_diff_le_0
% 5.13/5.50 thf(fact_2673_less__numeral__extra_I1_J,axiom,
% 5.13/5.50 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.13/5.50
% 5.13/5.50 % less_numeral_extra(1)
% 5.13/5.50 thf(fact_2674_less__numeral__extra_I1_J,axiom,
% 5.13/5.50 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.13/5.50
% 5.13/5.50 % less_numeral_extra(1)
% 5.13/5.50 thf(fact_2675_less__numeral__extra_I1_J,axiom,
% 5.13/5.50 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.13/5.50
% 5.13/5.50 % less_numeral_extra(1)
% 5.13/5.50 thf(fact_2676_less__numeral__extra_I1_J,axiom,
% 5.13/5.50 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.13/5.50
% 5.13/5.50 % less_numeral_extra(1)
% 5.13/5.50 thf(fact_2677_zero__less__one,axiom,
% 5.13/5.50 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.13/5.50
% 5.13/5.50 % zero_less_one
% 5.13/5.50 thf(fact_2678_zero__less__one,axiom,
% 5.13/5.50 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.13/5.50
% 5.13/5.50 % zero_less_one
% 5.13/5.50 thf(fact_2679_zero__less__one,axiom,
% 5.13/5.50 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.13/5.50
% 5.13/5.50 % zero_less_one
% 5.13/5.50 thf(fact_2680_zero__less__one,axiom,
% 5.13/5.50 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.13/5.50
% 5.13/5.50 % zero_less_one
% 5.13/5.50 thf(fact_2681_not__one__less__zero,axiom,
% 5.13/5.50 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.13/5.50
% 5.13/5.50 % not_one_less_zero
% 5.13/5.50 thf(fact_2682_not__one__less__zero,axiom,
% 5.13/5.50 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.13/5.50
% 5.13/5.50 % not_one_less_zero
% 5.13/5.50 thf(fact_2683_not__one__less__zero,axiom,
% 5.13/5.50 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.13/5.50
% 5.13/5.50 % not_one_less_zero
% 5.13/5.50 thf(fact_2684_not__one__less__zero,axiom,
% 5.13/5.50 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.13/5.50
% 5.13/5.50 % not_one_less_zero
% 5.13/5.50 thf(fact_2685_add__less__zeroD,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_real @ ( plus_plus_real @ X @ Y4 ) @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.13/5.50 | ( ord_less_real @ Y4 @ zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_less_zeroD
% 5.13/5.50 thf(fact_2686_add__less__zeroD,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y4 ) @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.13/5.50 | ( ord_less_rat @ Y4 @ zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_less_zeroD
% 5.13/5.50 thf(fact_2687_add__less__zeroD,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_int @ ( plus_plus_int @ X @ Y4 ) @ zero_zero_int )
% 5.13/5.50 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.13/5.50 | ( ord_less_int @ Y4 @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_less_zeroD
% 5.13/5.50 thf(fact_2688_add__neg__neg,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_neg
% 5.13/5.50 thf(fact_2689_add__neg__neg,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_neg
% 5.13/5.50 thf(fact_2690_add__neg__neg,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.13/5.50 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.13/5.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_neg
% 5.13/5.50 thf(fact_2691_add__neg__neg,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.50 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_neg
% 5.13/5.50 thf(fact_2692_add__pos__pos,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_pos
% 5.13/5.50 thf(fact_2693_add__pos__pos,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_pos
% 5.13/5.50 thf(fact_2694_add__pos__pos,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_pos
% 5.13/5.50 thf(fact_2695_add__pos__pos,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_pos
% 5.13/5.50 thf(fact_2696_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ~ ! [C3: nat] :
% 5.13/5.50 ( ( B
% 5.13/5.50 = ( plus_plus_nat @ A @ C3 ) )
% 5.13/5.50 => ( C3 = zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % canonically_ordered_monoid_add_class.lessE
% 5.13/5.50 thf(fact_2697_pos__add__strict,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ B @ C )
% 5.13/5.50 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_add_strict
% 5.13/5.50 thf(fact_2698_pos__add__strict,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ B @ C )
% 5.13/5.50 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_add_strict
% 5.13/5.50 thf(fact_2699_pos__add__strict,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ B @ C )
% 5.13/5.50 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_add_strict
% 5.13/5.50 thf(fact_2700_pos__add__strict,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ B @ C )
% 5.13/5.50 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_add_strict
% 5.13/5.50 thf(fact_2701_less__iff__diff__less__0,axiom,
% 5.13/5.50 ( ord_less_real
% 5.13/5.50 = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_iff_diff_less_0
% 5.13/5.50 thf(fact_2702_less__iff__diff__less__0,axiom,
% 5.13/5.50 ( ord_less_rat
% 5.13/5.50 = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_iff_diff_less_0
% 5.13/5.50 thf(fact_2703_less__iff__diff__less__0,axiom,
% 5.13/5.50 ( ord_less_int
% 5.13/5.50 = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_iff_diff_less_0
% 5.13/5.50 thf(fact_2704_power__mono,axiom,
% 5.13/5.50 ! [A: real,B: real,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_mono
% 5.13/5.50 thf(fact_2705_power__mono,axiom,
% 5.13/5.50 ! [A: rat,B: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_mono
% 5.13/5.50 thf(fact_2706_power__mono,axiom,
% 5.13/5.50 ! [A: nat,B: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_mono
% 5.13/5.50 thf(fact_2707_power__mono,axiom,
% 5.13/5.50 ! [A: int,B: int,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_mono
% 5.13/5.50 thf(fact_2708_zero__le__power,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power
% 5.13/5.50 thf(fact_2709_zero__le__power,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power
% 5.13/5.50 thf(fact_2710_zero__le__power,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power
% 5.13/5.50 thf(fact_2711_zero__le__power,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power
% 5.13/5.50 thf(fact_2712_zero__less__power,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_power
% 5.13/5.50 thf(fact_2713_zero__less__power,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_power
% 5.13/5.50 thf(fact_2714_zero__less__power,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_power
% 5.13/5.50 thf(fact_2715_zero__less__power,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_power
% 5.13/5.50 thf(fact_2716_power__0,axiom,
% 5.13/5.50 ! [A: rat] :
% 5.13/5.50 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.13/5.50 = one_one_rat ) ).
% 5.13/5.50
% 5.13/5.50 % power_0
% 5.13/5.50 thf(fact_2717_power__0,axiom,
% 5.13/5.50 ! [A: nat] :
% 5.13/5.50 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.13/5.50 = one_one_nat ) ).
% 5.13/5.50
% 5.13/5.50 % power_0
% 5.13/5.50 thf(fact_2718_power__0,axiom,
% 5.13/5.50 ! [A: real] :
% 5.13/5.50 ( ( power_power_real @ A @ zero_zero_nat )
% 5.13/5.50 = one_one_real ) ).
% 5.13/5.50
% 5.13/5.50 % power_0
% 5.13/5.50 thf(fact_2719_power__0,axiom,
% 5.13/5.50 ! [A: int] :
% 5.13/5.50 ( ( power_power_int @ A @ zero_zero_nat )
% 5.13/5.50 = one_one_int ) ).
% 5.13/5.50
% 5.13/5.50 % power_0
% 5.13/5.50 thf(fact_2720_power__0,axiom,
% 5.13/5.50 ! [A: complex] :
% 5.13/5.50 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.13/5.50 = one_one_complex ) ).
% 5.13/5.50
% 5.13/5.50 % power_0
% 5.13/5.50 thf(fact_2721_Ex__less__Suc2,axiom,
% 5.13/5.50 ! [N: nat,P: nat > $o] :
% 5.13/5.50 ( ( ? [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.13/5.50 & ( P @ I4 ) ) )
% 5.13/5.50 = ( ( P @ zero_zero_nat )
% 5.13/5.50 | ? [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ N )
% 5.13/5.50 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Ex_less_Suc2
% 5.13/5.50 thf(fact_2722_gr0__conv__Suc,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 = ( ? [M2: nat] :
% 5.13/5.50 ( N
% 5.13/5.50 = ( suc @ M2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % gr0_conv_Suc
% 5.13/5.50 thf(fact_2723_All__less__Suc2,axiom,
% 5.13/5.50 ! [N: nat,P: nat > $o] :
% 5.13/5.50 ( ( ! [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.13/5.50 => ( P @ I4 ) ) )
% 5.13/5.50 = ( ( P @ zero_zero_nat )
% 5.13/5.50 & ! [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ N )
% 5.13/5.50 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % All_less_Suc2
% 5.13/5.50 thf(fact_2724_gr0__implies__Suc,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ? [M4: nat] :
% 5.13/5.50 ( N
% 5.13/5.50 = ( suc @ M4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % gr0_implies_Suc
% 5.13/5.50 thf(fact_2725_less__Suc__eq__0__disj,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.13/5.50 = ( ( M = zero_zero_nat )
% 5.13/5.50 | ? [J3: nat] :
% 5.13/5.50 ( ( M
% 5.13/5.50 = ( suc @ J3 ) )
% 5.13/5.50 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_Suc_eq_0_disj
% 5.13/5.50 thf(fact_2726_one__is__add,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( suc @ zero_zero_nat )
% 5.13/5.50 = ( plus_plus_nat @ M @ N ) )
% 5.13/5.50 = ( ( ( M
% 5.13/5.50 = ( suc @ zero_zero_nat ) )
% 5.13/5.50 & ( N = zero_zero_nat ) )
% 5.13/5.50 | ( ( M = zero_zero_nat )
% 5.13/5.50 & ( N
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % one_is_add
% 5.13/5.50 thf(fact_2727_add__is__1,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( plus_plus_nat @ M @ N )
% 5.13/5.50 = ( suc @ zero_zero_nat ) )
% 5.13/5.50 = ( ( ( M
% 5.13/5.50 = ( suc @ zero_zero_nat ) )
% 5.13/5.50 & ( N = zero_zero_nat ) )
% 5.13/5.50 | ( ( M = zero_zero_nat )
% 5.13/5.50 & ( N
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_is_1
% 5.13/5.50 thf(fact_2728_ex__least__nat__le,axiom,
% 5.13/5.50 ! [P: nat > $o,N: nat] :
% 5.13/5.50 ( ( P @ N )
% 5.13/5.50 => ( ~ ( P @ zero_zero_nat )
% 5.13/5.50 => ? [K2: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ K2 @ N )
% 5.13/5.50 & ! [I: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I @ K2 )
% 5.13/5.50 => ~ ( P @ I ) )
% 5.13/5.50 & ( P @ K2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_least_nat_le
% 5.13/5.50 thf(fact_2729_option_Osize_I4_J,axiom,
% 5.13/5.50 ! [X22: nat] :
% 5.13/5.50 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % option.size(4)
% 5.13/5.50 thf(fact_2730_option_Osize_I4_J,axiom,
% 5.13/5.50 ! [X22: product_prod_nat_nat] :
% 5.13/5.50 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % option.size(4)
% 5.13/5.50 thf(fact_2731_option_Osize_I4_J,axiom,
% 5.13/5.50 ! [X22: num] :
% 5.13/5.50 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % option.size(4)
% 5.13/5.50 thf(fact_2732_less__imp__add__positive,axiom,
% 5.13/5.50 ! [I2: nat,J: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.50 => ? [K2: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.13/5.50 & ( ( plus_plus_nat @ I2 @ K2 )
% 5.13/5.50 = J ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_imp_add_positive
% 5.13/5.50 thf(fact_2733_option_Osize_I3_J,axiom,
% 5.13/5.50 ( ( size_size_option_nat @ none_nat )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % option.size(3)
% 5.13/5.50 thf(fact_2734_option_Osize_I3_J,axiom,
% 5.13/5.50 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % option.size(3)
% 5.13/5.50 thf(fact_2735_option_Osize_I3_J,axiom,
% 5.13/5.50 ( ( size_size_option_num @ none_num )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % option.size(3)
% 5.13/5.50 thf(fact_2736_diff__less,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % diff_less
% 5.13/5.50 thf(fact_2737_mult__less__mono1,axiom,
% 5.13/5.50 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_mono1
% 5.13/5.50 thf(fact_2738_mult__less__mono2,axiom,
% 5.13/5.50 ! [I2: nat,J: nat,K: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I2 @ J )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_mono2
% 5.13/5.50 thf(fact_2739_nat__mult__less__cancel1,axiom,
% 5.13/5.50 ! [K: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.50 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.50 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_mult_less_cancel1
% 5.13/5.50 thf(fact_2740_nat__mult__eq__cancel1,axiom,
% 5.13/5.50 ! [K: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.50 => ( ( ( times_times_nat @ K @ M )
% 5.13/5.50 = ( times_times_nat @ K @ N ) )
% 5.13/5.50 = ( M = N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_mult_eq_cancel1
% 5.13/5.50 thf(fact_2741_One__nat__def,axiom,
% 5.13/5.50 ( one_one_nat
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % One_nat_def
% 5.13/5.50 thf(fact_2742_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( divide_divide_nat @ M @ N )
% 5.13/5.50 = zero_zero_nat )
% 5.13/5.50 = ( ( ord_less_nat @ M @ N )
% 5.13/5.50 | ( N = zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Euclidean_Division.div_eq_0_iff
% 5.13/5.50 thf(fact_2743_diff__add__0,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.13/5.50 = zero_zero_nat ) ).
% 5.13/5.50
% 5.13/5.50 % diff_add_0
% 5.13/5.50 thf(fact_2744_nat__power__less__imp__less,axiom,
% 5.13/5.50 ! [I2: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.13/5.50 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 5.13/5.50 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_power_less_imp_less
% 5.13/5.50 thf(fact_2745_mult__eq__self__implies__10,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( M
% 5.13/5.50 = ( times_times_nat @ M @ N ) )
% 5.13/5.50 => ( ( N = one_one_nat )
% 5.13/5.50 | ( M = zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_eq_self_implies_10
% 5.13/5.50 thf(fact_2746_vebt__insert_Osimps_I2_J,axiom,
% 5.13/5.50 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.13/5.50 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) @ X )
% 5.13/5.50 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_insert.simps(2)
% 5.13/5.50 thf(fact_2747_field__le__mult__one__interval,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ! [Z: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.13/5.50 => ( ( ord_less_real @ Z @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ Y4 ) ) )
% 5.13/5.50 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.13/5.50
% 5.13/5.50 % field_le_mult_one_interval
% 5.13/5.50 thf(fact_2748_field__le__mult__one__interval,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ! [Z: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.13/5.50 => ( ( ord_less_rat @ Z @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ Y4 ) ) )
% 5.13/5.50 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.13/5.50
% 5.13/5.50 % field_le_mult_one_interval
% 5.13/5.50 thf(fact_2749_divide__le__eq,axiom,
% 5.13/5.50 ! [B: real,C: real,A: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_le_eq
% 5.13/5.50 thf(fact_2750_divide__le__eq,axiom,
% 5.13/5.50 ! [B: rat,C: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_le_eq
% 5.13/5.50 thf(fact_2751_le__divide__eq,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_divide_eq
% 5.13/5.50 thf(fact_2752_le__divide__eq,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_divide_eq
% 5.13/5.50 thf(fact_2753_divide__left__mono,axiom,
% 5.13/5.50 ! [B: real,A: real,C: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ B @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.50 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_left_mono
% 5.13/5.50 thf(fact_2754_divide__left__mono,axiom,
% 5.13/5.50 ! [B: rat,A: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ B @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.50 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_left_mono
% 5.13/5.50 thf(fact_2755_neg__divide__le__eq,axiom,
% 5.13/5.50 ! [C: real,B: real,A: real] :
% 5.13/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.50 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % neg_divide_le_eq
% 5.13/5.50 thf(fact_2756_neg__divide__le__eq,axiom,
% 5.13/5.50 ! [C: rat,B: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.50 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % neg_divide_le_eq
% 5.13/5.50 thf(fact_2757_neg__le__divide__eq,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.50 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % neg_le_divide_eq
% 5.13/5.50 thf(fact_2758_neg__le__divide__eq,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.50 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % neg_le_divide_eq
% 5.13/5.50 thf(fact_2759_pos__divide__le__eq,axiom,
% 5.13/5.50 ! [C: real,B: real,A: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.13/5.50 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_divide_le_eq
% 5.13/5.50 thf(fact_2760_pos__divide__le__eq,axiom,
% 5.13/5.50 ! [C: rat,B: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.13/5.50 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_divide_le_eq
% 5.13/5.50 thf(fact_2761_pos__le__divide__eq,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.13/5.50 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_le_divide_eq
% 5.13/5.50 thf(fact_2762_pos__le__divide__eq,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.50 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_le_divide_eq
% 5.13/5.50 thf(fact_2763_mult__imp__div__pos__le,axiom,
% 5.13/5.50 ! [Y4: real,X: real,Z2: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z2 @ Y4 ) )
% 5.13/5.50 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_imp_div_pos_le
% 5.13/5.50 thf(fact_2764_mult__imp__div__pos__le,axiom,
% 5.13/5.50 ! [Y4: rat,X: rat,Z2: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z2 @ Y4 ) )
% 5.13/5.50 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ Z2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_imp_div_pos_le
% 5.13/5.50 thf(fact_2765_mult__imp__le__div__pos,axiom,
% 5.13/5.50 ! [Y4: real,Z2: real,X: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ Y4 ) @ X )
% 5.13/5.50 => ( ord_less_eq_real @ Z2 @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_imp_le_div_pos
% 5.13/5.50 thf(fact_2766_mult__imp__le__div__pos,axiom,
% 5.13/5.50 ! [Y4: rat,Z2: rat,X: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ Y4 ) @ X )
% 5.13/5.50 => ( ord_less_eq_rat @ Z2 @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_imp_le_div_pos
% 5.13/5.50 thf(fact_2767_divide__left__mono__neg,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.13/5.50 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_left_mono_neg
% 5.13/5.50 thf(fact_2768_divide__left__mono__neg,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.13/5.50 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_left_mono_neg
% 5.13/5.50 thf(fact_2769_divide__le__eq__1,axiom,
% 5.13/5.50 ! [B: real,A: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 & ( ord_less_eq_real @ B @ A ) )
% 5.13/5.50 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.50 & ( ord_less_eq_real @ A @ B ) )
% 5.13/5.50 | ( A = zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_le_eq_1
% 5.13/5.50 thf(fact_2770_divide__le__eq__1,axiom,
% 5.13/5.50 ! [B: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 & ( ord_less_eq_rat @ B @ A ) )
% 5.13/5.50 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.50 & ( ord_less_eq_rat @ A @ B ) )
% 5.13/5.50 | ( A = zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_le_eq_1
% 5.13/5.50 thf(fact_2771_le__divide__eq__1,axiom,
% 5.13/5.50 ! [B: real,A: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 & ( ord_less_eq_real @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.50 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_divide_eq_1
% 5.13/5.50 thf(fact_2772_le__divide__eq__1,axiom,
% 5.13/5.50 ! [B: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 & ( ord_less_eq_rat @ A @ B ) )
% 5.13/5.50 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.50 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_divide_eq_1
% 5.13/5.50 thf(fact_2773_frac__le__eq,axiom,
% 5.13/5.50 ! [Y4: real,Z2: real,X: real,W2: real] :
% 5.13/5.50 ( ( Y4 != zero_zero_real )
% 5.13/5.50 => ( ( Z2 != zero_zero_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 5.13/5.50 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W2 @ Y4 ) ) @ ( times_times_real @ Y4 @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % frac_le_eq
% 5.13/5.50 thf(fact_2774_frac__le__eq,axiom,
% 5.13/5.50 ! [Y4: rat,Z2: rat,X: rat,W2: rat] :
% 5.13/5.50 ( ( Y4 != zero_zero_rat )
% 5.13/5.50 => ( ( Z2 != zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 5.13/5.50 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W2 @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % frac_le_eq
% 5.13/5.50 thf(fact_2775_frac__less__eq,axiom,
% 5.13/5.50 ! [Y4: real,Z2: real,X: real,W2: real] :
% 5.13/5.50 ( ( Y4 != zero_zero_real )
% 5.13/5.50 => ( ( Z2 != zero_zero_real )
% 5.13/5.50 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W2 @ Z2 ) )
% 5.13/5.50 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W2 @ Y4 ) ) @ ( times_times_real @ Y4 @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % frac_less_eq
% 5.13/5.50 thf(fact_2776_frac__less__eq,axiom,
% 5.13/5.50 ! [Y4: rat,Z2: rat,X: rat,W2: rat] :
% 5.13/5.50 ( ( Y4 != zero_zero_rat )
% 5.13/5.50 => ( ( Z2 != zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 5.13/5.50 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W2 @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % frac_less_eq
% 5.13/5.50 thf(fact_2777_linordered__field__no__ub,axiom,
% 5.13/5.50 ! [X5: real] :
% 5.13/5.50 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_field_no_ub
% 5.13/5.50 thf(fact_2778_linordered__field__no__ub,axiom,
% 5.13/5.50 ! [X5: rat] :
% 5.13/5.50 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_field_no_ub
% 5.13/5.50 thf(fact_2779_linordered__field__no__lb,axiom,
% 5.13/5.50 ! [X5: real] :
% 5.13/5.50 ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_field_no_lb
% 5.13/5.50 thf(fact_2780_linordered__field__no__lb,axiom,
% 5.13/5.50 ! [X5: rat] :
% 5.13/5.50 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 5.13/5.50
% 5.13/5.50 % linordered_field_no_lb
% 5.13/5.50 thf(fact_2781_mult__less__le__imp__less,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_real @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_le_imp_less
% 5.13/5.50 thf(fact_2782_mult__less__le__imp__less,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_rat @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_le_imp_less
% 5.13/5.50 thf(fact_2783_mult__less__le__imp__less,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_nat @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_le_imp_less
% 5.13/5.50 thf(fact_2784_mult__less__le__imp__less,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_eq_int @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_le_imp_less
% 5.13/5.50 thf(fact_2785_mult__le__less__imp__less,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_real @ C @ D )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_less_imp_less
% 5.13/5.50 thf(fact_2786_mult__le__less__imp__less,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_rat @ C @ D )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_less_imp_less
% 5.13/5.50 thf(fact_2787_mult__le__less__imp__less,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_nat @ C @ D )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_less_imp_less
% 5.13/5.50 thf(fact_2788_mult__le__less__imp__less,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_int @ C @ D )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_less_imp_less
% 5.13/5.50 thf(fact_2789_mult__right__le__imp__le,axiom,
% 5.13/5.50 ! [A: real,C: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_imp_le
% 5.13/5.50 thf(fact_2790_mult__right__le__imp__le,axiom,
% 5.13/5.50 ! [A: rat,C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_imp_le
% 5.13/5.50 thf(fact_2791_mult__right__le__imp__le,axiom,
% 5.13/5.50 ! [A: nat,C: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_imp_le
% 5.13/5.50 thf(fact_2792_mult__right__le__imp__le,axiom,
% 5.13/5.50 ! [A: int,C: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_imp_le
% 5.13/5.50 thf(fact_2793_mult__left__le__imp__le,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_imp_le
% 5.13/5.50 thf(fact_2794_mult__left__le__imp__le,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_imp_le
% 5.13/5.50 thf(fact_2795_mult__left__le__imp__le,axiom,
% 5.13/5.50 ! [C: nat,A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_imp_le
% 5.13/5.50 thf(fact_2796_mult__left__le__imp__le,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_imp_le
% 5.13/5.50 thf(fact_2797_mult__le__cancel__left__pos,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left_pos
% 5.13/5.50 thf(fact_2798_mult__le__cancel__left__pos,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left_pos
% 5.13/5.50 thf(fact_2799_mult__le__cancel__left__pos,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left_pos
% 5.13/5.50 thf(fact_2800_mult__le__cancel__left__neg,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left_neg
% 5.13/5.50 thf(fact_2801_mult__le__cancel__left__neg,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left_neg
% 5.13/5.50 thf(fact_2802_mult__le__cancel__left__neg,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left_neg
% 5.13/5.50 thf(fact_2803_mult__less__cancel__right,axiom,
% 5.13/5.50 ! [A: real,C: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right
% 5.13/5.50 thf(fact_2804_mult__less__cancel__right,axiom,
% 5.13/5.50 ! [A: rat,C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right
% 5.13/5.50 thf(fact_2805_mult__less__cancel__right,axiom,
% 5.13/5.50 ! [A: int,C: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right
% 5.13/5.50 thf(fact_2806_mult__strict__mono_H,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_real @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono'
% 5.13/5.50 thf(fact_2807_mult__strict__mono_H,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_rat @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono'
% 5.13/5.50 thf(fact_2808_mult__strict__mono_H,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_nat @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono'
% 5.13/5.50 thf(fact_2809_mult__strict__mono_H,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_int @ C @ D )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono'
% 5.13/5.50 thf(fact_2810_mult__right__less__imp__less,axiom,
% 5.13/5.50 ! [A: real,C: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_less_imp_less
% 5.13/5.50 thf(fact_2811_mult__right__less__imp__less,axiom,
% 5.13/5.50 ! [A: rat,C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_less_imp_less
% 5.13/5.50 thf(fact_2812_mult__right__less__imp__less,axiom,
% 5.13/5.50 ! [A: nat,C: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_less_imp_less
% 5.13/5.50 thf(fact_2813_mult__right__less__imp__less,axiom,
% 5.13/5.50 ! [A: int,C: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_less_imp_less
% 5.13/5.50 thf(fact_2814_mult__less__cancel__left,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left
% 5.13/5.50 thf(fact_2815_mult__less__cancel__left,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left
% 5.13/5.50 thf(fact_2816_mult__less__cancel__left,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left
% 5.13/5.50 thf(fact_2817_mult__strict__mono,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ( ord_less_real @ C @ D )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono
% 5.13/5.50 thf(fact_2818_mult__strict__mono,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ( ord_less_rat @ C @ D )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono
% 5.13/5.50 thf(fact_2819_mult__strict__mono,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( ord_less_nat @ C @ D )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono
% 5.13/5.50 thf(fact_2820_mult__strict__mono,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ B )
% 5.13/5.50 => ( ( ord_less_int @ C @ D )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_strict_mono
% 5.13/5.50 thf(fact_2821_mult__left__less__imp__less,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_less_imp_less
% 5.13/5.50 thf(fact_2822_mult__left__less__imp__less,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_less_imp_less
% 5.13/5.50 thf(fact_2823_mult__left__less__imp__less,axiom,
% 5.13/5.50 ! [C: nat,A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.13/5.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_less_imp_less
% 5.13/5.50 thf(fact_2824_mult__left__less__imp__less,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_less_imp_less
% 5.13/5.50 thf(fact_2825_mult__le__cancel__right,axiom,
% 5.13/5.50 ! [A: real,C: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right
% 5.13/5.50 thf(fact_2826_mult__le__cancel__right,axiom,
% 5.13/5.50 ! [A: rat,C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right
% 5.13/5.50 thf(fact_2827_mult__le__cancel__right,axiom,
% 5.13/5.50 ! [A: int,C: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right
% 5.13/5.50 thf(fact_2828_mult__le__cancel__left,axiom,
% 5.13/5.50 ! [C: real,A: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left
% 5.13/5.50 thf(fact_2829_mult__le__cancel__left,axiom,
% 5.13/5.50 ! [C: rat,A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left
% 5.13/5.50 thf(fact_2830_mult__le__cancel__left,axiom,
% 5.13/5.50 ! [C: int,A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ A @ B ) )
% 5.13/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left
% 5.13/5.50 thf(fact_2831_add__strict__increasing2,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ B @ C )
% 5.13/5.50 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing2
% 5.13/5.50 thf(fact_2832_add__strict__increasing2,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ B @ C )
% 5.13/5.50 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing2
% 5.13/5.50 thf(fact_2833_add__strict__increasing2,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ B @ C )
% 5.13/5.50 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing2
% 5.13/5.50 thf(fact_2834_add__strict__increasing2,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ B @ C )
% 5.13/5.50 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing2
% 5.13/5.50 thf(fact_2835_add__strict__increasing,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ B @ C )
% 5.13/5.50 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing
% 5.13/5.50 thf(fact_2836_add__strict__increasing,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ B @ C )
% 5.13/5.50 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing
% 5.13/5.50 thf(fact_2837_add__strict__increasing,axiom,
% 5.13/5.50 ! [A: nat,B: nat,C: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ B @ C )
% 5.13/5.50 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing
% 5.13/5.50 thf(fact_2838_add__strict__increasing,axiom,
% 5.13/5.50 ! [A: int,B: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ B @ C )
% 5.13/5.50 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_strict_increasing
% 5.13/5.50 thf(fact_2839_add__pos__nonneg,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_nonneg
% 5.13/5.50 thf(fact_2840_add__pos__nonneg,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_nonneg
% 5.13/5.50 thf(fact_2841_add__pos__nonneg,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_nonneg
% 5.13/5.50 thf(fact_2842_add__pos__nonneg,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_pos_nonneg
% 5.13/5.50 thf(fact_2843_add__nonpos__neg,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonpos_neg
% 5.13/5.50 thf(fact_2844_add__nonpos__neg,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonpos_neg
% 5.13/5.50 thf(fact_2845_add__nonpos__neg,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.13/5.50 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.13/5.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonpos_neg
% 5.13/5.50 thf(fact_2846_add__nonpos__neg,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.50 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonpos_neg
% 5.13/5.50 thf(fact_2847_add__nonneg__pos,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonneg_pos
% 5.13/5.50 thf(fact_2848_add__nonneg__pos,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonneg_pos
% 5.13/5.50 thf(fact_2849_add__nonneg__pos,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonneg_pos
% 5.13/5.50 thf(fact_2850_add__nonneg__pos,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_nonneg_pos
% 5.13/5.50 thf(fact_2851_add__neg__nonpos,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_nonpos
% 5.13/5.50 thf(fact_2852_add__neg__nonpos,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_nonpos
% 5.13/5.50 thf(fact_2853_add__neg__nonpos,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.13/5.50 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.13/5.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_nonpos
% 5.13/5.50 thf(fact_2854_add__neg__nonpos,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.50 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_neg_nonpos
% 5.13/5.50 thf(fact_2855_mult__left__le,axiom,
% 5.13/5.50 ! [C: real,A: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le
% 5.13/5.50 thf(fact_2856_mult__left__le,axiom,
% 5.13/5.50 ! [C: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le
% 5.13/5.50 thf(fact_2857_mult__left__le,axiom,
% 5.13/5.50 ! [C: nat,A: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le
% 5.13/5.50 thf(fact_2858_mult__left__le,axiom,
% 5.13/5.50 ! [C: int,A: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le
% 5.13/5.50 thf(fact_2859_mult__le__one,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_one
% 5.13/5.50 thf(fact_2860_mult__le__one,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_one
% 5.13/5.50 thf(fact_2861_mult__le__one,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.13/5.50 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_one
% 5.13/5.50 thf(fact_2862_mult__le__one,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_one
% 5.13/5.50 thf(fact_2863_mult__right__le__one__le,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ X @ Y4 ) @ X ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_one_le
% 5.13/5.50 thf(fact_2864_mult__right__le__one__le,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ Y4 @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y4 ) @ X ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_one_le
% 5.13/5.50 thf(fact_2865_mult__right__le__one__le,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_int @ Y4 @ one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( times_times_int @ X @ Y4 ) @ X ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_right_le_one_le
% 5.13/5.50 thf(fact_2866_mult__left__le__one__le,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ Y4 @ X ) @ X ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_one_le
% 5.13/5.50 thf(fact_2867_mult__left__le__one__le,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ Y4 @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ Y4 @ X ) @ X ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_one_le
% 5.13/5.50 thf(fact_2868_mult__left__le__one__le,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.50 => ( ( ord_less_eq_int @ Y4 @ one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( times_times_int @ Y4 @ X ) @ X ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_left_le_one_le
% 5.13/5.50 thf(fact_2869_sum__squares__le__zero__iff,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) @ zero_zero_real )
% 5.13/5.50 = ( ( X = zero_zero_real )
% 5.13/5.50 & ( Y4 = zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_le_zero_iff
% 5.13/5.50 thf(fact_2870_sum__squares__le__zero__iff,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) @ zero_zero_rat )
% 5.13/5.50 = ( ( X = zero_zero_rat )
% 5.13/5.50 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_le_zero_iff
% 5.13/5.50 thf(fact_2871_sum__squares__le__zero__iff,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) @ zero_zero_int )
% 5.13/5.50 = ( ( X = zero_zero_int )
% 5.13/5.50 & ( Y4 = zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_le_zero_iff
% 5.13/5.50 thf(fact_2872_sum__squares__ge__zero,axiom,
% 5.13/5.50 ! [X: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_ge_zero
% 5.13/5.50 thf(fact_2873_sum__squares__ge__zero,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_ge_zero
% 5.13/5.50 thf(fact_2874_sum__squares__ge__zero,axiom,
% 5.13/5.50 ! [X: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_ge_zero
% 5.13/5.50 thf(fact_2875_power__less__imp__less__base,axiom,
% 5.13/5.50 ! [A: real,N: nat,B: real] :
% 5.13/5.50 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ord_less_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_less_imp_less_base
% 5.13/5.50 thf(fact_2876_power__less__imp__less__base,axiom,
% 5.13/5.50 ! [A: rat,N: nat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_less_imp_less_base
% 5.13/5.50 thf(fact_2877_power__less__imp__less__base,axiom,
% 5.13/5.50 ! [A: nat,N: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_less_imp_less_base
% 5.13/5.50 thf(fact_2878_power__less__imp__less__base,axiom,
% 5.13/5.50 ! [A: int,N: nat,B: int] :
% 5.13/5.50 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ord_less_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_less_imp_less_base
% 5.13/5.50 thf(fact_2879_sum__squares__gt__zero__iff,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) )
% 5.13/5.50 = ( ( X != zero_zero_real )
% 5.13/5.50 | ( Y4 != zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_gt_zero_iff
% 5.13/5.50 thf(fact_2880_sum__squares__gt__zero__iff,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) )
% 5.13/5.50 = ( ( X != zero_zero_rat )
% 5.13/5.50 | ( Y4 != zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_gt_zero_iff
% 5.13/5.50 thf(fact_2881_sum__squares__gt__zero__iff,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) )
% 5.13/5.50 = ( ( X != zero_zero_int )
% 5.13/5.50 | ( Y4 != zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_squares_gt_zero_iff
% 5.13/5.50 thf(fact_2882_not__sum__squares__lt__zero,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) @ zero_zero_real ) ).
% 5.13/5.50
% 5.13/5.50 % not_sum_squares_lt_zero
% 5.13/5.50 thf(fact_2883_not__sum__squares__lt__zero,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) @ zero_zero_rat ) ).
% 5.13/5.50
% 5.13/5.50 % not_sum_squares_lt_zero
% 5.13/5.50 thf(fact_2884_not__sum__squares__lt__zero,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) @ zero_zero_int ) ).
% 5.13/5.50
% 5.13/5.50 % not_sum_squares_lt_zero
% 5.13/5.50 thf(fact_2885_zero__less__two,axiom,
% 5.13/5.50 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_two
% 5.13/5.50 thf(fact_2886_zero__less__two,axiom,
% 5.13/5.50 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_two
% 5.13/5.50 thf(fact_2887_zero__less__two,axiom,
% 5.13/5.50 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_two
% 5.13/5.50 thf(fact_2888_zero__less__two,axiom,
% 5.13/5.50 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.13/5.50
% 5.13/5.50 % zero_less_two
% 5.13/5.50 thf(fact_2889_power__le__one,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_one
% 5.13/5.50 thf(fact_2890_power__le__one,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_one
% 5.13/5.50 thf(fact_2891_power__le__one,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_one
% 5.13/5.50 thf(fact_2892_power__le__one,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_one
% 5.13/5.50 thf(fact_2893_divide__eq__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: complex,C: complex,W2: num] :
% 5.13/5.50 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.13/5.50 = ( numera6690914467698888265omplex @ W2 ) )
% 5.13/5.50 = ( ( ( C != zero_zero_complex )
% 5.13/5.50 => ( B
% 5.13/5.50 = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ( C = zero_zero_complex )
% 5.13/5.50 => ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.50 = zero_zero_complex ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_eq_eq_numeral(1)
% 5.13/5.50 thf(fact_2894_divide__eq__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: real,C: real,W2: num] :
% 5.13/5.50 ( ( ( divide_divide_real @ B @ C )
% 5.13/5.50 = ( numeral_numeral_real @ W2 ) )
% 5.13/5.50 = ( ( ( C != zero_zero_real )
% 5.13/5.50 => ( B
% 5.13/5.50 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ( C = zero_zero_real )
% 5.13/5.50 => ( ( numeral_numeral_real @ W2 )
% 5.13/5.50 = zero_zero_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_eq_eq_numeral(1)
% 5.13/5.50 thf(fact_2895_divide__eq__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: rat,C: rat,W2: num] :
% 5.13/5.50 ( ( ( divide_divide_rat @ B @ C )
% 5.13/5.50 = ( numeral_numeral_rat @ W2 ) )
% 5.13/5.50 = ( ( ( C != zero_zero_rat )
% 5.13/5.50 => ( B
% 5.13/5.50 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ( C = zero_zero_rat )
% 5.13/5.50 => ( ( numeral_numeral_rat @ W2 )
% 5.13/5.50 = zero_zero_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_eq_eq_numeral(1)
% 5.13/5.50 thf(fact_2896_eq__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: complex,C: complex] :
% 5.13/5.50 ( ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.50 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.13/5.50 = ( ( ( C != zero_zero_complex )
% 5.13/5.50 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C )
% 5.13/5.50 = B ) )
% 5.13/5.50 & ( ( C = zero_zero_complex )
% 5.13/5.50 => ( ( numera6690914467698888265omplex @ W2 )
% 5.13/5.50 = zero_zero_complex ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % eq_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_2897_eq__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: real,C: real] :
% 5.13/5.50 ( ( ( numeral_numeral_real @ W2 )
% 5.13/5.50 = ( divide_divide_real @ B @ C ) )
% 5.13/5.50 = ( ( ( C != zero_zero_real )
% 5.13/5.50 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C )
% 5.13/5.50 = B ) )
% 5.13/5.50 & ( ( C = zero_zero_real )
% 5.13/5.50 => ( ( numeral_numeral_real @ W2 )
% 5.13/5.50 = zero_zero_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % eq_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_2898_eq__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: rat,C: rat] :
% 5.13/5.50 ( ( ( numeral_numeral_rat @ W2 )
% 5.13/5.50 = ( divide_divide_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( C != zero_zero_rat )
% 5.13/5.50 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 5.13/5.50 = B ) )
% 5.13/5.50 & ( ( C = zero_zero_rat )
% 5.13/5.50 => ( ( numeral_numeral_rat @ W2 )
% 5.13/5.50 = zero_zero_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % eq_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_2899_power__inject__base,axiom,
% 5.13/5.50 ! [A: real,N: nat,B: real] :
% 5.13/5.50 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.13/5.50 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.50 => ( A = B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_inject_base
% 5.13/5.50 thf(fact_2900_power__inject__base,axiom,
% 5.13/5.50 ! [A: rat,N: nat,B: rat] :
% 5.13/5.50 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.13/5.50 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( A = B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_inject_base
% 5.13/5.50 thf(fact_2901_power__inject__base,axiom,
% 5.13/5.50 ! [A: nat,N: nat,B: nat] :
% 5.13/5.50 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.13/5.50 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( A = B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_inject_base
% 5.13/5.50 thf(fact_2902_power__inject__base,axiom,
% 5.13/5.50 ! [A: int,N: nat,B: int] :
% 5.13/5.50 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.13/5.50 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.50 => ( A = B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_inject_base
% 5.13/5.50 thf(fact_2903_power__le__imp__le__base,axiom,
% 5.13/5.50 ! [A: real,N: nat,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.13/5.50 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_imp_le_base
% 5.13/5.50 thf(fact_2904_power__le__imp__le__base,axiom,
% 5.13/5.50 ! [A: rat,N: nat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_imp_le_base
% 5.13/5.50 thf(fact_2905_power__le__imp__le__base,axiom,
% 5.13/5.50 ! [A: nat,N: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_imp_le_base
% 5.13/5.50 thf(fact_2906_power__le__imp__le__base,axiom,
% 5.13/5.50 ! [A: int,N: nat,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_le_imp_le_base
% 5.13/5.50 thf(fact_2907_div__add__self1,axiom,
% 5.13/5.50 ! [B: nat,A: nat] :
% 5.13/5.50 ( ( B != zero_zero_nat )
% 5.13/5.50 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.13/5.50 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_add_self1
% 5.13/5.50 thf(fact_2908_div__add__self1,axiom,
% 5.13/5.50 ! [B: int,A: int] :
% 5.13/5.50 ( ( B != zero_zero_int )
% 5.13/5.50 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.13/5.50 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_add_self1
% 5.13/5.50 thf(fact_2909_div__add__self2,axiom,
% 5.13/5.50 ! [B: nat,A: nat] :
% 5.13/5.50 ( ( B != zero_zero_nat )
% 5.13/5.50 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.13/5.50 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_add_self2
% 5.13/5.50 thf(fact_2910_div__add__self2,axiom,
% 5.13/5.50 ! [B: int,A: int] :
% 5.13/5.50 ( ( B != zero_zero_int )
% 5.13/5.50 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.13/5.50 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_add_self2
% 5.13/5.50 thf(fact_2911_numeral__1__eq__Suc__0,axiom,
% 5.13/5.50 ( ( numeral_numeral_nat @ one )
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % numeral_1_eq_Suc_0
% 5.13/5.50 thf(fact_2912_num_Osize_I5_J,axiom,
% 5.13/5.50 ! [X22: num] :
% 5.13/5.50 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.13/5.50 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % num.size(5)
% 5.13/5.50 thf(fact_2913_ex__least__nat__less,axiom,
% 5.13/5.50 ! [P: nat > $o,N: nat] :
% 5.13/5.50 ( ( P @ N )
% 5.13/5.50 => ( ~ ( P @ zero_zero_nat )
% 5.13/5.50 => ? [K2: nat] :
% 5.13/5.50 ( ( ord_less_nat @ K2 @ N )
% 5.13/5.50 & ! [I: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ I @ K2 )
% 5.13/5.50 => ~ ( P @ I ) )
% 5.13/5.50 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_least_nat_less
% 5.13/5.50 thf(fact_2914_diff__Suc__less,axiom,
% 5.13/5.50 ! [N: nat,I2: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 5.13/5.50
% 5.13/5.50 % diff_Suc_less
% 5.13/5.50 thf(fact_2915_one__less__mult,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.13/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.13/5.50 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % one_less_mult
% 5.13/5.50 thf(fact_2916_n__less__m__mult__n,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.13/5.50 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % n_less_m_mult_n
% 5.13/5.50 thf(fact_2917_n__less__n__mult__m,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.13/5.50 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % n_less_n_mult_m
% 5.13/5.50 thf(fact_2918_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: real,Xs2: list_real] :
% 5.13/5.50 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2919_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: complex,Xs2: list_complex] :
% 5.13/5.50 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2920_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.13/5.50 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2921_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2922_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: $o,Xs2: list_o] :
% 5.13/5.50 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2923_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: nat,Xs2: list_nat] :
% 5.13/5.50 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2924_length__pos__if__in__set,axiom,
% 5.13/5.50 ! [X: int,Xs2: list_int] :
% 5.13/5.50 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % length_pos_if_in_set
% 5.13/5.50 thf(fact_2925_nat__induct__non__zero,axiom,
% 5.13/5.50 ! [N: nat,P: nat > $o] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( P @ one_one_nat )
% 5.13/5.50 => ( ! [N3: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.13/5.50 => ( ( P @ N3 )
% 5.13/5.50 => ( P @ ( suc @ N3 ) ) ) )
% 5.13/5.50 => ( P @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_induct_non_zero
% 5.13/5.50 thf(fact_2926_nat__mult__le__cancel1,axiom,
% 5.13/5.50 ! [K: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.50 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.50 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_mult_le_cancel1
% 5.13/5.50 thf(fact_2927_power__gt__expt,axiom,
% 5.13/5.50 ! [N: nat,K: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.13/5.50 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_gt_expt
% 5.13/5.50 thf(fact_2928_div__le__mono2,axiom,
% 5.13/5.50 ! [M: nat,N: nat,K: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ( ord_less_eq_nat @ M @ N )
% 5.13/5.50 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_le_mono2
% 5.13/5.50 thf(fact_2929_div__greater__zero__iff,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.13/5.50 = ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_greater_zero_iff
% 5.13/5.50 thf(fact_2930_nat__diff__split,axiom,
% 5.13/5.50 ! [P: nat > $o,A: nat,B: nat] :
% 5.13/5.50 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.13/5.50 = ( ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( P @ zero_zero_nat ) )
% 5.13/5.50 & ! [D2: nat] :
% 5.13/5.50 ( ( A
% 5.13/5.50 = ( plus_plus_nat @ B @ D2 ) )
% 5.13/5.50 => ( P @ D2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_diff_split
% 5.13/5.50 thf(fact_2931_nat__diff__split__asm,axiom,
% 5.13/5.50 ! [P: nat > $o,A: nat,B: nat] :
% 5.13/5.50 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.13/5.50 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.13/5.50 & ~ ( P @ zero_zero_nat ) )
% 5.13/5.50 | ? [D2: nat] :
% 5.13/5.50 ( ( A
% 5.13/5.50 = ( plus_plus_nat @ B @ D2 ) )
% 5.13/5.50 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_diff_split_asm
% 5.13/5.50 thf(fact_2932_nat__one__le__power,axiom,
% 5.13/5.50 ! [I2: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.13/5.50 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_one_le_power
% 5.13/5.50 thf(fact_2933_div__less__iff__less__mult,axiom,
% 5.13/5.50 ! [Q2: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.13/5.50 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.13/5.50 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_less_iff_less_mult
% 5.13/5.50 thf(fact_2934_nat__mult__div__cancel1,axiom,
% 5.13/5.50 ! [K: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.13/5.50 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.13/5.50 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_mult_div_cancel1
% 5.13/5.50 thf(fact_2935_div__eq__dividend__iff,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ( ( divide_divide_nat @ M @ N )
% 5.13/5.50 = M )
% 5.13/5.50 = ( N = one_one_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_eq_dividend_iff
% 5.13/5.50 thf(fact_2936_div__less__dividend,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ one_one_nat @ N )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_less_dividend
% 5.13/5.50 thf(fact_2937_vebt__insert_Osimps_I3_J,axiom,
% 5.13/5.50 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.13/5.50 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ X )
% 5.13/5.50 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_insert.simps(3)
% 5.13/5.50 thf(fact_2938_scaling__mono,axiom,
% 5.13/5.50 ! [U2: real,V: real,R2: real,S2: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ U2 @ V )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.13/5.50 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.13/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ U2 @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U2 ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % scaling_mono
% 5.13/5.50 thf(fact_2939_scaling__mono,axiom,
% 5.13/5.50 ! [U2: rat,V: rat,R2: rat,S2: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ U2 @ V )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.13/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ U2 @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U2 ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % scaling_mono
% 5.13/5.50 thf(fact_2940_vebt__member_Osimps_I3_J,axiom,
% 5.13/5.50 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.13/5.50 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_member.simps(3)
% 5.13/5.50 thf(fact_2941_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.13/5.50 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.13/5.50 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.membermima.simps(2)
% 5.13/5.50 thf(fact_2942_mult__le__cancel__left1,axiom,
% 5.13/5.50 ! [C: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.13/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left1
% 5.13/5.50 thf(fact_2943_mult__le__cancel__left1,axiom,
% 5.13/5.50 ! [C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.13/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left1
% 5.13/5.50 thf(fact_2944_mult__le__cancel__left1,axiom,
% 5.13/5.50 ! [C: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.13/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left1
% 5.13/5.50 thf(fact_2945_mult__le__cancel__left2,axiom,
% 5.13/5.50 ! [C: real,A: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.13/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left2
% 5.13/5.50 thf(fact_2946_mult__le__cancel__left2,axiom,
% 5.13/5.50 ! [C: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.13/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left2
% 5.13/5.50 thf(fact_2947_mult__le__cancel__left2,axiom,
% 5.13/5.50 ! [C: int,A: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.13/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_left2
% 5.13/5.50 thf(fact_2948_mult__le__cancel__right1,axiom,
% 5.13/5.50 ! [C: real,B: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.13/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right1
% 5.13/5.50 thf(fact_2949_mult__le__cancel__right1,axiom,
% 5.13/5.50 ! [C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.13/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right1
% 5.13/5.50 thf(fact_2950_mult__le__cancel__right1,axiom,
% 5.13/5.50 ! [C: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.13/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right1
% 5.13/5.50 thf(fact_2951_mult__le__cancel__right2,axiom,
% 5.13/5.50 ! [A: real,C: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.13/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right2
% 5.13/5.50 thf(fact_2952_mult__le__cancel__right2,axiom,
% 5.13/5.50 ! [A: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.13/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right2
% 5.13/5.50 thf(fact_2953_mult__le__cancel__right2,axiom,
% 5.13/5.50 ! [A: int,C: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.13/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.13/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_le_cancel_right2
% 5.13/5.50 thf(fact_2954_mult__less__cancel__left1,axiom,
% 5.13/5.50 ! [C: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ one_one_real @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left1
% 5.13/5.50 thf(fact_2955_mult__less__cancel__left1,axiom,
% 5.13/5.50 ! [C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left1
% 5.13/5.50 thf(fact_2956_mult__less__cancel__left1,axiom,
% 5.13/5.50 ! [C: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.13/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ one_one_int @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left1
% 5.13/5.50 thf(fact_2957_mult__less__cancel__left2,axiom,
% 5.13/5.50 ! [C: real,A: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.13/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ A @ one_one_real ) )
% 5.13/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left2
% 5.13/5.50 thf(fact_2958_mult__less__cancel__left2,axiom,
% 5.13/5.50 ! [C: rat,A: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.13/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.13/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left2
% 5.13/5.50 thf(fact_2959_mult__less__cancel__left2,axiom,
% 5.13/5.50 ! [C: int,A: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.13/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ A @ one_one_int ) )
% 5.13/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_left2
% 5.13/5.50 thf(fact_2960_mult__less__cancel__right1,axiom,
% 5.13/5.50 ! [C: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ one_one_real @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right1
% 5.13/5.50 thf(fact_2961_mult__less__cancel__right1,axiom,
% 5.13/5.50 ! [C: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right1
% 5.13/5.50 thf(fact_2962_mult__less__cancel__right1,axiom,
% 5.13/5.50 ! [C: int,B: int] :
% 5.13/5.50 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ one_one_int @ B ) )
% 5.13/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right1
% 5.13/5.50 thf(fact_2963_mult__less__cancel__right2,axiom,
% 5.13/5.50 ! [A: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.13/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ A @ one_one_real ) )
% 5.13/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right2
% 5.13/5.50 thf(fact_2964_mult__less__cancel__right2,axiom,
% 5.13/5.50 ! [A: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.13/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.13/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right2
% 5.13/5.50 thf(fact_2965_mult__less__cancel__right2,axiom,
% 5.13/5.50 ! [A: int,C: int] :
% 5.13/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.13/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.13/5.50 => ( ord_less_int @ A @ one_one_int ) )
% 5.13/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_less_cancel_right2
% 5.13/5.50 thf(fact_2966_convex__bound__le,axiom,
% 5.13/5.50 ! [X: real,A: real,Y4: real,U2: real,V: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ X @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ Y4 @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ U2 )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.13/5.50 => ( ( ( plus_plus_real @ U2 @ V )
% 5.13/5.50 = one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U2 @ X ) @ ( times_times_real @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % convex_bound_le
% 5.13/5.50 thf(fact_2967_convex__bound__le,axiom,
% 5.13/5.50 ! [X: rat,A: rat,Y4: rat,U2: rat,V: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ X @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ Y4 @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ U2 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.13/5.50 => ( ( ( plus_plus_rat @ U2 @ V )
% 5.13/5.50 = one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U2 @ X ) @ ( times_times_rat @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % convex_bound_le
% 5.13/5.50 thf(fact_2968_convex__bound__le,axiom,
% 5.13/5.50 ! [X: int,A: int,Y4: int,U2: int,V: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ X @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ Y4 @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ U2 )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.13/5.50 => ( ( ( plus_plus_int @ U2 @ V )
% 5.13/5.50 = one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U2 @ X ) @ ( times_times_int @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % convex_bound_le
% 5.13/5.50 thf(fact_2969_divide__less__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: real,C: real,W2: num] :
% 5.13/5.50 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_less_eq_numeral(1)
% 5.13/5.50 thf(fact_2970_divide__less__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: rat,C: rat,W2: num] :
% 5.13/5.50 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_less_eq_numeral(1)
% 5.13/5.50 thf(fact_2971_less__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_2972_less__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_2973_power__Suc__less,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ A @ one_one_real )
% 5.13/5.50 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less
% 5.13/5.50 thf(fact_2974_power__Suc__less,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less
% 5.13/5.50 thf(fact_2975_power__Suc__less,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less
% 5.13/5.50 thf(fact_2976_power__Suc__less,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ A @ one_one_int )
% 5.13/5.50 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less
% 5.13/5.50 thf(fact_2977_power__Suc__le__self,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_le_self
% 5.13/5.50 thf(fact_2978_power__Suc__le__self,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_le_self
% 5.13/5.50 thf(fact_2979_power__Suc__le__self,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_le_self
% 5.13/5.50 thf(fact_2980_power__Suc__le__self,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_le_self
% 5.13/5.50 thf(fact_2981_power__Suc__less__one,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ A @ one_one_real )
% 5.13/5.50 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less_one
% 5.13/5.50 thf(fact_2982_power__Suc__less__one,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less_one
% 5.13/5.50 thf(fact_2983_power__Suc__less__one,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less_one
% 5.13/5.50 thf(fact_2984_power__Suc__less__one,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ A @ one_one_int )
% 5.13/5.50 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_Suc_less_one
% 5.13/5.50 thf(fact_2985_power__strict__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: real] :
% 5.13/5.50 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_real @ A @ one_one_real )
% 5.13/5.50 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_strict_decreasing
% 5.13/5.50 thf(fact_2986_power__strict__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: rat] :
% 5.13/5.50 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_strict_decreasing
% 5.13/5.50 thf(fact_2987_power__strict__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: nat] :
% 5.13/5.50 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_strict_decreasing
% 5.13/5.50 thf(fact_2988_power__strict__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: int] :
% 5.13/5.50 ( ( ord_less_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_int @ A @ one_one_int )
% 5.13/5.50 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_strict_decreasing
% 5.13/5.50 thf(fact_2989_power__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: real] :
% 5.13/5.50 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_decreasing
% 5.13/5.50 thf(fact_2990_power__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: rat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_decreasing
% 5.13/5.50 thf(fact_2991_power__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.13/5.50 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_decreasing
% 5.13/5.50 thf(fact_2992_power__decreasing,axiom,
% 5.13/5.50 ! [N: nat,N4: nat,A: int] :
% 5.13/5.50 ( ( ord_less_eq_nat @ N @ N4 )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.13/5.50 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_decreasing
% 5.13/5.50 thf(fact_2993_zero__power2,axiom,
% 5.13/5.50 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = zero_zero_rat ) ).
% 5.13/5.50
% 5.13/5.50 % zero_power2
% 5.13/5.50 thf(fact_2994_zero__power2,axiom,
% 5.13/5.50 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = zero_zero_nat ) ).
% 5.13/5.50
% 5.13/5.50 % zero_power2
% 5.13/5.50 thf(fact_2995_zero__power2,axiom,
% 5.13/5.50 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = zero_zero_real ) ).
% 5.13/5.50
% 5.13/5.50 % zero_power2
% 5.13/5.50 thf(fact_2996_zero__power2,axiom,
% 5.13/5.50 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = zero_zero_int ) ).
% 5.13/5.50
% 5.13/5.50 % zero_power2
% 5.13/5.50 thf(fact_2997_zero__power2,axiom,
% 5.13/5.50 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = zero_zero_complex ) ).
% 5.13/5.50
% 5.13/5.50 % zero_power2
% 5.13/5.50 thf(fact_2998_self__le__power,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % self_le_power
% 5.13/5.50 thf(fact_2999_self__le__power,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % self_le_power
% 5.13/5.50 thf(fact_3000_self__le__power,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % self_le_power
% 5.13/5.50 thf(fact_3001_self__le__power,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % self_le_power
% 5.13/5.50 thf(fact_3002_one__less__power,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_real @ one_one_real @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % one_less_power
% 5.13/5.50 thf(fact_3003_one__less__power,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_rat @ one_one_rat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % one_less_power
% 5.13/5.50 thf(fact_3004_one__less__power,axiom,
% 5.13/5.50 ! [A: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ one_one_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % one_less_power
% 5.13/5.50 thf(fact_3005_one__less__power,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_int @ one_one_int @ A )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % one_less_power
% 5.13/5.50 thf(fact_3006_numeral__2__eq__2,axiom,
% 5.13/5.50 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.13/5.50 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % numeral_2_eq_2
% 5.13/5.50 thf(fact_3007_pos2,axiom,
% 5.13/5.50 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos2
% 5.13/5.50 thf(fact_3008_power__diff,axiom,
% 5.13/5.50 ! [A: complex,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_complex )
% 5.13/5.50 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.50 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff
% 5.13/5.50 thf(fact_3009_power__diff,axiom,
% 5.13/5.50 ! [A: real,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_real )
% 5.13/5.50 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.50 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff
% 5.13/5.50 thf(fact_3010_power__diff,axiom,
% 5.13/5.50 ! [A: rat,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_rat )
% 5.13/5.50 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.50 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff
% 5.13/5.50 thf(fact_3011_power__diff,axiom,
% 5.13/5.50 ! [A: nat,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_nat )
% 5.13/5.50 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.50 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff
% 5.13/5.50 thf(fact_3012_power__diff,axiom,
% 5.13/5.50 ! [A: int,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_int )
% 5.13/5.50 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.13/5.50 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff
% 5.13/5.50 thf(fact_3013_div__if,axiom,
% 5.13/5.50 ( divide_divide_nat
% 5.13/5.50 = ( ^ [M2: nat,N2: nat] :
% 5.13/5.50 ( if_nat
% 5.13/5.50 @ ( ( ord_less_nat @ M2 @ N2 )
% 5.13/5.50 | ( N2 = zero_zero_nat ) )
% 5.13/5.50 @ zero_zero_nat
% 5.13/5.50 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_if
% 5.13/5.50 thf(fact_3014_Suc__pred_H,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( N
% 5.13/5.50 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Suc_pred'
% 5.13/5.50 thf(fact_3015_Suc__diff__eq__diff__pred,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.13/5.50 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Suc_diff_eq_diff_pred
% 5.13/5.50 thf(fact_3016_less__eq__div__iff__mult__less__eq,axiom,
% 5.13/5.50 ! [Q2: nat,M: nat,N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.13/5.50 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.13/5.50 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_eq_div_iff_mult_less_eq
% 5.13/5.50 thf(fact_3017_add__eq__if,axiom,
% 5.13/5.50 ( plus_plus_nat
% 5.13/5.50 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_eq_if
% 5.13/5.50 thf(fact_3018_dividend__less__times__div,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % dividend_less_times_div
% 5.13/5.50 thf(fact_3019_dividend__less__div__times,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % dividend_less_div_times
% 5.13/5.50 thf(fact_3020_split__div,axiom,
% 5.13/5.50 ! [P: nat > $o,M: nat,N: nat] :
% 5.13/5.50 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.13/5.50 = ( ( ( N = zero_zero_nat )
% 5.13/5.50 => ( P @ zero_zero_nat ) )
% 5.13/5.50 & ( ( N != zero_zero_nat )
% 5.13/5.50 => ! [I4: nat,J3: nat] :
% 5.13/5.50 ( ( ord_less_nat @ J3 @ N )
% 5.13/5.50 => ( ( M
% 5.13/5.50 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.13/5.50 => ( P @ I4 ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % split_div
% 5.13/5.50 thf(fact_3021_mult__commute__abs,axiom,
% 5.13/5.50 ! [C: real] :
% 5.13/5.50 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 5.13/5.50 = ( times_times_real @ C ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_commute_abs
% 5.13/5.50 thf(fact_3022_mult__commute__abs,axiom,
% 5.13/5.50 ! [C: rat] :
% 5.13/5.50 ( ( ^ [X2: rat] : ( times_times_rat @ X2 @ C ) )
% 5.13/5.50 = ( times_times_rat @ C ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_commute_abs
% 5.13/5.50 thf(fact_3023_mult__commute__abs,axiom,
% 5.13/5.50 ! [C: nat] :
% 5.13/5.50 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 5.13/5.50 = ( times_times_nat @ C ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_commute_abs
% 5.13/5.50 thf(fact_3024_mult__commute__abs,axiom,
% 5.13/5.50 ! [C: int] :
% 5.13/5.50 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 5.13/5.50 = ( times_times_int @ C ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_commute_abs
% 5.13/5.50 thf(fact_3025_mult__eq__if,axiom,
% 5.13/5.50 ( times_times_nat
% 5.13/5.50 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % mult_eq_if
% 5.13/5.50 thf(fact_3026_vebt__member_Osimps_I4_J,axiom,
% 5.13/5.50 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.13/5.50 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_member.simps(4)
% 5.13/5.50 thf(fact_3027_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.13/5.50 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.13/5.50 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 5.13/5.50 = ( ( X = Mi )
% 5.13/5.50 | ( X = Ma ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.membermima.simps(3)
% 5.13/5.50 thf(fact_3028_vebt__pred_Osimps_I5_J,axiom,
% 5.13/5.50 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.13/5.50 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 5.13/5.50 = none_nat ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_pred.simps(5)
% 5.13/5.50 thf(fact_3029_convex__bound__lt,axiom,
% 5.13/5.50 ! [X: real,A: real,Y4: real,U2: real,V: real] :
% 5.13/5.50 ( ( ord_less_real @ X @ A )
% 5.13/5.50 => ( ( ord_less_real @ Y4 @ A )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ U2 )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.13/5.50 => ( ( ( plus_plus_real @ U2 @ V )
% 5.13/5.50 = one_one_real )
% 5.13/5.50 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U2 @ X ) @ ( times_times_real @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % convex_bound_lt
% 5.13/5.50 thf(fact_3030_convex__bound__lt,axiom,
% 5.13/5.50 ! [X: rat,A: rat,Y4: rat,U2: rat,V: rat] :
% 5.13/5.50 ( ( ord_less_rat @ X @ A )
% 5.13/5.50 => ( ( ord_less_rat @ Y4 @ A )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ U2 )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.13/5.50 => ( ( ( plus_plus_rat @ U2 @ V )
% 5.13/5.50 = one_one_rat )
% 5.13/5.50 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U2 @ X ) @ ( times_times_rat @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % convex_bound_lt
% 5.13/5.50 thf(fact_3031_convex__bound__lt,axiom,
% 5.13/5.50 ! [X: int,A: int,Y4: int,U2: int,V: int] :
% 5.13/5.50 ( ( ord_less_int @ X @ A )
% 5.13/5.50 => ( ( ord_less_int @ Y4 @ A )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ U2 )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.13/5.50 => ( ( ( plus_plus_int @ U2 @ V )
% 5.13/5.50 = one_one_int )
% 5.13/5.50 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U2 @ X ) @ ( times_times_int @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % convex_bound_lt
% 5.13/5.50 thf(fact_3032_divide__le__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: real,C: real,W2: num] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_le_eq_numeral(1)
% 5.13/5.50 thf(fact_3033_divide__le__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [B: rat,C: rat,W2: num] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_le_eq_numeral(1)
% 5.13/5.50 thf(fact_3034_le__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: real,C: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.13/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.13/5.50 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_3035_le__divide__eq__numeral_I1_J,axiom,
% 5.13/5.50 ! [W2: num,B: rat,C: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 5.13/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.13/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.13/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_divide_eq_numeral(1)
% 5.13/5.50 thf(fact_3036_half__gt__zero,axiom,
% 5.13/5.50 ! [A: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % half_gt_zero
% 5.13/5.50 thf(fact_3037_half__gt__zero,axiom,
% 5.13/5.50 ! [A: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.13/5.50 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % half_gt_zero
% 5.13/5.50 thf(fact_3038_half__gt__zero__iff,axiom,
% 5.13/5.50 ! [A: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.13/5.50 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.13/5.50
% 5.13/5.50 % half_gt_zero_iff
% 5.13/5.50 thf(fact_3039_half__gt__zero__iff,axiom,
% 5.13/5.50 ! [A: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.13/5.50
% 5.13/5.50 % half_gt_zero_iff
% 5.13/5.50 thf(fact_3040_zero__le__power2,axiom,
% 5.13/5.50 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power2
% 5.13/5.50 thf(fact_3041_zero__le__power2,axiom,
% 5.13/5.50 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power2
% 5.13/5.50 thf(fact_3042_zero__le__power2,axiom,
% 5.13/5.50 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_power2
% 5.13/5.50 thf(fact_3043_power2__eq__imp__eq,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( X = Y4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_eq_imp_eq
% 5.13/5.50 thf(fact_3044_power2__eq__imp__eq,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( X = Y4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_eq_imp_eq
% 5.13/5.50 thf(fact_3045_power2__eq__imp__eq,axiom,
% 5.13/5.50 ! [X: nat,Y4: nat] :
% 5.13/5.50 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.13/5.50 => ( X = Y4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_eq_imp_eq
% 5.13/5.50 thf(fact_3046_power2__eq__imp__eq,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.50 => ( X = Y4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_eq_imp_eq
% 5.13/5.50 thf(fact_3047_power2__le__imp__le,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_le_imp_le
% 5.13/5.50 thf(fact_3048_power2__le__imp__le,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ord_less_eq_rat @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_le_imp_le
% 5.13/5.50 thf(fact_3049_power2__le__imp__le,axiom,
% 5.13/5.50 ! [X: nat,Y4: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.13/5.50 => ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_le_imp_le
% 5.13/5.50 thf(fact_3050_power2__le__imp__le,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.50 => ( ord_less_eq_int @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_le_imp_le
% 5.13/5.50 thf(fact_3051_power2__less__0,axiom,
% 5.13/5.50 ! [A: real] :
% 5.13/5.50 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_0
% 5.13/5.50 thf(fact_3052_power2__less__0,axiom,
% 5.13/5.50 ! [A: rat] :
% 5.13/5.50 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_0
% 5.13/5.50 thf(fact_3053_power2__less__0,axiom,
% 5.13/5.50 ! [A: int] :
% 5.13/5.50 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_0
% 5.13/5.50 thf(fact_3054_exp__add__not__zero__imp__left,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.50 != zero_zero_nat )
% 5.13/5.50 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.13/5.50 != zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % exp_add_not_zero_imp_left
% 5.13/5.50 thf(fact_3055_exp__add__not__zero__imp__left,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.50 != zero_zero_int )
% 5.13/5.50 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.13/5.50 != zero_zero_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % exp_add_not_zero_imp_left
% 5.13/5.50 thf(fact_3056_exp__add__not__zero__imp__right,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.50 != zero_zero_nat )
% 5.13/5.50 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.13/5.50 != zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % exp_add_not_zero_imp_right
% 5.13/5.50 thf(fact_3057_exp__add__not__zero__imp__right,axiom,
% 5.13/5.50 ! [M: nat,N: nat] :
% 5.13/5.50 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.13/5.50 != zero_zero_int )
% 5.13/5.50 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.13/5.50 != zero_zero_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % exp_add_not_zero_imp_right
% 5.13/5.50 thf(fact_3058_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.13/5.50 != zero_zero_nat )
% 5.13/5.50 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.13/5.50 != zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % exp_not_zero_imp_exp_diff_not_zero
% 5.13/5.50 thf(fact_3059_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.13/5.50 != zero_zero_int )
% 5.13/5.50 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.13/5.50 != zero_zero_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % exp_not_zero_imp_exp_diff_not_zero
% 5.13/5.50 thf(fact_3060_power__diff__power__eq,axiom,
% 5.13/5.50 ! [A: nat,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_nat )
% 5.13/5.50 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.13/5.50 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.13/5.50 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.13/5.50 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff_power_eq
% 5.13/5.50 thf(fact_3061_power__diff__power__eq,axiom,
% 5.13/5.50 ! [A: int,N: nat,M: nat] :
% 5.13/5.50 ( ( A != zero_zero_int )
% 5.13/5.50 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.13/5.50 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.13/5.50 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.13/5.50 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_diff_power_eq
% 5.13/5.50 thf(fact_3062_less__2__cases,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 => ( ( N = zero_zero_nat )
% 5.13/5.50 | ( N
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_2_cases
% 5.13/5.50 thf(fact_3063_less__2__cases__iff,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( ( N = zero_zero_nat )
% 5.13/5.50 | ( N
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_2_cases_iff
% 5.13/5.50 thf(fact_3064_nat__induct2,axiom,
% 5.13/5.50 ! [P: nat > $o,N: nat] :
% 5.13/5.50 ( ( P @ zero_zero_nat )
% 5.13/5.50 => ( ( P @ one_one_nat )
% 5.13/5.50 => ( ! [N3: nat] :
% 5.13/5.50 ( ( P @ N3 )
% 5.13/5.50 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.50 => ( P @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_induct2
% 5.13/5.50 thf(fact_3065_power__eq__if,axiom,
% 5.13/5.50 ( power_power_complex
% 5.13/5.50 = ( ^ [P4: complex,M2: nat] : ( if_complex @ ( M2 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P4 @ ( power_power_complex @ P4 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_eq_if
% 5.13/5.50 thf(fact_3066_power__eq__if,axiom,
% 5.13/5.50 ( power_power_real
% 5.13/5.50 = ( ^ [P4: real,M2: nat] : ( if_real @ ( M2 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P4 @ ( power_power_real @ P4 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_eq_if
% 5.13/5.50 thf(fact_3067_power__eq__if,axiom,
% 5.13/5.50 ( power_power_rat
% 5.13/5.50 = ( ^ [P4: rat,M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P4 @ ( power_power_rat @ P4 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_eq_if
% 5.13/5.50 thf(fact_3068_power__eq__if,axiom,
% 5.13/5.50 ( power_power_nat
% 5.13/5.50 = ( ^ [P4: nat,M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P4 @ ( power_power_nat @ P4 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_eq_if
% 5.13/5.50 thf(fact_3069_power__eq__if,axiom,
% 5.13/5.50 ( power_power_int
% 5.13/5.50 = ( ^ [P4: int,M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P4 @ ( power_power_int @ P4 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_eq_if
% 5.13/5.50 thf(fact_3070_power__minus__mult,axiom,
% 5.13/5.50 ! [N: nat,A: complex] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.13/5.50 = ( power_power_complex @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_minus_mult
% 5.13/5.50 thf(fact_3071_power__minus__mult,axiom,
% 5.13/5.50 ! [N: nat,A: real] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.13/5.50 = ( power_power_real @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_minus_mult
% 5.13/5.50 thf(fact_3072_power__minus__mult,axiom,
% 5.13/5.50 ! [N: nat,A: rat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.13/5.50 = ( power_power_rat @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_minus_mult
% 5.13/5.50 thf(fact_3073_power__minus__mult,axiom,
% 5.13/5.50 ! [N: nat,A: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.13/5.50 = ( power_power_nat @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_minus_mult
% 5.13/5.50 thf(fact_3074_power__minus__mult,axiom,
% 5.13/5.50 ! [N: nat,A: int] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.13/5.50 = ( power_power_int @ A @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power_minus_mult
% 5.13/5.50 thf(fact_3075_le__div__geq,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_eq_nat @ N @ M )
% 5.13/5.50 => ( ( divide_divide_nat @ M @ N )
% 5.13/5.50 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % le_div_geq
% 5.13/5.50 thf(fact_3076_split__div_H,axiom,
% 5.13/5.50 ! [P: nat > $o,M: nat,N: nat] :
% 5.13/5.50 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.13/5.50 = ( ( ( N = zero_zero_nat )
% 5.13/5.50 & ( P @ zero_zero_nat ) )
% 5.13/5.50 | ? [Q4: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.13/5.50 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.13/5.50 & ( P @ Q4 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % split_div'
% 5.13/5.50 thf(fact_3077_vebt__pred_Osimps_I6_J,axiom,
% 5.13/5.50 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.13/5.50 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 5.13/5.50 = none_nat ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_pred.simps(6)
% 5.13/5.50 thf(fact_3078_power2__less__imp__less,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ord_less_real @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_imp_less
% 5.13/5.50 thf(fact_3079_power2__less__imp__less,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ord_less_rat @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_imp_less
% 5.13/5.50 thf(fact_3080_power2__less__imp__less,axiom,
% 5.13/5.50 ! [X: nat,Y4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.13/5.50 => ( ord_less_nat @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_imp_less
% 5.13/5.50 thf(fact_3081_power2__less__imp__less,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.13/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.13/5.50 => ( ord_less_int @ X @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % power2_less_imp_less
% 5.13/5.50 thf(fact_3082_sum__power2__ge__zero,axiom,
% 5.13/5.50 ! [X: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_ge_zero
% 5.13/5.50 thf(fact_3083_sum__power2__ge__zero,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_ge_zero
% 5.13/5.50 thf(fact_3084_sum__power2__ge__zero,axiom,
% 5.13/5.50 ! [X: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_ge_zero
% 5.13/5.50 thf(fact_3085_sum__power2__le__zero__iff,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.13/5.50 = ( ( X = zero_zero_real )
% 5.13/5.50 & ( Y4 = zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_le_zero_iff
% 5.13/5.50 thf(fact_3086_sum__power2__le__zero__iff,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.13/5.50 = ( ( X = zero_zero_rat )
% 5.13/5.50 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_le_zero_iff
% 5.13/5.50 thf(fact_3087_sum__power2__le__zero__iff,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.13/5.50 = ( ( X = zero_zero_int )
% 5.13/5.50 & ( Y4 = zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_le_zero_iff
% 5.13/5.50 thf(fact_3088_not__sum__power2__lt__zero,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.13/5.50
% 5.13/5.50 % not_sum_power2_lt_zero
% 5.13/5.50 thf(fact_3089_not__sum__power2__lt__zero,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.13/5.50
% 5.13/5.50 % not_sum_power2_lt_zero
% 5.13/5.50 thf(fact_3090_not__sum__power2__lt__zero,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.13/5.50
% 5.13/5.50 % not_sum_power2_lt_zero
% 5.13/5.50 thf(fact_3091_sum__power2__gt__zero__iff,axiom,
% 5.13/5.50 ! [X: real,Y4: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.50 = ( ( X != zero_zero_real )
% 5.13/5.50 | ( Y4 != zero_zero_real ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_gt_zero_iff
% 5.13/5.50 thf(fact_3092_sum__power2__gt__zero__iff,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat] :
% 5.13/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.50 = ( ( X != zero_zero_rat )
% 5.13/5.50 | ( Y4 != zero_zero_rat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_gt_zero_iff
% 5.13/5.50 thf(fact_3093_sum__power2__gt__zero__iff,axiom,
% 5.13/5.50 ! [X: int,Y4: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.50 = ( ( X != zero_zero_int )
% 5.13/5.50 | ( Y4 != zero_zero_int ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % sum_power2_gt_zero_iff
% 5.13/5.50 thf(fact_3094_zero__le__even__power_H,axiom,
% 5.13/5.50 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_even_power'
% 5.13/5.50 thf(fact_3095_zero__le__even__power_H,axiom,
% 5.13/5.50 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_even_power'
% 5.13/5.50 thf(fact_3096_zero__le__even__power_H,axiom,
% 5.13/5.50 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zero_le_even_power'
% 5.13/5.50 thf(fact_3097_nat__bit__induct,axiom,
% 5.13/5.50 ! [P: nat > $o,N: nat] :
% 5.13/5.50 ( ( P @ zero_zero_nat )
% 5.13/5.50 => ( ! [N3: nat] :
% 5.13/5.50 ( ( P @ N3 )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.13/5.50 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.13/5.50 => ( ! [N3: nat] :
% 5.13/5.50 ( ( P @ N3 )
% 5.13/5.50 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.13/5.50 => ( P @ N ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % nat_bit_induct
% 5.13/5.50 thf(fact_3098_div__2__gt__zero,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_2_gt_zero
% 5.13/5.50 thf(fact_3099_Suc__n__div__2__gt__zero,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Suc_n_div_2_gt_zero
% 5.13/5.50 thf(fact_3100_times__divide__times__eq,axiom,
% 5.13/5.50 ! [X: complex,Y4: complex,Z2: complex,W2: complex] :
% 5.13/5.50 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ Z2 @ W2 ) )
% 5.13/5.50 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z2 ) @ ( times_times_complex @ Y4 @ W2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % times_divide_times_eq
% 5.13/5.50 thf(fact_3101_times__divide__times__eq,axiom,
% 5.13/5.50 ! [X: real,Y4: real,Z2: real,W2: real] :
% 5.13/5.50 ( ( times_times_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ Z2 @ W2 ) )
% 5.13/5.50 = ( divide_divide_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ Y4 @ W2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % times_divide_times_eq
% 5.13/5.50 thf(fact_3102_times__divide__times__eq,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat,Z2: rat,W2: rat] :
% 5.13/5.50 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ Z2 @ W2 ) )
% 5.13/5.50 = ( divide_divide_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ Y4 @ W2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % times_divide_times_eq
% 5.13/5.50 thf(fact_3103_divide__divide__times__eq,axiom,
% 5.13/5.50 ! [X: complex,Y4: complex,Z2: complex,W2: complex] :
% 5.13/5.50 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ Z2 @ W2 ) )
% 5.13/5.50 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W2 ) @ ( times_times_complex @ Y4 @ Z2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_divide_times_eq
% 5.13/5.50 thf(fact_3104_divide__divide__times__eq,axiom,
% 5.13/5.50 ! [X: real,Y4: real,Z2: real,W2: real] :
% 5.13/5.50 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ Z2 @ W2 ) )
% 5.13/5.50 = ( divide_divide_real @ ( times_times_real @ X @ W2 ) @ ( times_times_real @ Y4 @ Z2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_divide_times_eq
% 5.13/5.50 thf(fact_3105_divide__divide__times__eq,axiom,
% 5.13/5.50 ! [X: rat,Y4: rat,Z2: rat,W2: rat] :
% 5.13/5.50 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ Z2 @ W2 ) )
% 5.13/5.50 = ( divide_divide_rat @ ( times_times_rat @ X @ W2 ) @ ( times_times_rat @ Y4 @ Z2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_divide_times_eq
% 5.13/5.50 thf(fact_3106_divide__divide__eq__left_H,axiom,
% 5.13/5.50 ! [A: complex,B: complex,C: complex] :
% 5.13/5.50 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.13/5.50 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_divide_eq_left'
% 5.13/5.50 thf(fact_3107_divide__divide__eq__left_H,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.13/5.50 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_divide_eq_left'
% 5.13/5.50 thf(fact_3108_divide__divide__eq__left_H,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.13/5.50 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % divide_divide_eq_left'
% 5.13/5.50 thf(fact_3109_add__divide__distrib,axiom,
% 5.13/5.50 ! [A: complex,B: complex,C: complex] :
% 5.13/5.50 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.13/5.50 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_divide_distrib
% 5.13/5.50 thf(fact_3110_add__divide__distrib,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.13/5.50 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_divide_distrib
% 5.13/5.50 thf(fact_3111_add__divide__distrib,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.13/5.50 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % add_divide_distrib
% 5.13/5.50 thf(fact_3112_diff__divide__distrib,axiom,
% 5.13/5.50 ! [A: complex,B: complex,C: complex] :
% 5.13/5.50 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.13/5.50 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % diff_divide_distrib
% 5.13/5.50 thf(fact_3113_diff__divide__distrib,axiom,
% 5.13/5.50 ! [A: real,B: real,C: real] :
% 5.13/5.50 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.13/5.50 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % diff_divide_distrib
% 5.13/5.50 thf(fact_3114_diff__divide__distrib,axiom,
% 5.13/5.50 ! [A: rat,B: rat,C: rat] :
% 5.13/5.50 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.13/5.50 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % diff_divide_distrib
% 5.13/5.50 thf(fact_3115_odd__0__le__power__imp__0__le,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.13/5.50 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.13/5.50
% 5.13/5.50 % odd_0_le_power_imp_0_le
% 5.13/5.50 thf(fact_3116_odd__0__le__power__imp__0__le,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.13/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.13/5.50
% 5.13/5.50 % odd_0_le_power_imp_0_le
% 5.13/5.50 thf(fact_3117_odd__0__le__power__imp__0__le,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.13/5.50 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.13/5.50
% 5.13/5.50 % odd_0_le_power_imp_0_le
% 5.13/5.50 thf(fact_3118_odd__power__less__zero,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_real @ A @ zero_zero_real )
% 5.13/5.50 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.13/5.50
% 5.13/5.50 % odd_power_less_zero
% 5.13/5.50 thf(fact_3119_odd__power__less__zero,axiom,
% 5.13/5.50 ! [A: rat,N: nat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.13/5.50 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.13/5.50
% 5.13/5.50 % odd_power_less_zero
% 5.13/5.50 thf(fact_3120_odd__power__less__zero,axiom,
% 5.13/5.50 ! [A: int,N: nat] :
% 5.13/5.50 ( ( ord_less_int @ A @ zero_zero_int )
% 5.13/5.50 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % odd_power_less_zero
% 5.13/5.50 thf(fact_3121_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.13/5.50 ! [X: nat,N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.exp_split_high_low(1)
% 5.13/5.50 thf(fact_3122_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.13/5.50 ! [X: nat,N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.exp_split_high_low(2)
% 5.13/5.50 thf(fact_3123_arith__geo__mean,axiom,
% 5.13/5.50 ! [U2: real,X: real,Y4: real] :
% 5.13/5.50 ( ( ( power_power_real @ U2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( times_times_real @ X @ Y4 ) )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.13/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ord_less_eq_real @ U2 @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % arith_geo_mean
% 5.13/5.50 thf(fact_3124_arith__geo__mean,axiom,
% 5.13/5.50 ! [U2: rat,X: rat,Y4: rat] :
% 5.13/5.50 ( ( ( power_power_rat @ U2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.13/5.50 = ( times_times_rat @ X @ Y4 ) )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.13/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.13/5.50 => ( ord_less_eq_rat @ U2 @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % arith_geo_mean
% 5.13/5.50 thf(fact_3125_less__half__sum,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_half_sum
% 5.13/5.50 thf(fact_3126_less__half__sum,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % less_half_sum
% 5.13/5.50 thf(fact_3127_gt__half__sum,axiom,
% 5.13/5.50 ! [A: real,B: real] :
% 5.13/5.50 ( ( ord_less_real @ A @ B )
% 5.13/5.50 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.13/5.50
% 5.13/5.50 % gt_half_sum
% 5.13/5.50 thf(fact_3128_gt__half__sum,axiom,
% 5.13/5.50 ! [A: rat,B: rat] :
% 5.13/5.50 ( ( ord_less_rat @ A @ B )
% 5.13/5.50 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.13/5.50
% 5.13/5.50 % gt_half_sum
% 5.13/5.50 thf(fact_3129_vebt__pred_Oelims,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT,Xa2: nat,Y4: option_nat] :
% 5.13/5.50 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.13/5.50 = Y4 )
% 5.13/5.50 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.13/5.50 => ( ( Xa2 = zero_zero_nat )
% 5.13/5.50 => ( Y4 != none_nat ) ) )
% 5.13/5.50 => ( ! [A3: $o] :
% 5.13/5.50 ( ? [Uw2: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.13/5.50 => ( ( Xa2
% 5.13/5.50 = ( suc @ zero_zero_nat ) )
% 5.13/5.50 => ~ ( ( A3
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A3
% 5.13/5.50 => ( Y4 = none_nat ) ) ) ) )
% 5.13/5.50 => ( ! [A3: $o,B2: $o] :
% 5.13/5.50 ( ( X
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.13/5.50 => ( ? [Va3: nat] :
% 5.13/5.50 ( Xa2
% 5.13/5.50 = ( suc @ ( suc @ Va3 ) ) )
% 5.13/5.50 => ~ ( ( B2
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ one_one_nat ) ) )
% 5.13/5.50 & ( ~ B2
% 5.13/5.50 => ( ( A3
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A3
% 5.13/5.50 => ( Y4 = none_nat ) ) ) ) ) ) )
% 5.13/5.50 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.13/5.50 => ( Y4 != none_nat ) )
% 5.13/5.50 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.13/5.50 => ( Y4 != none_nat ) )
% 5.13/5.50 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.13/5.50 => ( Y4 != none_nat ) )
% 5.13/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.13/5.50 ( ( X
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.13/5.50 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ Ma2 ) ) )
% 5.13/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( 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 ) )
% 5.13/5.50 @ ( if_option_nat
% 5.13/5.50 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.13/5.50 != none_nat )
% 5.13/5.50 & ( 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 ) ) ) ) ) ) ) )
% 5.13/5.50 @ ( 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 ) ) ) ) ) )
% 5.13/5.50 @ ( if_option_nat
% 5.13/5.50 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.13/5.50 = none_nat )
% 5.13/5.50 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.13/5.50 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.13/5.50 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_pred.elims
% 5.13/5.50 thf(fact_3130_inrange,axiom,
% 5.13/5.50 ! [T: vEBT_VEBT,N: nat] :
% 5.13/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.50 => ( 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 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % inrange
% 5.13/5.50 thf(fact_3131_set__bit__0,axiom,
% 5.13/5.50 ! [A: int] :
% 5.13/5.50 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.13/5.50 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % set_bit_0
% 5.13/5.50 thf(fact_3132_set__bit__0,axiom,
% 5.13/5.50 ! [A: nat] :
% 5.13/5.50 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.13/5.50 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % set_bit_0
% 5.13/5.50 thf(fact_3133_invar__vebt_Osimps,axiom,
% 5.13/5.50 ( vEBT_invar_vebt
% 5.13/5.50 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.13/5.50 ( ( ? [A4: $o,B3: $o] :
% 5.13/5.50 ( A1
% 5.13/5.50 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.13/5.50 & ( A22
% 5.13/5.50 = ( suc @ zero_zero_nat ) ) )
% 5.13/5.50 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.13/5.50 ( ( A1
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.13/5.50 & ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.13/5.50 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.13/5.50 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.13/5.50 & ( A22
% 5.13/5.50 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.13/5.50 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 5.13/5.50 & ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.13/5.50 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.13/5.50 ( ( A1
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.13/5.50 & ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.13/5.50 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.13/5.50 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.13/5.50 & ( A22
% 5.13/5.50 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.13/5.50 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 5.13/5.50 & ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.13/5.50 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.13/5.50 ( ( A1
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.13/5.50 & ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.13/5.50 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.13/5.50 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.13/5.50 & ( A22
% 5.13/5.50 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.13/5.50 & ! [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.13/5.50 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X6 ) )
% 5.13/5.50 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.13/5.50 & ( ( Mi3 = Ma3 )
% 5.13/5.50 => ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.13/5.50 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.13/5.50 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.13/5.50 & ( ( Mi3 != Ma3 )
% 5.13/5.50 => ! [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.13/5.50 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.13/5.50 = I4 )
% 5.13/5.50 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.13/5.50 & ! [X2: nat] :
% 5.13/5.50 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 5.13/5.50 = I4 )
% 5.13/5.50 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 5.13/5.50 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.13/5.50 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.13/5.50 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.13/5.50 ( ( A1
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.13/5.50 & ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.13/5.50 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.13/5.50 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.13/5.50 & ( A22
% 5.13/5.50 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.13/5.50 & ! [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.13/5.50 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X6 ) )
% 5.13/5.50 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.13/5.50 & ( ( Mi3 = Ma3 )
% 5.13/5.50 => ! [X2: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.13/5.50 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.13/5.50 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.13/5.50 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.13/5.50 & ( ( Mi3 != Ma3 )
% 5.13/5.50 => ! [I4: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.13/5.50 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.13/5.50 = I4 )
% 5.13/5.50 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.13/5.50 & ! [X2: nat] :
% 5.13/5.50 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 5.13/5.50 = I4 )
% 5.13/5.50 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 5.13/5.50 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.13/5.50 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % invar_vebt.simps
% 5.13/5.50 thf(fact_3134_invar__vebt_Ocases,axiom,
% 5.13/5.50 ! [A12: vEBT_VEBT,A23: nat] :
% 5.13/5.50 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.13/5.50 => ( ( ? [A3: $o,B2: $o] :
% 5.13/5.50 ( A12
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.13/5.50 => ( A23
% 5.13/5.50 != ( suc @ zero_zero_nat ) ) )
% 5.13/5.50 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.13/5.50 ( ( A12
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.13/5.50 => ( ( A23 = Deg2 )
% 5.13/5.50 => ( ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.13/5.50 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.13/5.50 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( M4 = N3 )
% 5.13/5.50 => ( ( Deg2
% 5.13/5.50 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.13/5.50 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.13/5.50 => ~ ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.13/5.50 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.13/5.50 ( ( A12
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.13/5.50 => ( ( A23 = Deg2 )
% 5.13/5.50 => ( ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.13/5.50 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.13/5.50 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( M4
% 5.13/5.50 = ( suc @ N3 ) )
% 5.13/5.50 => ( ( Deg2
% 5.13/5.50 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.13/5.50 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.13/5.50 => ~ ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.13/5.50 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.13/5.50 ( ( A12
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.13/5.50 => ( ( A23 = Deg2 )
% 5.13/5.50 => ( ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.13/5.50 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.13/5.50 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( M4 = N3 )
% 5.13/5.50 => ( ( Deg2
% 5.13/5.50 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.13/5.50 => ( ! [I: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X6 ) )
% 5.13/5.50 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.13/5.50 => ( ( ( Mi2 = Ma2 )
% 5.13/5.50 => ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.13/5.50 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.13/5.50 => ~ ( ( Mi2 != Ma2 )
% 5.13/5.50 => ! [I: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.13/5.50 = I )
% 5.13/5.50 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.13/5.50 & ! [X5: nat] :
% 5.13/5.50 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.13/5.50 = I )
% 5.13/5.50 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.13/5.50 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.13/5.50 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.13/5.50 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.13/5.50 ( ( A12
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.13/5.50 => ( ( A23 = Deg2 )
% 5.13/5.50 => ( ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.13/5.50 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.13/5.50 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.13/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( M4
% 5.13/5.50 = ( suc @ N3 ) )
% 5.13/5.50 => ( ( Deg2
% 5.13/5.50 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.13/5.50 => ( ! [I: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X6 ) )
% 5.13/5.50 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.13/5.50 => ( ( ( Mi2 = Ma2 )
% 5.13/5.50 => ! [X5: vEBT_VEBT] :
% 5.13/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.13/5.50 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.13/5.50 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.13/5.50 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.13/5.50 => ~ ( ( Mi2 != Ma2 )
% 5.13/5.50 => ! [I: nat] :
% 5.13/5.50 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.13/5.50 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.13/5.50 = I )
% 5.13/5.50 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.13/5.50 & ! [X5: nat] :
% 5.13/5.50 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.13/5.50 = I )
% 5.13/5.50 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.13/5.50 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.13/5.50 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % invar_vebt.cases
% 5.13/5.50 thf(fact_3135_div__geq,axiom,
% 5.13/5.50 ! [N: nat,M: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ~ ( ord_less_nat @ M @ N )
% 5.13/5.50 => ( ( divide_divide_nat @ M @ N )
% 5.13/5.50 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_geq
% 5.13/5.50 thf(fact_3136_empty__subsetI,axiom,
% 5.13/5.50 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.13/5.50
% 5.13/5.50 % empty_subsetI
% 5.13/5.50 thf(fact_3137_empty__subsetI,axiom,
% 5.13/5.50 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.13/5.50
% 5.13/5.50 % empty_subsetI
% 5.13/5.50 thf(fact_3138_empty__subsetI,axiom,
% 5.13/5.50 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.13/5.50
% 5.13/5.50 % empty_subsetI
% 5.13/5.50 thf(fact_3139_subset__empty,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.13/5.50 = ( A2 = bot_bot_set_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % subset_empty
% 5.13/5.50 thf(fact_3140_subset__empty,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.13/5.50 = ( A2 = bot_bot_set_real ) ) ).
% 5.13/5.50
% 5.13/5.50 % subset_empty
% 5.13/5.50 thf(fact_3141_subset__empty,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.13/5.50 = ( A2 = bot_bot_set_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % subset_empty
% 5.13/5.50 thf(fact_3142_Leaf__0__not,axiom,
% 5.13/5.50 ! [A: $o,B: $o] :
% 5.13/5.50 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.13/5.50
% 5.13/5.50 % Leaf_0_not
% 5.13/5.50 thf(fact_3143_deg1Leaf,axiom,
% 5.13/5.50 ! [T: vEBT_VEBT] :
% 5.13/5.50 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.13/5.50 = ( ? [A4: $o,B3: $o] :
% 5.13/5.50 ( T
% 5.13/5.50 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % deg1Leaf
% 5.13/5.50 thf(fact_3144_deg__1__Leaf,axiom,
% 5.13/5.50 ! [T: vEBT_VEBT] :
% 5.13/5.50 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.13/5.50 => ? [A3: $o,B2: $o] :
% 5.13/5.50 ( T
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % deg_1_Leaf
% 5.13/5.50 thf(fact_3145_deg__1__Leafy,axiom,
% 5.13/5.50 ! [T: vEBT_VEBT,N: nat] :
% 5.13/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.13/5.50 => ( ( N = one_one_nat )
% 5.13/5.50 => ? [A3: $o,B2: $o] :
% 5.13/5.50 ( T
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % deg_1_Leafy
% 5.13/5.50 thf(fact_3146_zdiv__numeral__Bit0,axiom,
% 5.13/5.50 ! [V: num,W2: num] :
% 5.13/5.50 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.13/5.50 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % zdiv_numeral_Bit0
% 5.13/5.50 thf(fact_3147_Diff__empty,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 5.13/5.50 = A2 ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_empty
% 5.13/5.50 thf(fact_3148_Diff__empty,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 5.13/5.50 = A2 ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_empty
% 5.13/5.50 thf(fact_3149_Diff__empty,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 5.13/5.50 = A2 ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_empty
% 5.13/5.50 thf(fact_3150_empty__Diff,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 5.13/5.50 = bot_bot_set_int ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Diff
% 5.13/5.50 thf(fact_3151_empty__Diff,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 5.13/5.50 = bot_bot_set_real ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Diff
% 5.13/5.50 thf(fact_3152_empty__Diff,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 5.13/5.50 = bot_bot_set_nat ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Diff
% 5.13/5.50 thf(fact_3153_Diff__cancel,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ( minus_minus_set_int @ A2 @ A2 )
% 5.13/5.50 = bot_bot_set_int ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_cancel
% 5.13/5.50 thf(fact_3154_Diff__cancel,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ( minus_minus_set_real @ A2 @ A2 )
% 5.13/5.50 = bot_bot_set_real ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_cancel
% 5.13/5.50 thf(fact_3155_Diff__cancel,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ( minus_minus_set_nat @ A2 @ A2 )
% 5.13/5.50 = bot_bot_set_nat ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_cancel
% 5.13/5.50 thf(fact_3156_empty__iff,axiom,
% 5.13/5.50 ! [C: complex] :
% 5.13/5.50 ~ ( member_complex @ C @ bot_bot_set_complex ) ).
% 5.13/5.50
% 5.13/5.50 % empty_iff
% 5.13/5.50 thf(fact_3157_empty__iff,axiom,
% 5.13/5.50 ! [C: product_prod_nat_nat] :
% 5.13/5.50 ~ ( member8440522571783428010at_nat @ C @ bot_bo2099793752762293965at_nat ) ).
% 5.13/5.50
% 5.13/5.50 % empty_iff
% 5.13/5.50 thf(fact_3158_empty__iff,axiom,
% 5.13/5.50 ! [C: nat] :
% 5.13/5.50 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 5.13/5.50
% 5.13/5.50 % empty_iff
% 5.13/5.50 thf(fact_3159_empty__iff,axiom,
% 5.13/5.50 ! [C: int] :
% 5.13/5.50 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 5.13/5.50
% 5.13/5.50 % empty_iff
% 5.13/5.50 thf(fact_3160_empty__iff,axiom,
% 5.13/5.50 ! [C: real] :
% 5.13/5.50 ~ ( member_real @ C @ bot_bot_set_real ) ).
% 5.13/5.50
% 5.13/5.50 % empty_iff
% 5.13/5.50 thf(fact_3161_all__not__in__conv,axiom,
% 5.13/5.50 ! [A2: set_complex] :
% 5.13/5.50 ( ( ! [X2: complex] :
% 5.13/5.50 ~ ( member_complex @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 = bot_bot_set_complex ) ) ).
% 5.13/5.50
% 5.13/5.50 % all_not_in_conv
% 5.13/5.50 thf(fact_3162_all__not__in__conv,axiom,
% 5.13/5.50 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.13/5.50 ( ( ! [X2: product_prod_nat_nat] :
% 5.13/5.50 ~ ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % all_not_in_conv
% 5.13/5.50 thf(fact_3163_all__not__in__conv,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ( ! [X2: nat] :
% 5.13/5.50 ~ ( member_nat @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 = bot_bot_set_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % all_not_in_conv
% 5.13/5.50 thf(fact_3164_all__not__in__conv,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ( ! [X2: int] :
% 5.13/5.50 ~ ( member_int @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 = bot_bot_set_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % all_not_in_conv
% 5.13/5.50 thf(fact_3165_all__not__in__conv,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ( ! [X2: real] :
% 5.13/5.50 ~ ( member_real @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 = bot_bot_set_real ) ) ).
% 5.13/5.50
% 5.13/5.50 % all_not_in_conv
% 5.13/5.50 thf(fact_3166_Collect__empty__eq,axiom,
% 5.13/5.50 ! [P: complex > $o] :
% 5.13/5.50 ( ( ( collect_complex @ P )
% 5.13/5.50 = bot_bot_set_complex )
% 5.13/5.50 = ( ! [X2: complex] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Collect_empty_eq
% 5.13/5.50 thf(fact_3167_Collect__empty__eq,axiom,
% 5.13/5.50 ! [P: product_prod_nat_nat > $o] :
% 5.13/5.50 ( ( ( collec3392354462482085612at_nat @ P )
% 5.13/5.50 = bot_bo2099793752762293965at_nat )
% 5.13/5.50 = ( ! [X2: product_prod_nat_nat] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Collect_empty_eq
% 5.13/5.50 thf(fact_3168_Collect__empty__eq,axiom,
% 5.13/5.50 ! [P: list_nat > $o] :
% 5.13/5.50 ( ( ( collect_list_nat @ P )
% 5.13/5.50 = bot_bot_set_list_nat )
% 5.13/5.50 = ( ! [X2: list_nat] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Collect_empty_eq
% 5.13/5.50 thf(fact_3169_Collect__empty__eq,axiom,
% 5.13/5.50 ! [P: nat > $o] :
% 5.13/5.50 ( ( ( collect_nat @ P )
% 5.13/5.50 = bot_bot_set_nat )
% 5.13/5.50 = ( ! [X2: nat] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Collect_empty_eq
% 5.13/5.50 thf(fact_3170_Collect__empty__eq,axiom,
% 5.13/5.50 ! [P: int > $o] :
% 5.13/5.50 ( ( ( collect_int @ P )
% 5.13/5.50 = bot_bot_set_int )
% 5.13/5.50 = ( ! [X2: int] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Collect_empty_eq
% 5.13/5.50 thf(fact_3171_Collect__empty__eq,axiom,
% 5.13/5.50 ! [P: real > $o] :
% 5.13/5.50 ( ( ( collect_real @ P )
% 5.13/5.50 = bot_bot_set_real )
% 5.13/5.50 = ( ! [X2: real] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % Collect_empty_eq
% 5.13/5.50 thf(fact_3172_empty__Collect__eq,axiom,
% 5.13/5.50 ! [P: complex > $o] :
% 5.13/5.50 ( ( bot_bot_set_complex
% 5.13/5.50 = ( collect_complex @ P ) )
% 5.13/5.50 = ( ! [X2: complex] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Collect_eq
% 5.13/5.50 thf(fact_3173_empty__Collect__eq,axiom,
% 5.13/5.50 ! [P: product_prod_nat_nat > $o] :
% 5.13/5.50 ( ( bot_bo2099793752762293965at_nat
% 5.13/5.50 = ( collec3392354462482085612at_nat @ P ) )
% 5.13/5.50 = ( ! [X2: product_prod_nat_nat] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Collect_eq
% 5.13/5.50 thf(fact_3174_empty__Collect__eq,axiom,
% 5.13/5.50 ! [P: list_nat > $o] :
% 5.13/5.50 ( ( bot_bot_set_list_nat
% 5.13/5.50 = ( collect_list_nat @ P ) )
% 5.13/5.50 = ( ! [X2: list_nat] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Collect_eq
% 5.13/5.50 thf(fact_3175_empty__Collect__eq,axiom,
% 5.13/5.50 ! [P: nat > $o] :
% 5.13/5.50 ( ( bot_bot_set_nat
% 5.13/5.50 = ( collect_nat @ P ) )
% 5.13/5.50 = ( ! [X2: nat] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Collect_eq
% 5.13/5.50 thf(fact_3176_empty__Collect__eq,axiom,
% 5.13/5.50 ! [P: int > $o] :
% 5.13/5.50 ( ( bot_bot_set_int
% 5.13/5.50 = ( collect_int @ P ) )
% 5.13/5.50 = ( ! [X2: int] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Collect_eq
% 5.13/5.50 thf(fact_3177_empty__Collect__eq,axiom,
% 5.13/5.50 ! [P: real > $o] :
% 5.13/5.50 ( ( bot_bot_set_real
% 5.13/5.50 = ( collect_real @ P ) )
% 5.13/5.50 = ( ! [X2: real] :
% 5.13/5.50 ~ ( P @ X2 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_Collect_eq
% 5.13/5.50 thf(fact_3178_VEBT_Oinject_I2_J,axiom,
% 5.13/5.50 ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 5.13/5.50 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.13/5.50 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 5.13/5.50 = ( ( X21 = Y21 )
% 5.13/5.50 & ( X222 = Y22 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT.inject(2)
% 5.13/5.50 thf(fact_3179_i0__less,axiom,
% 5.13/5.50 ! [N: extended_enat] :
% 5.13/5.50 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.13/5.50 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.13/5.50
% 5.13/5.50 % i0_less
% 5.13/5.50 thf(fact_3180_idiff__0__right,axiom,
% 5.13/5.50 ! [N: extended_enat] :
% 5.13/5.50 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.13/5.50 = N ) ).
% 5.13/5.50
% 5.13/5.50 % idiff_0_right
% 5.13/5.50 thf(fact_3181_idiff__0,axiom,
% 5.13/5.50 ! [N: extended_enat] :
% 5.13/5.50 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.13/5.50 = zero_z5237406670263579293d_enat ) ).
% 5.13/5.50
% 5.13/5.50 % idiff_0
% 5.13/5.50 thf(fact_3182_half__nonnegative__int__iff,axiom,
% 5.13/5.50 ! [K: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.13/5.50 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.13/5.50
% 5.13/5.50 % half_nonnegative_int_iff
% 5.13/5.50 thf(fact_3183_half__negative__int__iff,axiom,
% 5.13/5.50 ! [K: int] :
% 5.13/5.50 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.13/5.50 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % half_negative_int_iff
% 5.13/5.50 thf(fact_3184_Diff__eq__empty__iff,axiom,
% 5.13/5.50 ! [A2: set_int,B5: set_int] :
% 5.13/5.50 ( ( ( minus_minus_set_int @ A2 @ B5 )
% 5.13/5.50 = bot_bot_set_int )
% 5.13/5.50 = ( ord_less_eq_set_int @ A2 @ B5 ) ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_eq_empty_iff
% 5.13/5.50 thf(fact_3185_Diff__eq__empty__iff,axiom,
% 5.13/5.50 ! [A2: set_real,B5: set_real] :
% 5.13/5.50 ( ( ( minus_minus_set_real @ A2 @ B5 )
% 5.13/5.50 = bot_bot_set_real )
% 5.13/5.50 = ( ord_less_eq_set_real @ A2 @ B5 ) ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_eq_empty_iff
% 5.13/5.50 thf(fact_3186_Diff__eq__empty__iff,axiom,
% 5.13/5.50 ! [A2: set_nat,B5: set_nat] :
% 5.13/5.50 ( ( ( minus_minus_set_nat @ A2 @ B5 )
% 5.13/5.50 = bot_bot_set_nat )
% 5.13/5.50 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ).
% 5.13/5.50
% 5.13/5.50 % Diff_eq_empty_iff
% 5.13/5.50 thf(fact_3187_not__real__square__gt__zero,axiom,
% 5.13/5.50 ! [X: real] :
% 5.13/5.50 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.13/5.50 = ( X = zero_zero_real ) ) ).
% 5.13/5.50
% 5.13/5.50 % not_real_square_gt_zero
% 5.13/5.50 thf(fact_3188_VEBT_Osize_I4_J,axiom,
% 5.13/5.50 ! [X21: $o,X222: $o] :
% 5.13/5.50 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.13/5.50 = zero_zero_nat ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT.size(4)
% 5.13/5.50 thf(fact_3189_VEBT_Odistinct_I1_J,axiom,
% 5.13/5.50 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.13/5.50 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.13/5.50 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT.distinct(1)
% 5.13/5.50 thf(fact_3190_VEBT_Oexhaust,axiom,
% 5.13/5.50 ! [Y4: vEBT_VEBT] :
% 5.13/5.50 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.13/5.50 ( Y4
% 5.13/5.50 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.13/5.50 => ~ ! [X212: $o,X223: $o] :
% 5.13/5.50 ( Y4
% 5.13/5.50 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT.exhaust
% 5.13/5.50 thf(fact_3191_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.13/5.50 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.13/5.50 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.membermima.simps(1)
% 5.13/5.50 thf(fact_3192_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.13/5.50 ! [Uu: $o] :
% 5.13/5.50 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.simps(3)
% 5.13/5.50 thf(fact_3193_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.13/5.50 ! [Uv: $o] :
% 5.13/5.50 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.simps(2)
% 5.13/5.50 thf(fact_3194_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.13/5.50 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.simps(1)
% 5.13/5.50 thf(fact_3195_neg__zdiv__mult__2,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.13/5.50 => ( ( 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 ) )
% 5.13/5.50 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % neg_zdiv_mult_2
% 5.13/5.50 thf(fact_3196_pos__zdiv__mult__2,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.13/5.50 => ( ( 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 ) )
% 5.13/5.50 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % pos_zdiv_mult_2
% 5.13/5.50 thf(fact_3197_not__iless0,axiom,
% 5.13/5.50 ! [N: extended_enat] :
% 5.13/5.50 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.13/5.50
% 5.13/5.50 % not_iless0
% 5.13/5.50 thf(fact_3198_enat__0__less__mult__iff,axiom,
% 5.13/5.50 ! [M: extended_enat,N: extended_enat] :
% 5.13/5.50 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.13/5.50 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.13/5.50 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % enat_0_less_mult_iff
% 5.13/5.50 thf(fact_3199_iadd__is__0,axiom,
% 5.13/5.50 ! [M: extended_enat,N: extended_enat] :
% 5.13/5.50 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.13/5.50 = zero_z5237406670263579293d_enat )
% 5.13/5.50 = ( ( M = zero_z5237406670263579293d_enat )
% 5.13/5.50 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % iadd_is_0
% 5.13/5.50 thf(fact_3200_ile0__eq,axiom,
% 5.13/5.50 ! [N: extended_enat] :
% 5.13/5.50 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.13/5.50 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.13/5.50
% 5.13/5.50 % ile0_eq
% 5.13/5.50 thf(fact_3201_i0__lb,axiom,
% 5.13/5.50 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.13/5.50
% 5.13/5.50 % i0_lb
% 5.13/5.50 thf(fact_3202_ex__nat__less,axiom,
% 5.13/5.50 ! [N: nat,P: nat > $o] :
% 5.13/5.50 ( ( ? [M2: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ M2 @ N )
% 5.13/5.50 & ( P @ M2 ) ) )
% 5.13/5.50 = ( ? [X2: nat] :
% 5.13/5.50 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.13/5.50 & ( P @ X2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_nat_less
% 5.13/5.50 thf(fact_3203_all__nat__less,axiom,
% 5.13/5.50 ! [N: nat,P: nat > $o] :
% 5.13/5.50 ( ( ! [M2: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ M2 @ N )
% 5.13/5.50 => ( P @ M2 ) ) )
% 5.13/5.50 = ( ! [X2: nat] :
% 5.13/5.50 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.13/5.50 => ( P @ X2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % all_nat_less
% 5.13/5.50 thf(fact_3204_vebt__buildup_Osimps_I1_J,axiom,
% 5.13/5.50 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.13/5.50 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_buildup.simps(1)
% 5.13/5.50 thf(fact_3205_not__exp__less__eq__0__int,axiom,
% 5.13/5.50 ! [N: nat] :
% 5.13/5.50 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.13/5.50
% 5.13/5.50 % not_exp_less_eq_0_int
% 5.13/5.50 thf(fact_3206_invar__vebt_Ointros_I1_J,axiom,
% 5.13/5.50 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % invar_vebt.intros(1)
% 5.13/5.50 thf(fact_3207_int__power__div__base,axiom,
% 5.13/5.50 ! [M: nat,K: int] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.13/5.50 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.13/5.50 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.13/5.50 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % int_power_div_base
% 5.13/5.50 thf(fact_3208_vebt__member_Osimps_I1_J,axiom,
% 5.13/5.50 ! [A: $o,B: $o,X: nat] :
% 5.13/5.50 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.13/5.50 = ( ( ( X = zero_zero_nat )
% 5.13/5.50 => A )
% 5.13/5.50 & ( ( X != zero_zero_nat )
% 5.13/5.50 => ( ( ( X = one_one_nat )
% 5.13/5.50 => B )
% 5.13/5.50 & ( X = one_one_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_member.simps(1)
% 5.13/5.50 thf(fact_3209_vebt__buildup_Osimps_I2_J,axiom,
% 5.13/5.50 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.13/5.50 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_buildup.simps(2)
% 5.13/5.50 thf(fact_3210_VEBT__internal_OminNull_Ocases,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT] :
% 5.13/5.50 ( ( X
% 5.13/5.50 != ( vEBT_Leaf @ $false @ $false ) )
% 5.13/5.50 => ( ! [Uv2: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.13/5.50 => ( ! [Uu3: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.13/5.50 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.13/5.50 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.cases
% 5.13/5.50 thf(fact_3211_vebt__insert_Osimps_I1_J,axiom,
% 5.13/5.50 ! [X: nat,A: $o,B: $o] :
% 5.13/5.50 ( ( ( X = zero_zero_nat )
% 5.13/5.50 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.13/5.50 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.13/5.50 & ( ( X != zero_zero_nat )
% 5.13/5.50 => ( ( ( X = one_one_nat )
% 5.13/5.50 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.13/5.50 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.13/5.50 & ( ( X != one_one_nat )
% 5.13/5.50 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.13/5.50 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_insert.simps(1)
% 5.13/5.50 thf(fact_3212_vebt__pred_Osimps_I1_J,axiom,
% 5.13/5.50 ! [Uu: $o,Uv: $o] :
% 5.13/5.50 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.13/5.50 = none_nat ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_pred.simps(1)
% 5.13/5.50 thf(fact_3213_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.13/5.50 ! [A: $o,B: $o,X: nat] :
% 5.13/5.50 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.13/5.50 = ( ( ( X = zero_zero_nat )
% 5.13/5.50 => A )
% 5.13/5.50 & ( ( X != zero_zero_nat )
% 5.13/5.50 => ( ( ( X = one_one_nat )
% 5.13/5.50 => B )
% 5.13/5.50 & ( X = one_one_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.naive_member.simps(1)
% 5.13/5.50 thf(fact_3214_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT] :
% 5.13/5.50 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.13/5.50 => ( ! [Uv2: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.13/5.50 => ( ! [Uu3: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.13/5.50 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.elims(3)
% 5.13/5.50 thf(fact_3215_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT] :
% 5.13/5.50 ( ( vEBT_VEBT_minNull @ X )
% 5.13/5.50 => ( ( X
% 5.13/5.50 != ( vEBT_Leaf @ $false @ $false ) )
% 5.13/5.50 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.elims(2)
% 5.13/5.50 thf(fact_3216_not__psubset__empty,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 5.13/5.50
% 5.13/5.50 % not_psubset_empty
% 5.13/5.50 thf(fact_3217_not__psubset__empty,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 5.13/5.50
% 5.13/5.50 % not_psubset_empty
% 5.13/5.50 thf(fact_3218_not__psubset__empty,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 5.13/5.50
% 5.13/5.50 % not_psubset_empty
% 5.13/5.50 thf(fact_3219_emptyE,axiom,
% 5.13/5.50 ! [A: complex] :
% 5.13/5.50 ~ ( member_complex @ A @ bot_bot_set_complex ) ).
% 5.13/5.50
% 5.13/5.50 % emptyE
% 5.13/5.50 thf(fact_3220_emptyE,axiom,
% 5.13/5.50 ! [A: product_prod_nat_nat] :
% 5.13/5.50 ~ ( member8440522571783428010at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 5.13/5.50
% 5.13/5.50 % emptyE
% 5.13/5.50 thf(fact_3221_emptyE,axiom,
% 5.13/5.50 ! [A: nat] :
% 5.13/5.50 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 5.13/5.50
% 5.13/5.50 % emptyE
% 5.13/5.50 thf(fact_3222_emptyE,axiom,
% 5.13/5.50 ! [A: int] :
% 5.13/5.50 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 5.13/5.50
% 5.13/5.50 % emptyE
% 5.13/5.50 thf(fact_3223_emptyE,axiom,
% 5.13/5.50 ! [A: real] :
% 5.13/5.50 ~ ( member_real @ A @ bot_bot_set_real ) ).
% 5.13/5.50
% 5.13/5.50 % emptyE
% 5.13/5.50 thf(fact_3224_equals0D,axiom,
% 5.13/5.50 ! [A2: set_complex,A: complex] :
% 5.13/5.50 ( ( A2 = bot_bot_set_complex )
% 5.13/5.50 => ~ ( member_complex @ A @ A2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0D
% 5.13/5.50 thf(fact_3225_equals0D,axiom,
% 5.13/5.50 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 5.13/5.50 ( ( A2 = bot_bo2099793752762293965at_nat )
% 5.13/5.50 => ~ ( member8440522571783428010at_nat @ A @ A2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0D
% 5.13/5.50 thf(fact_3226_equals0D,axiom,
% 5.13/5.50 ! [A2: set_nat,A: nat] :
% 5.13/5.50 ( ( A2 = bot_bot_set_nat )
% 5.13/5.50 => ~ ( member_nat @ A @ A2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0D
% 5.13/5.50 thf(fact_3227_equals0D,axiom,
% 5.13/5.50 ! [A2: set_int,A: int] :
% 5.13/5.50 ( ( A2 = bot_bot_set_int )
% 5.13/5.50 => ~ ( member_int @ A @ A2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0D
% 5.13/5.50 thf(fact_3228_equals0D,axiom,
% 5.13/5.50 ! [A2: set_real,A: real] :
% 5.13/5.50 ( ( A2 = bot_bot_set_real )
% 5.13/5.50 => ~ ( member_real @ A @ A2 ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0D
% 5.13/5.50 thf(fact_3229_equals0I,axiom,
% 5.13/5.50 ! [A2: set_complex] :
% 5.13/5.50 ( ! [Y3: complex] :
% 5.13/5.50 ~ ( member_complex @ Y3 @ A2 )
% 5.13/5.50 => ( A2 = bot_bot_set_complex ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0I
% 5.13/5.50 thf(fact_3230_equals0I,axiom,
% 5.13/5.50 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.13/5.50 ( ! [Y3: product_prod_nat_nat] :
% 5.13/5.50 ~ ( member8440522571783428010at_nat @ Y3 @ A2 )
% 5.13/5.50 => ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0I
% 5.13/5.50 thf(fact_3231_equals0I,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ! [Y3: nat] :
% 5.13/5.50 ~ ( member_nat @ Y3 @ A2 )
% 5.13/5.50 => ( A2 = bot_bot_set_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0I
% 5.13/5.50 thf(fact_3232_equals0I,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ! [Y3: int] :
% 5.13/5.50 ~ ( member_int @ Y3 @ A2 )
% 5.13/5.50 => ( A2 = bot_bot_set_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0I
% 5.13/5.50 thf(fact_3233_equals0I,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ! [Y3: real] :
% 5.13/5.50 ~ ( member_real @ Y3 @ A2 )
% 5.13/5.50 => ( A2 = bot_bot_set_real ) ) ).
% 5.13/5.50
% 5.13/5.50 % equals0I
% 5.13/5.50 thf(fact_3234_ex__in__conv,axiom,
% 5.13/5.50 ! [A2: set_complex] :
% 5.13/5.50 ( ( ? [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 != bot_bot_set_complex ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_in_conv
% 5.13/5.50 thf(fact_3235_ex__in__conv,axiom,
% 5.13/5.50 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.13/5.50 ( ( ? [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 != bot_bo2099793752762293965at_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_in_conv
% 5.13/5.50 thf(fact_3236_ex__in__conv,axiom,
% 5.13/5.50 ! [A2: set_nat] :
% 5.13/5.50 ( ( ? [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 != bot_bot_set_nat ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_in_conv
% 5.13/5.50 thf(fact_3237_ex__in__conv,axiom,
% 5.13/5.50 ! [A2: set_int] :
% 5.13/5.50 ( ( ? [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 != bot_bot_set_int ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_in_conv
% 5.13/5.50 thf(fact_3238_ex__in__conv,axiom,
% 5.13/5.50 ! [A2: set_real] :
% 5.13/5.50 ( ( ? [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.13/5.50 = ( A2 != bot_bot_set_real ) ) ).
% 5.13/5.50
% 5.13/5.50 % ex_in_conv
% 5.13/5.50 thf(fact_3239_bot__set__def,axiom,
% 5.13/5.50 ( bot_bot_set_complex
% 5.13/5.50 = ( collect_complex @ bot_bot_complex_o ) ) ).
% 5.13/5.50
% 5.13/5.50 % bot_set_def
% 5.13/5.50 thf(fact_3240_bot__set__def,axiom,
% 5.13/5.50 ( bot_bo2099793752762293965at_nat
% 5.13/5.50 = ( collec3392354462482085612at_nat @ bot_bo482883023278783056_nat_o ) ) ).
% 5.13/5.50
% 5.13/5.50 % bot_set_def
% 5.13/5.50 thf(fact_3241_bot__set__def,axiom,
% 5.13/5.50 ( bot_bot_set_list_nat
% 5.13/5.50 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 5.13/5.50
% 5.13/5.50 % bot_set_def
% 5.13/5.50 thf(fact_3242_bot__set__def,axiom,
% 5.13/5.50 ( bot_bot_set_nat
% 5.13/5.50 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 5.13/5.50
% 5.13/5.50 % bot_set_def
% 5.13/5.50 thf(fact_3243_bot__set__def,axiom,
% 5.13/5.50 ( bot_bot_set_int
% 5.13/5.50 = ( collect_int @ bot_bot_int_o ) ) ).
% 5.13/5.50
% 5.13/5.50 % bot_set_def
% 5.13/5.50 thf(fact_3244_bot__set__def,axiom,
% 5.13/5.50 ( bot_bot_set_real
% 5.13/5.50 = ( collect_real @ bot_bot_real_o ) ) ).
% 5.13/5.50
% 5.13/5.50 % bot_set_def
% 5.13/5.50 thf(fact_3245_realpow__pos__nth2,axiom,
% 5.13/5.50 ! [A: real,N: nat] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ? [R3: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.13/5.50 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.13/5.50 = A ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % realpow_pos_nth2
% 5.13/5.50 thf(fact_3246_real__arch__pow__inv,axiom,
% 5.13/5.50 ! [Y4: real,X: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.13/5.50 => ( ( ord_less_real @ X @ one_one_real )
% 5.13/5.50 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y4 ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % real_arch_pow_inv
% 5.13/5.50 thf(fact_3247_vebt__mint_Ocases,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT] :
% 5.13/5.50 ( ! [A3: $o,B2: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Leaf @ A3 @ B2 ) )
% 5.13/5.50 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.13/5.50 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_mint.cases
% 5.13/5.50 thf(fact_3248_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT,Y4: $o] :
% 5.13/5.50 ( ( ( vEBT_VEBT_minNull @ X )
% 5.13/5.50 = Y4 )
% 5.13/5.50 => ( ( ( X
% 5.13/5.50 = ( vEBT_Leaf @ $false @ $false ) )
% 5.13/5.50 => ~ Y4 )
% 5.13/5.50 => ( ( ? [Uv2: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.13/5.50 => Y4 )
% 5.13/5.50 => ( ( ? [Uu3: $o] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.13/5.50 => Y4 )
% 5.13/5.50 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.13/5.50 => ~ Y4 )
% 5.13/5.50 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.13/5.50 => Y4 ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % VEBT_internal.minNull.elims(1)
% 5.13/5.50 thf(fact_3249_realpow__pos__nth,axiom,
% 5.13/5.50 ! [N: nat,A: real] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ? [R3: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.13/5.50 & ( ( power_power_real @ R3 @ N )
% 5.13/5.50 = A ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % realpow_pos_nth
% 5.13/5.50 thf(fact_3250_realpow__pos__nth__unique,axiom,
% 5.13/5.50 ! [N: nat,A: real] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.13/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.13/5.50 => ? [X3: real] :
% 5.13/5.50 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.13/5.50 & ( ( power_power_real @ X3 @ N )
% 5.13/5.50 = A )
% 5.13/5.50 & ! [Y5: real] :
% 5.13/5.50 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 5.13/5.50 & ( ( power_power_real @ Y5 @ N )
% 5.13/5.50 = A ) )
% 5.13/5.50 => ( Y5 = X3 ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % realpow_pos_nth_unique
% 5.13/5.50 thf(fact_3251_empty__def,axiom,
% 5.13/5.50 ( bot_bot_set_complex
% 5.13/5.50 = ( collect_complex
% 5.13/5.50 @ ^ [X2: complex] : $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_def
% 5.13/5.50 thf(fact_3252_empty__def,axiom,
% 5.13/5.50 ( bot_bo2099793752762293965at_nat
% 5.13/5.50 = ( collec3392354462482085612at_nat
% 5.13/5.50 @ ^ [X2: product_prod_nat_nat] : $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_def
% 5.13/5.50 thf(fact_3253_empty__def,axiom,
% 5.13/5.50 ( bot_bot_set_list_nat
% 5.13/5.50 = ( collect_list_nat
% 5.13/5.50 @ ^ [X2: list_nat] : $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_def
% 5.13/5.50 thf(fact_3254_empty__def,axiom,
% 5.13/5.50 ( bot_bot_set_nat
% 5.13/5.50 = ( collect_nat
% 5.13/5.50 @ ^ [X2: nat] : $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_def
% 5.13/5.50 thf(fact_3255_empty__def,axiom,
% 5.13/5.50 ( bot_bot_set_int
% 5.13/5.50 = ( collect_int
% 5.13/5.50 @ ^ [X2: int] : $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_def
% 5.13/5.50 thf(fact_3256_empty__def,axiom,
% 5.13/5.50 ( bot_bot_set_real
% 5.13/5.50 = ( collect_real
% 5.13/5.50 @ ^ [X2: real] : $false ) ) ).
% 5.13/5.50
% 5.13/5.50 % empty_def
% 5.13/5.50 thf(fact_3257_vebt__pred_Osimps_I2_J,axiom,
% 5.13/5.50 ! [A: $o,Uw: $o] :
% 5.13/5.50 ( ( A
% 5.13/5.50 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A
% 5.13/5.50 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.13/5.50 = none_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_pred.simps(2)
% 5.13/5.50 thf(fact_3258_vebt__mint_Osimps_I1_J,axiom,
% 5.13/5.50 ! [A: $o,B: $o] :
% 5.13/5.50 ( ( A
% 5.13/5.50 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A
% 5.13/5.50 => ( ( B
% 5.13/5.50 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.13/5.50 = ( some_nat @ one_one_nat ) ) )
% 5.13/5.50 & ( ~ B
% 5.13/5.50 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.13/5.50 = none_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_mint.simps(1)
% 5.13/5.50 thf(fact_3259_vebt__maxt_Osimps_I1_J,axiom,
% 5.13/5.50 ! [B: $o,A: $o] :
% 5.13/5.50 ( ( B
% 5.13/5.50 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.13/5.50 = ( some_nat @ one_one_nat ) ) )
% 5.13/5.50 & ( ~ B
% 5.13/5.50 => ( ( A
% 5.13/5.50 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A
% 5.13/5.50 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.13/5.50 = none_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_maxt.simps(1)
% 5.13/5.50 thf(fact_3260_vebt__pred_Osimps_I3_J,axiom,
% 5.13/5.50 ! [B: $o,A: $o,Va: nat] :
% 5.13/5.50 ( ( B
% 5.13/5.50 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.13/5.50 = ( some_nat @ one_one_nat ) ) )
% 5.13/5.50 & ( ~ B
% 5.13/5.50 => ( ( A
% 5.13/5.50 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A
% 5.13/5.50 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.13/5.50 = none_nat ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_pred.simps(3)
% 5.13/5.50 thf(fact_3261_vebt__mint_Oelims,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT,Y4: option_nat] :
% 5.13/5.50 ( ( ( vEBT_vebt_mint @ X )
% 5.13/5.50 = Y4 )
% 5.13/5.50 => ( ! [A3: $o,B2: $o] :
% 5.13/5.50 ( ( X
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.13/5.50 => ~ ( ( A3
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A3
% 5.13/5.50 => ( ( B2
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ one_one_nat ) ) )
% 5.13/5.50 & ( ~ B2
% 5.13/5.50 => ( Y4 = none_nat ) ) ) ) ) )
% 5.13/5.50 => ( ( ? [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.13/5.50 => ( Y4 != none_nat ) )
% 5.13/5.50 => ~ ! [Mi2: nat] :
% 5.13/5.50 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.13/5.50 => ( Y4
% 5.13/5.50 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_mint.elims
% 5.13/5.50 thf(fact_3262_vebt__maxt_Oelims,axiom,
% 5.13/5.50 ! [X: vEBT_VEBT,Y4: option_nat] :
% 5.13/5.50 ( ( ( vEBT_vebt_maxt @ X )
% 5.13/5.50 = Y4 )
% 5.13/5.50 => ( ! [A3: $o,B2: $o] :
% 5.13/5.50 ( ( X
% 5.13/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.13/5.50 => ~ ( ( B2
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ one_one_nat ) ) )
% 5.13/5.50 & ( ~ B2
% 5.13/5.50 => ( ( A3
% 5.13/5.50 => ( Y4
% 5.13/5.50 = ( some_nat @ zero_zero_nat ) ) )
% 5.13/5.50 & ( ~ A3
% 5.13/5.50 => ( Y4 = none_nat ) ) ) ) ) )
% 5.13/5.50 => ( ( ? [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.13/5.50 => ( Y4 != none_nat ) )
% 5.13/5.50 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.13/5.50 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.13/5.50 ( X
% 5.13/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.13/5.50 => ( Y4
% 5.13/5.50 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % vebt_maxt.elims
% 5.13/5.50 thf(fact_3263_div__positive,axiom,
% 5.13/5.50 ! [B: nat,A: nat] :
% 5.13/5.50 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.13/5.50 => ( ( ord_less_eq_nat @ B @ A )
% 5.13/5.50 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_positive
% 5.13/5.50 thf(fact_3264_div__positive,axiom,
% 5.13/5.50 ! [B: int,A: int] :
% 5.13/5.50 ( ( ord_less_int @ zero_zero_int @ B )
% 5.13/5.50 => ( ( ord_less_eq_int @ B @ A )
% 5.13/5.50 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % div_positive
% 5.13/5.50 thf(fact_3265_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.13/5.50 ! [A: nat,B: nat] :
% 5.13/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.13/5.50 => ( ( ord_less_nat @ A @ B )
% 5.13/5.50 => ( ( divide_divide_nat @ A @ B )
% 5.13/5.50 = zero_zero_nat ) ) ) ).
% 5.13/5.50
% 5.13/5.50 % unique_euclidean_semiring_numeral_class.div_less
% 5.13/5.50 thf(fact_3266_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.13/5.50 ! [A: int,B: int] :
% 5.13/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.50 => ( ( ord_less_int @ A @ B )
% 5.24/5.50 => ( ( divide_divide_int @ A @ B )
% 5.24/5.50 = zero_zero_int ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unique_euclidean_semiring_numeral_class.div_less
% 5.24/5.50 thf(fact_3267_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.24/5.50 ! [C: nat,A: nat,B: nat] :
% 5.24/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.24/5.50 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.50 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.24/5.50 thf(fact_3268_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.24/5.50 ! [C: int,A: int,B: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.24/5.50 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.50 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.24/5.50 thf(fact_3269_discrete,axiom,
% 5.24/5.50 ( ord_less_nat
% 5.24/5.50 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % discrete
% 5.24/5.50 thf(fact_3270_discrete,axiom,
% 5.24/5.50 ( ord_less_int
% 5.24/5.50 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % discrete
% 5.24/5.50 thf(fact_3271_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.50 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.24/5.50 => ( ! [A3: $o,B2: $o] :
% 5.24/5.50 ( ( X
% 5.24/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.50 => ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.50 => A3 )
% 5.24/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.50 => B2 )
% 5.24/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.24/5.50 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.24/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [S: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.24/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.naive_member.elims(3)
% 5.24/5.50 thf(fact_3272_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.50 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.24/5.50 => ( ! [A3: $o,B2: $o] :
% 5.24/5.50 ( ( X
% 5.24/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.50 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.50 => A3 )
% 5.24/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.50 => B2 )
% 5.24/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.24/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [S: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.24/5.50 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.naive_member.elims(2)
% 5.24/5.50 thf(fact_3273_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.50 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.24/5.50 = Y4 )
% 5.24/5.50 => ( ! [A3: $o,B2: $o] :
% 5.24/5.50 ( ( X
% 5.24/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.50 => A3 )
% 5.24/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.50 => B2 )
% 5.24/5.50 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.24/5.50 => ( ( ? [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.24/5.50 => Y4 )
% 5.24/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [S: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.naive_member.elims(1)
% 5.24/5.50 thf(fact_3274_vebt__member_Oelims_I2_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.50 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.24/5.50 => ( ! [A3: $o,B2: $o] :
% 5.24/5.50 ( ( X
% 5.24/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.50 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.50 => A3 )
% 5.24/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.50 => B2 )
% 5.24/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.24/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Summary2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.50 => ~ ( ( Xa2 != Mi2 )
% 5.24/5.50 => ( ( Xa2 != Ma2 )
% 5.24/5.50 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.50 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.50 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % vebt_member.elims(2)
% 5.24/5.50 thf(fact_3275_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.50 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.24/5.50 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.50 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.24/5.50 => ( ! [Mi2: nat,Ma2: nat] :
% 5.24/5.50 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.24/5.50 => ( ( Xa2 = Mi2 )
% 5.24/5.50 | ( Xa2 = Ma2 ) ) )
% 5.24/5.50 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Vc2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.24/5.50 => ( ( Xa2 = Mi2 )
% 5.24/5.50 | ( Xa2 = Ma2 )
% 5.24/5.50 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.24/5.50 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Vd2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.24/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.membermima.elims(3)
% 5.24/5.50 thf(fact_3276_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.50 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.24/5.50 = Y4 )
% 5.24/5.50 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.50 => Y4 )
% 5.24/5.50 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.24/5.50 => Y4 )
% 5.24/5.50 => ( ! [Mi2: nat,Ma2: nat] :
% 5.24/5.50 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( Xa2 = Mi2 )
% 5.24/5.50 | ( Xa2 = Ma2 ) ) ) ) )
% 5.24/5.50 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Vc2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( Xa2 = Mi2 )
% 5.24/5.50 | ( Xa2 = Ma2 )
% 5.24/5.50 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.24/5.50 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Vd2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.membermima.elims(1)
% 5.24/5.50 thf(fact_3277_vebt__member_Oelims_I3_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.50 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.24/5.50 => ( ! [A3: $o,B2: $o] :
% 5.24/5.50 ( ( X
% 5.24/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.50 => ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.50 => A3 )
% 5.24/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.50 => B2 )
% 5.24/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.24/5.50 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.24/5.50 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.24/5.50 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.24/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Summary2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.50 => ( ( Xa2 != Mi2 )
% 5.24/5.50 => ( ( Xa2 != Ma2 )
% 5.24/5.50 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.50 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.50 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % vebt_member.elims(3)
% 5.24/5.50 thf(fact_3278_vebt__member_Oelims_I1_J,axiom,
% 5.24/5.50 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.50 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.24/5.50 = Y4 )
% 5.24/5.50 => ( ! [A3: $o,B2: $o] :
% 5.24/5.50 ( ( X
% 5.24/5.50 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.50 => A3 )
% 5.24/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.50 => B2 )
% 5.24/5.50 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.24/5.50 => ( ( ? [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.24/5.50 => Y4 )
% 5.24/5.50 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.24/5.50 => Y4 )
% 5.24/5.50 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.24/5.50 => Y4 )
% 5.24/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.24/5.50 ( ? [Summary2: vEBT_VEBT] :
% 5.24/5.50 ( X
% 5.24/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.50 => ( Y4
% 5.24/5.50 = ( ~ ( ( Xa2 != Mi2 )
% 5.24/5.50 => ( ( Xa2 != Ma2 )
% 5.24/5.50 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.50 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.50 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.50 => ( 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 ) ) ) ) ) )
% 5.24/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % vebt_member.elims(1)
% 5.24/5.50 thf(fact_3279_divmod__step__eq,axiom,
% 5.24/5.50 ! [L2: num,R2: nat,Q2: nat] :
% 5.24/5.50 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.24/5.50 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.24/5.50 = ( 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 ) ) ) ) )
% 5.24/5.50 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.24/5.50 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.24/5.50 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % divmod_step_eq
% 5.24/5.50 thf(fact_3280_divmod__step__eq,axiom,
% 5.24/5.50 ! [L2: num,R2: int,Q2: int] :
% 5.24/5.50 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.24/5.50 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.50 = ( 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 ) ) ) ) )
% 5.24/5.50 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.24/5.50 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.50 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % divmod_step_eq
% 5.24/5.50 thf(fact_3281_divmod__step__eq,axiom,
% 5.24/5.50 ! [L2: num,R2: code_integer,Q2: code_integer] :
% 5.24/5.50 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.24/5.50 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.24/5.50 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.24/5.50 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.24/5.50 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.24/5.50 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % divmod_step_eq
% 5.24/5.50 thf(fact_3282_atLeastatMost__empty,axiom,
% 5.24/5.50 ! [B: rat,A: rat] :
% 5.24/5.50 ( ( ord_less_rat @ B @ A )
% 5.24/5.50 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.24/5.50 = bot_bot_set_rat ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty
% 5.24/5.50 thf(fact_3283_atLeastatMost__empty,axiom,
% 5.24/5.50 ! [B: num,A: num] :
% 5.24/5.50 ( ( ord_less_num @ B @ A )
% 5.24/5.50 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.24/5.50 = bot_bot_set_num ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty
% 5.24/5.50 thf(fact_3284_atLeastatMost__empty,axiom,
% 5.24/5.50 ! [B: nat,A: nat] :
% 5.24/5.50 ( ( ord_less_nat @ B @ A )
% 5.24/5.50 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.24/5.50 = bot_bot_set_nat ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty
% 5.24/5.50 thf(fact_3285_atLeastatMost__empty,axiom,
% 5.24/5.50 ! [B: int,A: int] :
% 5.24/5.50 ( ( ord_less_int @ B @ A )
% 5.24/5.50 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.24/5.50 = bot_bot_set_int ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty
% 5.24/5.50 thf(fact_3286_atLeastatMost__empty,axiom,
% 5.24/5.50 ! [B: real,A: real] :
% 5.24/5.50 ( ( ord_less_real @ B @ A )
% 5.24/5.50 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.24/5.50 = bot_bot_set_real ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty
% 5.24/5.50 thf(fact_3287_atLeastatMost__subset__iff,axiom,
% 5.24/5.50 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.24/5.50 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.24/5.50 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_subset_iff
% 5.24/5.50 thf(fact_3288_atLeastatMost__subset__iff,axiom,
% 5.24/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.24/5.50 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_rat @ C @ A )
% 5.24/5.50 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_subset_iff
% 5.24/5.50 thf(fact_3289_atLeastatMost__subset__iff,axiom,
% 5.24/5.50 ! [A: num,B: num,C: num,D: num] :
% 5.24/5.50 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_num @ C @ A )
% 5.24/5.50 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_subset_iff
% 5.24/5.50 thf(fact_3290_atLeastatMost__subset__iff,axiom,
% 5.24/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.24/5.50 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_nat @ C @ A )
% 5.24/5.50 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_subset_iff
% 5.24/5.50 thf(fact_3291_atLeastatMost__subset__iff,axiom,
% 5.24/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.24/5.50 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_int @ C @ A )
% 5.24/5.50 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_subset_iff
% 5.24/5.50 thf(fact_3292_atLeastatMost__subset__iff,axiom,
% 5.24/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.50 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_real @ C @ A )
% 5.24/5.50 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_subset_iff
% 5.24/5.50 thf(fact_3293_atLeastatMost__empty__iff,axiom,
% 5.24/5.50 ! [A: set_nat,B: set_nat] :
% 5.24/5.50 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.24/5.50 = bot_bot_set_set_nat )
% 5.24/5.50 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff
% 5.24/5.50 thf(fact_3294_atLeastatMost__empty__iff,axiom,
% 5.24/5.50 ! [A: rat,B: rat] :
% 5.24/5.50 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.24/5.50 = bot_bot_set_rat )
% 5.24/5.50 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff
% 5.24/5.50 thf(fact_3295_atLeastatMost__empty__iff,axiom,
% 5.24/5.50 ! [A: num,B: num] :
% 5.24/5.50 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.24/5.50 = bot_bot_set_num )
% 5.24/5.50 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff
% 5.24/5.50 thf(fact_3296_atLeastatMost__empty__iff,axiom,
% 5.24/5.50 ! [A: nat,B: nat] :
% 5.24/5.50 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.24/5.50 = bot_bot_set_nat )
% 5.24/5.50 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff
% 5.24/5.50 thf(fact_3297_atLeastatMost__empty__iff,axiom,
% 5.24/5.50 ! [A: int,B: int] :
% 5.24/5.50 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.24/5.50 = bot_bot_set_int )
% 5.24/5.50 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff
% 5.24/5.50 thf(fact_3298_atLeastatMost__empty__iff,axiom,
% 5.24/5.50 ! [A: real,B: real] :
% 5.24/5.50 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.24/5.50 = bot_bot_set_real )
% 5.24/5.50 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff
% 5.24/5.50 thf(fact_3299_atLeastatMost__empty__iff2,axiom,
% 5.24/5.50 ! [A: set_nat,B: set_nat] :
% 5.24/5.50 ( ( bot_bot_set_set_nat
% 5.24/5.50 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff2
% 5.24/5.50 thf(fact_3300_atLeastatMost__empty__iff2,axiom,
% 5.24/5.50 ! [A: rat,B: rat] :
% 5.24/5.50 ( ( bot_bot_set_rat
% 5.24/5.50 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff2
% 5.24/5.50 thf(fact_3301_atLeastatMost__empty__iff2,axiom,
% 5.24/5.50 ! [A: num,B: num] :
% 5.24/5.50 ( ( bot_bot_set_num
% 5.24/5.50 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff2
% 5.24/5.50 thf(fact_3302_atLeastatMost__empty__iff2,axiom,
% 5.24/5.50 ! [A: nat,B: nat] :
% 5.24/5.50 ( ( bot_bot_set_nat
% 5.24/5.50 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff2
% 5.24/5.50 thf(fact_3303_atLeastatMost__empty__iff2,axiom,
% 5.24/5.50 ! [A: int,B: int] :
% 5.24/5.50 ( ( bot_bot_set_int
% 5.24/5.50 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff2
% 5.24/5.50 thf(fact_3304_atLeastatMost__empty__iff2,axiom,
% 5.24/5.50 ! [A: real,B: real] :
% 5.24/5.50 ( ( bot_bot_set_real
% 5.24/5.50 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.24/5.50 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_empty_iff2
% 5.24/5.50 thf(fact_3305_atLeastAtMost__iff,axiom,
% 5.24/5.50 ! [I2: set_nat,L2: set_nat,U2: set_nat] :
% 5.24/5.50 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L2 @ U2 ) )
% 5.24/5.50 = ( ( ord_less_eq_set_nat @ L2 @ I2 )
% 5.24/5.50 & ( ord_less_eq_set_nat @ I2 @ U2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastAtMost_iff
% 5.24/5.50 thf(fact_3306_atLeastAtMost__iff,axiom,
% 5.24/5.50 ! [I2: rat,L2: rat,U2: rat] :
% 5.24/5.50 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L2 @ U2 ) )
% 5.24/5.50 = ( ( ord_less_eq_rat @ L2 @ I2 )
% 5.24/5.50 & ( ord_less_eq_rat @ I2 @ U2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastAtMost_iff
% 5.24/5.50 thf(fact_3307_atLeastAtMost__iff,axiom,
% 5.24/5.50 ! [I2: num,L2: num,U2: num] :
% 5.24/5.50 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U2 ) )
% 5.24/5.50 = ( ( ord_less_eq_num @ L2 @ I2 )
% 5.24/5.50 & ( ord_less_eq_num @ I2 @ U2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastAtMost_iff
% 5.24/5.50 thf(fact_3308_atLeastAtMost__iff,axiom,
% 5.24/5.50 ! [I2: nat,L2: nat,U2: nat] :
% 5.24/5.50 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U2 ) )
% 5.24/5.50 = ( ( ord_less_eq_nat @ L2 @ I2 )
% 5.24/5.50 & ( ord_less_eq_nat @ I2 @ U2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastAtMost_iff
% 5.24/5.50 thf(fact_3309_atLeastAtMost__iff,axiom,
% 5.24/5.50 ! [I2: int,L2: int,U2: int] :
% 5.24/5.50 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U2 ) )
% 5.24/5.50 = ( ( ord_less_eq_int @ L2 @ I2 )
% 5.24/5.50 & ( ord_less_eq_int @ I2 @ U2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastAtMost_iff
% 5.24/5.50 thf(fact_3310_atLeastAtMost__iff,axiom,
% 5.24/5.50 ! [I2: real,L2: real,U2: real] :
% 5.24/5.50 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U2 ) )
% 5.24/5.50 = ( ( ord_less_eq_real @ L2 @ I2 )
% 5.24/5.50 & ( ord_less_eq_real @ I2 @ U2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastAtMost_iff
% 5.24/5.50 thf(fact_3311_Icc__eq__Icc,axiom,
% 5.24/5.50 ! [L2: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.24/5.50 ( ( ( set_or4548717258645045905et_nat @ L2 @ H2 )
% 5.24/5.50 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.24/5.50 = ( ( ( L2 = L3 )
% 5.24/5.50 & ( H2 = H3 ) )
% 5.24/5.50 | ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.24/5.50 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % Icc_eq_Icc
% 5.24/5.50 thf(fact_3312_Icc__eq__Icc,axiom,
% 5.24/5.50 ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 5.24/5.50 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.24/5.50 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.24/5.50 = ( ( ( L2 = L3 )
% 5.24/5.50 & ( H2 = H3 ) )
% 5.24/5.50 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.24/5.50 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % Icc_eq_Icc
% 5.24/5.50 thf(fact_3313_Icc__eq__Icc,axiom,
% 5.24/5.50 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.24/5.50 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.24/5.50 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.24/5.50 = ( ( ( L2 = L3 )
% 5.24/5.50 & ( H2 = H3 ) )
% 5.24/5.50 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.24/5.50 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % Icc_eq_Icc
% 5.24/5.50 thf(fact_3314_Icc__eq__Icc,axiom,
% 5.24/5.50 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.24/5.50 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.24/5.50 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.24/5.50 = ( ( ( L2 = L3 )
% 5.24/5.50 & ( H2 = H3 ) )
% 5.24/5.50 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.24/5.50 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % Icc_eq_Icc
% 5.24/5.50 thf(fact_3315_Icc__eq__Icc,axiom,
% 5.24/5.50 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.24/5.50 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.24/5.50 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.24/5.50 = ( ( ( L2 = L3 )
% 5.24/5.50 & ( H2 = H3 ) )
% 5.24/5.50 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.24/5.50 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % Icc_eq_Icc
% 5.24/5.50 thf(fact_3316_Icc__eq__Icc,axiom,
% 5.24/5.50 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.24/5.50 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.24/5.50 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.24/5.50 = ( ( ( L2 = L3 )
% 5.24/5.50 & ( H2 = H3 ) )
% 5.24/5.50 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.24/5.50 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % Icc_eq_Icc
% 5.24/5.50 thf(fact_3317_double__eq__0__iff,axiom,
% 5.24/5.50 ! [A: real] :
% 5.24/5.50 ( ( ( plus_plus_real @ A @ A )
% 5.24/5.50 = zero_zero_real )
% 5.24/5.50 = ( A = zero_zero_real ) ) ).
% 5.24/5.50
% 5.24/5.50 % double_eq_0_iff
% 5.24/5.50 thf(fact_3318_double__eq__0__iff,axiom,
% 5.24/5.50 ! [A: rat] :
% 5.24/5.50 ( ( ( plus_plus_rat @ A @ A )
% 5.24/5.50 = zero_zero_rat )
% 5.24/5.50 = ( A = zero_zero_rat ) ) ).
% 5.24/5.50
% 5.24/5.50 % double_eq_0_iff
% 5.24/5.50 thf(fact_3319_double__eq__0__iff,axiom,
% 5.24/5.50 ! [A: int] :
% 5.24/5.50 ( ( ( plus_plus_int @ A @ A )
% 5.24/5.50 = zero_zero_int )
% 5.24/5.50 = ( A = zero_zero_int ) ) ).
% 5.24/5.50
% 5.24/5.50 % double_eq_0_iff
% 5.24/5.50 thf(fact_3320_unset__bit__0,axiom,
% 5.24/5.50 ! [A: nat] :
% 5.24/5.50 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.24/5.50 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unset_bit_0
% 5.24/5.50 thf(fact_3321_unset__bit__0,axiom,
% 5.24/5.50 ! [A: int] :
% 5.24/5.50 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.24/5.50 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unset_bit_0
% 5.24/5.50 thf(fact_3322_zle__diff1__eq,axiom,
% 5.24/5.50 ! [W2: int,Z2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z2 @ one_one_int ) )
% 5.24/5.50 = ( ord_less_int @ W2 @ Z2 ) ) ).
% 5.24/5.50
% 5.24/5.50 % zle_diff1_eq
% 5.24/5.50 thf(fact_3323_zle__add1__eq__le,axiom,
% 5.24/5.50 ! [W2: int,Z2: int] :
% 5.24/5.50 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 5.24/5.50 = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 5.24/5.50
% 5.24/5.50 % zle_add1_eq_le
% 5.24/5.50 thf(fact_3324_div__pos__pos__trivial,axiom,
% 5.24/5.50 ! [K: int,L2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.50 => ( ( ord_less_int @ K @ L2 )
% 5.24/5.50 => ( ( divide_divide_int @ K @ L2 )
% 5.24/5.50 = zero_zero_int ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % div_pos_pos_trivial
% 5.24/5.50 thf(fact_3325_div__neg__neg__trivial,axiom,
% 5.24/5.50 ! [K: int,L2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.24/5.50 => ( ( ord_less_int @ L2 @ K )
% 5.24/5.50 => ( ( divide_divide_int @ K @ L2 )
% 5.24/5.50 = zero_zero_int ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % div_neg_neg_trivial
% 5.24/5.50 thf(fact_3326_add1__zle__eq,axiom,
% 5.24/5.50 ! [W2: int,Z2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 )
% 5.24/5.50 = ( ord_less_int @ W2 @ Z2 ) ) ).
% 5.24/5.50
% 5.24/5.50 % add1_zle_eq
% 5.24/5.50 thf(fact_3327_le__imp__0__less,axiom,
% 5.24/5.50 ! [Z2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.50 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % le_imp_0_less
% 5.24/5.50 thf(fact_3328_split__zdiv,axiom,
% 5.24/5.50 ! [P: int > $o,N: int,K: int] :
% 5.24/5.50 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.24/5.50 = ( ( ( K = zero_zero_int )
% 5.24/5.50 => ( P @ zero_zero_int ) )
% 5.24/5.50 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.50 => ! [I4: int,J3: int] :
% 5.24/5.50 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.24/5.50 & ( ord_less_int @ J3 @ K )
% 5.24/5.50 & ( N
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.24/5.50 => ( P @ I4 ) ) )
% 5.24/5.50 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.24/5.50 => ! [I4: int,J3: int] :
% 5.24/5.50 ( ( ( ord_less_int @ K @ J3 )
% 5.24/5.50 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.24/5.50 & ( N
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.24/5.50 => ( P @ I4 ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % split_zdiv
% 5.24/5.50 thf(fact_3329_odd__less__0__iff,axiom,
% 5.24/5.50 ! [Z2: int] :
% 5.24/5.50 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
% 5.24/5.50 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.50
% 5.24/5.50 % odd_less_0_iff
% 5.24/5.50 thf(fact_3330_div__pos__geq,axiom,
% 5.24/5.50 ! [L2: int,K: int] :
% 5.24/5.50 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.24/5.50 => ( ( ord_less_eq_int @ L2 @ K )
% 5.24/5.50 => ( ( divide_divide_int @ K @ L2 )
% 5.24/5.50 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % div_pos_geq
% 5.24/5.50 thf(fact_3331_q__pos__lemma,axiom,
% 5.24/5.50 ! [B4: int,Q5: int,R4: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.24/5.50 => ( ( ord_less_int @ R4 @ B4 )
% 5.24/5.50 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.24/5.50 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % q_pos_lemma
% 5.24/5.50 thf(fact_3332_int__div__neg__eq,axiom,
% 5.24/5.50 ! [A: int,B: int,Q2: int,R2: int] :
% 5.24/5.50 ( ( A
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.24/5.50 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.24/5.50 => ( ( ord_less_int @ B @ R2 )
% 5.24/5.50 => ( ( divide_divide_int @ A @ B )
% 5.24/5.50 = Q2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_div_neg_eq
% 5.24/5.50 thf(fact_3333_int__div__pos__eq,axiom,
% 5.24/5.50 ! [A: int,B: int,Q2: int,R2: int] :
% 5.24/5.50 ( ( A
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.24/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.24/5.50 => ( ( ord_less_int @ R2 @ B )
% 5.24/5.50 => ( ( divide_divide_int @ A @ B )
% 5.24/5.50 = Q2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_div_pos_eq
% 5.24/5.50 thf(fact_3334_zless__imp__add1__zle,axiom,
% 5.24/5.50 ! [W2: int,Z2: int] :
% 5.24/5.50 ( ( ord_less_int @ W2 @ Z2 )
% 5.24/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 ) ) ).
% 5.24/5.50
% 5.24/5.50 % zless_imp_add1_zle
% 5.24/5.50 thf(fact_3335_zdiv__mono2__lemma,axiom,
% 5.24/5.50 ! [B: int,Q2: int,R2: int,B4: int,Q5: int,R4: int] :
% 5.24/5.50 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.24/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.24/5.50 => ( ( ord_less_int @ R4 @ B4 )
% 5.24/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.24/5.50 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.24/5.50 => ( ( ord_less_eq_int @ B4 @ B )
% 5.24/5.50 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % zdiv_mono2_lemma
% 5.24/5.50 thf(fact_3336_zdiv__mono2__neg__lemma,axiom,
% 5.24/5.50 ! [B: int,Q2: int,R2: int,B4: int,Q5: int,R4: int] :
% 5.24/5.50 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.24/5.50 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.24/5.50 => ( ( ord_less_int @ R2 @ B )
% 5.24/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.24/5.50 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.24/5.50 => ( ( ord_less_eq_int @ B4 @ B )
% 5.24/5.50 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % zdiv_mono2_neg_lemma
% 5.24/5.50 thf(fact_3337_unique__quotient__lemma,axiom,
% 5.24/5.50 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.24/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.24/5.50 => ( ( ord_less_int @ R4 @ B )
% 5.24/5.50 => ( ( ord_less_int @ R2 @ B )
% 5.24/5.50 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unique_quotient_lemma
% 5.24/5.50 thf(fact_3338_unique__quotient__lemma__neg,axiom,
% 5.24/5.50 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.24/5.50 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.24/5.50 => ( ( ord_less_int @ B @ R2 )
% 5.24/5.50 => ( ( ord_less_int @ B @ R4 )
% 5.24/5.50 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % unique_quotient_lemma_neg
% 5.24/5.50 thf(fact_3339_odd__nonzero,axiom,
% 5.24/5.50 ! [Z2: int] :
% 5.24/5.50 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 )
% 5.24/5.50 != zero_zero_int ) ).
% 5.24/5.50
% 5.24/5.50 % odd_nonzero
% 5.24/5.50 thf(fact_3340_int__ge__induct,axiom,
% 5.24/5.50 ! [K: int,I2: int,P: int > $o] :
% 5.24/5.50 ( ( ord_less_eq_int @ K @ I2 )
% 5.24/5.50 => ( ( P @ K )
% 5.24/5.50 => ( ! [I3: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ K @ I3 )
% 5.24/5.50 => ( ( P @ I3 )
% 5.24/5.50 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.24/5.50 => ( P @ I2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_ge_induct
% 5.24/5.50 thf(fact_3341_int__induct,axiom,
% 5.24/5.50 ! [P: int > $o,K: int,I2: int] :
% 5.24/5.50 ( ( P @ K )
% 5.24/5.50 => ( ! [I3: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ K @ I3 )
% 5.24/5.50 => ( ( P @ I3 )
% 5.24/5.50 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.24/5.50 => ( ! [I3: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ I3 @ K )
% 5.24/5.50 => ( ( P @ I3 )
% 5.24/5.50 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.24/5.50 => ( P @ I2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_induct
% 5.24/5.50 thf(fact_3342_int__le__induct,axiom,
% 5.24/5.50 ! [I2: int,K: int,P: int > $o] :
% 5.24/5.50 ( ( ord_less_eq_int @ I2 @ K )
% 5.24/5.50 => ( ( P @ K )
% 5.24/5.50 => ( ! [I3: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ I3 @ K )
% 5.24/5.50 => ( ( P @ I3 )
% 5.24/5.50 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.24/5.50 => ( P @ I2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_le_induct
% 5.24/5.50 thf(fact_3343_zdiv__zmult2__eq,axiom,
% 5.24/5.50 ! [C: int,A: int,B: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.24/5.50 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.50 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % zdiv_zmult2_eq
% 5.24/5.50 thf(fact_3344_imult__is__0,axiom,
% 5.24/5.50 ! [M: extended_enat,N: extended_enat] :
% 5.24/5.50 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.24/5.50 = zero_z5237406670263579293d_enat )
% 5.24/5.50 = ( ( M = zero_z5237406670263579293d_enat )
% 5.24/5.50 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % imult_is_0
% 5.24/5.50 thf(fact_3345_zero__one__enat__neq_I1_J,axiom,
% 5.24/5.50 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.24/5.50
% 5.24/5.50 % zero_one_enat_neq(1)
% 5.24/5.50 thf(fact_3346_times__int__code_I2_J,axiom,
% 5.24/5.50 ! [L2: int] :
% 5.24/5.50 ( ( times_times_int @ zero_zero_int @ L2 )
% 5.24/5.50 = zero_zero_int ) ).
% 5.24/5.50
% 5.24/5.50 % times_int_code(2)
% 5.24/5.50 thf(fact_3347_times__int__code_I1_J,axiom,
% 5.24/5.50 ! [K: int] :
% 5.24/5.50 ( ( times_times_int @ K @ zero_zero_int )
% 5.24/5.50 = zero_zero_int ) ).
% 5.24/5.50
% 5.24/5.50 % times_int_code(1)
% 5.24/5.50 thf(fact_3348_int__one__le__iff__zero__less,axiom,
% 5.24/5.50 ! [Z2: int] :
% 5.24/5.50 ( ( ord_less_eq_int @ one_one_int @ Z2 )
% 5.24/5.50 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_one_le_iff_zero_less
% 5.24/5.50 thf(fact_3349_int__div__less__self,axiom,
% 5.24/5.50 ! [X: int,K: int] :
% 5.24/5.50 ( ( ord_less_int @ zero_zero_int @ X )
% 5.24/5.50 => ( ( ord_less_int @ one_one_int @ K )
% 5.24/5.50 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_div_less_self
% 5.24/5.50 thf(fact_3350_pos__zmult__eq__1__iff,axiom,
% 5.24/5.50 ! [M: int,N: int] :
% 5.24/5.50 ( ( ord_less_int @ zero_zero_int @ M )
% 5.24/5.50 => ( ( ( times_times_int @ M @ N )
% 5.24/5.50 = one_one_int )
% 5.24/5.50 = ( ( M = one_one_int )
% 5.24/5.50 & ( N = one_one_int ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % pos_zmult_eq_1_iff
% 5.24/5.50 thf(fact_3351_zmult__zless__mono2,axiom,
% 5.24/5.50 ! [I2: int,J: int,K: int] :
% 5.24/5.50 ( ( ord_less_int @ I2 @ J )
% 5.24/5.50 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.50 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % zmult_zless_mono2
% 5.24/5.50 thf(fact_3352_plus__int__code_I2_J,axiom,
% 5.24/5.50 ! [L2: int] :
% 5.24/5.50 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 5.24/5.50 = L2 ) ).
% 5.24/5.50
% 5.24/5.50 % plus_int_code(2)
% 5.24/5.50 thf(fact_3353_plus__int__code_I1_J,axiom,
% 5.24/5.50 ! [K: int] :
% 5.24/5.50 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.24/5.50 = K ) ).
% 5.24/5.50
% 5.24/5.50 % plus_int_code(1)
% 5.24/5.50 thf(fact_3354_bot__enat__def,axiom,
% 5.24/5.50 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.24/5.50
% 5.24/5.50 % bot_enat_def
% 5.24/5.50 thf(fact_3355_int__less__induct,axiom,
% 5.24/5.50 ! [I2: int,K: int,P: int > $o] :
% 5.24/5.50 ( ( ord_less_int @ I2 @ K )
% 5.24/5.50 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.24/5.50 => ( ! [I3: int] :
% 5.24/5.50 ( ( ord_less_int @ I3 @ K )
% 5.24/5.50 => ( ( P @ I3 )
% 5.24/5.50 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.24/5.50 => ( P @ I2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_less_induct
% 5.24/5.50 thf(fact_3356_int__distrib_I3_J,axiom,
% 5.24/5.50 ! [Z1: int,Z22: int,W2: int] :
% 5.24/5.50 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 5.24/5.50 = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_distrib(3)
% 5.24/5.50 thf(fact_3357_int__distrib_I4_J,axiom,
% 5.24/5.50 ! [W2: int,Z1: int,Z22: int] :
% 5.24/5.50 ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.24/5.50 = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_distrib(4)
% 5.24/5.50 thf(fact_3358_int__distrib_I2_J,axiom,
% 5.24/5.50 ! [W2: int,Z1: int,Z22: int] :
% 5.24/5.50 ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_distrib(2)
% 5.24/5.50 thf(fact_3359_int__distrib_I1_J,axiom,
% 5.24/5.50 ! [Z1: int,Z22: int,W2: int] :
% 5.24/5.50 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 5.24/5.50 = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_distrib(1)
% 5.24/5.50 thf(fact_3360_zless__add1__eq,axiom,
% 5.24/5.50 ! [W2: int,Z2: int] :
% 5.24/5.50 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 5.24/5.50 = ( ( ord_less_int @ W2 @ Z2 )
% 5.24/5.50 | ( W2 = Z2 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % zless_add1_eq
% 5.24/5.50 thf(fact_3361_int__gr__induct,axiom,
% 5.24/5.50 ! [K: int,I2: int,P: int > $o] :
% 5.24/5.50 ( ( ord_less_int @ K @ I2 )
% 5.24/5.50 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.24/5.50 => ( ! [I3: int] :
% 5.24/5.50 ( ( ord_less_int @ K @ I3 )
% 5.24/5.50 => ( ( P @ I3 )
% 5.24/5.50 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.24/5.50 => ( P @ I2 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % int_gr_induct
% 5.24/5.50 thf(fact_3362_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.24/5.50 ! [X: produc8306885398267862888on_nat] :
% 5.24/5.50 ( ! [Uu3: nat > nat > nat,Uv2: option_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc8929957630744042906on_nat @ Uu3 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.24/5.50 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.24/5.50 => ~ ! [F2: nat > nat > nat,A3: nat,B2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B2 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.option_shift.cases
% 5.24/5.50 thf(fact_3363_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.24/5.50 ! [X: produc5542196010084753463at_nat] :
% 5.24/5.50 ( ! [Uu3: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc2899441246263362727at_nat @ Uu3 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.24/5.50 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.24/5.50 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.option_shift.cases
% 5.24/5.50 thf(fact_3364_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.24/5.50 ! [X: produc1193250871479095198on_num] :
% 5.24/5.50 ( ! [Uu3: num > num > num,Uv2: option_num] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc5778274026573060048on_num @ Uu3 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.24/5.50 => ( ! [Uw2: num > num > num,V2: num] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.24/5.50 => ~ ! [F2: num > num > num,A3: num,B2: num] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B2 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.option_shift.cases
% 5.24/5.50 thf(fact_3365_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.24/5.50 ! [X: produc2233624965454879586on_nat] :
% 5.24/5.50 ( ! [Uu3: nat > nat > $o,Uv2: option_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc4035269172776083154on_nat @ Uu3 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.24/5.50 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.24/5.50 => ~ ! [F2: nat > nat > $o,X3: nat,Y3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.option_comp_shift.cases
% 5.24/5.50 thf(fact_3366_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.24/5.50 ! [X: produc5491161045314408544at_nat] :
% 5.24/5.50 ( ! [Uu3: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc3994169339658061776at_nat @ Uu3 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.24/5.50 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.24/5.50 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.option_comp_shift.cases
% 5.24/5.50 thf(fact_3367_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.24/5.50 ! [X: produc7036089656553540234on_num] :
% 5.24/5.50 ( ! [Uu3: num > num > $o,Uv2: option_num] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc3576312749637752826on_num @ Uu3 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.24/5.50 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.24/5.50 => ~ ! [F2: num > num > $o,X3: num,Y3: num] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.option_comp_shift.cases
% 5.24/5.50 thf(fact_3368_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.24/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.24/5.50 ( ! [Uu3: $o,Uv2: $o,D3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ D3 ) )
% 5.24/5.50 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.valid'.cases
% 5.24/5.50 thf(fact_3369_bounded__Max__nat,axiom,
% 5.24/5.50 ! [P: nat > $o,X: nat,M7: nat] :
% 5.24/5.50 ( ( P @ X )
% 5.24/5.50 => ( ! [X3: nat] :
% 5.24/5.50 ( ( P @ X3 )
% 5.24/5.50 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 5.24/5.50 => ~ ! [M4: nat] :
% 5.24/5.50 ( ( P @ M4 )
% 5.24/5.50 => ~ ! [X5: nat] :
% 5.24/5.50 ( ( P @ X5 )
% 5.24/5.50 => ( ord_less_eq_nat @ X5 @ M4 ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % bounded_Max_nat
% 5.24/5.50 thf(fact_3370_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.24/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.24/5.50 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.24/5.50 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.24/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ X3 ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.naive_member.cases
% 5.24/5.50 thf(fact_3371_vebt__insert_Ocases,axiom,
% 5.24/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.24/5.50 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.24/5.50 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ X3 ) )
% 5.24/5.50 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X3 ) )
% 5.24/5.50 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) )
% 5.24/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % vebt_insert.cases
% 5.24/5.50 thf(fact_3372_vebt__pred_Ocases,axiom,
% 5.24/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.24/5.50 ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ zero_zero_nat ) )
% 5.24/5.50 => ( ! [A3: $o,Uw2: $o] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.24/5.50 => ( ! [A3: $o,B2: $o,Va3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va3 ) ) ) )
% 5.24/5.50 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.24/5.50 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 5.24/5.50 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 5.24/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % vebt_pred.cases
% 5.24/5.50 thf(fact_3373_VEBT__internal_Omembermima_Ocases,axiom,
% 5.24/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.24/5.50 ( ! [Uu3: $o,Uv2: $o,Uw2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Uw2 ) )
% 5.24/5.50 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.24/5.50 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 5.24/5.50 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X3 ) )
% 5.24/5.50 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % VEBT_internal.membermima.cases
% 5.24/5.50 thf(fact_3374_vebt__member_Ocases,axiom,
% 5.24/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.24/5.50 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.24/5.50 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) @ X3 ) )
% 5.24/5.50 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 5.24/5.50 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.24/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.24/5.50 ( X
% 5.24/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % vebt_member.cases
% 5.24/5.50 thf(fact_3375_atLeastatMost__psubset__iff,axiom,
% 5.24/5.50 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.24/5.50 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.24/5.50 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.24/5.50 & ( ord_less_eq_set_nat @ B @ D )
% 5.24/5.50 & ( ( ord_less_set_nat @ C @ A )
% 5.24/5.50 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.24/5.50 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_psubset_iff
% 5.24/5.50 thf(fact_3376_atLeastatMost__psubset__iff,axiom,
% 5.24/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.24/5.50 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.24/5.50 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_rat @ C @ A )
% 5.24/5.50 & ( ord_less_eq_rat @ B @ D )
% 5.24/5.50 & ( ( ord_less_rat @ C @ A )
% 5.24/5.50 | ( ord_less_rat @ B @ D ) ) ) )
% 5.24/5.50 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_psubset_iff
% 5.24/5.50 thf(fact_3377_atLeastatMost__psubset__iff,axiom,
% 5.24/5.50 ! [A: num,B: num,C: num,D: num] :
% 5.24/5.50 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.24/5.50 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_num @ C @ A )
% 5.24/5.50 & ( ord_less_eq_num @ B @ D )
% 5.24/5.50 & ( ( ord_less_num @ C @ A )
% 5.24/5.50 | ( ord_less_num @ B @ D ) ) ) )
% 5.24/5.50 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_psubset_iff
% 5.24/5.50 thf(fact_3378_atLeastatMost__psubset__iff,axiom,
% 5.24/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.24/5.50 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.24/5.50 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.24/5.50 | ( ( ord_less_eq_nat @ C @ A )
% 5.24/5.50 & ( ord_less_eq_nat @ B @ D )
% 5.24/5.50 & ( ( ord_less_nat @ C @ A )
% 5.24/5.50 | ( ord_less_nat @ B @ D ) ) ) )
% 5.24/5.50 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.24/5.50
% 5.24/5.50 % atLeastatMost_psubset_iff
% 5.24/5.50 thf(fact_3379_atLeastatMost__psubset__iff,axiom,
% 5.24/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.24/5.50 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.24/5.51 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.24/5.51 | ( ( ord_less_eq_int @ C @ A )
% 5.24/5.51 & ( ord_less_eq_int @ B @ D )
% 5.24/5.51 & ( ( ord_less_int @ C @ A )
% 5.24/5.51 | ( ord_less_int @ B @ D ) ) ) )
% 5.24/5.51 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % atLeastatMost_psubset_iff
% 5.24/5.51 thf(fact_3380_atLeastatMost__psubset__iff,axiom,
% 5.24/5.51 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.51 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.24/5.51 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.24/5.51 | ( ( ord_less_eq_real @ C @ A )
% 5.24/5.51 & ( ord_less_eq_real @ B @ D )
% 5.24/5.51 & ( ( ord_less_real @ C @ A )
% 5.24/5.51 | ( ord_less_real @ B @ D ) ) ) )
% 5.24/5.51 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % atLeastatMost_psubset_iff
% 5.24/5.51 thf(fact_3381_cpmi,axiom,
% 5.24/5.51 ! [D4: int,P: int > $o,P5: int > $o,B5: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ B5 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P5 @ X3 )
% 5.24/5.51 = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.24/5.51 = ( ? [X2: int] :
% 5.24/5.51 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 & ( P5 @ X2 ) )
% 5.24/5.51 | ? [X2: int] :
% 5.24/5.51 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 & ? [Y: int] :
% 5.24/5.51 ( ( member_int @ Y @ B5 )
% 5.24/5.51 & ( P @ ( plus_plus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cpmi
% 5.24/5.51 thf(fact_3382_cppi,axiom,
% 5.24/5.51 ! [D4: int,P: int > $o,P5: int > $o,A2: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ A2 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P5 @ X3 )
% 5.24/5.51 = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.24/5.51 = ( ? [X2: int] :
% 5.24/5.51 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 & ( P5 @ X2 ) )
% 5.24/5.51 | ? [X2: int] :
% 5.24/5.51 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 & ? [Y: int] :
% 5.24/5.51 ( ( member_int @ Y @ A2 )
% 5.24/5.51 & ( P @ ( minus_minus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cppi
% 5.24/5.51 thf(fact_3383_incr__mult__lemma,axiom,
% 5.24/5.51 ! [D: int,P: int > $o,K: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ( P @ X5 )
% 5.24/5.51 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % incr_mult_lemma
% 5.24/5.51 thf(fact_3384_aset_I8_J,axiom,
% 5.24/5.51 ! [D4: int,A2: set_int,T: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ T @ X5 )
% 5.24/5.51 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(8)
% 5.24/5.51 thf(fact_3385_aset_I6_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,A2: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ X5 @ T )
% 5.24/5.51 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(6)
% 5.24/5.51 thf(fact_3386_bset_I8_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,B5: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ T @ X5 )
% 5.24/5.51 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(8)
% 5.24/5.51 thf(fact_3387_bset_I6_J,axiom,
% 5.24/5.51 ! [D4: int,B5: set_int,T: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ X5 @ T )
% 5.24/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(6)
% 5.24/5.51 thf(fact_3388_vebt__pred_Opelims,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat,Y4: option_nat] :
% 5.24/5.51 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.24/5.51 = Y4 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.51 => ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => ( ( Y4 = none_nat )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.24/5.51 => ( ! [A3: $o,Uw2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.24/5.51 => ( ( Xa2
% 5.24/5.51 = ( suc @ zero_zero_nat ) )
% 5.24/5.51 => ( ( ( A3
% 5.24/5.51 => ( Y4
% 5.24/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.24/5.51 & ( ~ A3
% 5.24/5.51 => ( Y4 = none_nat ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ! [Va3: nat] :
% 5.24/5.51 ( ( Xa2
% 5.24/5.51 = ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.51 => ( ( ( B2
% 5.24/5.51 => ( Y4
% 5.24/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.24/5.51 & ( ~ B2
% 5.24/5.51 => ( ( A3
% 5.24/5.51 => ( Y4
% 5.24/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.24/5.51 & ( ~ A3
% 5.24/5.51 => ( Y4 = none_nat ) ) ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.24/5.51 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.24/5.51 => ( ( Y4 = none_nat )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.24/5.51 => ( ( Y4 = none_nat )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.24/5.51 => ( ( Y4 = none_nat )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.51 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 => ( Y4
% 5.24/5.51 = ( some_nat @ Ma2 ) ) )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 => ( Y4
% 5.24/5.51 = ( 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 ) )
% 5.24/5.51 @ ( if_option_nat
% 5.24/5.51 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.51 != none_nat )
% 5.24/5.51 & ( 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 ) ) ) ) ) ) ) )
% 5.24/5.51 @ ( 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 ) ) ) ) ) )
% 5.24/5.51 @ ( if_option_nat
% 5.24/5.51 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.51 = none_nat )
% 5.24/5.51 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.24/5.51 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.24/5.51 @ none_nat ) ) ) )
% 5.24/5.51 => ~ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % vebt_pred.pelims
% 5.24/5.51 thf(fact_3389_minf_I7_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(7)
% 5.24/5.51 thf(fact_3390_minf_I7_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(7)
% 5.24/5.51 thf(fact_3391_minf_I7_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(7)
% 5.24/5.51 thf(fact_3392_minf_I7_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(7)
% 5.24/5.51 thf(fact_3393_minf_I7_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(7)
% 5.24/5.51 thf(fact_3394_minf_I5_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ( ord_less_real @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(5)
% 5.24/5.51 thf(fact_3395_minf_I5_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ( ord_less_rat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(5)
% 5.24/5.51 thf(fact_3396_minf_I5_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ( ord_less_num @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(5)
% 5.24/5.51 thf(fact_3397_minf_I5_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ( ord_less_nat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(5)
% 5.24/5.51 thf(fact_3398_minf_I5_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ( ord_less_int @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(5)
% 5.24/5.51 thf(fact_3399_minf_I4_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(4)
% 5.24/5.51 thf(fact_3400_minf_I4_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(4)
% 5.24/5.51 thf(fact_3401_minf_I4_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(4)
% 5.24/5.51 thf(fact_3402_minf_I4_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(4)
% 5.24/5.51 thf(fact_3403_minf_I4_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(4)
% 5.24/5.51 thf(fact_3404_minf_I3_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(3)
% 5.24/5.51 thf(fact_3405_minf_I3_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(3)
% 5.24/5.51 thf(fact_3406_minf_I3_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(3)
% 5.24/5.51 thf(fact_3407_minf_I3_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(3)
% 5.24/5.51 thf(fact_3408_minf_I3_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(3)
% 5.24/5.51 thf(fact_3409_minf_I2_J,axiom,
% 5.24/5.51 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.24/5.51 ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(2)
% 5.24/5.51 thf(fact_3410_minf_I2_J,axiom,
% 5.24/5.51 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.24/5.51 ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(2)
% 5.24/5.51 thf(fact_3411_minf_I2_J,axiom,
% 5.24/5.51 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.24/5.51 ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(2)
% 5.24/5.51 thf(fact_3412_minf_I2_J,axiom,
% 5.24/5.51 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.24/5.51 ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(2)
% 5.24/5.51 thf(fact_3413_minf_I2_J,axiom,
% 5.24/5.51 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.24/5.51 ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(2)
% 5.24/5.51 thf(fact_3414_minf_I1_J,axiom,
% 5.24/5.51 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.24/5.51 ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(1)
% 5.24/5.51 thf(fact_3415_minf_I1_J,axiom,
% 5.24/5.51 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.24/5.51 ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(1)
% 5.24/5.51 thf(fact_3416_minf_I1_J,axiom,
% 5.24/5.51 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.24/5.51 ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(1)
% 5.24/5.51 thf(fact_3417_minf_I1_J,axiom,
% 5.24/5.51 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.24/5.51 ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(1)
% 5.24/5.51 thf(fact_3418_minf_I1_J,axiom,
% 5.24/5.51 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.24/5.51 ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ X3 @ Z5 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(1)
% 5.24/5.51 thf(fact_3419_pinf_I7_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ( ord_less_real @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(7)
% 5.24/5.51 thf(fact_3420_pinf_I7_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ( ord_less_rat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(7)
% 5.24/5.51 thf(fact_3421_pinf_I7_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ( ord_less_num @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(7)
% 5.24/5.51 thf(fact_3422_pinf_I7_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ( ord_less_nat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(7)
% 5.24/5.51 thf(fact_3423_pinf_I7_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ( ord_less_int @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(7)
% 5.24/5.51 thf(fact_3424_pinf_I5_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(5)
% 5.24/5.51 thf(fact_3425_pinf_I5_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(5)
% 5.24/5.51 thf(fact_3426_pinf_I5_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(5)
% 5.24/5.51 thf(fact_3427_pinf_I5_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(5)
% 5.24/5.51 thf(fact_3428_pinf_I5_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(5)
% 5.24/5.51 thf(fact_3429_pinf_I4_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(4)
% 5.24/5.51 thf(fact_3430_pinf_I4_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(4)
% 5.24/5.51 thf(fact_3431_pinf_I4_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(4)
% 5.24/5.51 thf(fact_3432_pinf_I4_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(4)
% 5.24/5.51 thf(fact_3433_pinf_I4_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(4)
% 5.24/5.51 thf(fact_3434_pinf_I3_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(3)
% 5.24/5.51 thf(fact_3435_pinf_I3_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(3)
% 5.24/5.51 thf(fact_3436_pinf_I3_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(3)
% 5.24/5.51 thf(fact_3437_pinf_I3_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(3)
% 5.24/5.51 thf(fact_3438_pinf_I3_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ( X5 != T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(3)
% 5.24/5.51 thf(fact_3439_pinf_I2_J,axiom,
% 5.24/5.51 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.24/5.51 ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(2)
% 5.24/5.51 thf(fact_3440_pinf_I2_J,axiom,
% 5.24/5.51 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.24/5.51 ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(2)
% 5.24/5.51 thf(fact_3441_pinf_I2_J,axiom,
% 5.24/5.51 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.24/5.51 ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(2)
% 5.24/5.51 thf(fact_3442_pinf_I2_J,axiom,
% 5.24/5.51 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.24/5.51 ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(2)
% 5.24/5.51 thf(fact_3443_pinf_I2_J,axiom,
% 5.24/5.51 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.24/5.51 ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(2)
% 5.24/5.51 thf(fact_3444_pinf_I1_J,axiom,
% 5.24/5.51 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 5.24/5.51 ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: real] :
% 5.24/5.51 ! [X3: real] :
% 5.24/5.51 ( ( ord_less_real @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(1)
% 5.24/5.51 thf(fact_3445_pinf_I1_J,axiom,
% 5.24/5.51 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.24/5.51 ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: rat] :
% 5.24/5.51 ! [X3: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(1)
% 5.24/5.51 thf(fact_3446_pinf_I1_J,axiom,
% 5.24/5.51 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 5.24/5.51 ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: num] :
% 5.24/5.51 ! [X3: num] :
% 5.24/5.51 ( ( ord_less_num @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(1)
% 5.24/5.51 thf(fact_3447_pinf_I1_J,axiom,
% 5.24/5.51 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.24/5.51 ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: nat] :
% 5.24/5.51 ! [X3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(1)
% 5.24/5.51 thf(fact_3448_pinf_I1_J,axiom,
% 5.24/5.51 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 5.24/5.51 ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ Z5 @ X3 )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 = ( Q6 @ X3 ) ) )
% 5.24/5.51 => ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P5 @ X5 )
% 5.24/5.51 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(1)
% 5.24/5.51 thf(fact_3449_pinf_I6_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(6)
% 5.24/5.51 thf(fact_3450_pinf_I6_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(6)
% 5.24/5.51 thf(fact_3451_pinf_I6_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(6)
% 5.24/5.51 thf(fact_3452_pinf_I6_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(6)
% 5.24/5.51 thf(fact_3453_pinf_I6_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(6)
% 5.24/5.51 thf(fact_3454_pinf_I8_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.51 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(8)
% 5.24/5.51 thf(fact_3455_pinf_I8_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.51 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(8)
% 5.24/5.51 thf(fact_3456_pinf_I8_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ Z @ X5 )
% 5.24/5.51 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(8)
% 5.24/5.51 thf(fact_3457_pinf_I8_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.51 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(8)
% 5.24/5.51 thf(fact_3458_pinf_I8_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.51 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % pinf(8)
% 5.24/5.51 thf(fact_3459_minf_I6_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(6)
% 5.24/5.51 thf(fact_3460_minf_I6_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(6)
% 5.24/5.51 thf(fact_3461_minf_I6_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(6)
% 5.24/5.51 thf(fact_3462_minf_I6_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(6)
% 5.24/5.51 thf(fact_3463_minf_I6_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(6)
% 5.24/5.51 thf(fact_3464_minf_I8_J,axiom,
% 5.24/5.51 ! [T: real] :
% 5.24/5.51 ? [Z: real] :
% 5.24/5.51 ! [X5: real] :
% 5.24/5.51 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(8)
% 5.24/5.51 thf(fact_3465_minf_I8_J,axiom,
% 5.24/5.51 ! [T: rat] :
% 5.24/5.51 ? [Z: rat] :
% 5.24/5.51 ! [X5: rat] :
% 5.24/5.51 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(8)
% 5.24/5.51 thf(fact_3466_minf_I8_J,axiom,
% 5.24/5.51 ! [T: num] :
% 5.24/5.51 ? [Z: num] :
% 5.24/5.51 ! [X5: num] :
% 5.24/5.51 ( ( ord_less_num @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(8)
% 5.24/5.51 thf(fact_3467_minf_I8_J,axiom,
% 5.24/5.51 ! [T: nat] :
% 5.24/5.51 ? [Z: nat] :
% 5.24/5.51 ! [X5: nat] :
% 5.24/5.51 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(8)
% 5.24/5.51 thf(fact_3468_minf_I8_J,axiom,
% 5.24/5.51 ! [T: int] :
% 5.24/5.51 ? [Z: int] :
% 5.24/5.51 ! [X5: int] :
% 5.24/5.51 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.51 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.24/5.51
% 5.24/5.51 % minf(8)
% 5.24/5.51 thf(fact_3469_inf__period_I2_J,axiom,
% 5.24/5.51 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.24/5.51 ( ! [X3: real,K2: real] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: real,K2: real] :
% 5.24/5.51 ( ( Q @ X3 )
% 5.24/5.51 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: real,K4: real] :
% 5.24/5.51 ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.24/5.51 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % inf_period(2)
% 5.24/5.51 thf(fact_3470_inf__period_I2_J,axiom,
% 5.24/5.51 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.24/5.51 ( ! [X3: rat,K2: rat] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: rat,K2: rat] :
% 5.24/5.51 ( ( Q @ X3 )
% 5.24/5.51 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: rat,K4: rat] :
% 5.24/5.51 ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.24/5.51 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % inf_period(2)
% 5.24/5.51 thf(fact_3471_inf__period_I2_J,axiom,
% 5.24/5.51 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.24/5.51 ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( Q @ X3 )
% 5.24/5.51 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: int,K4: int] :
% 5.24/5.51 ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.24/5.51 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % inf_period(2)
% 5.24/5.51 thf(fact_3472_inf__period_I1_J,axiom,
% 5.24/5.51 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.24/5.51 ( ! [X3: real,K2: real] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: real,K2: real] :
% 5.24/5.51 ( ( Q @ X3 )
% 5.24/5.51 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: real,K4: real] :
% 5.24/5.51 ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.24/5.51 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % inf_period(1)
% 5.24/5.51 thf(fact_3473_inf__period_I1_J,axiom,
% 5.24/5.51 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.24/5.51 ( ! [X3: rat,K2: rat] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: rat,K2: rat] :
% 5.24/5.51 ( ( Q @ X3 )
% 5.24/5.51 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: rat,K4: rat] :
% 5.24/5.51 ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.24/5.51 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % inf_period(1)
% 5.24/5.51 thf(fact_3474_inf__period_I1_J,axiom,
% 5.24/5.51 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.24/5.51 ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( Q @ X3 )
% 5.24/5.51 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: int,K4: int] :
% 5.24/5.51 ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.24/5.51 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % inf_period(1)
% 5.24/5.51 thf(fact_3475_aset_I2_J,axiom,
% 5.24/5.51 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.24/5.51 ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ A2 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ A2 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 5.24/5.51 | ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(2)
% 5.24/5.51 thf(fact_3476_aset_I1_J,axiom,
% 5.24/5.51 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.24/5.51 ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ A2 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ A2 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 5.24/5.51 & ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(1)
% 5.24/5.51 thf(fact_3477_bset_I2_J,axiom,
% 5.24/5.51 ! [D4: int,B5: set_int,P: int > $o,Q: int > $o] :
% 5.24/5.51 ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ B5 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ B5 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 | ( Q @ X5 ) )
% 5.24/5.51 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 5.24/5.51 | ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(2)
% 5.24/5.51 thf(fact_3478_bset_I1_J,axiom,
% 5.24/5.51 ! [D4: int,B5: set_int,P: int > $o,Q: int > $o] :
% 5.24/5.51 ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ B5 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb: int] :
% 5.24/5.51 ( ( member_int @ Xb @ B5 )
% 5.24/5.51 => ( X3
% 5.24/5.51 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.24/5.51 => ( ( Q @ X3 )
% 5.24/5.51 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ( P @ X5 )
% 5.24/5.51 & ( Q @ X5 ) )
% 5.24/5.51 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 5.24/5.51 & ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(1)
% 5.24/5.51 thf(fact_3479_plusinfinity,axiom,
% 5.24/5.51 ! [D: int,P5: int > $o,P: int > $o] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P5 @ X3 )
% 5.24/5.51 = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ Z5 @ X3 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P5 @ X3 ) ) )
% 5.24/5.51 => ( ? [X_12: int] : ( P5 @ X_12 )
% 5.24/5.51 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % plusinfinity
% 5.24/5.51 thf(fact_3480_minusinfinity,axiom,
% 5.24/5.51 ! [D: int,P1: int > $o,P: int > $o] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P1 @ X3 )
% 5.24/5.51 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.24/5.51 => ( ? [Z5: int] :
% 5.24/5.51 ! [X3: int] :
% 5.24/5.51 ( ( ord_less_int @ X3 @ Z5 )
% 5.24/5.51 => ( ( P @ X3 )
% 5.24/5.51 = ( P1 @ X3 ) ) )
% 5.24/5.51 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.24/5.51 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minusinfinity
% 5.24/5.51 thf(fact_3481_decr__mult__lemma,axiom,
% 5.24/5.51 ! [D: int,P: int > $o,K: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.51 => ( ! [X3: int] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ( P @ X5 )
% 5.24/5.51 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % decr_mult_lemma
% 5.24/5.51 thf(fact_3482_periodic__finite__ex,axiom,
% 5.24/5.51 ! [D: int,P: int > $o] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.51 => ( ! [X3: int,K2: int] :
% 5.24/5.51 ( ( P @ X3 )
% 5.24/5.51 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.24/5.51 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.24/5.51 = ( ? [X2: int] :
% 5.24/5.51 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % periodic_finite_ex
% 5.24/5.51 thf(fact_3483_bset_I3_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,B5: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( X5 = T )
% 5.24/5.51 => ( ( minus_minus_int @ X5 @ D4 )
% 5.24/5.51 = T ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(3)
% 5.24/5.51 thf(fact_3484_bset_I4_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,B5: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ T @ B5 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( X5 != T )
% 5.24/5.51 => ( ( minus_minus_int @ X5 @ D4 )
% 5.24/5.51 != T ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(4)
% 5.24/5.51 thf(fact_3485_bset_I5_J,axiom,
% 5.24/5.51 ! [D4: int,B5: set_int,T: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_int @ X5 @ T )
% 5.24/5.51 => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(5)
% 5.24/5.51 thf(fact_3486_bset_I7_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,B5: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ T @ B5 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_int @ T @ X5 )
% 5.24/5.51 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % bset(7)
% 5.24/5.51 thf(fact_3487_aset_I3_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,A2: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( X5 = T )
% 5.24/5.51 => ( ( plus_plus_int @ X5 @ D4 )
% 5.24/5.51 = T ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(3)
% 5.24/5.51 thf(fact_3488_aset_I4_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,A2: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ T @ A2 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( X5 != T )
% 5.24/5.51 => ( ( plus_plus_int @ X5 @ D4 )
% 5.24/5.51 != T ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(4)
% 5.24/5.51 thf(fact_3489_aset_I5_J,axiom,
% 5.24/5.51 ! [D4: int,T: int,A2: set_int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ( ( member_int @ T @ A2 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_int @ X5 @ T )
% 5.24/5.51 => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(5)
% 5.24/5.51 thf(fact_3490_aset_I7_J,axiom,
% 5.24/5.51 ! [D4: int,A2: set_int,T: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.24/5.51 => ! [X5: int] :
% 5.24/5.51 ( ! [Xa3: int] :
% 5.24/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.51 => ! [Xb3: int] :
% 5.24/5.51 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.51 => ( X5
% 5.24/5.51 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.51 => ( ( ord_less_int @ T @ X5 )
% 5.24/5.51 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % aset(7)
% 5.24/5.51 thf(fact_3491_vebt__member_Opelims_I3_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.51 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.24/5.51 => ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => A3 )
% 5.24/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.51 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.51 => B2 )
% 5.24/5.51 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.24/5.51 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.24/5.51 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.24/5.51 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.24/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 => ( ( Xa2 != Mi2 )
% 5.24/5.51 => ( ( Xa2 != Ma2 )
% 5.24/5.51 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.51 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % vebt_member.pelims(3)
% 5.24/5.51 thf(fact_3492_vebt__member_Opelims_I1_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.51 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.24/5.51 = Y4 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => A3 )
% 5.24/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.51 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.51 => B2 )
% 5.24/5.51 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.24/5.51 => ( ~ Y4
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.24/5.51 => ( ~ Y4
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.24/5.51 => ( ~ Y4
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( Xa2 != Mi2 )
% 5.24/5.51 => ( ( Xa2 != Ma2 )
% 5.24/5.51 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.51 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.24/5.51 => ~ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % vebt_member.pelims(1)
% 5.24/5.51 thf(fact_3493_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.51 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.24/5.51 => ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => A3 )
% 5.24/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.51 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.51 => B2 )
% 5.24/5.51 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.24/5.51 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.24/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) )
% 5.24/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % VEBT_internal.naive_member.pelims(3)
% 5.24/5.51 thf(fact_3494_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.51 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.24/5.51 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => A3 )
% 5.24/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.51 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.51 => B2 )
% 5.24/5.51 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.24/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) )
% 5.24/5.51 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % VEBT_internal.naive_member.pelims(2)
% 5.24/5.51 thf(fact_3495_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.51 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.24/5.51 = Y4 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => A3 )
% 5.24/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.51 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.51 => B2 )
% 5.24/5.51 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.24/5.51 => ( ~ Y4
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % VEBT_internal.naive_member.pelims(1)
% 5.24/5.51 thf(fact_3496_vebt__member_Opelims_I2_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.51 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [A3: $o,B2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.24/5.51 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.51 => A3 )
% 5.24/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.51 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.51 => B2 )
% 5.24/5.51 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.24/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 => ~ ( ( Xa2 != Mi2 )
% 5.24/5.51 => ( ( Xa2 != Ma2 )
% 5.24/5.51 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.24/5.51 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.24/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % vebt_member.pelims(2)
% 5.24/5.51 thf(fact_3497_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.51 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.24/5.51 = Y4 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.51 => ( ~ Y4
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.24/5.51 => ( ~ Y4
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( Xa2 = Mi2 )
% 5.24/5.51 | ( Xa2 = Ma2 ) ) )
% 5.24/5.51 => ~ ( 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 ) ) ) )
% 5.24/5.51 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( Xa2 = Mi2 )
% 5.24/5.51 | ( Xa2 = Ma2 )
% 5.24/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.24/5.51 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.24/5.51 => ( ( Y4
% 5.24/5.51 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % VEBT_internal.membermima.pelims(1)
% 5.24/5.51 thf(fact_3498_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.51 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) ) )
% 5.24/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.24/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.24/5.51 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 => ( ( Xa2 = Mi2 )
% 5.24/5.51 | ( Xa2 = Ma2 ) ) ) )
% 5.24/5.51 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.24/5.51 => ( ( Xa2 = Mi2 )
% 5.24/5.51 | ( Xa2 = Ma2 )
% 5.24/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.24/5.51 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.24/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % VEBT_internal.membermima.pelims(3)
% 5.24/5.51 thf(fact_3499_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.24/5.51 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.51 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.51 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 => ~ ( ( Xa2 = Mi2 )
% 5.24/5.51 | ( Xa2 = Ma2 ) ) ) )
% 5.24/5.51 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.24/5.51 => ~ ( ( Xa2 = Mi2 )
% 5.24/5.51 | ( Xa2 = Ma2 )
% 5.24/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.24/5.51 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.24/5.51 ( ( X
% 5.24/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.24/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.24/5.51 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.24/5.51 => ( 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 ) ) ) ) ) )
% 5.24/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % VEBT_internal.membermima.pelims(2)
% 5.24/5.51 thf(fact_3500_mult__le__cancel__iff2,axiom,
% 5.24/5.51 ! [Z2: real,X: real,Y4: real] :
% 5.24/5.51 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.24/5.51 => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ X ) @ ( times_times_real @ Z2 @ Y4 ) )
% 5.24/5.51 = ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_le_cancel_iff2
% 5.24/5.51 thf(fact_3501_mult__le__cancel__iff2,axiom,
% 5.24/5.51 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.51 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.24/5.51 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ ( times_times_rat @ Z2 @ Y4 ) )
% 5.24/5.51 = ( ord_less_eq_rat @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_le_cancel_iff2
% 5.24/5.51 thf(fact_3502_mult__le__cancel__iff2,axiom,
% 5.24/5.51 ! [Z2: int,X: int,Y4: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ ( times_times_int @ Z2 @ X ) @ ( times_times_int @ Z2 @ Y4 ) )
% 5.24/5.51 = ( ord_less_eq_int @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_le_cancel_iff2
% 5.24/5.51 thf(fact_3503_mult__le__cancel__iff1,axiom,
% 5.24/5.51 ! [Z2: real,X: real,Y4: real] :
% 5.24/5.51 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.24/5.51 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_le_cancel_iff1
% 5.24/5.51 thf(fact_3504_mult__le__cancel__iff1,axiom,
% 5.24/5.51 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.51 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.24/5.51 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_less_eq_rat @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_le_cancel_iff1
% 5.24/5.51 thf(fact_3505_mult__le__cancel__iff1,axiom,
% 5.24/5.51 ! [Z2: int,X: int,Y4: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z2 ) @ ( times_times_int @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_less_eq_int @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_le_cancel_iff1
% 5.24/5.51 thf(fact_3506_divides__aux__eq,axiom,
% 5.24/5.51 ! [Q2: nat,R2: nat] :
% 5.24/5.51 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.24/5.51 = ( R2 = zero_zero_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % divides_aux_eq
% 5.24/5.51 thf(fact_3507_divides__aux__eq,axiom,
% 5.24/5.51 ! [Q2: int,R2: int] :
% 5.24/5.51 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 = ( R2 = zero_zero_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % divides_aux_eq
% 5.24/5.51 thf(fact_3508_neg__eucl__rel__int__mult__2,axiom,
% 5.24/5.51 ! [B: int,A: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.24/5.51 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % neg_eucl_rel_int_mult_2
% 5.24/5.51 thf(fact_3509_low__def,axiom,
% 5.24/5.51 ( vEBT_VEBT_low
% 5.24/5.51 = ( ^ [X2: nat,N2: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % low_def
% 5.24/5.51 thf(fact_3510_obtain__set__pred,axiom,
% 5.24/5.51 ! [Z2: nat,X: nat,A2: set_nat] :
% 5.24/5.51 ( ( ord_less_nat @ Z2 @ X )
% 5.24/5.51 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z2 )
% 5.24/5.51 => ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % obtain_set_pred
% 5.24/5.51 thf(fact_3511_set__vebt__finite,axiom,
% 5.24/5.51 ! [T: vEBT_VEBT,N: nat] :
% 5.24/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.24/5.51 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_vebt_finite
% 5.24/5.51 thf(fact_3512_pred__none__empty,axiom,
% 5.24/5.51 ! [Xs2: set_nat,A: nat] :
% 5.24/5.51 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.24/5.51 => ( ( finite_finite_nat @ Xs2 )
% 5.24/5.51 => ~ ? [X5: nat] :
% 5.24/5.51 ( ( member_nat @ X5 @ Xs2 )
% 5.24/5.51 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pred_none_empty
% 5.24/5.51 thf(fact_3513_mod__mod__trivial,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mod_trivial
% 5.24/5.51 thf(fact_3514_mod__mod__trivial,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mod_trivial
% 5.24/5.51 thf(fact_3515_mod__mod__trivial,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mod_trivial
% 5.24/5.51 thf(fact_3516_mod__add__self2,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_self2
% 5.24/5.51 thf(fact_3517_mod__add__self2,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_self2
% 5.24/5.51 thf(fact_3518_mod__add__self2,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_self2
% 5.24/5.51 thf(fact_3519_mod__add__self1,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_self1
% 5.24/5.51 thf(fact_3520_mod__add__self1,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_self1
% 5.24/5.51 thf(fact_3521_mod__add__self1,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_self1
% 5.24/5.51 thf(fact_3522_minus__mod__self2,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_self2
% 5.24/5.51 thf(fact_3523_minus__mod__self2,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_self2
% 5.24/5.51 thf(fact_3524_List_Ofinite__set,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % List.finite_set
% 5.24/5.51 thf(fact_3525_List_Ofinite__set,axiom,
% 5.24/5.51 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % List.finite_set
% 5.24/5.51 thf(fact_3526_List_Ofinite__set,axiom,
% 5.24/5.51 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % List.finite_set
% 5.24/5.51 thf(fact_3527_List_Ofinite__set,axiom,
% 5.24/5.51 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % List.finite_set
% 5.24/5.51 thf(fact_3528_mod__less,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ( ord_less_nat @ M @ N )
% 5.24/5.51 => ( ( modulo_modulo_nat @ M @ N )
% 5.24/5.51 = M ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_less
% 5.24/5.51 thf(fact_3529_mod__mult__self2__is__0,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self2_is_0
% 5.24/5.51 thf(fact_3530_mod__mult__self2__is__0,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self2_is_0
% 5.24/5.51 thf(fact_3531_mod__mult__self2__is__0,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self2_is_0
% 5.24/5.51 thf(fact_3532_mod__mult__self1__is__0,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self1_is_0
% 5.24/5.51 thf(fact_3533_mod__mult__self1__is__0,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self1_is_0
% 5.24/5.51 thf(fact_3534_mod__mult__self1__is__0,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self1_is_0
% 5.24/5.51 thf(fact_3535_mod__by__1,axiom,
% 5.24/5.51 ! [A: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % mod_by_1
% 5.24/5.51 thf(fact_3536_mod__by__1,axiom,
% 5.24/5.51 ! [A: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % mod_by_1
% 5.24/5.51 thf(fact_3537_mod__by__1,axiom,
% 5.24/5.51 ! [A: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % mod_by_1
% 5.24/5.51 thf(fact_3538_bits__mod__by__1,axiom,
% 5.24/5.51 ! [A: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % bits_mod_by_1
% 5.24/5.51 thf(fact_3539_bits__mod__by__1,axiom,
% 5.24/5.51 ! [A: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % bits_mod_by_1
% 5.24/5.51 thf(fact_3540_bits__mod__by__1,axiom,
% 5.24/5.51 ! [A: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % bits_mod_by_1
% 5.24/5.51 thf(fact_3541_mod__div__trivial,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_trivial
% 5.24/5.51 thf(fact_3542_mod__div__trivial,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_trivial
% 5.24/5.51 thf(fact_3543_mod__div__trivial,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_trivial
% 5.24/5.51 thf(fact_3544_bits__mod__div__trivial,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % bits_mod_div_trivial
% 5.24/5.51 thf(fact_3545_bits__mod__div__trivial,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % bits_mod_div_trivial
% 5.24/5.51 thf(fact_3546_bits__mod__div__trivial,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % bits_mod_div_trivial
% 5.24/5.51 thf(fact_3547_mod__mult__self4,axiom,
% 5.24/5.51 ! [B: nat,C: nat,A: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self4
% 5.24/5.51 thf(fact_3548_mod__mult__self4,axiom,
% 5.24/5.51 ! [B: int,C: int,A: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self4
% 5.24/5.51 thf(fact_3549_mod__mult__self4,axiom,
% 5.24/5.51 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self4
% 5.24/5.51 thf(fact_3550_mod__mult__self3,axiom,
% 5.24/5.51 ! [C: nat,B: nat,A: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self3
% 5.24/5.51 thf(fact_3551_mod__mult__self3,axiom,
% 5.24/5.51 ! [C: int,B: int,A: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self3
% 5.24/5.51 thf(fact_3552_mod__mult__self3,axiom,
% 5.24/5.51 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self3
% 5.24/5.51 thf(fact_3553_mod__mult__self2,axiom,
% 5.24/5.51 ! [A: nat,B: nat,C: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self2
% 5.24/5.51 thf(fact_3554_mod__mult__self2,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self2
% 5.24/5.51 thf(fact_3555_mod__mult__self2,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self2
% 5.24/5.51 thf(fact_3556_mod__mult__self1,axiom,
% 5.24/5.51 ! [A: nat,C: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self1
% 5.24/5.51 thf(fact_3557_mod__mult__self1,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self1
% 5.24/5.51 thf(fact_3558_mod__mult__self1,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_self1
% 5.24/5.51 thf(fact_3559_infinite__Icc__iff,axiom,
% 5.24/5.51 ! [A: rat,B: rat] :
% 5.24/5.51 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.24/5.51 = ( ord_less_rat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_Icc_iff
% 5.24/5.51 thf(fact_3560_infinite__Icc__iff,axiom,
% 5.24/5.51 ! [A: real,B: real] :
% 5.24/5.51 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.24/5.51 = ( ord_less_real @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_Icc_iff
% 5.24/5.51 thf(fact_3561_mod__by__Suc__0,axiom,
% 5.24/5.51 ! [M: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % mod_by_Suc_0
% 5.24/5.51 thf(fact_3562_Suc__mod__mult__self4,axiom,
% 5.24/5.51 ! [N: nat,K: nat,M: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % Suc_mod_mult_self4
% 5.24/5.51 thf(fact_3563_Suc__mod__mult__self3,axiom,
% 5.24/5.51 ! [K: nat,N: nat,M: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % Suc_mod_mult_self3
% 5.24/5.51 thf(fact_3564_Suc__mod__mult__self2,axiom,
% 5.24/5.51 ! [M: nat,N: nat,K: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % Suc_mod_mult_self2
% 5.24/5.51 thf(fact_3565_Suc__mod__mult__self1,axiom,
% 5.24/5.51 ! [M: nat,K: nat,N: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % Suc_mod_mult_self1
% 5.24/5.51 thf(fact_3566_one__mod__two__eq__one,axiom,
% 5.24/5.51 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_nat ) ).
% 5.24/5.51
% 5.24/5.51 % one_mod_two_eq_one
% 5.24/5.51 thf(fact_3567_one__mod__two__eq__one,axiom,
% 5.24/5.51 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_int ) ).
% 5.24/5.51
% 5.24/5.51 % one_mod_two_eq_one
% 5.24/5.51 thf(fact_3568_one__mod__two__eq__one,axiom,
% 5.24/5.51 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_Code_integer ) ).
% 5.24/5.51
% 5.24/5.51 % one_mod_two_eq_one
% 5.24/5.51 thf(fact_3569_bits__one__mod__two__eq__one,axiom,
% 5.24/5.51 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_nat ) ).
% 5.24/5.51
% 5.24/5.51 % bits_one_mod_two_eq_one
% 5.24/5.51 thf(fact_3570_bits__one__mod__two__eq__one,axiom,
% 5.24/5.51 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_int ) ).
% 5.24/5.51
% 5.24/5.51 % bits_one_mod_two_eq_one
% 5.24/5.51 thf(fact_3571_bits__one__mod__two__eq__one,axiom,
% 5.24/5.51 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_Code_integer ) ).
% 5.24/5.51
% 5.24/5.51 % bits_one_mod_two_eq_one
% 5.24/5.51 thf(fact_3572_mod2__Suc__Suc,axiom,
% 5.24/5.51 ! [M: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod2_Suc_Suc
% 5.24/5.51 thf(fact_3573_Suc__times__numeral__mod__eq,axiom,
% 5.24/5.51 ! [K: num,N: nat] :
% 5.24/5.51 ( ( ( numeral_numeral_nat @ K )
% 5.24/5.51 != one_one_nat )
% 5.24/5.51 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.51 = one_one_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % Suc_times_numeral_mod_eq
% 5.24/5.51 thf(fact_3574_not__mod__2__eq__1__eq__0,axiom,
% 5.24/5.51 ! [A: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 != one_one_nat )
% 5.24/5.51 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = zero_zero_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod_2_eq_1_eq_0
% 5.24/5.51 thf(fact_3575_not__mod__2__eq__1__eq__0,axiom,
% 5.24/5.51 ! [A: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 != one_one_int )
% 5.24/5.51 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 = zero_zero_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod_2_eq_1_eq_0
% 5.24/5.51 thf(fact_3576_not__mod__2__eq__1__eq__0,axiom,
% 5.24/5.51 ! [A: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 != one_one_Code_integer )
% 5.24/5.51 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod_2_eq_1_eq_0
% 5.24/5.51 thf(fact_3577_not__mod__2__eq__0__eq__1,axiom,
% 5.24/5.51 ! [A: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 != zero_zero_nat )
% 5.24/5.51 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod_2_eq_0_eq_1
% 5.24/5.51 thf(fact_3578_not__mod__2__eq__0__eq__1,axiom,
% 5.24/5.51 ! [A: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 != zero_zero_int )
% 5.24/5.51 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod_2_eq_0_eq_1
% 5.24/5.51 thf(fact_3579_not__mod__2__eq__0__eq__1,axiom,
% 5.24/5.51 ! [A: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 != zero_z3403309356797280102nteger )
% 5.24/5.51 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_Code_integer ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod_2_eq_0_eq_1
% 5.24/5.51 thf(fact_3580_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.24/5.51 ! [N: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 != ( suc @ zero_zero_nat ) )
% 5.24/5.51 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = zero_zero_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % not_mod2_eq_Suc_0_eq_0
% 5.24/5.51 thf(fact_3581_add__self__mod__2,axiom,
% 5.24/5.51 ! [M: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % add_self_mod_2
% 5.24/5.51 thf(fact_3582_mod2__gr__0,axiom,
% 5.24/5.51 ! [M: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.51 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = one_one_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod2_gr_0
% 5.24/5.51 thf(fact_3583_unique__quotient,axiom,
% 5.24/5.51 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.24/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.24/5.51 => ( Q2 = Q5 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_quotient
% 5.24/5.51 thf(fact_3584_unique__remainder,axiom,
% 5.24/5.51 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.24/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.24/5.51 => ( R2 = R4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_remainder
% 5.24/5.51 thf(fact_3585_mod__mult__right__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat,C: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_right_eq
% 5.24/5.51 thf(fact_3586_mod__mult__right__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_right_eq
% 5.24/5.51 thf(fact_3587_mod__mult__right__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_right_eq
% 5.24/5.51 thf(fact_3588_mod__mult__left__eq,axiom,
% 5.24/5.51 ! [A: nat,C: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_left_eq
% 5.24/5.51 thf(fact_3589_mod__mult__left__eq,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_left_eq
% 5.24/5.51 thf(fact_3590_mod__mult__left__eq,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_left_eq
% 5.24/5.51 thf(fact_3591_mult__mod__right,axiom,
% 5.24/5.51 ! [C: nat,A: nat,B: nat] :
% 5.24/5.51 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.24/5.51 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_mod_right
% 5.24/5.51 thf(fact_3592_mult__mod__right,axiom,
% 5.24/5.51 ! [C: int,A: int,B: int] :
% 5.24/5.51 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.24/5.51 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_mod_right
% 5.24/5.51 thf(fact_3593_mult__mod__right,axiom,
% 5.24/5.51 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_mod_right
% 5.24/5.51 thf(fact_3594_mod__mult__mult2,axiom,
% 5.24/5.51 ! [A: nat,C: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.24/5.51 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_mult2
% 5.24/5.51 thf(fact_3595_mod__mult__mult2,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.24/5.51 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_mult2
% 5.24/5.51 thf(fact_3596_mod__mult__mult2,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.51 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_mult2
% 5.24/5.51 thf(fact_3597_mod__mult__cong,axiom,
% 5.24/5.51 ! [A: nat,C: nat,A5: nat,B: nat,B4: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ A @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_cong
% 5.24/5.51 thf(fact_3598_mod__mult__cong,axiom,
% 5.24/5.51 ! [A: int,C: int,A5: int,B: int,B4: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ C )
% 5.24/5.51 = ( modulo_modulo_int @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo_modulo_int @ B @ C )
% 5.24/5.51 = ( modulo_modulo_int @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( times_times_int @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_cong
% 5.24/5.51 thf(fact_3599_mod__mult__cong,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B4: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_cong
% 5.24/5.51 thf(fact_3600_mod__mult__eq,axiom,
% 5.24/5.51 ! [A: nat,C: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_eq
% 5.24/5.51 thf(fact_3601_mod__mult__eq,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_eq
% 5.24/5.51 thf(fact_3602_mod__mult__eq,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_eq
% 5.24/5.51 thf(fact_3603_mod__add__right__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat,C: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_right_eq
% 5.24/5.51 thf(fact_3604_mod__add__right__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_right_eq
% 5.24/5.51 thf(fact_3605_mod__add__right__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_right_eq
% 5.24/5.51 thf(fact_3606_mod__add__left__eq,axiom,
% 5.24/5.51 ! [A: nat,C: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_left_eq
% 5.24/5.51 thf(fact_3607_mod__add__left__eq,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_left_eq
% 5.24/5.51 thf(fact_3608_mod__add__left__eq,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_left_eq
% 5.24/5.51 thf(fact_3609_mod__add__cong,axiom,
% 5.24/5.51 ! [A: nat,C: nat,A5: nat,B: nat,B4: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ A @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_cong
% 5.24/5.51 thf(fact_3610_mod__add__cong,axiom,
% 5.24/5.51 ! [A: int,C: int,A5: int,B: int,B4: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ C )
% 5.24/5.51 = ( modulo_modulo_int @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo_modulo_int @ B @ C )
% 5.24/5.51 = ( modulo_modulo_int @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_cong
% 5.24/5.51 thf(fact_3611_mod__add__cong,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B4: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_cong
% 5.24/5.51 thf(fact_3612_mod__add__eq,axiom,
% 5.24/5.51 ! [A: nat,C: nat,B: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_eq
% 5.24/5.51 thf(fact_3613_mod__add__eq,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_eq
% 5.24/5.51 thf(fact_3614_mod__add__eq,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_add_eq
% 5.24/5.51 thf(fact_3615_mod__diff__right__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_right_eq
% 5.24/5.51 thf(fact_3616_mod__diff__right__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_right_eq
% 5.24/5.51 thf(fact_3617_mod__diff__left__eq,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_left_eq
% 5.24/5.51 thf(fact_3618_mod__diff__left__eq,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_left_eq
% 5.24/5.51 thf(fact_3619_mod__diff__cong,axiom,
% 5.24/5.51 ! [A: int,C: int,A5: int,B: int,B4: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ C )
% 5.24/5.51 = ( modulo_modulo_int @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo_modulo_int @ B @ C )
% 5.24/5.51 = ( modulo_modulo_int @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_cong
% 5.24/5.51 thf(fact_3620_mod__diff__cong,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B4: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.24/5.51 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_cong
% 5.24/5.51 thf(fact_3621_mod__diff__eq,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_eq
% 5.24/5.51 thf(fact_3622_mod__diff__eq,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_diff_eq
% 5.24/5.51 thf(fact_3623_power__mod,axiom,
% 5.24/5.51 ! [A: nat,B: nat,N: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % power_mod
% 5.24/5.51 thf(fact_3624_power__mod,axiom,
% 5.24/5.51 ! [A: int,B: int,N: nat] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % power_mod
% 5.24/5.51 thf(fact_3625_power__mod,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,N: nat] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % power_mod
% 5.24/5.51 thf(fact_3626_mod__Suc__Suc__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_Suc_Suc_eq
% 5.24/5.51 thf(fact_3627_mod__Suc__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_Suc_eq
% 5.24/5.51 thf(fact_3628_mod__less__eq__dividend,axiom,
% 5.24/5.51 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.24/5.51
% 5.24/5.51 % mod_less_eq_dividend
% 5.24/5.51 thf(fact_3629_finite__nat__set__iff__bounded,axiom,
% 5.24/5.51 ( finite_finite_nat
% 5.24/5.51 = ( ^ [N6: set_nat] :
% 5.24/5.51 ? [M2: nat] :
% 5.24/5.51 ! [X2: nat] :
% 5.24/5.51 ( ( member_nat @ X2 @ N6 )
% 5.24/5.51 => ( ord_less_nat @ X2 @ M2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_nat_set_iff_bounded
% 5.24/5.51 thf(fact_3630_bounded__nat__set__is__finite,axiom,
% 5.24/5.51 ! [N4: set_nat,N: nat] :
% 5.24/5.51 ( ! [X3: nat] :
% 5.24/5.51 ( ( member_nat @ X3 @ N4 )
% 5.24/5.51 => ( ord_less_nat @ X3 @ N ) )
% 5.24/5.51 => ( finite_finite_nat @ N4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % bounded_nat_set_is_finite
% 5.24/5.51 thf(fact_3631_finite__nat__set__iff__bounded__le,axiom,
% 5.24/5.51 ( finite_finite_nat
% 5.24/5.51 = ( ^ [N6: set_nat] :
% 5.24/5.51 ? [M2: nat] :
% 5.24/5.51 ! [X2: nat] :
% 5.24/5.51 ( ( member_nat @ X2 @ N6 )
% 5.24/5.51 => ( ord_less_eq_nat @ X2 @ M2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_nat_set_iff_bounded_le
% 5.24/5.51 thf(fact_3632_finite__list,axiom,
% 5.24/5.51 ! [A2: set_VEBT_VEBT] :
% 5.24/5.51 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.24/5.51 => ? [Xs3: list_VEBT_VEBT] :
% 5.24/5.51 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.24/5.51 = A2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_list
% 5.24/5.51 thf(fact_3633_finite__list,axiom,
% 5.24/5.51 ! [A2: set_int] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ? [Xs3: list_int] :
% 5.24/5.51 ( ( set_int2 @ Xs3 )
% 5.24/5.51 = A2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_list
% 5.24/5.51 thf(fact_3634_finite__list,axiom,
% 5.24/5.51 ! [A2: set_nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ? [Xs3: list_nat] :
% 5.24/5.51 ( ( set_nat2 @ Xs3 )
% 5.24/5.51 = A2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_list
% 5.24/5.51 thf(fact_3635_finite__list,axiom,
% 5.24/5.51 ! [A2: set_complex] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.51 => ? [Xs3: list_complex] :
% 5.24/5.51 ( ( set_complex2 @ Xs3 )
% 5.24/5.51 = A2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_list
% 5.24/5.51 thf(fact_3636_finite__M__bounded__by__nat,axiom,
% 5.24/5.51 ! [P: nat > $o,I2: nat] :
% 5.24/5.51 ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [K3: nat] :
% 5.24/5.51 ( ( P @ K3 )
% 5.24/5.51 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_M_bounded_by_nat
% 5.24/5.51 thf(fact_3637_finite__less__ub,axiom,
% 5.24/5.51 ! [F: nat > nat,U2: nat] :
% 5.24/5.51 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_less_ub
% 5.24/5.51 thf(fact_3638_finite__lists__length__eq,axiom,
% 5.24/5.51 ! [A2: set_complex,N: nat] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.51 => ( finite8712137658972009173omplex
% 5.24/5.51 @ ( collect_list_complex
% 5.24/5.51 @ ^ [Xs: list_complex] :
% 5.24/5.51 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.24/5.51 = N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_eq
% 5.24/5.51 thf(fact_3639_finite__lists__length__eq,axiom,
% 5.24/5.51 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.24/5.51 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.24/5.51 => ( finite3004134309566078307T_VEBT
% 5.24/5.51 @ ( collec5608196760682091941T_VEBT
% 5.24/5.51 @ ^ [Xs: list_VEBT_VEBT] :
% 5.24/5.51 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.24/5.51 = N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_eq
% 5.24/5.51 thf(fact_3640_finite__lists__length__eq,axiom,
% 5.24/5.51 ! [A2: set_o,N: nat] :
% 5.24/5.51 ( ( finite_finite_o @ A2 )
% 5.24/5.51 => ( finite_finite_list_o
% 5.24/5.51 @ ( collect_list_o
% 5.24/5.51 @ ^ [Xs: list_o] :
% 5.24/5.51 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ( size_size_list_o @ Xs )
% 5.24/5.51 = N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_eq
% 5.24/5.51 thf(fact_3641_finite__lists__length__eq,axiom,
% 5.24/5.51 ! [A2: set_int,N: nat] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ( finite3922522038869484883st_int
% 5.24/5.51 @ ( collect_list_int
% 5.24/5.51 @ ^ [Xs: list_int] :
% 5.24/5.51 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ( size_size_list_int @ Xs )
% 5.24/5.51 = N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_eq
% 5.24/5.51 thf(fact_3642_finite__lists__length__eq,axiom,
% 5.24/5.51 ! [A2: set_nat,N: nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ( finite8100373058378681591st_nat
% 5.24/5.51 @ ( collect_list_nat
% 5.24/5.51 @ ^ [Xs: list_nat] :
% 5.24/5.51 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ( size_size_list_nat @ Xs )
% 5.24/5.51 = N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_eq
% 5.24/5.51 thf(fact_3643_eucl__rel__int__by0,axiom,
% 5.24/5.51 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.24/5.51
% 5.24/5.51 % eucl_rel_int_by0
% 5.24/5.51 thf(fact_3644_div__int__unique,axiom,
% 5.24/5.51 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 => ( ( divide_divide_int @ K @ L2 )
% 5.24/5.51 = Q2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_int_unique
% 5.24/5.51 thf(fact_3645_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.51 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.24/5.51 thf(fact_3646_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.24/5.51 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.24/5.51 thf(fact_3647_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.51 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.24/5.51 thf(fact_3648_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.24/5.51 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.24/5.51 thf(fact_3649_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.24/5.51 thf(fact_3650_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.51 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.24/5.51 thf(fact_3651_mod__eq__self__iff__div__eq__0,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ A @ B )
% 5.24/5.51 = A )
% 5.24/5.51 = ( ( divide_divide_nat @ A @ B )
% 5.24/5.51 = zero_zero_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eq_self_iff_div_eq_0
% 5.24/5.51 thf(fact_3652_mod__eq__self__iff__div__eq__0,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ B )
% 5.24/5.51 = A )
% 5.24/5.51 = ( ( divide_divide_int @ A @ B )
% 5.24/5.51 = zero_zero_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eq_self_iff_div_eq_0
% 5.24/5.51 thf(fact_3653_mod__eq__self__iff__div__eq__0,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.24/5.51 = A )
% 5.24/5.51 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eq_self_iff_div_eq_0
% 5.24/5.51 thf(fact_3654_cong__exp__iff__simps_I9_J,axiom,
% 5.24/5.51 ! [M: num,Q2: num,N: num] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.51 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.24/5.51 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(9)
% 5.24/5.51 thf(fact_3655_cong__exp__iff__simps_I9_J,axiom,
% 5.24/5.51 ! [M: num,Q2: num,N: num] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.51 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.24/5.51 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(9)
% 5.24/5.51 thf(fact_3656_cong__exp__iff__simps_I9_J,axiom,
% 5.24/5.51 ! [M: num,Q2: num,N: num] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.51 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(9)
% 5.24/5.51 thf(fact_3657_cong__exp__iff__simps_I4_J,axiom,
% 5.24/5.51 ! [M: num,N: num] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.24/5.51 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(4)
% 5.24/5.51 thf(fact_3658_cong__exp__iff__simps_I4_J,axiom,
% 5.24/5.51 ! [M: num,N: num] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.24/5.51 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(4)
% 5.24/5.51 thf(fact_3659_cong__exp__iff__simps_I4_J,axiom,
% 5.24/5.51 ! [M: num,N: num] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(4)
% 5.24/5.51 thf(fact_3660_mod__eqE,axiom,
% 5.24/5.51 ! [A: int,C: int,B: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ A @ C )
% 5.24/5.51 = ( modulo_modulo_int @ B @ C ) )
% 5.24/5.51 => ~ ! [D3: int] :
% 5.24/5.51 ( B
% 5.24/5.51 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eqE
% 5.24/5.51 thf(fact_3661_mod__eqE,axiom,
% 5.24/5.51 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.24/5.51 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.24/5.51 => ~ ! [D3: code_integer] :
% 5.24/5.51 ( B
% 5.24/5.51 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eqE
% 5.24/5.51 thf(fact_3662_div__add1__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat,C: nat] :
% 5.24/5.51 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_add1_eq
% 5.24/5.51 thf(fact_3663_div__add1__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_add1_eq
% 5.24/5.51 thf(fact_3664_div__add1__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_add1_eq
% 5.24/5.51 thf(fact_3665_mod__Suc,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.51 = N )
% 5.24/5.51 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.24/5.51 = zero_zero_nat ) )
% 5.24/5.51 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.51 != N )
% 5.24/5.51 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.24/5.51 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_Suc
% 5.24/5.51 thf(fact_3666_mod__induct,axiom,
% 5.24/5.51 ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 5.24/5.51 ( ( P @ N )
% 5.24/5.51 => ( ( ord_less_nat @ N @ P6 )
% 5.24/5.51 => ( ( ord_less_nat @ M @ P6 )
% 5.24/5.51 => ( ! [N3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ N3 @ P6 )
% 5.24/5.51 => ( ( P @ N3 )
% 5.24/5.51 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P6 ) ) ) )
% 5.24/5.51 => ( P @ M ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_induct
% 5.24/5.51 thf(fact_3667_mod__less__divisor,axiom,
% 5.24/5.51 ! [N: nat,M: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.51 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_less_divisor
% 5.24/5.51 thf(fact_3668_mod__Suc__le__divisor,axiom,
% 5.24/5.51 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.24/5.51
% 5.24/5.51 % mod_Suc_le_divisor
% 5.24/5.51 thf(fact_3669_mod__eq__0D,axiom,
% 5.24/5.51 ! [M: nat,D: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ M @ D )
% 5.24/5.51 = zero_zero_nat )
% 5.24/5.51 => ? [Q3: nat] :
% 5.24/5.51 ( M
% 5.24/5.51 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eq_0D
% 5.24/5.51 thf(fact_3670_mod__geq,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ~ ( ord_less_nat @ M @ N )
% 5.24/5.51 => ( ( modulo_modulo_nat @ M @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_geq
% 5.24/5.51 thf(fact_3671_mod__if,axiom,
% 5.24/5.51 ( modulo_modulo_nat
% 5.24/5.51 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M2 @ N2 ) @ M2 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_if
% 5.24/5.51 thf(fact_3672_le__mod__geq,axiom,
% 5.24/5.51 ! [N: nat,M: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.51 => ( ( modulo_modulo_nat @ M @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % le_mod_geq
% 5.24/5.51 thf(fact_3673_nat__mod__eq__iff,axiom,
% 5.24/5.51 ! [X: nat,N: nat,Y4: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ X @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ Y4 @ N ) )
% 5.24/5.51 = ( ? [Q1: nat,Q22: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 5.24/5.51 = ( plus_plus_nat @ Y4 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_mod_eq_iff
% 5.24/5.51 thf(fact_3674_infinite__Icc,axiom,
% 5.24/5.51 ! [A: rat,B: rat] :
% 5.24/5.51 ( ( ord_less_rat @ A @ B )
% 5.24/5.51 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_Icc
% 5.24/5.51 thf(fact_3675_infinite__Icc,axiom,
% 5.24/5.51 ! [A: real,B: real] :
% 5.24/5.51 ( ( ord_less_real @ A @ B )
% 5.24/5.51 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_Icc
% 5.24/5.51 thf(fact_3676_finite__lists__length__le,axiom,
% 5.24/5.51 ! [A2: set_complex,N: nat] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.51 => ( finite8712137658972009173omplex
% 5.24/5.51 @ ( collect_list_complex
% 5.24/5.51 @ ^ [Xs: list_complex] :
% 5.24/5.51 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_le
% 5.24/5.51 thf(fact_3677_finite__lists__length__le,axiom,
% 5.24/5.51 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.24/5.51 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.24/5.51 => ( finite3004134309566078307T_VEBT
% 5.24/5.51 @ ( collec5608196760682091941T_VEBT
% 5.24/5.51 @ ^ [Xs: list_VEBT_VEBT] :
% 5.24/5.51 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_le
% 5.24/5.51 thf(fact_3678_finite__lists__length__le,axiom,
% 5.24/5.51 ! [A2: set_o,N: nat] :
% 5.24/5.51 ( ( finite_finite_o @ A2 )
% 5.24/5.51 => ( finite_finite_list_o
% 5.24/5.51 @ ( collect_list_o
% 5.24/5.51 @ ^ [Xs: list_o] :
% 5.24/5.51 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_le
% 5.24/5.51 thf(fact_3679_finite__lists__length__le,axiom,
% 5.24/5.51 ! [A2: set_int,N: nat] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ( finite3922522038869484883st_int
% 5.24/5.51 @ ( collect_list_int
% 5.24/5.51 @ ^ [Xs: list_int] :
% 5.24/5.51 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_le
% 5.24/5.51 thf(fact_3680_finite__lists__length__le,axiom,
% 5.24/5.51 ! [A2: set_nat,N: nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ( finite8100373058378681591st_nat
% 5.24/5.51 @ ( collect_list_nat
% 5.24/5.51 @ ^ [Xs: list_nat] :
% 5.24/5.51 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_lists_length_le
% 5.24/5.51 thf(fact_3681_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.51 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.24/5.51 = A ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_less
% 5.24/5.51 thf(fact_3682_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.24/5.51 => ( ( ord_less_nat @ A @ B )
% 5.24/5.51 => ( ( modulo_modulo_nat @ A @ B )
% 5.24/5.51 = A ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_less
% 5.24/5.51 thf(fact_3683_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.51 => ( ( ord_less_int @ A @ B )
% 5.24/5.51 => ( ( modulo_modulo_int @ A @ B )
% 5.24/5.51 = A ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_less
% 5.24/5.51 thf(fact_3684_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.51 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.24/5.51 thf(fact_3685_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.24/5.51 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.24/5.51 thf(fact_3686_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.24/5.51 thf(fact_3687_cong__exp__iff__simps_I2_J,axiom,
% 5.24/5.51 ! [N: num,Q2: num] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 = zero_zero_nat )
% 5.24/5.51 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.24/5.51 = zero_zero_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(2)
% 5.24/5.51 thf(fact_3688_cong__exp__iff__simps_I2_J,axiom,
% 5.24/5.51 ! [N: num,Q2: num] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 = zero_zero_int )
% 5.24/5.51 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.24/5.51 = zero_zero_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(2)
% 5.24/5.51 thf(fact_3689_cong__exp__iff__simps_I2_J,axiom,
% 5.24/5.51 ! [N: num,Q2: num] :
% 5.24/5.51 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 = zero_z3403309356797280102nteger )
% 5.24/5.51 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(2)
% 5.24/5.51 thf(fact_3690_cong__exp__iff__simps_I1_J,axiom,
% 5.24/5.51 ! [N: num] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.24/5.51 = zero_zero_nat ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(1)
% 5.24/5.51 thf(fact_3691_cong__exp__iff__simps_I1_J,axiom,
% 5.24/5.51 ! [N: num] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(1)
% 5.24/5.51 thf(fact_3692_cong__exp__iff__simps_I1_J,axiom,
% 5.24/5.51 ! [N: num] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(1)
% 5.24/5.51 thf(fact_3693_cong__exp__iff__simps_I6_J,axiom,
% 5.24/5.51 ! [Q2: num,N: num] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(6)
% 5.24/5.51 thf(fact_3694_cong__exp__iff__simps_I6_J,axiom,
% 5.24/5.51 ! [Q2: num,N: num] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(6)
% 5.24/5.51 thf(fact_3695_cong__exp__iff__simps_I6_J,axiom,
% 5.24/5.51 ! [Q2: num,N: num] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(6)
% 5.24/5.51 thf(fact_3696_cong__exp__iff__simps_I8_J,axiom,
% 5.24/5.51 ! [M: num,Q2: num] :
% 5.24/5.51 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(8)
% 5.24/5.51 thf(fact_3697_cong__exp__iff__simps_I8_J,axiom,
% 5.24/5.51 ! [M: num,Q2: num] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(8)
% 5.24/5.51 thf(fact_3698_cong__exp__iff__simps_I8_J,axiom,
% 5.24/5.51 ! [M: num,Q2: num] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.51 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % cong_exp_iff_simps(8)
% 5.24/5.51 thf(fact_3699_mult__div__mod__eq,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mult_div_mod_eq
% 5.24/5.51 thf(fact_3700_mult__div__mod__eq,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mult_div_mod_eq
% 5.24/5.51 thf(fact_3701_mult__div__mod__eq,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mult_div_mod_eq
% 5.24/5.51 thf(fact_3702_mod__mult__div__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_div_eq
% 5.24/5.51 thf(fact_3703_mod__mult__div__eq,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_div_eq
% 5.24/5.51 thf(fact_3704_mod__mult__div__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult_div_eq
% 5.24/5.51 thf(fact_3705_mod__div__mult__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_mult_eq
% 5.24/5.51 thf(fact_3706_mod__div__mult__eq,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_mult_eq
% 5.24/5.51 thf(fact_3707_mod__div__mult__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_mult_eq
% 5.24/5.51 thf(fact_3708_div__mult__mod__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % div_mult_mod_eq
% 5.24/5.51 thf(fact_3709_div__mult__mod__eq,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % div_mult_mod_eq
% 5.24/5.51 thf(fact_3710_div__mult__mod__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.24/5.51 = A ) ).
% 5.24/5.51
% 5.24/5.51 % div_mult_mod_eq
% 5.24/5.51 thf(fact_3711_mod__div__decomp,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( A
% 5.24/5.51 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_decomp
% 5.24/5.51 thf(fact_3712_mod__div__decomp,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( A
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_decomp
% 5.24/5.51 thf(fact_3713_mod__div__decomp,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( A
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_div_decomp
% 5.24/5.51 thf(fact_3714_cancel__div__mod__rules_I1_J,axiom,
% 5.24/5.51 ! [A: nat,B: nat,C: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.24/5.51 = ( plus_plus_nat @ A @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % cancel_div_mod_rules(1)
% 5.24/5.51 thf(fact_3715_cancel__div__mod__rules_I1_J,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.24/5.51 = ( plus_plus_int @ A @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % cancel_div_mod_rules(1)
% 5.24/5.51 thf(fact_3716_cancel__div__mod__rules_I1_J,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % cancel_div_mod_rules(1)
% 5.24/5.51 thf(fact_3717_cancel__div__mod__rules_I2_J,axiom,
% 5.24/5.51 ! [B: nat,A: nat,C: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.24/5.51 = ( plus_plus_nat @ A @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % cancel_div_mod_rules(2)
% 5.24/5.51 thf(fact_3718_cancel__div__mod__rules_I2_J,axiom,
% 5.24/5.51 ! [B: int,A: int,C: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.24/5.51 = ( plus_plus_int @ A @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % cancel_div_mod_rules(2)
% 5.24/5.51 thf(fact_3719_cancel__div__mod__rules_I2_J,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.51 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.24/5.51
% 5.24/5.51 % cancel_div_mod_rules(2)
% 5.24/5.51 thf(fact_3720_div__mult1__eq,axiom,
% 5.24/5.51 ! [A: nat,B: nat,C: nat] :
% 5.24/5.51 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_mult1_eq
% 5.24/5.51 thf(fact_3721_div__mult1__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,C: int] :
% 5.24/5.51 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_mult1_eq
% 5.24/5.51 thf(fact_3722_div__mult1__eq,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.51 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_mult1_eq
% 5.24/5.51 thf(fact_3723_minus__mult__div__eq__mod,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mult_div_eq_mod
% 5.24/5.51 thf(fact_3724_minus__mult__div__eq__mod,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mult_div_eq_mod
% 5.24/5.51 thf(fact_3725_minus__mult__div__eq__mod,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mult_div_eq_mod
% 5.24/5.51 thf(fact_3726_minus__mod__eq__mult__div,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.24/5.51 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_eq_mult_div
% 5.24/5.51 thf(fact_3727_minus__mod__eq__mult__div,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.24/5.51 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_eq_mult_div
% 5.24/5.51 thf(fact_3728_minus__mod__eq__mult__div,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.24/5.51 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_eq_mult_div
% 5.24/5.51 thf(fact_3729_minus__mod__eq__div__mult,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.24/5.51 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_eq_div_mult
% 5.24/5.51 thf(fact_3730_minus__mod__eq__div__mult,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.24/5.51 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_eq_div_mult
% 5.24/5.51 thf(fact_3731_minus__mod__eq__div__mult,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.24/5.51 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_mod_eq_div_mult
% 5.24/5.51 thf(fact_3732_minus__div__mult__eq__mod,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_div_mult_eq_mod
% 5.24/5.51 thf(fact_3733_minus__div__mult__eq__mod,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_div_mult_eq_mod
% 5.24/5.51 thf(fact_3734_minus__div__mult__eq__mod,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.24/5.51
% 5.24/5.51 % minus_div_mult_eq_mod
% 5.24/5.51 thf(fact_3735_mod__le__divisor,axiom,
% 5.24/5.51 ! [N: nat,M: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.51 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_le_divisor
% 5.24/5.51 thf(fact_3736_div__less__mono,axiom,
% 5.24/5.51 ! [A2: nat,B5: nat,N: nat] :
% 5.24/5.51 ( ( ord_less_nat @ A2 @ B5 )
% 5.24/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.51 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.24/5.51 = zero_zero_nat )
% 5.24/5.51 => ( ( ( modulo_modulo_nat @ B5 @ N )
% 5.24/5.51 = zero_zero_nat )
% 5.24/5.51 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_less_mono
% 5.24/5.51 thf(fact_3737_mod__eq__nat1E,axiom,
% 5.24/5.51 ! [M: nat,Q2: nat,N: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.24/5.51 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.24/5.51 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.51 => ~ ! [S: nat] :
% 5.24/5.51 ( M
% 5.24/5.51 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eq_nat1E
% 5.24/5.51 thf(fact_3738_mod__eq__nat2E,axiom,
% 5.24/5.51 ! [M: nat,Q2: nat,N: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.24/5.51 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.24/5.51 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.51 => ~ ! [S: nat] :
% 5.24/5.51 ( N
% 5.24/5.51 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_eq_nat2E
% 5.24/5.51 thf(fact_3739_nat__mod__eq__lemma,axiom,
% 5.24/5.51 ! [X: nat,N: nat,Y4: nat] :
% 5.24/5.51 ( ( ( modulo_modulo_nat @ X @ N )
% 5.24/5.51 = ( modulo_modulo_nat @ Y4 @ N ) )
% 5.24/5.51 => ( ( ord_less_eq_nat @ Y4 @ X )
% 5.24/5.51 => ? [Q3: nat] :
% 5.24/5.51 ( X
% 5.24/5.51 = ( plus_plus_nat @ Y4 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_mod_eq_lemma
% 5.24/5.51 thf(fact_3740_eucl__rel__int__dividesI,axiom,
% 5.24/5.51 ! [L2: int,K: int,Q2: int] :
% 5.24/5.51 ( ( L2 != zero_zero_int )
% 5.24/5.51 => ( ( K
% 5.24/5.51 = ( times_times_int @ Q2 @ L2 ) )
% 5.24/5.51 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % eucl_rel_int_dividesI
% 5.24/5.51 thf(fact_3741_mod__mult2__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.51 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.24/5.51 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_mult2_eq
% 5.24/5.51 thf(fact_3742_div__mod__decomp,axiom,
% 5.24/5.51 ! [A2: nat,N: nat] :
% 5.24/5.51 ( A2
% 5.24/5.51 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_mod_decomp
% 5.24/5.51 thf(fact_3743_modulo__nat__def,axiom,
% 5.24/5.51 ( modulo_modulo_nat
% 5.24/5.51 = ( ^ [M2: nat,N2: nat] : ( minus_minus_nat @ M2 @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % modulo_nat_def
% 5.24/5.51 thf(fact_3744_split__mod,axiom,
% 5.24/5.51 ! [P: nat > $o,M: nat,N: nat] :
% 5.24/5.51 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.51 = ( ( ( N = zero_zero_nat )
% 5.24/5.51 => ( P @ M ) )
% 5.24/5.51 & ( ( N != zero_zero_nat )
% 5.24/5.51 => ! [I4: nat,J3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ J3 @ N )
% 5.24/5.51 => ( ( M
% 5.24/5.51 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.24/5.51 => ( P @ J3 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % split_mod
% 5.24/5.51 thf(fact_3745_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.24/5.51 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.24/5.51 thf(fact_3746_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.24/5.51 ! [C: nat,A: nat,B: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.24/5.51 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.51 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.24/5.51 thf(fact_3747_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.24/5.51 ! [C: int,A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.24/5.51 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.24/5.51 thf(fact_3748_Suc__times__mod__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.24/5.51 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.24/5.51 = one_one_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % Suc_times_mod_eq
% 5.24/5.51 thf(fact_3749_divmod__digit__0_I2_J,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.24/5.51 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_0(2)
% 5.24/5.51 thf(fact_3750_divmod__digit__0_I2_J,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_0(2)
% 5.24/5.51 thf(fact_3751_divmod__digit__0_I2_J,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.51 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_0(2)
% 5.24/5.51 thf(fact_3752_bits__stable__imp__add__self,axiom,
% 5.24/5.51 ! [A: nat] :
% 5.24/5.51 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.51 = A )
% 5.24/5.51 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.51 = zero_zero_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % bits_stable_imp_add_self
% 5.24/5.51 thf(fact_3753_bits__stable__imp__add__self,axiom,
% 5.24/5.51 ! [A: int] :
% 5.24/5.51 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.51 = A )
% 5.24/5.51 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.24/5.51 = zero_zero_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % bits_stable_imp_add_self
% 5.24/5.51 thf(fact_3754_bits__stable__imp__add__self,axiom,
% 5.24/5.51 ! [A: code_integer] :
% 5.24/5.51 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.51 = A )
% 5.24/5.51 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.24/5.51 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.51
% 5.24/5.51 % bits_stable_imp_add_self
% 5.24/5.51 thf(fact_3755_div__exp__mod__exp__eq,axiom,
% 5.24/5.51 ! [A: nat,N: nat,M: nat] :
% 5.24/5.51 ( ( 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 ) )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_exp_mod_exp_eq
% 5.24/5.51 thf(fact_3756_div__exp__mod__exp__eq,axiom,
% 5.24/5.51 ! [A: int,N: nat,M: nat] :
% 5.24/5.51 ( ( 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 ) )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_exp_mod_exp_eq
% 5.24/5.51 thf(fact_3757_div__exp__mod__exp__eq,axiom,
% 5.24/5.51 ! [A: code_integer,N: nat,M: nat] :
% 5.24/5.51 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_exp_mod_exp_eq
% 5.24/5.51 thf(fact_3758_verit__le__mono__div,axiom,
% 5.24/5.51 ! [A2: nat,B5: nat,N: nat] :
% 5.24/5.51 ( ( ord_less_nat @ A2 @ B5 )
% 5.24/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.51 => ( ord_less_eq_nat
% 5.24/5.51 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.24/5.51 @ ( if_nat
% 5.24/5.51 @ ( ( modulo_modulo_nat @ B5 @ N )
% 5.24/5.51 = zero_zero_nat )
% 5.24/5.51 @ one_one_nat
% 5.24/5.51 @ zero_zero_nat ) )
% 5.24/5.51 @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % verit_le_mono_div
% 5.24/5.51 thf(fact_3759_divmod__digit__0_I1_J,axiom,
% 5.24/5.51 ! [B: nat,A: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.24/5.51 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_0(1)
% 5.24/5.51 thf(fact_3760_divmod__digit__0_I1_J,axiom,
% 5.24/5.51 ! [B: int,A: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_0(1)
% 5.24/5.51 thf(fact_3761_divmod__digit__0_I1_J,axiom,
% 5.24/5.51 ! [B: code_integer,A: code_integer] :
% 5.24/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.51 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_0(1)
% 5.24/5.51 thf(fact_3762_mult__exp__mod__exp__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat,A: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 = ( 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 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_exp_mod_exp_eq
% 5.24/5.51 thf(fact_3763_mult__exp__mod__exp__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat,A: int] :
% 5.24/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 = ( 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 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_exp_mod_exp_eq
% 5.24/5.51 thf(fact_3764_mult__exp__mod__exp__eq,axiom,
% 5.24/5.51 ! [M: nat,N: nat,A: code_integer] :
% 5.24/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.51 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.51 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_exp_mod_exp_eq
% 5.24/5.51 thf(fact_3765_eucl__rel__int__iff,axiom,
% 5.24/5.51 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 = ( ( K
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R2 ) )
% 5.24/5.51 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.24/5.51 & ( ord_less_int @ R2 @ L2 ) ) )
% 5.24/5.51 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.24/5.51 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.24/5.51 => ( ( ord_less_int @ L2 @ R2 )
% 5.24/5.51 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.24/5.51 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.24/5.51 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % eucl_rel_int_iff
% 5.24/5.51 thf(fact_3766_mod__double__modulus,axiom,
% 5.24/5.51 ! [M: code_integer,X: code_integer] :
% 5.24/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.24/5.51 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.24/5.51 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.24/5.51 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_double_modulus
% 5.24/5.51 thf(fact_3767_mod__double__modulus,axiom,
% 5.24/5.51 ! [M: nat,X: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.24/5.51 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( modulo_modulo_nat @ X @ M ) )
% 5.24/5.51 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_double_modulus
% 5.24/5.51 thf(fact_3768_mod__double__modulus,axiom,
% 5.24/5.51 ! [M: int,X: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ M )
% 5.24/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.24/5.51 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( modulo_modulo_int @ X @ M ) )
% 5.24/5.51 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.24/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_double_modulus
% 5.24/5.51 thf(fact_3769_divmod__digit__1_I2_J,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.51 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.51 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_1(2)
% 5.24/5.51 thf(fact_3770_divmod__digit__1_I2_J,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.24/5.51 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.24/5.51 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_1(2)
% 5.24/5.51 thf(fact_3771_divmod__digit__1_I2_J,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.51 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.24/5.51 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_1(2)
% 5.24/5.51 thf(fact_3772_unset__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: nat] :
% 5.24/5.51 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unset_bit_Suc
% 5.24/5.51 thf(fact_3773_unset__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: code_integer] :
% 5.24/5.51 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unset_bit_Suc
% 5.24/5.51 thf(fact_3774_unset__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: int] :
% 5.24/5.51 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % unset_bit_Suc
% 5.24/5.51 thf(fact_3775_set__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: code_integer] :
% 5.24/5.51 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_bit_Suc
% 5.24/5.51 thf(fact_3776_set__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: int] :
% 5.24/5.51 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_bit_Suc
% 5.24/5.51 thf(fact_3777_set__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: nat] :
% 5.24/5.51 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_bit_Suc
% 5.24/5.51 thf(fact_3778_divmod__digit__1_I1_J,axiom,
% 5.24/5.51 ! [A: code_integer,B: code_integer] :
% 5.24/5.51 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.51 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.51 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.24/5.51 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_1(1)
% 5.24/5.51 thf(fact_3779_divmod__digit__1_I1_J,axiom,
% 5.24/5.51 ! [A: nat,B: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.24/5.51 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.24/5.51 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 => ( ( 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 )
% 5.24/5.51 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_1(1)
% 5.24/5.51 thf(fact_3780_divmod__digit__1_I1_J,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.51 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.24/5.51 => ( ( 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 )
% 5.24/5.51 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % divmod_digit_1(1)
% 5.24/5.51 thf(fact_3781_mult__less__iff1,axiom,
% 5.24/5.51 ! [Z2: real,X: real,Y4: real] :
% 5.24/5.51 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.24/5.51 => ( ( ord_less_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_less_real @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_less_iff1
% 5.24/5.51 thf(fact_3782_mult__less__iff1,axiom,
% 5.24/5.51 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.51 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.24/5.51 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_less_rat @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_less_iff1
% 5.24/5.51 thf(fact_3783_mult__less__iff1,axiom,
% 5.24/5.51 ! [Z2: int,X: int,Y4: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.51 => ( ( ord_less_int @ ( times_times_int @ X @ Z2 ) @ ( times_times_int @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_less_int @ X @ Y4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mult_less_iff1
% 5.24/5.51 thf(fact_3784_pos__eucl__rel__int__mult__2,axiom,
% 5.24/5.51 ! [B: int,A: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.24/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pos_eucl_rel_int_mult_2
% 5.24/5.51 thf(fact_3785_finite__Collect__le__nat,axiom,
% 5.24/5.51 ! [K: nat] :
% 5.24/5.51 ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_le_nat
% 5.24/5.51 thf(fact_3786_finite__Collect__less__nat,axiom,
% 5.24/5.51 ! [K: nat] :
% 5.24/5.51 ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_less_nat
% 5.24/5.51 thf(fact_3787_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: real > $o,Q: real > real > $o] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [X2: real] :
% 5.24/5.51 ? [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [X2: real] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3788_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: real > $o,Q: nat > real > $o] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [X2: nat] :
% 5.24/5.51 ? [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [X2: nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3789_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: real > $o,Q: complex > real > $o] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [X2: complex] :
% 5.24/5.51 ? [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [X2: complex] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3790_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: nat > $o,Q: real > nat > $o] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [X2: real] :
% 5.24/5.51 ? [Y: nat] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: nat] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [X2: real] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3791_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: nat > $o,Q: nat > nat > $o] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [X2: nat] :
% 5.24/5.51 ? [Y: nat] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: nat] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [X2: nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3792_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: nat > $o,Q: complex > nat > $o] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [X2: complex] :
% 5.24/5.51 ? [Y: nat] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: nat] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [X2: complex] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3793_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: complex > $o,Q: real > complex > $o] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [X2: real] :
% 5.24/5.51 ? [Y: complex] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: complex] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [X2: real] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3794_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: complex > $o,Q: nat > complex > $o] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [X2: nat] :
% 5.24/5.51 ? [Y: complex] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: complex] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [X2: nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3795_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: complex > $o,Q: complex > complex > $o] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [X2: complex] :
% 5.24/5.51 ? [Y: complex] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: complex] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [X2: complex] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3796_finite__Collect__bounded__ex,axiom,
% 5.24/5.51 ! [P: real > $o,Q: list_nat > real > $o] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite8100373058378681591st_nat
% 5.24/5.51 @ ( collect_list_nat
% 5.24/5.51 @ ^ [X2: list_nat] :
% 5.24/5.51 ? [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 & ( Q @ X2 @ Y ) ) ) )
% 5.24/5.51 = ( ! [Y: real] :
% 5.24/5.51 ( ( P @ Y )
% 5.24/5.51 => ( finite8100373058378681591st_nat
% 5.24/5.51 @ ( collect_list_nat
% 5.24/5.51 @ ^ [X2: list_nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_Collect_bounded_ex
% 5.24/5.51 thf(fact_3797_finite__roots__unity,axiom,
% 5.24/5.51 ! [N: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Z4: real] :
% 5.24/5.51 ( ( power_power_real @ Z4 @ N )
% 5.24/5.51 = one_one_real ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_roots_unity
% 5.24/5.51 thf(fact_3798_finite__roots__unity,axiom,
% 5.24/5.51 ! [N: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Z4: complex] :
% 5.24/5.51 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.51 = one_one_complex ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_roots_unity
% 5.24/5.51 thf(fact_3799_flip__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: code_integer] :
% 5.24/5.51 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.24/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % flip_bit_Suc
% 5.24/5.51 thf(fact_3800_flip__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: int] :
% 5.24/5.51 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % flip_bit_Suc
% 5.24/5.51 thf(fact_3801_flip__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,A: nat] :
% 5.24/5.51 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % flip_bit_Suc
% 5.24/5.51 thf(fact_3802_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3803_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3804_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3805_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3806_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3807_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3808_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3809_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3810_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3811_product__nth,axiom,
% 5.24/5.51 ! [N: nat,Xs2: list_nat,Ys: list_o] :
% 5.24/5.51 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.24/5.51 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs2 @ Ys ) @ N )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % product_nth
% 5.24/5.51 thf(fact_3812_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_int,X: int > complex,Y4: int > complex] :
% 5.24/5.51 ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3813_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_real,X: real > complex,Y4: real > complex] :
% 5.24/5.51 ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3814_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_nat,X: nat > complex,Y4: nat > complex] :
% 5.24/5.51 ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3815_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_complex,X: complex > complex,Y4: complex > complex] :
% 5.24/5.51 ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_complex ) ) ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3816_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_int,X: int > real,Y4: int > real] :
% 5.24/5.51 ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3817_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_real,X: real > real,Y4: real > real] :
% 5.24/5.51 ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3818_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_nat,X: nat > real,Y4: nat > real] :
% 5.24/5.51 ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3819_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_complex,X: complex > real,Y4: complex > real] :
% 5.24/5.51 ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_real ) ) ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3820_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_int,X: int > rat,Y4: int > rat] :
% 5.24/5.51 ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_rat ) ) ) )
% 5.24/5.51 => ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_rat ) ) ) )
% 5.24/5.51 => ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_rat @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_rat ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3821_prod_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_real,X: real > rat,Y4: real > rat] :
% 5.24/5.51 ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != one_one_rat ) ) ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != one_one_rat ) ) ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( times_times_rat @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != one_one_rat ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.finite_Collect_op
% 5.24/5.51 thf(fact_3822_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_int,X: int > complex,Y4: int > complex] :
% 5.24/5.51 ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3823_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_real,X: real > complex,Y4: real > complex] :
% 5.24/5.51 ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3824_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_nat,X: nat > complex,Y4: nat > complex] :
% 5.24/5.51 ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3825_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_complex,X: complex > complex,Y4: complex > complex] :
% 5.24/5.51 ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_complex ) ) ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_complex @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_complex ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3826_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_int,X: int > real,Y4: int > real] :
% 5.24/5.51 ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3827_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_real,X: real > real,Y4: real > real] :
% 5.24/5.51 ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3828_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_nat,X: nat > real,Y4: nat > real] :
% 5.24/5.51 ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [I4: nat] :
% 5.24/5.51 ( ( member_nat @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3829_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_complex,X: complex > real,Y4: complex > real] :
% 5.24/5.51 ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_real ) ) ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [I4: complex] :
% 5.24/5.51 ( ( member_complex @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3830_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_int,X: int > rat,Y4: int > rat] :
% 5.24/5.51 ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_rat ) ) ) )
% 5.24/5.51 => ( ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_rat ) ) ) )
% 5.24/5.51 => ( finite_finite_int
% 5.24/5.51 @ ( collect_int
% 5.24/5.51 @ ^ [I4: int] :
% 5.24/5.51 ( ( member_int @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3831_sum_Ofinite__Collect__op,axiom,
% 5.24/5.51 ! [I5: set_real,X: real > rat,Y4: real > rat] :
% 5.24/5.51 ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( X @ I4 )
% 5.24/5.51 != zero_zero_rat ) ) ) )
% 5.24/5.51 => ( ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( Y4 @ I4 )
% 5.24/5.51 != zero_zero_rat ) ) ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [I4: real] :
% 5.24/5.51 ( ( member_real @ I4 @ I5 )
% 5.24/5.51 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y4 @ I4 ) )
% 5.24/5.51 != zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % sum.finite_Collect_op
% 5.24/5.51 thf(fact_3832_mod__pos__pos__trivial,axiom,
% 5.24/5.51 ! [K: int,L2: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.51 => ( ( ord_less_int @ K @ L2 )
% 5.24/5.51 => ( ( modulo_modulo_int @ K @ L2 )
% 5.24/5.51 = K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_pos_pos_trivial
% 5.24/5.51 thf(fact_3833_mod__neg__neg__trivial,axiom,
% 5.24/5.51 ! [K: int,L2: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.24/5.51 => ( ( ord_less_int @ L2 @ K )
% 5.24/5.51 => ( ( modulo_modulo_int @ K @ L2 )
% 5.24/5.51 = K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_neg_neg_trivial
% 5.24/5.51 thf(fact_3834_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.24/5.51 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3835_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.24/5.51 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3836_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.24/5.51 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3837_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.24/5.51 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3838_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.24/5.51 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3839_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_o,Ys: list_o] :
% 5.24/5.51 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3840_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_o,Ys: list_nat] :
% 5.24/5.51 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3841_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_o,Ys: list_int] :
% 5.24/5.51 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3842_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.24/5.51 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3843_length__product,axiom,
% 5.24/5.51 ! [Xs2: list_nat,Ys: list_o] :
% 5.24/5.51 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.24/5.51 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_product
% 5.24/5.51 thf(fact_3844_zmod__numeral__Bit0,axiom,
% 5.24/5.51 ! [V: num,W2: num] :
% 5.24/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.24/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % zmod_numeral_Bit0
% 5.24/5.51 thf(fact_3845_neg__mod__bound,axiom,
% 5.24/5.51 ! [L2: int,K: int] :
% 5.24/5.51 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.24/5.51 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % neg_mod_bound
% 5.24/5.51 thf(fact_3846_Euclidean__Division_Opos__mod__bound,axiom,
% 5.24/5.51 ! [L2: int,K: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.24/5.51 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % Euclidean_Division.pos_mod_bound
% 5.24/5.51 thf(fact_3847_zmod__eq__0D,axiom,
% 5.24/5.51 ! [M: int,D: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ M @ D )
% 5.24/5.51 = zero_zero_int )
% 5.24/5.51 => ? [Q3: int] :
% 5.24/5.51 ( M
% 5.24/5.51 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % zmod_eq_0D
% 5.24/5.51 thf(fact_3848_zmod__eq__0__iff,axiom,
% 5.24/5.51 ! [M: int,D: int] :
% 5.24/5.51 ( ( ( modulo_modulo_int @ M @ D )
% 5.24/5.51 = zero_zero_int )
% 5.24/5.51 = ( ? [Q4: int] :
% 5.24/5.51 ( M
% 5.24/5.51 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % zmod_eq_0_iff
% 5.24/5.51 thf(fact_3849_finite__maxlen,axiom,
% 5.24/5.51 ! [M7: set_list_VEBT_VEBT] :
% 5.24/5.51 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.24/5.51 => ? [N3: nat] :
% 5.24/5.51 ! [X5: list_VEBT_VEBT] :
% 5.24/5.51 ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 5.24/5.51 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_maxlen
% 5.24/5.51 thf(fact_3850_finite__maxlen,axiom,
% 5.24/5.51 ! [M7: set_list_o] :
% 5.24/5.51 ( ( finite_finite_list_o @ M7 )
% 5.24/5.51 => ? [N3: nat] :
% 5.24/5.51 ! [X5: list_o] :
% 5.24/5.51 ( ( member_list_o @ X5 @ M7 )
% 5.24/5.51 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_maxlen
% 5.24/5.51 thf(fact_3851_finite__maxlen,axiom,
% 5.24/5.51 ! [M7: set_list_nat] :
% 5.24/5.51 ( ( finite8100373058378681591st_nat @ M7 )
% 5.24/5.51 => ? [N3: nat] :
% 5.24/5.51 ! [X5: list_nat] :
% 5.24/5.51 ( ( member_list_nat @ X5 @ M7 )
% 5.24/5.51 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_maxlen
% 5.24/5.51 thf(fact_3852_finite__maxlen,axiom,
% 5.24/5.51 ! [M7: set_list_int] :
% 5.24/5.51 ( ( finite3922522038869484883st_int @ M7 )
% 5.24/5.51 => ? [N3: nat] :
% 5.24/5.51 ! [X5: list_int] :
% 5.24/5.51 ( ( member_list_int @ X5 @ M7 )
% 5.24/5.51 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_maxlen
% 5.24/5.51 thf(fact_3853_mod__int__unique,axiom,
% 5.24/5.51 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.51 => ( ( modulo_modulo_int @ K @ L2 )
% 5.24/5.51 = R2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_int_unique
% 5.24/5.51 thf(fact_3854_Euclidean__Division_Opos__mod__sign,axiom,
% 5.24/5.51 ! [L2: int,K: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.24/5.51 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % Euclidean_Division.pos_mod_sign
% 5.24/5.51 thf(fact_3855_neg__mod__sign,axiom,
% 5.24/5.51 ! [L2: int,K: int] :
% 5.24/5.51 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.24/5.51 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % neg_mod_sign
% 5.24/5.51 thf(fact_3856_zdiv__mono__strict,axiom,
% 5.24/5.51 ! [A2: int,B5: int,N: int] :
% 5.24/5.51 ( ( ord_less_int @ A2 @ B5 )
% 5.24/5.51 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.24/5.51 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.24/5.51 = zero_zero_int )
% 5.24/5.51 => ( ( ( modulo_modulo_int @ B5 @ N )
% 5.24/5.51 = zero_zero_int )
% 5.24/5.51 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B5 @ N ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % zdiv_mono_strict
% 5.24/5.51 thf(fact_3857_div__mod__decomp__int,axiom,
% 5.24/5.51 ! [A2: int,N: int] :
% 5.24/5.51 ( A2
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % div_mod_decomp_int
% 5.24/5.51 thf(fact_3858_eucl__rel__int,axiom,
% 5.24/5.51 ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % eucl_rel_int
% 5.24/5.51 thf(fact_3859_mod__pos__neg__trivial,axiom,
% 5.24/5.51 ! [K: int,L2: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.51 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.24/5.51 => ( ( modulo_modulo_int @ K @ L2 )
% 5.24/5.51 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % mod_pos_neg_trivial
% 5.24/5.51 thf(fact_3860_split__zmod,axiom,
% 5.24/5.51 ! [P: int > $o,N: int,K: int] :
% 5.24/5.51 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.24/5.51 = ( ( ( K = zero_zero_int )
% 5.24/5.51 => ( P @ N ) )
% 5.24/5.51 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.51 => ! [I4: int,J3: int] :
% 5.24/5.51 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.24/5.51 & ( ord_less_int @ J3 @ K )
% 5.24/5.51 & ( N
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.24/5.51 => ( P @ J3 ) ) )
% 5.24/5.51 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.24/5.51 => ! [I4: int,J3: int] :
% 5.24/5.51 ( ( ( ord_less_int @ K @ J3 )
% 5.24/5.51 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.24/5.51 & ( N
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.24/5.51 => ( P @ J3 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % split_zmod
% 5.24/5.51 thf(fact_3861_int__mod__neg__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( A
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.24/5.51 => ( ( ord_less_int @ B @ R2 )
% 5.24/5.51 => ( ( modulo_modulo_int @ A @ B )
% 5.24/5.51 = R2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % int_mod_neg_eq
% 5.24/5.51 thf(fact_3862_int__mod__pos__eq,axiom,
% 5.24/5.51 ! [A: int,B: int,Q2: int,R2: int] :
% 5.24/5.51 ( ( A
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.24/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.24/5.51 => ( ( ord_less_int @ R2 @ B )
% 5.24/5.51 => ( ( modulo_modulo_int @ A @ B )
% 5.24/5.51 = R2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % int_mod_pos_eq
% 5.24/5.51 thf(fact_3863_zmod__zmult2__eq,axiom,
% 5.24/5.51 ! [C: int,A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.24/5.51 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % zmod_zmult2_eq
% 5.24/5.51 thf(fact_3864_verit__le__mono__div__int,axiom,
% 5.24/5.51 ! [A2: int,B5: int,N: int] :
% 5.24/5.51 ( ( ord_less_int @ A2 @ B5 )
% 5.24/5.51 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.24/5.51 => ( ord_less_eq_int
% 5.24/5.51 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.24/5.51 @ ( if_int
% 5.24/5.51 @ ( ( modulo_modulo_int @ B5 @ N )
% 5.24/5.51 = zero_zero_int )
% 5.24/5.51 @ one_one_int
% 5.24/5.51 @ zero_zero_int ) )
% 5.24/5.51 @ ( divide_divide_int @ B5 @ N ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % verit_le_mono_div_int
% 5.24/5.51 thf(fact_3865_split__neg__lemma,axiom,
% 5.24/5.51 ! [K: int,P: int > int > $o,N: int] :
% 5.24/5.51 ( ( ord_less_int @ K @ zero_zero_int )
% 5.24/5.51 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.24/5.51 = ( ! [I4: int,J3: int] :
% 5.24/5.51 ( ( ( ord_less_int @ K @ J3 )
% 5.24/5.51 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.24/5.51 & ( N
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.24/5.51 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % split_neg_lemma
% 5.24/5.51 thf(fact_3866_split__pos__lemma,axiom,
% 5.24/5.51 ! [K: int,P: int > int > $o,N: int] :
% 5.24/5.51 ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.51 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.24/5.51 = ( ! [I4: int,J3: int] :
% 5.24/5.51 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.24/5.51 & ( ord_less_int @ J3 @ K )
% 5.24/5.51 & ( N
% 5.24/5.51 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.24/5.51 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % split_pos_lemma
% 5.24/5.51 thf(fact_3867_finite__has__maximal2,axiom,
% 5.24/5.51 ! [A2: set_real,A: real] :
% 5.24/5.51 ( ( finite_finite_real @ A2 )
% 5.24/5.51 => ( ( member_real @ A @ A2 )
% 5.24/5.51 => ? [X3: real] :
% 5.24/5.51 ( ( member_real @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_real @ A @ X3 )
% 5.24/5.51 & ! [Xa: real] :
% 5.24/5.51 ( ( member_real @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal2
% 5.24/5.51 thf(fact_3868_finite__has__maximal2,axiom,
% 5.24/5.51 ! [A2: set_set_nat,A: set_nat] :
% 5.24/5.51 ( ( finite1152437895449049373et_nat @ A2 )
% 5.24/5.51 => ( ( member_set_nat @ A @ A2 )
% 5.24/5.51 => ? [X3: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_set_nat @ A @ X3 )
% 5.24/5.51 & ! [Xa: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal2
% 5.24/5.51 thf(fact_3869_finite__has__maximal2,axiom,
% 5.24/5.51 ! [A2: set_rat,A: rat] :
% 5.24/5.51 ( ( finite_finite_rat @ A2 )
% 5.24/5.51 => ( ( member_rat @ A @ A2 )
% 5.24/5.51 => ? [X3: rat] :
% 5.24/5.51 ( ( member_rat @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_rat @ A @ X3 )
% 5.24/5.51 & ! [Xa: rat] :
% 5.24/5.51 ( ( member_rat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal2
% 5.24/5.51 thf(fact_3870_finite__has__maximal2,axiom,
% 5.24/5.51 ! [A2: set_num,A: num] :
% 5.24/5.51 ( ( finite_finite_num @ A2 )
% 5.24/5.51 => ( ( member_num @ A @ A2 )
% 5.24/5.51 => ? [X3: num] :
% 5.24/5.51 ( ( member_num @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_num @ A @ X3 )
% 5.24/5.51 & ! [Xa: num] :
% 5.24/5.51 ( ( member_num @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal2
% 5.24/5.51 thf(fact_3871_finite__has__maximal2,axiom,
% 5.24/5.51 ! [A2: set_nat,A: nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ( ( member_nat @ A @ A2 )
% 5.24/5.51 => ? [X3: nat] :
% 5.24/5.51 ( ( member_nat @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ A @ X3 )
% 5.24/5.51 & ! [Xa: nat] :
% 5.24/5.51 ( ( member_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal2
% 5.24/5.51 thf(fact_3872_finite__has__maximal2,axiom,
% 5.24/5.51 ! [A2: set_int,A: int] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ( ( member_int @ A @ A2 )
% 5.24/5.51 => ? [X3: int] :
% 5.24/5.51 ( ( member_int @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_int @ A @ X3 )
% 5.24/5.51 & ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal2
% 5.24/5.51 thf(fact_3873_finite__has__minimal2,axiom,
% 5.24/5.51 ! [A2: set_real,A: real] :
% 5.24/5.51 ( ( finite_finite_real @ A2 )
% 5.24/5.51 => ( ( member_real @ A @ A2 )
% 5.24/5.51 => ? [X3: real] :
% 5.24/5.51 ( ( member_real @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_real @ X3 @ A )
% 5.24/5.51 & ! [Xa: real] :
% 5.24/5.51 ( ( member_real @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal2
% 5.24/5.51 thf(fact_3874_finite__has__minimal2,axiom,
% 5.24/5.51 ! [A2: set_set_nat,A: set_nat] :
% 5.24/5.51 ( ( finite1152437895449049373et_nat @ A2 )
% 5.24/5.51 => ( ( member_set_nat @ A @ A2 )
% 5.24/5.51 => ? [X3: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_set_nat @ X3 @ A )
% 5.24/5.51 & ! [Xa: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal2
% 5.24/5.51 thf(fact_3875_finite__has__minimal2,axiom,
% 5.24/5.51 ! [A2: set_rat,A: rat] :
% 5.24/5.51 ( ( finite_finite_rat @ A2 )
% 5.24/5.51 => ( ( member_rat @ A @ A2 )
% 5.24/5.51 => ? [X3: rat] :
% 5.24/5.51 ( ( member_rat @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_rat @ X3 @ A )
% 5.24/5.51 & ! [Xa: rat] :
% 5.24/5.51 ( ( member_rat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal2
% 5.24/5.51 thf(fact_3876_finite__has__minimal2,axiom,
% 5.24/5.51 ! [A2: set_num,A: num] :
% 5.24/5.51 ( ( finite_finite_num @ A2 )
% 5.24/5.51 => ( ( member_num @ A @ A2 )
% 5.24/5.51 => ? [X3: num] :
% 5.24/5.51 ( ( member_num @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_num @ X3 @ A )
% 5.24/5.51 & ! [Xa: num] :
% 5.24/5.51 ( ( member_num @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal2
% 5.24/5.51 thf(fact_3877_finite__has__minimal2,axiom,
% 5.24/5.51 ! [A2: set_nat,A: nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ( ( member_nat @ A @ A2 )
% 5.24/5.51 => ? [X3: nat] :
% 5.24/5.51 ( ( member_nat @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_nat @ X3 @ A )
% 5.24/5.51 & ! [Xa: nat] :
% 5.24/5.51 ( ( member_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal2
% 5.24/5.51 thf(fact_3878_finite__has__minimal2,axiom,
% 5.24/5.51 ! [A2: set_int,A: int] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ( ( member_int @ A @ A2 )
% 5.24/5.51 => ? [X3: int] :
% 5.24/5.51 ( ( member_int @ X3 @ A2 )
% 5.24/5.51 & ( ord_less_eq_int @ X3 @ A )
% 5.24/5.51 & ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal2
% 5.24/5.51 thf(fact_3879_finite_OemptyI,axiom,
% 5.24/5.51 finite3207457112153483333omplex @ bot_bot_set_complex ).
% 5.24/5.51
% 5.24/5.51 % finite.emptyI
% 5.24/5.51 thf(fact_3880_finite_OemptyI,axiom,
% 5.24/5.51 finite_finite_nat @ bot_bot_set_nat ).
% 5.24/5.51
% 5.24/5.51 % finite.emptyI
% 5.24/5.51 thf(fact_3881_finite_OemptyI,axiom,
% 5.24/5.51 finite_finite_int @ bot_bot_set_int ).
% 5.24/5.51
% 5.24/5.51 % finite.emptyI
% 5.24/5.51 thf(fact_3882_finite_OemptyI,axiom,
% 5.24/5.51 finite_finite_real @ bot_bot_set_real ).
% 5.24/5.51
% 5.24/5.51 % finite.emptyI
% 5.24/5.51 thf(fact_3883_infinite__imp__nonempty,axiom,
% 5.24/5.51 ! [S3: set_complex] :
% 5.24/5.51 ( ~ ( finite3207457112153483333omplex @ S3 )
% 5.24/5.51 => ( S3 != bot_bot_set_complex ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_imp_nonempty
% 5.24/5.51 thf(fact_3884_infinite__imp__nonempty,axiom,
% 5.24/5.51 ! [S3: set_nat] :
% 5.24/5.51 ( ~ ( finite_finite_nat @ S3 )
% 5.24/5.51 => ( S3 != bot_bot_set_nat ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_imp_nonempty
% 5.24/5.51 thf(fact_3885_infinite__imp__nonempty,axiom,
% 5.24/5.51 ! [S3: set_int] :
% 5.24/5.51 ( ~ ( finite_finite_int @ S3 )
% 5.24/5.51 => ( S3 != bot_bot_set_int ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_imp_nonempty
% 5.24/5.51 thf(fact_3886_infinite__imp__nonempty,axiom,
% 5.24/5.51 ! [S3: set_real] :
% 5.24/5.51 ( ~ ( finite_finite_real @ S3 )
% 5.24/5.51 => ( S3 != bot_bot_set_real ) ) ).
% 5.24/5.51
% 5.24/5.51 % infinite_imp_nonempty
% 5.24/5.51 thf(fact_3887_pos__zmod__mult__2,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % pos_zmod_mult_2
% 5.24/5.51 thf(fact_3888_finite__image__set,axiom,
% 5.24/5.51 ! [P: real > $o,F: real > real] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3889_finite__image__set,axiom,
% 5.24/5.51 ! [P: real > $o,F: real > nat] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [Uu2: nat] :
% 5.24/5.51 ? [X2: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3890_finite__image__set,axiom,
% 5.24/5.51 ! [P: real > $o,F: real > complex] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Uu2: complex] :
% 5.24/5.51 ? [X2: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3891_finite__image__set,axiom,
% 5.24/5.51 ! [P: nat > $o,F: nat > real] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: nat] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3892_finite__image__set,axiom,
% 5.24/5.51 ! [P: nat > $o,F: nat > nat] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [Uu2: nat] :
% 5.24/5.51 ? [X2: nat] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3893_finite__image__set,axiom,
% 5.24/5.51 ! [P: nat > $o,F: nat > complex] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Uu2: complex] :
% 5.24/5.51 ? [X2: nat] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3894_finite__image__set,axiom,
% 5.24/5.51 ! [P: complex > $o,F: complex > real] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: complex] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3895_finite__image__set,axiom,
% 5.24/5.51 ! [P: complex > $o,F: complex > nat] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [Uu2: nat] :
% 5.24/5.51 ? [X2: complex] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3896_finite__image__set,axiom,
% 5.24/5.51 ! [P: complex > $o,F: complex > complex] :
% 5.24/5.51 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Uu2: complex] :
% 5.24/5.51 ? [X2: complex] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3897_finite__image__set,axiom,
% 5.24/5.51 ! [P: real > $o,F: real > list_nat] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( finite8100373058378681591st_nat
% 5.24/5.51 @ ( collect_list_nat
% 5.24/5.51 @ ^ [Uu2: list_nat] :
% 5.24/5.51 ? [X2: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 ) )
% 5.24/5.51 & ( P @ X2 ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set
% 5.24/5.51 thf(fact_3898_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: real > $o,F: real > real > real] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: real,Y: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3899_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: real > $o,F: real > real > nat] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [Uu2: nat] :
% 5.24/5.51 ? [X2: real,Y: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3900_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: real > $o,F: real > real > complex] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Uu2: complex] :
% 5.24/5.51 ? [X2: real,Y: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3901_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: nat > $o,F: real > nat > real] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: real,Y: nat] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3902_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: nat > $o,F: real > nat > nat] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [Uu2: nat] :
% 5.24/5.51 ? [X2: real,Y: nat] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3903_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: nat > $o,F: real > nat > complex] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Uu2: complex] :
% 5.24/5.51 ? [X2: real,Y: nat] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3904_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: complex > $o,F: real > complex > real] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex @ ( collect_complex @ Q ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: real,Y: complex] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3905_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: complex > $o,F: real > complex > nat] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex @ ( collect_complex @ Q ) )
% 5.24/5.51 => ( finite_finite_nat
% 5.24/5.51 @ ( collect_nat
% 5.24/5.51 @ ^ [Uu2: nat] :
% 5.24/5.51 ? [X2: real,Y: complex] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3906_finite__image__set2,axiom,
% 5.24/5.51 ! [P: real > $o,Q: complex > $o,F: real > complex > complex] :
% 5.24/5.51 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.24/5.51 => ( ( finite3207457112153483333omplex @ ( collect_complex @ Q ) )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Uu2: complex] :
% 5.24/5.51 ? [X2: real,Y: complex] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3907_finite__image__set2,axiom,
% 5.24/5.51 ! [P: nat > $o,Q: real > $o,F: nat > real > real] :
% 5.24/5.51 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.24/5.51 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.24/5.51 => ( finite_finite_real
% 5.24/5.51 @ ( collect_real
% 5.24/5.51 @ ^ [Uu2: real] :
% 5.24/5.51 ? [X2: nat,Y: real] :
% 5.24/5.51 ( ( Uu2
% 5.24/5.51 = ( F @ X2 @ Y ) )
% 5.24/5.51 & ( P @ X2 )
% 5.24/5.51 & ( Q @ Y ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_image_set2
% 5.24/5.51 thf(fact_3908_neg__zmod__mult__2,axiom,
% 5.24/5.51 ! [A: int,B: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.24/5.51 => ( ( 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 ) )
% 5.24/5.51 = ( 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 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % neg_zmod_mult_2
% 5.24/5.51 thf(fact_3909_finite__has__minimal,axiom,
% 5.24/5.51 ! [A2: set_real] :
% 5.24/5.51 ( ( finite_finite_real @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_real )
% 5.24/5.51 => ? [X3: real] :
% 5.24/5.51 ( ( member_real @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: real] :
% 5.24/5.51 ( ( member_real @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal
% 5.24/5.51 thf(fact_3910_finite__has__minimal,axiom,
% 5.24/5.51 ! [A2: set_set_nat] :
% 5.24/5.51 ( ( finite1152437895449049373et_nat @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_set_nat )
% 5.24/5.51 => ? [X3: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal
% 5.24/5.51 thf(fact_3911_finite__has__minimal,axiom,
% 5.24/5.51 ! [A2: set_rat] :
% 5.24/5.51 ( ( finite_finite_rat @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_rat )
% 5.24/5.51 => ? [X3: rat] :
% 5.24/5.51 ( ( member_rat @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: rat] :
% 5.24/5.51 ( ( member_rat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal
% 5.24/5.51 thf(fact_3912_finite__has__minimal,axiom,
% 5.24/5.51 ! [A2: set_num] :
% 5.24/5.51 ( ( finite_finite_num @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_num )
% 5.24/5.51 => ? [X3: num] :
% 5.24/5.51 ( ( member_num @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: num] :
% 5.24/5.51 ( ( member_num @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal
% 5.24/5.51 thf(fact_3913_finite__has__minimal,axiom,
% 5.24/5.51 ! [A2: set_nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_nat )
% 5.24/5.51 => ? [X3: nat] :
% 5.24/5.51 ( ( member_nat @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: nat] :
% 5.24/5.51 ( ( member_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal
% 5.24/5.51 thf(fact_3914_finite__has__minimal,axiom,
% 5.24/5.51 ! [A2: set_int] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_int )
% 5.24/5.51 => ? [X3: int] :
% 5.24/5.51 ( ( member_int @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_minimal
% 5.24/5.51 thf(fact_3915_finite__has__maximal,axiom,
% 5.24/5.51 ! [A2: set_real] :
% 5.24/5.51 ( ( finite_finite_real @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_real )
% 5.24/5.51 => ? [X3: real] :
% 5.24/5.51 ( ( member_real @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: real] :
% 5.24/5.51 ( ( member_real @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal
% 5.24/5.51 thf(fact_3916_finite__has__maximal,axiom,
% 5.24/5.51 ! [A2: set_set_nat] :
% 5.24/5.51 ( ( finite1152437895449049373et_nat @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_set_nat )
% 5.24/5.51 => ? [X3: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: set_nat] :
% 5.24/5.51 ( ( member_set_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal
% 5.24/5.51 thf(fact_3917_finite__has__maximal,axiom,
% 5.24/5.51 ! [A2: set_rat] :
% 5.24/5.51 ( ( finite_finite_rat @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_rat )
% 5.24/5.51 => ? [X3: rat] :
% 5.24/5.51 ( ( member_rat @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: rat] :
% 5.24/5.51 ( ( member_rat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal
% 5.24/5.51 thf(fact_3918_finite__has__maximal,axiom,
% 5.24/5.51 ! [A2: set_num] :
% 5.24/5.51 ( ( finite_finite_num @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_num )
% 5.24/5.51 => ? [X3: num] :
% 5.24/5.51 ( ( member_num @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: num] :
% 5.24/5.51 ( ( member_num @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal
% 5.24/5.51 thf(fact_3919_finite__has__maximal,axiom,
% 5.24/5.51 ! [A2: set_nat] :
% 5.24/5.51 ( ( finite_finite_nat @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_nat )
% 5.24/5.51 => ? [X3: nat] :
% 5.24/5.51 ( ( member_nat @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: nat] :
% 5.24/5.51 ( ( member_nat @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal
% 5.24/5.51 thf(fact_3920_finite__has__maximal,axiom,
% 5.24/5.51 ! [A2: set_int] :
% 5.24/5.51 ( ( finite_finite_int @ A2 )
% 5.24/5.51 => ( ( A2 != bot_bot_set_int )
% 5.24/5.51 => ? [X3: int] :
% 5.24/5.51 ( ( member_int @ X3 @ A2 )
% 5.24/5.51 & ! [Xa: int] :
% 5.24/5.51 ( ( member_int @ Xa @ A2 )
% 5.24/5.51 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.24/5.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_has_maximal
% 5.24/5.51 thf(fact_3921_arcosh__1,axiom,
% 5.24/5.51 ( ( arcosh_real @ one_one_real )
% 5.24/5.51 = zero_zero_real ) ).
% 5.24/5.51
% 5.24/5.51 % arcosh_1
% 5.24/5.51 thf(fact_3922_finite__nth__roots,axiom,
% 5.24/5.51 ! [N: nat,C: complex] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.51 => ( finite3207457112153483333omplex
% 5.24/5.51 @ ( collect_complex
% 5.24/5.51 @ ^ [Z4: complex] :
% 5.24/5.51 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.51 = C ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % finite_nth_roots
% 5.24/5.51 thf(fact_3923_prod_Oinject,axiom,
% 5.24/5.51 ! [X1: int,X22: int,Y1: int,Y2: int] :
% 5.24/5.51 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.24/5.51 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 5.24/5.51 = ( ( X1 = Y1 )
% 5.24/5.51 & ( X22 = Y2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.inject
% 5.24/5.51 thf(fact_3924_prod_Oinject,axiom,
% 5.24/5.51 ! [X1: code_integer > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: code_integer > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 5.24/5.51 ( ( ( produc6137756002093451184nteger @ X1 @ X22 )
% 5.24/5.51 = ( produc6137756002093451184nteger @ Y1 @ Y2 ) )
% 5.24/5.51 = ( ( X1 = Y1 )
% 5.24/5.51 & ( X22 = Y2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.inject
% 5.24/5.51 thf(fact_3925_prod_Oinject,axiom,
% 5.24/5.51 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 5.24/5.51 ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 5.24/5.51 = ( produc8603105652947943368nteger @ Y1 @ Y2 ) )
% 5.24/5.51 = ( ( X1 = Y1 )
% 5.24/5.51 & ( X22 = Y2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.inject
% 5.24/5.51 thf(fact_3926_prod_Oinject,axiom,
% 5.24/5.51 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 5.24/5.51 ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 5.24/5.51 = ( produc5700946648718959541nt_int @ Y1 @ Y2 ) )
% 5.24/5.51 = ( ( X1 = Y1 )
% 5.24/5.51 & ( X22 = Y2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.inject
% 5.24/5.51 thf(fact_3927_prod_Oinject,axiom,
% 5.24/5.51 ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 5.24/5.51 ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 5.24/5.51 = ( produc4305682042979456191nt_int @ Y1 @ Y2 ) )
% 5.24/5.51 = ( ( X1 = Y1 )
% 5.24/5.51 & ( X22 = Y2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod.inject
% 5.24/5.51 thf(fact_3928_old_Oprod_Oinject,axiom,
% 5.24/5.51 ! [A: int,B: int,A5: int,B4: int] :
% 5.24/5.51 ( ( ( product_Pair_int_int @ A @ B )
% 5.24/5.51 = ( product_Pair_int_int @ A5 @ B4 ) )
% 5.24/5.51 = ( ( A = A5 )
% 5.24/5.51 & ( B = B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.inject
% 5.24/5.51 thf(fact_3929_old_Oprod_Oinject,axiom,
% 5.24/5.51 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.24/5.51 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.24/5.51 = ( produc6137756002093451184nteger @ A5 @ B4 ) )
% 5.24/5.51 = ( ( A = A5 )
% 5.24/5.51 & ( B = B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.inject
% 5.24/5.51 thf(fact_3930_old_Oprod_Oinject,axiom,
% 5.24/5.51 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.24/5.51 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.24/5.51 = ( produc8603105652947943368nteger @ A5 @ B4 ) )
% 5.24/5.51 = ( ( A = A5 )
% 5.24/5.51 & ( B = B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.inject
% 5.24/5.51 thf(fact_3931_old_Oprod_Oinject,axiom,
% 5.24/5.51 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.24/5.51 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.24/5.51 = ( produc5700946648718959541nt_int @ A5 @ B4 ) )
% 5.24/5.51 = ( ( A = A5 )
% 5.24/5.51 & ( B = B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.inject
% 5.24/5.51 thf(fact_3932_old_Oprod_Oinject,axiom,
% 5.24/5.51 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.24/5.51 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.24/5.51 = ( produc4305682042979456191nt_int @ A5 @ B4 ) )
% 5.24/5.51 = ( ( A = A5 )
% 5.24/5.51 & ( B = B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.inject
% 5.24/5.51 thf(fact_3933_old_Oprod_Oexhaust,axiom,
% 5.24/5.51 ! [Y4: product_prod_int_int] :
% 5.24/5.51 ~ ! [A3: int,B2: int] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( product_Pair_int_int @ A3 @ B2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.exhaust
% 5.24/5.51 thf(fact_3934_old_Oprod_Oexhaust,axiom,
% 5.24/5.51 ! [Y4: produc8763457246119570046nteger] :
% 5.24/5.51 ~ ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc6137756002093451184nteger @ A3 @ B2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.exhaust
% 5.24/5.51 thf(fact_3935_old_Oprod_Oexhaust,axiom,
% 5.24/5.51 ! [Y4: produc1908205239877642774nteger] :
% 5.24/5.51 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc8603105652947943368nteger @ A3 @ B2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.exhaust
% 5.24/5.51 thf(fact_3936_old_Oprod_Oexhaust,axiom,
% 5.24/5.51 ! [Y4: produc2285326912895808259nt_int] :
% 5.24/5.51 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc5700946648718959541nt_int @ A3 @ B2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.exhaust
% 5.24/5.51 thf(fact_3937_old_Oprod_Oexhaust,axiom,
% 5.24/5.51 ! [Y4: produc7773217078559923341nt_int] :
% 5.24/5.51 ~ ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc4305682042979456191nt_int @ A3 @ B2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % old.prod.exhaust
% 5.24/5.51 thf(fact_3938_surj__pair,axiom,
% 5.24/5.51 ! [P6: product_prod_int_int] :
% 5.24/5.51 ? [X3: int,Y3: int] :
% 5.24/5.51 ( P6
% 5.24/5.51 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 5.24/5.51
% 5.24/5.51 % surj_pair
% 5.24/5.51 thf(fact_3939_surj__pair,axiom,
% 5.24/5.51 ! [P6: produc8763457246119570046nteger] :
% 5.24/5.51 ? [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.51 ( P6
% 5.24/5.51 = ( produc6137756002093451184nteger @ X3 @ Y3 ) ) ).
% 5.24/5.51
% 5.24/5.51 % surj_pair
% 5.24/5.51 thf(fact_3940_surj__pair,axiom,
% 5.24/5.51 ! [P6: produc1908205239877642774nteger] :
% 5.24/5.51 ? [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.51 ( P6
% 5.24/5.51 = ( produc8603105652947943368nteger @ X3 @ Y3 ) ) ).
% 5.24/5.51
% 5.24/5.51 % surj_pair
% 5.24/5.51 thf(fact_3941_surj__pair,axiom,
% 5.24/5.51 ! [P6: produc2285326912895808259nt_int] :
% 5.24/5.51 ? [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.24/5.51 ( P6
% 5.24/5.51 = ( produc5700946648718959541nt_int @ X3 @ Y3 ) ) ).
% 5.24/5.51
% 5.24/5.51 % surj_pair
% 5.24/5.51 thf(fact_3942_surj__pair,axiom,
% 5.24/5.51 ! [P6: produc7773217078559923341nt_int] :
% 5.24/5.51 ? [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.24/5.51 ( P6
% 5.24/5.51 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) ) ).
% 5.24/5.51
% 5.24/5.51 % surj_pair
% 5.24/5.51 thf(fact_3943_prod__cases,axiom,
% 5.24/5.51 ! [P: product_prod_int_int > $o,P6: product_prod_int_int] :
% 5.24/5.51 ( ! [A3: int,B2: int] : ( P @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.51 => ( P @ P6 ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases
% 5.24/5.51 thf(fact_3944_prod__cases,axiom,
% 5.24/5.51 ! [P: produc8763457246119570046nteger > $o,P6: produc8763457246119570046nteger] :
% 5.24/5.51 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.24/5.51 => ( P @ P6 ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases
% 5.24/5.51 thf(fact_3945_prod__cases,axiom,
% 5.24/5.51 ! [P: produc1908205239877642774nteger > $o,P6: produc1908205239877642774nteger] :
% 5.24/5.51 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 5.24/5.51 => ( P @ P6 ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases
% 5.24/5.51 thf(fact_3946_prod__cases,axiom,
% 5.24/5.51 ! [P: produc2285326912895808259nt_int > $o,P6: produc2285326912895808259nt_int] :
% 5.24/5.51 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 5.24/5.51 => ( P @ P6 ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases
% 5.24/5.51 thf(fact_3947_prod__cases,axiom,
% 5.24/5.51 ! [P: produc7773217078559923341nt_int > $o,P6: produc7773217078559923341nt_int] :
% 5.24/5.51 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.24/5.51 => ( P @ P6 ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases
% 5.24/5.51 thf(fact_3948_Pair__inject,axiom,
% 5.24/5.51 ! [A: int,B: int,A5: int,B4: int] :
% 5.24/5.51 ( ( ( product_Pair_int_int @ A @ B )
% 5.24/5.51 = ( product_Pair_int_int @ A5 @ B4 ) )
% 5.24/5.51 => ~ ( ( A = A5 )
% 5.24/5.51 => ( B != B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % Pair_inject
% 5.24/5.51 thf(fact_3949_Pair__inject,axiom,
% 5.24/5.51 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.24/5.51 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.24/5.51 = ( produc6137756002093451184nteger @ A5 @ B4 ) )
% 5.24/5.51 => ~ ( ( A = A5 )
% 5.24/5.51 => ( B != B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % Pair_inject
% 5.24/5.51 thf(fact_3950_Pair__inject,axiom,
% 5.24/5.51 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.24/5.51 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.24/5.51 = ( produc8603105652947943368nteger @ A5 @ B4 ) )
% 5.24/5.51 => ~ ( ( A = A5 )
% 5.24/5.51 => ( B != B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % Pair_inject
% 5.24/5.51 thf(fact_3951_Pair__inject,axiom,
% 5.24/5.51 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.24/5.51 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.24/5.51 = ( produc5700946648718959541nt_int @ A5 @ B4 ) )
% 5.24/5.51 => ~ ( ( A = A5 )
% 5.24/5.51 => ( B != B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % Pair_inject
% 5.24/5.51 thf(fact_3952_Pair__inject,axiom,
% 5.24/5.51 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.24/5.51 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.24/5.51 = ( produc4305682042979456191nt_int @ A5 @ B4 ) )
% 5.24/5.51 => ~ ( ( A = A5 )
% 5.24/5.51 => ( B != B4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % Pair_inject
% 5.24/5.51 thf(fact_3953_prod__cases3,axiom,
% 5.24/5.51 ! [Y4: produc8763457246119570046nteger] :
% 5.24/5.51 ~ ! [A3: code_integer > option6357759511663192854e_term,B2: code_integer,C3: code_integer] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc6137756002093451184nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases3
% 5.24/5.51 thf(fact_3954_prod__cases3,axiom,
% 5.24/5.51 ! [Y4: produc1908205239877642774nteger] :
% 5.24/5.51 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases3
% 5.24/5.51 thf(fact_3955_prod__cases3,axiom,
% 5.24/5.51 ! [Y4: produc2285326912895808259nt_int] :
% 5.24/5.51 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases3
% 5.24/5.51 thf(fact_3956_prod__cases3,axiom,
% 5.24/5.51 ! [Y4: produc7773217078559923341nt_int] :
% 5.24/5.51 ~ ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] :
% 5.24/5.51 ( Y4
% 5.24/5.51 != ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_cases3
% 5.24/5.51 thf(fact_3957_prod__induct3,axiom,
% 5.24/5.51 ! [P: produc8763457246119570046nteger > $o,X: produc8763457246119570046nteger] :
% 5.24/5.51 ( ! [A3: code_integer > option6357759511663192854e_term,B2: code_integer,C3: code_integer] : ( P @ ( produc6137756002093451184nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) )
% 5.24/5.51 => ( P @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_induct3
% 5.24/5.51 thf(fact_3958_prod__induct3,axiom,
% 5.24/5.51 ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 5.24/5.51 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] : ( P @ ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) )
% 5.24/5.51 => ( P @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_induct3
% 5.24/5.51 thf(fact_3959_prod__induct3,axiom,
% 5.24/5.51 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 5.24/5.51 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 5.24/5.51 => ( P @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_induct3
% 5.24/5.51 thf(fact_3960_prod__induct3,axiom,
% 5.24/5.51 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 5.24/5.51 ( ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 5.24/5.51 => ( P @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % prod_induct3
% 5.24/5.51 thf(fact_3961_insert__simp__norm,axiom,
% 5.24/5.51 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.24/5.51 => ( ( ord_less_nat @ Mi @ X )
% 5.24/5.51 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.24/5.51 => ( ( X != Ma )
% 5.24/5.51 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % insert_simp_norm
% 5.24/5.51 thf(fact_3962_insert__simp__excp,axiom,
% 5.24/5.51 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.24/5.51 => ( ( ord_less_nat @ X @ Mi )
% 5.24/5.51 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.24/5.51 => ( ( X != Ma )
% 5.24/5.51 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.24/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % insert_simp_excp
% 5.24/5.51 thf(fact_3963_gcd__nat__induct,axiom,
% 5.24/5.51 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.24/5.51 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.24/5.51 => ( ! [M4: nat,N3: nat] :
% 5.24/5.51 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.24/5.51 => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 5.24/5.51 => ( P @ M4 @ N3 ) ) )
% 5.24/5.51 => ( P @ M @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % gcd_nat_induct
% 5.24/5.51 thf(fact_3964_concat__bit__Suc,axiom,
% 5.24/5.51 ! [N: nat,K: int,L2: int] :
% 5.24/5.51 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 5.24/5.51 = ( 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 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % concat_bit_Suc
% 5.24/5.51 thf(fact_3965_dbl__simps_I3_J,axiom,
% 5.24/5.51 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.24/5.51 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(3)
% 5.24/5.51 thf(fact_3966_dbl__simps_I3_J,axiom,
% 5.24/5.51 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.24/5.51 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(3)
% 5.24/5.51 thf(fact_3967_dbl__simps_I3_J,axiom,
% 5.24/5.51 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.24/5.51 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(3)
% 5.24/5.51 thf(fact_3968_dbl__simps_I3_J,axiom,
% 5.24/5.51 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.24/5.51 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(3)
% 5.24/5.51 thf(fact_3969_max__bot,axiom,
% 5.24/5.51 ! [X: set_nat] :
% 5.24/5.51 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot
% 5.24/5.51 thf(fact_3970_max__bot,axiom,
% 5.24/5.51 ! [X: set_int] :
% 5.24/5.51 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot
% 5.24/5.51 thf(fact_3971_max__bot,axiom,
% 5.24/5.51 ! [X: set_real] :
% 5.24/5.51 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot
% 5.24/5.51 thf(fact_3972_max__bot,axiom,
% 5.24/5.51 ! [X: nat] :
% 5.24/5.51 ( ( ord_max_nat @ bot_bot_nat @ X )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot
% 5.24/5.51 thf(fact_3973_max__bot,axiom,
% 5.24/5.51 ! [X: extended_enat] :
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot
% 5.24/5.51 thf(fact_3974_max__bot2,axiom,
% 5.24/5.51 ! [X: set_nat] :
% 5.24/5.51 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot2
% 5.24/5.51 thf(fact_3975_max__bot2,axiom,
% 5.24/5.51 ! [X: set_int] :
% 5.24/5.51 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot2
% 5.24/5.51 thf(fact_3976_max__bot2,axiom,
% 5.24/5.51 ! [X: set_real] :
% 5.24/5.51 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot2
% 5.24/5.51 thf(fact_3977_max__bot2,axiom,
% 5.24/5.51 ! [X: nat] :
% 5.24/5.51 ( ( ord_max_nat @ X @ bot_bot_nat )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot2
% 5.24/5.51 thf(fact_3978_max__bot2,axiom,
% 5.24/5.51 ! [X: extended_enat] :
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ X @ bot_bo4199563552545308370d_enat )
% 5.24/5.51 = X ) ).
% 5.24/5.51
% 5.24/5.51 % max_bot2
% 5.24/5.51 thf(fact_3979_length__list__update,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.24/5.51 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 5.24/5.51 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_list_update
% 5.24/5.51 thf(fact_3980_length__list__update,axiom,
% 5.24/5.51 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.24/5.51 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 5.24/5.51 = ( size_size_list_o @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_list_update
% 5.24/5.51 thf(fact_3981_length__list__update,axiom,
% 5.24/5.51 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.24/5.51 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 5.24/5.51 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_list_update
% 5.24/5.51 thf(fact_3982_length__list__update,axiom,
% 5.24/5.51 ! [Xs2: list_int,I2: nat,X: int] :
% 5.24/5.51 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 5.24/5.51 = ( size_size_list_int @ Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % length_list_update
% 5.24/5.51 thf(fact_3983_max__Suc__Suc,axiom,
% 5.24/5.51 ! [M: nat,N: nat] :
% 5.24/5.51 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.24/5.51 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_Suc_Suc
% 5.24/5.51 thf(fact_3984_nth__list__update__neq,axiom,
% 5.24/5.51 ! [I2: nat,J: nat,Xs2: list_nat,X: nat] :
% 5.24/5.51 ( ( I2 != J )
% 5.24/5.51 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.51 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_neq
% 5.24/5.51 thf(fact_3985_nth__list__update__neq,axiom,
% 5.24/5.51 ! [I2: nat,J: nat,Xs2: list_int,X: int] :
% 5.24/5.51 ( ( I2 != J )
% 5.24/5.51 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.51 = ( nth_int @ Xs2 @ J ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_neq
% 5.24/5.51 thf(fact_3986_nth__list__update__neq,axiom,
% 5.24/5.51 ! [I2: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.24/5.51 ( ( I2 != J )
% 5.24/5.51 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.51 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_neq
% 5.24/5.51 thf(fact_3987_list__update__id,axiom,
% 5.24/5.51 ! [Xs2: list_nat,I2: nat] :
% 5.24/5.51 ( ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ I2 ) )
% 5.24/5.51 = Xs2 ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_id
% 5.24/5.51 thf(fact_3988_list__update__id,axiom,
% 5.24/5.51 ! [Xs2: list_int,I2: nat] :
% 5.24/5.51 ( ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ I2 ) )
% 5.24/5.51 = Xs2 ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_id
% 5.24/5.51 thf(fact_3989_list__update__id,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,I2: nat] :
% 5.24/5.51 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) )
% 5.24/5.51 = Xs2 ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_id
% 5.24/5.51 thf(fact_3990_dbl__simps_I2_J,axiom,
% 5.24/5.51 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.24/5.51 = zero_zero_complex ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(2)
% 5.24/5.51 thf(fact_3991_dbl__simps_I2_J,axiom,
% 5.24/5.51 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.24/5.51 = zero_zero_real ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(2)
% 5.24/5.51 thf(fact_3992_dbl__simps_I2_J,axiom,
% 5.24/5.51 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.24/5.51 = zero_zero_rat ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(2)
% 5.24/5.51 thf(fact_3993_dbl__simps_I2_J,axiom,
% 5.24/5.51 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.24/5.51 = zero_zero_int ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(2)
% 5.24/5.51 thf(fact_3994_max__number__of_I1_J,axiom,
% 5.24/5.51 ! [U2: num,V: num] :
% 5.24/5.51 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U2 ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.24/5.51 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U2 ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.24/5.51 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.24/5.51 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U2 ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.24/5.51 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U2 ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.24/5.51 = ( numera1916890842035813515d_enat @ U2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_number_of(1)
% 5.24/5.51 thf(fact_3995_max__number__of_I1_J,axiom,
% 5.24/5.51 ! [U2: num,V: num] :
% 5.24/5.51 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.51 => ( ( ord_max_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.51 = ( numeral_numeral_real @ V ) ) )
% 5.24/5.51 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.51 => ( ( ord_max_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.51 = ( numeral_numeral_real @ U2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_number_of(1)
% 5.24/5.51 thf(fact_3996_max__number__of_I1_J,axiom,
% 5.24/5.51 ! [U2: num,V: num] :
% 5.24/5.51 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U2 ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.51 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U2 ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.51 = ( numeral_numeral_rat @ V ) ) )
% 5.24/5.51 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U2 ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.51 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U2 ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.51 = ( numeral_numeral_rat @ U2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_number_of(1)
% 5.24/5.51 thf(fact_3997_max__number__of_I1_J,axiom,
% 5.24/5.51 ! [U2: num,V: num] :
% 5.24/5.51 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U2 ) @ ( numeral_numeral_nat @ V ) )
% 5.24/5.51 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U2 ) @ ( numeral_numeral_nat @ V ) )
% 5.24/5.51 = ( numeral_numeral_nat @ V ) ) )
% 5.24/5.51 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U2 ) @ ( numeral_numeral_nat @ V ) )
% 5.24/5.51 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U2 ) @ ( numeral_numeral_nat @ V ) )
% 5.24/5.51 = ( numeral_numeral_nat @ U2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_number_of(1)
% 5.24/5.51 thf(fact_3998_max__number__of_I1_J,axiom,
% 5.24/5.51 ! [U2: num,V: num] :
% 5.24/5.51 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U2 ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.51 => ( ( ord_max_int @ ( numeral_numeral_int @ U2 ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.51 = ( numeral_numeral_int @ V ) ) )
% 5.24/5.51 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U2 ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.51 => ( ( ord_max_int @ ( numeral_numeral_int @ U2 ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.51 = ( numeral_numeral_int @ U2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_number_of(1)
% 5.24/5.51 thf(fact_3999_max__0__1_I3_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.24/5.51 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(3)
% 5.24/5.51 thf(fact_4000_max__0__1_I3_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.24/5.51 = ( numeral_numeral_real @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(3)
% 5.24/5.51 thf(fact_4001_max__0__1_I3_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.24/5.51 = ( numeral_numeral_rat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(3)
% 5.24/5.51 thf(fact_4002_max__0__1_I3_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.24/5.51 = ( numeral_numeral_nat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(3)
% 5.24/5.51 thf(fact_4003_max__0__1_I3_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.24/5.51 = ( numeral_numeral_int @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(3)
% 5.24/5.51 thf(fact_4004_max__0__1_I4_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.24/5.51 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(4)
% 5.24/5.51 thf(fact_4005_max__0__1_I4_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.24/5.51 = ( numeral_numeral_real @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(4)
% 5.24/5.51 thf(fact_4006_max__0__1_I4_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.24/5.51 = ( numeral_numeral_rat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(4)
% 5.24/5.51 thf(fact_4007_max__0__1_I4_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.24/5.51 = ( numeral_numeral_nat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(4)
% 5.24/5.51 thf(fact_4008_max__0__1_I4_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.24/5.51 = ( numeral_numeral_int @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(4)
% 5.24/5.51 thf(fact_4009_max__0__1_I2_J,axiom,
% 5.24/5.51 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.24/5.51 = one_one_real ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(2)
% 5.24/5.51 thf(fact_4010_max__0__1_I2_J,axiom,
% 5.24/5.51 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.24/5.51 = one_one_rat ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(2)
% 5.24/5.51 thf(fact_4011_max__0__1_I2_J,axiom,
% 5.24/5.51 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.24/5.51 = one_one_nat ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(2)
% 5.24/5.51 thf(fact_4012_max__0__1_I2_J,axiom,
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.24/5.51 = one_on7984719198319812577d_enat ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(2)
% 5.24/5.51 thf(fact_4013_max__0__1_I2_J,axiom,
% 5.24/5.51 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.24/5.51 = one_one_int ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(2)
% 5.24/5.51 thf(fact_4014_max__0__1_I1_J,axiom,
% 5.24/5.51 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.24/5.51 = one_one_real ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(1)
% 5.24/5.51 thf(fact_4015_max__0__1_I1_J,axiom,
% 5.24/5.51 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.24/5.51 = one_one_rat ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(1)
% 5.24/5.51 thf(fact_4016_max__0__1_I1_J,axiom,
% 5.24/5.51 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.24/5.51 = one_one_nat ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(1)
% 5.24/5.51 thf(fact_4017_max__0__1_I1_J,axiom,
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.24/5.51 = one_on7984719198319812577d_enat ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(1)
% 5.24/5.51 thf(fact_4018_max__0__1_I1_J,axiom,
% 5.24/5.51 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.24/5.51 = one_one_int ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(1)
% 5.24/5.51 thf(fact_4019_max__0__1_I5_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.24/5.51 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(5)
% 5.24/5.51 thf(fact_4020_max__0__1_I5_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.24/5.51 = ( numeral_numeral_real @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(5)
% 5.24/5.51 thf(fact_4021_max__0__1_I5_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.24/5.51 = ( numeral_numeral_rat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(5)
% 5.24/5.51 thf(fact_4022_max__0__1_I5_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.24/5.51 = ( numeral_numeral_nat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(5)
% 5.24/5.51 thf(fact_4023_max__0__1_I5_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.24/5.51 = ( numeral_numeral_int @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(5)
% 5.24/5.51 thf(fact_4024_max__0__1_I6_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.24/5.51 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(6)
% 5.24/5.51 thf(fact_4025_max__0__1_I6_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.24/5.51 = ( numeral_numeral_real @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(6)
% 5.24/5.51 thf(fact_4026_max__0__1_I6_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 5.24/5.51 = ( numeral_numeral_rat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(6)
% 5.24/5.51 thf(fact_4027_max__0__1_I6_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.24/5.51 = ( numeral_numeral_nat @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(6)
% 5.24/5.51 thf(fact_4028_max__0__1_I6_J,axiom,
% 5.24/5.51 ! [X: num] :
% 5.24/5.51 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.24/5.51 = ( numeral_numeral_int @ X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_0_1(6)
% 5.24/5.51 thf(fact_4029_list__update__beyond,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 5.24/5.51 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.24/5.51 = Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_beyond
% 5.24/5.51 thf(fact_4030_list__update__beyond,axiom,
% 5.24/5.51 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.24/5.51 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 5.24/5.51 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.24/5.51 = Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_beyond
% 5.24/5.51 thf(fact_4031_list__update__beyond,axiom,
% 5.24/5.51 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 5.24/5.51 => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.24/5.51 = Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_beyond
% 5.24/5.51 thf(fact_4032_list__update__beyond,axiom,
% 5.24/5.51 ! [Xs2: list_int,I2: nat,X: int] :
% 5.24/5.51 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 5.24/5.51 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.24/5.51 = Xs2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % list_update_beyond
% 5.24/5.51 thf(fact_4033_dbl__simps_I5_J,axiom,
% 5.24/5.51 ! [K: num] :
% 5.24/5.51 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.24/5.51 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(5)
% 5.24/5.51 thf(fact_4034_dbl__simps_I5_J,axiom,
% 5.24/5.51 ! [K: num] :
% 5.24/5.51 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.24/5.51 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(5)
% 5.24/5.51 thf(fact_4035_dbl__simps_I5_J,axiom,
% 5.24/5.51 ! [K: num] :
% 5.24/5.51 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.24/5.51 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(5)
% 5.24/5.51 thf(fact_4036_dbl__simps_I5_J,axiom,
% 5.24/5.51 ! [K: num] :
% 5.24/5.51 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.24/5.51 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_simps(5)
% 5.24/5.51 thf(fact_4037_nth__list__update__eq,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.24/5.51 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_eq
% 5.24/5.51 thf(fact_4038_nth__list__update__eq,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.24/5.51 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_eq
% 5.24/5.51 thf(fact_4039_nth__list__update__eq,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.24/5.51 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_eq
% 5.24/5.51 thf(fact_4040_nth__list__update__eq,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_int,X: int] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.24/5.51 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % nth_list_update_eq
% 5.24/5.51 thf(fact_4041_set__swap,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.24/5.51 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.24/5.51 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.24/5.51 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_swap
% 5.24/5.51 thf(fact_4042_set__swap,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_o,J: nat] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.24/5.51 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.24/5.51 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.24/5.51 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_swap
% 5.24/5.51 thf(fact_4043_set__swap,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_nat,J: nat] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.24/5.51 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.24/5.51 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.24/5.51 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_swap
% 5.24/5.51 thf(fact_4044_set__swap,axiom,
% 5.24/5.51 ! [I2: nat,Xs2: list_int,J: nat] :
% 5.24/5.51 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.24/5.51 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.24/5.51 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.24/5.51 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_swap
% 5.24/5.51 thf(fact_4045_max__def,axiom,
% 5.24/5.51 ( ord_ma741700101516333627d_enat
% 5.24/5.51 = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def
% 5.24/5.51 thf(fact_4046_max__def,axiom,
% 5.24/5.51 ( ord_max_set_nat
% 5.24/5.51 = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def
% 5.24/5.51 thf(fact_4047_max__def,axiom,
% 5.24/5.51 ( ord_max_rat
% 5.24/5.51 = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def
% 5.24/5.51 thf(fact_4048_max__def,axiom,
% 5.24/5.51 ( ord_max_num
% 5.24/5.51 = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def
% 5.24/5.51 thf(fact_4049_max__def,axiom,
% 5.24/5.51 ( ord_max_nat
% 5.24/5.51 = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def
% 5.24/5.51 thf(fact_4050_max__def,axiom,
% 5.24/5.51 ( ord_max_int
% 5.24/5.51 = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def
% 5.24/5.51 thf(fact_4051_max__absorb1,axiom,
% 5.24/5.51 ! [Y4: extended_enat,X: extended_enat] :
% 5.24/5.51 ( ( ord_le2932123472753598470d_enat @ Y4 @ X )
% 5.24/5.51 => ( ( ord_ma741700101516333627d_enat @ X @ Y4 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb1
% 5.24/5.51 thf(fact_4052_max__absorb1,axiom,
% 5.24/5.51 ! [Y4: set_nat,X: set_nat] :
% 5.24/5.51 ( ( ord_less_eq_set_nat @ Y4 @ X )
% 5.24/5.51 => ( ( ord_max_set_nat @ X @ Y4 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb1
% 5.24/5.51 thf(fact_4053_max__absorb1,axiom,
% 5.24/5.51 ! [Y4: rat,X: rat] :
% 5.24/5.51 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.24/5.51 => ( ( ord_max_rat @ X @ Y4 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb1
% 5.24/5.51 thf(fact_4054_max__absorb1,axiom,
% 5.24/5.51 ! [Y4: num,X: num] :
% 5.24/5.51 ( ( ord_less_eq_num @ Y4 @ X )
% 5.24/5.51 => ( ( ord_max_num @ X @ Y4 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb1
% 5.24/5.51 thf(fact_4055_max__absorb1,axiom,
% 5.24/5.51 ! [Y4: nat,X: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ Y4 @ X )
% 5.24/5.51 => ( ( ord_max_nat @ X @ Y4 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb1
% 5.24/5.51 thf(fact_4056_max__absorb1,axiom,
% 5.24/5.51 ! [Y4: int,X: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ Y4 @ X )
% 5.24/5.51 => ( ( ord_max_int @ X @ Y4 )
% 5.24/5.51 = X ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb1
% 5.24/5.51 thf(fact_4057_max__absorb2,axiom,
% 5.24/5.51 ! [X: extended_enat,Y4: extended_enat] :
% 5.24/5.51 ( ( ord_le2932123472753598470d_enat @ X @ Y4 )
% 5.24/5.51 => ( ( ord_ma741700101516333627d_enat @ X @ Y4 )
% 5.24/5.51 = Y4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb2
% 5.24/5.51 thf(fact_4058_max__absorb2,axiom,
% 5.24/5.51 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.51 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.24/5.51 => ( ( ord_max_set_nat @ X @ Y4 )
% 5.24/5.51 = Y4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb2
% 5.24/5.51 thf(fact_4059_max__absorb2,axiom,
% 5.24/5.51 ! [X: rat,Y4: rat] :
% 5.24/5.51 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.24/5.51 => ( ( ord_max_rat @ X @ Y4 )
% 5.24/5.51 = Y4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb2
% 5.24/5.51 thf(fact_4060_max__absorb2,axiom,
% 5.24/5.51 ! [X: num,Y4: num] :
% 5.24/5.51 ( ( ord_less_eq_num @ X @ Y4 )
% 5.24/5.51 => ( ( ord_max_num @ X @ Y4 )
% 5.24/5.51 = Y4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb2
% 5.24/5.51 thf(fact_4061_max__absorb2,axiom,
% 5.24/5.51 ! [X: nat,Y4: nat] :
% 5.24/5.51 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.24/5.51 => ( ( ord_max_nat @ X @ Y4 )
% 5.24/5.51 = Y4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb2
% 5.24/5.51 thf(fact_4062_max__absorb2,axiom,
% 5.24/5.51 ! [X: int,Y4: int] :
% 5.24/5.51 ( ( ord_less_eq_int @ X @ Y4 )
% 5.24/5.51 => ( ( ord_max_int @ X @ Y4 )
% 5.24/5.51 = Y4 ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_absorb2
% 5.24/5.51 thf(fact_4063_max__add__distrib__right,axiom,
% 5.24/5.51 ! [X: real,Y4: real,Z2: real] :
% 5.24/5.51 ( ( plus_plus_real @ X @ ( ord_max_real @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_max_real @ ( plus_plus_real @ X @ Y4 ) @ ( plus_plus_real @ X @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_right
% 5.24/5.51 thf(fact_4064_max__add__distrib__right,axiom,
% 5.24/5.51 ! [X: rat,Y4: rat,Z2: rat] :
% 5.24/5.51 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( plus_plus_rat @ X @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_right
% 5.24/5.51 thf(fact_4065_max__add__distrib__right,axiom,
% 5.24/5.51 ! [X: nat,Y4: nat,Z2: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y4 ) @ ( plus_plus_nat @ X @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_right
% 5.24/5.51 thf(fact_4066_max__add__distrib__right,axiom,
% 5.24/5.51 ! [X: int,Y4: int,Z2: int] :
% 5.24/5.51 ( ( plus_plus_int @ X @ ( ord_max_int @ Y4 @ Z2 ) )
% 5.24/5.51 = ( ord_max_int @ ( plus_plus_int @ X @ Y4 ) @ ( plus_plus_int @ X @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_right
% 5.24/5.51 thf(fact_4067_max__add__distrib__left,axiom,
% 5.24/5.51 ! [X: real,Y4: real,Z2: real] :
% 5.24/5.51 ( ( plus_plus_real @ ( ord_max_real @ X @ Y4 ) @ Z2 )
% 5.24/5.51 = ( ord_max_real @ ( plus_plus_real @ X @ Z2 ) @ ( plus_plus_real @ Y4 @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_left
% 5.24/5.51 thf(fact_4068_max__add__distrib__left,axiom,
% 5.24/5.51 ! [X: rat,Y4: rat,Z2: rat] :
% 5.24/5.51 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y4 ) @ Z2 )
% 5.24/5.51 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z2 ) @ ( plus_plus_rat @ Y4 @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_left
% 5.24/5.51 thf(fact_4069_max__add__distrib__left,axiom,
% 5.24/5.51 ! [X: nat,Y4: nat,Z2: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y4 ) @ Z2 )
% 5.24/5.51 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z2 ) @ ( plus_plus_nat @ Y4 @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_left
% 5.24/5.51 thf(fact_4070_max__add__distrib__left,axiom,
% 5.24/5.51 ! [X: int,Y4: int,Z2: int] :
% 5.24/5.51 ( ( plus_plus_int @ ( ord_max_int @ X @ Y4 ) @ Z2 )
% 5.24/5.51 = ( ord_max_int @ ( plus_plus_int @ X @ Z2 ) @ ( plus_plus_int @ Y4 @ Z2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_add_distrib_left
% 5.24/5.51 thf(fact_4071_nat__add__max__right,axiom,
% 5.24/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.24/5.51 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_add_max_right
% 5.24/5.51 thf(fact_4072_nat__add__max__left,axiom,
% 5.24/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.24/5.51 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_add_max_left
% 5.24/5.51 thf(fact_4073_nat__mult__max__right,axiom,
% 5.24/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.51 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.24/5.51 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_mult_max_right
% 5.24/5.51 thf(fact_4074_nat__mult__max__left,axiom,
% 5.24/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.51 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.24/5.51 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_mult_max_left
% 5.24/5.51 thf(fact_4075_max__def__raw,axiom,
% 5.24/5.51 ( ord_ma741700101516333627d_enat
% 5.24/5.51 = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def_raw
% 5.24/5.51 thf(fact_4076_max__def__raw,axiom,
% 5.24/5.51 ( ord_max_set_nat
% 5.24/5.51 = ( ^ [A4: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def_raw
% 5.24/5.51 thf(fact_4077_max__def__raw,axiom,
% 5.24/5.51 ( ord_max_rat
% 5.24/5.51 = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def_raw
% 5.24/5.51 thf(fact_4078_max__def__raw,axiom,
% 5.24/5.51 ( ord_max_num
% 5.24/5.51 = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def_raw
% 5.24/5.51 thf(fact_4079_max__def__raw,axiom,
% 5.24/5.51 ( ord_max_nat
% 5.24/5.51 = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def_raw
% 5.24/5.51 thf(fact_4080_max__def__raw,axiom,
% 5.24/5.51 ( ord_max_int
% 5.24/5.51 = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % max_def_raw
% 5.24/5.51 thf(fact_4081_concat__bit__assoc,axiom,
% 5.24/5.51 ! [N: nat,K: int,M: nat,L2: int,R2: int] :
% 5.24/5.51 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R2 ) )
% 5.24/5.51 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 ) ) ).
% 5.24/5.51
% 5.24/5.51 % concat_bit_assoc
% 5.24/5.51 thf(fact_4082_nat__minus__add__max,axiom,
% 5.24/5.51 ! [N: nat,M: nat] :
% 5.24/5.51 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.24/5.51 = ( ord_max_nat @ N @ M ) ) ).
% 5.24/5.51
% 5.24/5.51 % nat_minus_add_max
% 5.24/5.51 thf(fact_4083_set__update__subsetI,axiom,
% 5.24/5.51 ! [Xs2: list_real,A2: set_real,X: real,I2: nat] :
% 5.24/5.51 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 5.24/5.51 => ( ( member_real @ X @ A2 )
% 5.24/5.51 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_update_subsetI
% 5.24/5.51 thf(fact_4084_set__update__subsetI,axiom,
% 5.24/5.51 ! [Xs2: list_complex,A2: set_complex,X: complex,I2: nat] :
% 5.24/5.51 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.24/5.51 => ( ( member_complex @ X @ A2 )
% 5.24/5.51 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_update_subsetI
% 5.24/5.51 thf(fact_4085_set__update__subsetI,axiom,
% 5.24/5.51 ! [Xs2: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,I2: nat] :
% 5.24/5.51 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 5.24/5.51 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.24/5.51 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_update_subsetI
% 5.24/5.51 thf(fact_4086_set__update__subsetI,axiom,
% 5.24/5.51 ! [Xs2: list_int,A2: set_int,X: int,I2: nat] :
% 5.24/5.51 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.24/5.51 => ( ( member_int @ X @ A2 )
% 5.24/5.51 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_update_subsetI
% 5.24/5.51 thf(fact_4087_set__update__subsetI,axiom,
% 5.24/5.51 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I2: nat] :
% 5.24/5.51 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.24/5.51 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.24/5.51 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_update_subsetI
% 5.24/5.51 thf(fact_4088_set__update__subsetI,axiom,
% 5.24/5.51 ! [Xs2: list_nat,A2: set_nat,X: nat,I2: nat] :
% 5.24/5.51 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.24/5.51 => ( ( member_nat @ X @ A2 )
% 5.24/5.51 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % set_update_subsetI
% 5.24/5.51 thf(fact_4089_dbl__def,axiom,
% 5.24/5.51 ( neg_numeral_dbl_real
% 5.24/5.51 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_def
% 5.24/5.51 thf(fact_4090_dbl__def,axiom,
% 5.24/5.51 ( neg_numeral_dbl_rat
% 5.24/5.51 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_def
% 5.24/5.51 thf(fact_4091_dbl__def,axiom,
% 5.24/5.51 ( neg_numeral_dbl_int
% 5.24/5.51 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.24/5.51
% 5.24/5.51 % dbl_def
% 5.24/5.51 thf(fact_4092_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_real,X: real] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.24/5.52 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4093_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_complex,X: complex] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.24/5.52 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4094_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.24/5.52 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4095_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.24/5.52 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4096_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_o,X: $o] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.24/5.52 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4097_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_nat,X: nat] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.24/5.52 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4098_set__update__memI,axiom,
% 5.24/5.52 ! [N: nat,Xs2: list_int,X: int] :
% 5.24/5.52 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.24/5.52 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_update_memI
% 5.24/5.52 thf(fact_4099_list__update__same__conv,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.24/5.52 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.24/5.52 = Xs2 )
% 5.24/5.52 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.24/5.52 = X ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % list_update_same_conv
% 5.24/5.52 thf(fact_4100_list__update__same__conv,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.24/5.52 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.24/5.52 = Xs2 )
% 5.24/5.52 = ( ( nth_o @ Xs2 @ I2 )
% 5.24/5.52 = X ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % list_update_same_conv
% 5.24/5.52 thf(fact_4101_list__update__same__conv,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.24/5.52 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.24/5.52 = Xs2 )
% 5.24/5.52 = ( ( nth_nat @ Xs2 @ I2 )
% 5.24/5.52 = X ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % list_update_same_conv
% 5.24/5.52 thf(fact_4102_list__update__same__conv,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_int,X: int] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.24/5.52 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.24/5.52 = Xs2 )
% 5.24/5.52 = ( ( nth_int @ Xs2 @ I2 )
% 5.24/5.52 = X ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % list_update_same_conv
% 5.24/5.52 thf(fact_4103_nth__list__update,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.24/5.52 => ( ( ( I2 = J )
% 5.24/5.52 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = X ) )
% 5.24/5.52 & ( ( I2 != J )
% 5.24/5.52 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nth_list_update
% 5.24/5.52 thf(fact_4104_nth__list__update,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_o,X: $o,J: nat] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.24/5.52 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = ( ( ( I2 = J )
% 5.24/5.52 => X )
% 5.24/5.52 & ( ( I2 != J )
% 5.24/5.52 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nth_list_update
% 5.24/5.52 thf(fact_4105_nth__list__update,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_nat,J: nat,X: nat] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.24/5.52 => ( ( ( I2 = J )
% 5.24/5.52 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = X ) )
% 5.24/5.52 & ( ( I2 != J )
% 5.24/5.52 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nth_list_update
% 5.24/5.52 thf(fact_4106_nth__list__update,axiom,
% 5.24/5.52 ! [I2: nat,Xs2: list_int,J: nat,X: int] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.24/5.52 => ( ( ( I2 = J )
% 5.24/5.52 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = X ) )
% 5.24/5.52 & ( ( I2 != J )
% 5.24/5.52 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.24/5.52 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nth_list_update
% 5.24/5.52 thf(fact_4107_small__lazy_H_Ocases,axiom,
% 5.24/5.52 ! [X: product_prod_int_int] :
% 5.24/5.52 ~ ! [D3: int,I3: int] :
% 5.24/5.52 ( X
% 5.24/5.52 != ( product_Pair_int_int @ D3 @ I3 ) ) ).
% 5.24/5.52
% 5.24/5.52 % small_lazy'.cases
% 5.24/5.52 thf(fact_4108_exhaustive__int_H_Ocases,axiom,
% 5.24/5.52 ! [X: produc7773217078559923341nt_int] :
% 5.24/5.52 ~ ! [F2: int > option6357759511663192854e_term,D3: int,I3: int] :
% 5.24/5.52 ( X
% 5.24/5.52 != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % exhaustive_int'.cases
% 5.24/5.52 thf(fact_4109_full__exhaustive__int_H_Ocases,axiom,
% 5.24/5.52 ! [X: produc2285326912895808259nt_int] :
% 5.24/5.52 ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I3: int] :
% 5.24/5.52 ( X
% 5.24/5.52 != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % full_exhaustive_int'.cases
% 5.24/5.52 thf(fact_4110_Euclid__induct,axiom,
% 5.24/5.52 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.24/5.52 ( ! [A3: nat,B2: nat] :
% 5.24/5.52 ( ( P @ A3 @ B2 )
% 5.24/5.52 = ( P @ B2 @ A3 ) )
% 5.24/5.52 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.24/5.52 => ( ! [A3: nat,B2: nat] :
% 5.24/5.52 ( ( P @ A3 @ B2 )
% 5.24/5.52 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 5.24/5.52 => ( P @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % Euclid_induct
% 5.24/5.52 thf(fact_4111_vebt__insert_Osimps_I5_J,axiom,
% 5.24/5.52 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.24/5.52 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.24/5.52 = ( if_VEBT_VEBT
% 5.24/5.52 @ ( ( 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 ) )
% 5.24/5.52 & ~ ( ( X = Mi )
% 5.24/5.52 | ( X = Ma ) ) )
% 5.24/5.52 @ ( 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 ) )
% 5.24/5.52 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % vebt_insert.simps(5)
% 5.24/5.52 thf(fact_4112_vebt__insert_Oelims,axiom,
% 5.24/5.52 ! [X: vEBT_VEBT,Xa2: nat,Y4: vEBT_VEBT] :
% 5.24/5.52 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.24/5.52 = Y4 )
% 5.24/5.52 => ( ! [A3: $o,B2: $o] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.52 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.24/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.24/5.52 & ( ( Xa2 != one_one_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) ) )
% 5.24/5.52 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) ) )
% 5.24/5.52 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) )
% 5.24/5.52 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.24/5.52 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 != ( if_VEBT_VEBT
% 5.24/5.52 @ ( ( 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 ) )
% 5.24/5.52 & ~ ( ( Xa2 = Mi2 )
% 5.24/5.52 | ( Xa2 = Ma2 ) ) )
% 5.24/5.52 @ ( 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 ) )
% 5.24/5.52 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % vebt_insert.elims
% 5.24/5.52 thf(fact_4113_vebt__insert_Opelims,axiom,
% 5.24/5.52 ! [X: vEBT_VEBT,Xa2: nat,Y4: vEBT_VEBT] :
% 5.24/5.52 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.24/5.52 = Y4 )
% 5.24/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.52 => ( ! [A3: $o,B2: $o] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.52 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.24/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.24/5.52 & ( ( Xa2 != one_one_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) )
% 5.24/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.24/5.52 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 5.24/5.52 => ( ( Y4
% 5.24/5.52 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 5.24/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 5.24/5.52 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 5.24/5.52 => ( ( Y4
% 5.24/5.52 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 5.24/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 5.24/5.52 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.52 => ( ( Y4
% 5.24/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.24/5.52 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.24/5.52 => ( ( Y4
% 5.24/5.52 = ( if_VEBT_VEBT
% 5.24/5.52 @ ( ( 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 ) )
% 5.24/5.52 & ~ ( ( Xa2 = Mi2 )
% 5.24/5.52 | ( Xa2 = Ma2 ) ) )
% 5.24/5.52 @ ( 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 ) )
% 5.24/5.52 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.24/5.52 => ~ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % vebt_insert.pelims
% 5.24/5.52 thf(fact_4114_max__less__iff__conj,axiom,
% 5.24/5.52 ! [X: extended_enat,Y4: extended_enat,Z2: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y4 ) @ Z2 )
% 5.24/5.52 = ( ( ord_le72135733267957522d_enat @ X @ Z2 )
% 5.24/5.52 & ( ord_le72135733267957522d_enat @ Y4 @ Z2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max_less_iff_conj
% 5.24/5.52 thf(fact_4115_max__less__iff__conj,axiom,
% 5.24/5.52 ! [X: real,Y4: real,Z2: real] :
% 5.24/5.52 ( ( ord_less_real @ ( ord_max_real @ X @ Y4 ) @ Z2 )
% 5.24/5.52 = ( ( ord_less_real @ X @ Z2 )
% 5.24/5.52 & ( ord_less_real @ Y4 @ Z2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max_less_iff_conj
% 5.24/5.52 thf(fact_4116_max__less__iff__conj,axiom,
% 5.24/5.52 ! [X: rat,Y4: rat,Z2: rat] :
% 5.24/5.52 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y4 ) @ Z2 )
% 5.24/5.52 = ( ( ord_less_rat @ X @ Z2 )
% 5.24/5.52 & ( ord_less_rat @ Y4 @ Z2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max_less_iff_conj
% 5.24/5.52 thf(fact_4117_max__less__iff__conj,axiom,
% 5.24/5.52 ! [X: num,Y4: num,Z2: num] :
% 5.24/5.52 ( ( ord_less_num @ ( ord_max_num @ X @ Y4 ) @ Z2 )
% 5.24/5.52 = ( ( ord_less_num @ X @ Z2 )
% 5.24/5.52 & ( ord_less_num @ Y4 @ Z2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max_less_iff_conj
% 5.24/5.52 thf(fact_4118_max__less__iff__conj,axiom,
% 5.24/5.52 ! [X: nat,Y4: nat,Z2: nat] :
% 5.24/5.52 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y4 ) @ Z2 )
% 5.24/5.52 = ( ( ord_less_nat @ X @ Z2 )
% 5.24/5.52 & ( ord_less_nat @ Y4 @ Z2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max_less_iff_conj
% 5.24/5.52 thf(fact_4119_max__less__iff__conj,axiom,
% 5.24/5.52 ! [X: int,Y4: int,Z2: int] :
% 5.24/5.52 ( ( ord_less_int @ ( ord_max_int @ X @ Y4 ) @ Z2 )
% 5.24/5.52 = ( ( ord_less_int @ X @ Z2 )
% 5.24/5.52 & ( ord_less_int @ Y4 @ Z2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max_less_iff_conj
% 5.24/5.52 thf(fact_4120_max_Oabsorb4,axiom,
% 5.24/5.52 ! [A: extended_enat,B: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.24/5.52 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb4
% 5.24/5.52 thf(fact_4121_max_Oabsorb4,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( ord_less_real @ A @ B )
% 5.24/5.52 => ( ( ord_max_real @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb4
% 5.24/5.52 thf(fact_4122_max_Oabsorb4,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( ord_less_rat @ A @ B )
% 5.24/5.52 => ( ( ord_max_rat @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb4
% 5.24/5.52 thf(fact_4123_max_Oabsorb4,axiom,
% 5.24/5.52 ! [A: num,B: num] :
% 5.24/5.52 ( ( ord_less_num @ A @ B )
% 5.24/5.52 => ( ( ord_max_num @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb4
% 5.24/5.52 thf(fact_4124_max_Oabsorb4,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( ord_less_nat @ A @ B )
% 5.24/5.52 => ( ( ord_max_nat @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb4
% 5.24/5.52 thf(fact_4125_max_Oabsorb4,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( ord_less_int @ A @ B )
% 5.24/5.52 => ( ( ord_max_int @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb4
% 5.24/5.52 thf(fact_4126_max_Oabsorb3,axiom,
% 5.24/5.52 ! [B: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.24/5.52 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb3
% 5.24/5.52 thf(fact_4127_max_Oabsorb3,axiom,
% 5.24/5.52 ! [B: real,A: real] :
% 5.24/5.52 ( ( ord_less_real @ B @ A )
% 5.24/5.52 => ( ( ord_max_real @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb3
% 5.24/5.52 thf(fact_4128_max_Oabsorb3,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ B @ A )
% 5.24/5.52 => ( ( ord_max_rat @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb3
% 5.24/5.52 thf(fact_4129_max_Oabsorb3,axiom,
% 5.24/5.52 ! [B: num,A: num] :
% 5.24/5.52 ( ( ord_less_num @ B @ A )
% 5.24/5.52 => ( ( ord_max_num @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb3
% 5.24/5.52 thf(fact_4130_max_Oabsorb3,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_nat @ B @ A )
% 5.24/5.52 => ( ( ord_max_nat @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb3
% 5.24/5.52 thf(fact_4131_max_Oabsorb3,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( ord_less_int @ B @ A )
% 5.24/5.52 => ( ( ord_max_int @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb3
% 5.24/5.52 thf(fact_4132_max_Oabsorb1,axiom,
% 5.24/5.52 ! [B: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.24/5.52 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb1
% 5.24/5.52 thf(fact_4133_max_Oabsorb1,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ B @ A )
% 5.24/5.52 => ( ( ord_max_rat @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb1
% 5.24/5.52 thf(fact_4134_max_Oabsorb1,axiom,
% 5.24/5.52 ! [B: num,A: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ B @ A )
% 5.24/5.52 => ( ( ord_max_num @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb1
% 5.24/5.52 thf(fact_4135_max_Oabsorb1,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ B @ A )
% 5.24/5.52 => ( ( ord_max_nat @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb1
% 5.24/5.52 thf(fact_4136_max_Oabsorb1,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ B @ A )
% 5.24/5.52 => ( ( ord_max_int @ A @ B )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb1
% 5.24/5.52 thf(fact_4137_max_Oabsorb2,axiom,
% 5.24/5.52 ! [A: extended_enat,B: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.24/5.52 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb2
% 5.24/5.52 thf(fact_4138_max_Oabsorb2,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.52 => ( ( ord_max_rat @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb2
% 5.24/5.52 thf(fact_4139_max_Oabsorb2,axiom,
% 5.24/5.52 ! [A: num,B: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ A @ B )
% 5.24/5.52 => ( ( ord_max_num @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb2
% 5.24/5.52 thf(fact_4140_max_Oabsorb2,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.24/5.52 => ( ( ord_max_nat @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb2
% 5.24/5.52 thf(fact_4141_max_Oabsorb2,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ A @ B )
% 5.24/5.52 => ( ( ord_max_int @ A @ B )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb2
% 5.24/5.52 thf(fact_4142_max_Obounded__iff,axiom,
% 5.24/5.52 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.24/5.52 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.24/5.52 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.bounded_iff
% 5.24/5.52 thf(fact_4143_max_Obounded__iff,axiom,
% 5.24/5.52 ! [B: rat,C: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.24/5.52 = ( ( ord_less_eq_rat @ B @ A )
% 5.24/5.52 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.bounded_iff
% 5.24/5.52 thf(fact_4144_max_Obounded__iff,axiom,
% 5.24/5.52 ! [B: num,C: num,A: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.24/5.52 = ( ( ord_less_eq_num @ B @ A )
% 5.24/5.52 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.bounded_iff
% 5.24/5.52 thf(fact_4145_max_Obounded__iff,axiom,
% 5.24/5.52 ! [B: nat,C: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.24/5.52 = ( ( ord_less_eq_nat @ B @ A )
% 5.24/5.52 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.bounded_iff
% 5.24/5.52 thf(fact_4146_max_Obounded__iff,axiom,
% 5.24/5.52 ! [B: int,C: int,A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.24/5.52 = ( ( ord_less_eq_int @ B @ A )
% 5.24/5.52 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.bounded_iff
% 5.24/5.52 thf(fact_4147_max__enat__simps_I2_J,axiom,
% 5.24/5.52 ! [Q2: extended_enat] :
% 5.24/5.52 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.24/5.52 = Q2 ) ).
% 5.24/5.52
% 5.24/5.52 % max_enat_simps(2)
% 5.24/5.52 thf(fact_4148_max__enat__simps_I3_J,axiom,
% 5.24/5.52 ! [Q2: extended_enat] :
% 5.24/5.52 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.24/5.52 = Q2 ) ).
% 5.24/5.52
% 5.24/5.52 % max_enat_simps(3)
% 5.24/5.52 thf(fact_4149_prod__decode__aux_Ocases,axiom,
% 5.24/5.52 ! [X: product_prod_nat_nat] :
% 5.24/5.52 ~ ! [K2: nat,M4: nat] :
% 5.24/5.52 ( X
% 5.24/5.52 != ( product_Pair_nat_nat @ K2 @ M4 ) ) ).
% 5.24/5.52
% 5.24/5.52 % prod_decode_aux.cases
% 5.24/5.52 thf(fact_4150_list__decode_Ocases,axiom,
% 5.24/5.52 ! [X: nat] :
% 5.24/5.52 ( ( X != zero_zero_nat )
% 5.24/5.52 => ~ ! [N3: nat] :
% 5.24/5.52 ( X
% 5.24/5.52 != ( suc @ N3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % list_decode.cases
% 5.24/5.52 thf(fact_4151_max_Omono,axiom,
% 5.24/5.52 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.24/5.52 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.24/5.52 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.mono
% 5.24/5.52 thf(fact_4152_max_Omono,axiom,
% 5.24/5.52 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ C @ A )
% 5.24/5.52 => ( ( ord_less_eq_rat @ D @ B )
% 5.24/5.52 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.mono
% 5.24/5.52 thf(fact_4153_max_Omono,axiom,
% 5.24/5.52 ! [C: num,A: num,D: num,B: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ C @ A )
% 5.24/5.52 => ( ( ord_less_eq_num @ D @ B )
% 5.24/5.52 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.mono
% 5.24/5.52 thf(fact_4154_max_Omono,axiom,
% 5.24/5.52 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ C @ A )
% 5.24/5.52 => ( ( ord_less_eq_nat @ D @ B )
% 5.24/5.52 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.mono
% 5.24/5.52 thf(fact_4155_max_Omono,axiom,
% 5.24/5.52 ! [C: int,A: int,D: int,B: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ C @ A )
% 5.24/5.52 => ( ( ord_less_eq_int @ D @ B )
% 5.24/5.52 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.mono
% 5.24/5.52 thf(fact_4156_max_OorderE,axiom,
% 5.24/5.52 ! [B: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.24/5.52 => ( A
% 5.24/5.52 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderE
% 5.24/5.52 thf(fact_4157_max_OorderE,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ B @ A )
% 5.24/5.52 => ( A
% 5.24/5.52 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderE
% 5.24/5.52 thf(fact_4158_max_OorderE,axiom,
% 5.24/5.52 ! [B: num,A: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ B @ A )
% 5.24/5.52 => ( A
% 5.24/5.52 = ( ord_max_num @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderE
% 5.24/5.52 thf(fact_4159_max_OorderE,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ B @ A )
% 5.24/5.52 => ( A
% 5.24/5.52 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderE
% 5.24/5.52 thf(fact_4160_max_OorderE,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ B @ A )
% 5.24/5.52 => ( A
% 5.24/5.52 = ( ord_max_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderE
% 5.24/5.52 thf(fact_4161_max_OorderI,axiom,
% 5.24/5.52 ! [A: extended_enat,B: extended_enat] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.24/5.52 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderI
% 5.24/5.52 thf(fact_4162_max_OorderI,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( ord_max_rat @ A @ B ) )
% 5.24/5.52 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderI
% 5.24/5.52 thf(fact_4163_max_OorderI,axiom,
% 5.24/5.52 ! [A: num,B: num] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( ord_max_num @ A @ B ) )
% 5.24/5.52 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderI
% 5.24/5.52 thf(fact_4164_max_OorderI,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( ord_max_nat @ A @ B ) )
% 5.24/5.52 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderI
% 5.24/5.52 thf(fact_4165_max_OorderI,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( ord_max_int @ A @ B ) )
% 5.24/5.52 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.orderI
% 5.24/5.52 thf(fact_4166_max_OboundedE,axiom,
% 5.24/5.52 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.24/5.52 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedE
% 5.24/5.52 thf(fact_4167_max_OboundedE,axiom,
% 5.24/5.52 ! [B: rat,C: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.24/5.52 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedE
% 5.24/5.52 thf(fact_4168_max_OboundedE,axiom,
% 5.24/5.52 ! [B: num,C: num,A: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.24/5.52 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedE
% 5.24/5.52 thf(fact_4169_max_OboundedE,axiom,
% 5.24/5.52 ! [B: nat,C: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.24/5.52 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedE
% 5.24/5.52 thf(fact_4170_max_OboundedE,axiom,
% 5.24/5.52 ! [B: int,C: int,A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.24/5.52 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedE
% 5.24/5.52 thf(fact_4171_max_OboundedI,axiom,
% 5.24/5.52 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.24/5.52 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.24/5.52 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedI
% 5.24/5.52 thf(fact_4172_max_OboundedI,axiom,
% 5.24/5.52 ! [B: rat,A: rat,C: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ B @ A )
% 5.24/5.52 => ( ( ord_less_eq_rat @ C @ A )
% 5.24/5.52 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedI
% 5.24/5.52 thf(fact_4173_max_OboundedI,axiom,
% 5.24/5.52 ! [B: num,A: num,C: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ B @ A )
% 5.24/5.52 => ( ( ord_less_eq_num @ C @ A )
% 5.24/5.52 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedI
% 5.24/5.52 thf(fact_4174_max_OboundedI,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ B @ A )
% 5.24/5.52 => ( ( ord_less_eq_nat @ C @ A )
% 5.24/5.52 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedI
% 5.24/5.52 thf(fact_4175_max_OboundedI,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ B @ A )
% 5.24/5.52 => ( ( ord_less_eq_int @ C @ A )
% 5.24/5.52 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.boundedI
% 5.24/5.52 thf(fact_4176_max_Oorder__iff,axiom,
% 5.24/5.52 ( ord_le2932123472753598470d_enat
% 5.24/5.52 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.order_iff
% 5.24/5.52 thf(fact_4177_max_Oorder__iff,axiom,
% 5.24/5.52 ( ord_less_eq_rat
% 5.24/5.52 = ( ^ [B3: rat,A4: rat] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( ord_max_rat @ A4 @ B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.order_iff
% 5.24/5.52 thf(fact_4178_max_Oorder__iff,axiom,
% 5.24/5.52 ( ord_less_eq_num
% 5.24/5.52 = ( ^ [B3: num,A4: num] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( ord_max_num @ A4 @ B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.order_iff
% 5.24/5.52 thf(fact_4179_max_Oorder__iff,axiom,
% 5.24/5.52 ( ord_less_eq_nat
% 5.24/5.52 = ( ^ [B3: nat,A4: nat] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( ord_max_nat @ A4 @ B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.order_iff
% 5.24/5.52 thf(fact_4180_max_Oorder__iff,axiom,
% 5.24/5.52 ( ord_less_eq_int
% 5.24/5.52 = ( ^ [B3: int,A4: int] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( ord_max_int @ A4 @ B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.order_iff
% 5.24/5.52 thf(fact_4181_max_Ocobounded1,axiom,
% 5.24/5.52 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded1
% 5.24/5.52 thf(fact_4182_max_Ocobounded1,axiom,
% 5.24/5.52 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded1
% 5.24/5.52 thf(fact_4183_max_Ocobounded1,axiom,
% 5.24/5.52 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded1
% 5.24/5.52 thf(fact_4184_max_Ocobounded1,axiom,
% 5.24/5.52 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded1
% 5.24/5.52 thf(fact_4185_max_Ocobounded1,axiom,
% 5.24/5.52 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded1
% 5.24/5.52 thf(fact_4186_max_Ocobounded2,axiom,
% 5.24/5.52 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded2
% 5.24/5.52 thf(fact_4187_max_Ocobounded2,axiom,
% 5.24/5.52 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded2
% 5.24/5.52 thf(fact_4188_max_Ocobounded2,axiom,
% 5.24/5.52 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded2
% 5.24/5.52 thf(fact_4189_max_Ocobounded2,axiom,
% 5.24/5.52 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded2
% 5.24/5.52 thf(fact_4190_max_Ocobounded2,axiom,
% 5.24/5.52 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.cobounded2
% 5.24/5.52 thf(fact_4191_le__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: extended_enat,X: extended_enat,Y4: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ Z2 @ ( ord_ma741700101516333627d_enat @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_le2932123472753598470d_enat @ Z2 @ X )
% 5.24/5.52 | ( ord_le2932123472753598470d_enat @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_max_iff_disj
% 5.24/5.52 thf(fact_4192_le__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ Z2 @ ( ord_max_rat @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_eq_rat @ Z2 @ X )
% 5.24/5.52 | ( ord_less_eq_rat @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_max_iff_disj
% 5.24/5.52 thf(fact_4193_le__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: num,X: num,Y4: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ Z2 @ ( ord_max_num @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_eq_num @ Z2 @ X )
% 5.24/5.52 | ( ord_less_eq_num @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_max_iff_disj
% 5.24/5.52 thf(fact_4194_le__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: nat,X: nat,Y4: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ Z2 @ ( ord_max_nat @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_eq_nat @ Z2 @ X )
% 5.24/5.52 | ( ord_less_eq_nat @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_max_iff_disj
% 5.24/5.52 thf(fact_4195_le__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: int,X: int,Y4: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ Z2 @ ( ord_max_int @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_eq_int @ Z2 @ X )
% 5.24/5.52 | ( ord_less_eq_int @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_max_iff_disj
% 5.24/5.52 thf(fact_4196_max_Oabsorb__iff1,axiom,
% 5.24/5.52 ( ord_le2932123472753598470d_enat
% 5.24/5.52 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.24/5.52 ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 5.24/5.52 = A4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff1
% 5.24/5.52 thf(fact_4197_max_Oabsorb__iff1,axiom,
% 5.24/5.52 ( ord_less_eq_rat
% 5.24/5.52 = ( ^ [B3: rat,A4: rat] :
% 5.24/5.52 ( ( ord_max_rat @ A4 @ B3 )
% 5.24/5.52 = A4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff1
% 5.24/5.52 thf(fact_4198_max_Oabsorb__iff1,axiom,
% 5.24/5.52 ( ord_less_eq_num
% 5.24/5.52 = ( ^ [B3: num,A4: num] :
% 5.24/5.52 ( ( ord_max_num @ A4 @ B3 )
% 5.24/5.52 = A4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff1
% 5.24/5.52 thf(fact_4199_max_Oabsorb__iff1,axiom,
% 5.24/5.52 ( ord_less_eq_nat
% 5.24/5.52 = ( ^ [B3: nat,A4: nat] :
% 5.24/5.52 ( ( ord_max_nat @ A4 @ B3 )
% 5.24/5.52 = A4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff1
% 5.24/5.52 thf(fact_4200_max_Oabsorb__iff1,axiom,
% 5.24/5.52 ( ord_less_eq_int
% 5.24/5.52 = ( ^ [B3: int,A4: int] :
% 5.24/5.52 ( ( ord_max_int @ A4 @ B3 )
% 5.24/5.52 = A4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff1
% 5.24/5.52 thf(fact_4201_max_Oabsorb__iff2,axiom,
% 5.24/5.52 ( ord_le2932123472753598470d_enat
% 5.24/5.52 = ( ^ [A4: extended_enat,B3: extended_enat] :
% 5.24/5.52 ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 5.24/5.52 = B3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff2
% 5.24/5.52 thf(fact_4202_max_Oabsorb__iff2,axiom,
% 5.24/5.52 ( ord_less_eq_rat
% 5.24/5.52 = ( ^ [A4: rat,B3: rat] :
% 5.24/5.52 ( ( ord_max_rat @ A4 @ B3 )
% 5.24/5.52 = B3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff2
% 5.24/5.52 thf(fact_4203_max_Oabsorb__iff2,axiom,
% 5.24/5.52 ( ord_less_eq_num
% 5.24/5.52 = ( ^ [A4: num,B3: num] :
% 5.24/5.52 ( ( ord_max_num @ A4 @ B3 )
% 5.24/5.52 = B3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff2
% 5.24/5.52 thf(fact_4204_max_Oabsorb__iff2,axiom,
% 5.24/5.52 ( ord_less_eq_nat
% 5.24/5.52 = ( ^ [A4: nat,B3: nat] :
% 5.24/5.52 ( ( ord_max_nat @ A4 @ B3 )
% 5.24/5.52 = B3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff2
% 5.24/5.52 thf(fact_4205_max_Oabsorb__iff2,axiom,
% 5.24/5.52 ( ord_less_eq_int
% 5.24/5.52 = ( ^ [A4: int,B3: int] :
% 5.24/5.52 ( ( ord_max_int @ A4 @ B3 )
% 5.24/5.52 = B3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.absorb_iff2
% 5.24/5.52 thf(fact_4206_max_OcoboundedI1,axiom,
% 5.24/5.52 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.24/5.52 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI1
% 5.24/5.52 thf(fact_4207_max_OcoboundedI1,axiom,
% 5.24/5.52 ! [C: rat,A: rat,B: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ C @ A )
% 5.24/5.52 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI1
% 5.24/5.52 thf(fact_4208_max_OcoboundedI1,axiom,
% 5.24/5.52 ! [C: num,A: num,B: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ C @ A )
% 5.24/5.52 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI1
% 5.24/5.52 thf(fact_4209_max_OcoboundedI1,axiom,
% 5.24/5.52 ! [C: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ C @ A )
% 5.24/5.52 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI1
% 5.24/5.52 thf(fact_4210_max_OcoboundedI1,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ C @ A )
% 5.24/5.52 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI1
% 5.24/5.52 thf(fact_4211_max_OcoboundedI2,axiom,
% 5.24/5.52 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.24/5.52 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI2
% 5.24/5.52 thf(fact_4212_max_OcoboundedI2,axiom,
% 5.24/5.52 ! [C: rat,B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ C @ B )
% 5.24/5.52 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI2
% 5.24/5.52 thf(fact_4213_max_OcoboundedI2,axiom,
% 5.24/5.52 ! [C: num,B: num,A: num] :
% 5.24/5.52 ( ( ord_less_eq_num @ C @ B )
% 5.24/5.52 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI2
% 5.24/5.52 thf(fact_4214_max_OcoboundedI2,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ C @ B )
% 5.24/5.52 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI2
% 5.24/5.52 thf(fact_4215_max_OcoboundedI2,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ C @ B )
% 5.24/5.52 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.coboundedI2
% 5.24/5.52 thf(fact_4216_less__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: extended_enat,X: extended_enat,Y4: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ Z2 @ ( ord_ma741700101516333627d_enat @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_le72135733267957522d_enat @ Z2 @ X )
% 5.24/5.52 | ( ord_le72135733267957522d_enat @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_max_iff_disj
% 5.24/5.52 thf(fact_4217_less__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: real,X: real,Y4: real] :
% 5.24/5.52 ( ( ord_less_real @ Z2 @ ( ord_max_real @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_real @ Z2 @ X )
% 5.24/5.52 | ( ord_less_real @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_max_iff_disj
% 5.24/5.52 thf(fact_4218_less__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.52 ( ( ord_less_rat @ Z2 @ ( ord_max_rat @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_rat @ Z2 @ X )
% 5.24/5.52 | ( ord_less_rat @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_max_iff_disj
% 5.24/5.52 thf(fact_4219_less__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: num,X: num,Y4: num] :
% 5.24/5.52 ( ( ord_less_num @ Z2 @ ( ord_max_num @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_num @ Z2 @ X )
% 5.24/5.52 | ( ord_less_num @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_max_iff_disj
% 5.24/5.52 thf(fact_4220_less__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: nat,X: nat,Y4: nat] :
% 5.24/5.52 ( ( ord_less_nat @ Z2 @ ( ord_max_nat @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_nat @ Z2 @ X )
% 5.24/5.52 | ( ord_less_nat @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_max_iff_disj
% 5.24/5.52 thf(fact_4221_less__max__iff__disj,axiom,
% 5.24/5.52 ! [Z2: int,X: int,Y4: int] :
% 5.24/5.52 ( ( ord_less_int @ Z2 @ ( ord_max_int @ X @ Y4 ) )
% 5.24/5.52 = ( ( ord_less_int @ Z2 @ X )
% 5.24/5.52 | ( ord_less_int @ Z2 @ Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_max_iff_disj
% 5.24/5.52 thf(fact_4222_max_Ostrict__boundedE,axiom,
% 5.24/5.52 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.24/5.52 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_boundedE
% 5.24/5.52 thf(fact_4223_max_Ostrict__boundedE,axiom,
% 5.24/5.52 ! [B: real,C: real,A: real] :
% 5.24/5.52 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_real @ B @ A )
% 5.24/5.52 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_boundedE
% 5.24/5.52 thf(fact_4224_max_Ostrict__boundedE,axiom,
% 5.24/5.52 ! [B: rat,C: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_rat @ B @ A )
% 5.24/5.52 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_boundedE
% 5.24/5.52 thf(fact_4225_max_Ostrict__boundedE,axiom,
% 5.24/5.52 ! [B: num,C: num,A: num] :
% 5.24/5.52 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_num @ B @ A )
% 5.24/5.52 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_boundedE
% 5.24/5.52 thf(fact_4226_max_Ostrict__boundedE,axiom,
% 5.24/5.52 ! [B: nat,C: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_nat @ B @ A )
% 5.24/5.52 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_boundedE
% 5.24/5.52 thf(fact_4227_max_Ostrict__boundedE,axiom,
% 5.24/5.52 ! [B: int,C: int,A: int] :
% 5.24/5.52 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.24/5.52 => ~ ( ( ord_less_int @ B @ A )
% 5.24/5.52 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_boundedE
% 5.24/5.52 thf(fact_4228_max_Ostrict__order__iff,axiom,
% 5.24/5.52 ( ord_le72135733267957522d_enat
% 5.24/5.52 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.24/5.52 ( ( A4
% 5.24/5.52 = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) )
% 5.24/5.52 & ( A4 != B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_order_iff
% 5.24/5.52 thf(fact_4229_max_Ostrict__order__iff,axiom,
% 5.24/5.52 ( ord_less_real
% 5.24/5.52 = ( ^ [B3: real,A4: real] :
% 5.24/5.52 ( ( A4
% 5.24/5.52 = ( ord_max_real @ A4 @ B3 ) )
% 5.24/5.52 & ( A4 != B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_order_iff
% 5.24/5.52 thf(fact_4230_max_Ostrict__order__iff,axiom,
% 5.24/5.52 ( ord_less_rat
% 5.24/5.52 = ( ^ [B3: rat,A4: rat] :
% 5.24/5.52 ( ( A4
% 5.24/5.52 = ( ord_max_rat @ A4 @ B3 ) )
% 5.24/5.52 & ( A4 != B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_order_iff
% 5.24/5.52 thf(fact_4231_max_Ostrict__order__iff,axiom,
% 5.24/5.52 ( ord_less_num
% 5.24/5.52 = ( ^ [B3: num,A4: num] :
% 5.24/5.52 ( ( A4
% 5.24/5.52 = ( ord_max_num @ A4 @ B3 ) )
% 5.24/5.52 & ( A4 != B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_order_iff
% 5.24/5.52 thf(fact_4232_max_Ostrict__order__iff,axiom,
% 5.24/5.52 ( ord_less_nat
% 5.24/5.52 = ( ^ [B3: nat,A4: nat] :
% 5.24/5.52 ( ( A4
% 5.24/5.52 = ( ord_max_nat @ A4 @ B3 ) )
% 5.24/5.52 & ( A4 != B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_order_iff
% 5.24/5.52 thf(fact_4233_max_Ostrict__order__iff,axiom,
% 5.24/5.52 ( ord_less_int
% 5.24/5.52 = ( ^ [B3: int,A4: int] :
% 5.24/5.52 ( ( A4
% 5.24/5.52 = ( ord_max_int @ A4 @ B3 ) )
% 5.24/5.52 & ( A4 != B3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_order_iff
% 5.24/5.52 thf(fact_4234_max_Ostrict__coboundedI1,axiom,
% 5.24/5.52 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.24/5.52 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI1
% 5.24/5.52 thf(fact_4235_max_Ostrict__coboundedI1,axiom,
% 5.24/5.52 ! [C: real,A: real,B: real] :
% 5.24/5.52 ( ( ord_less_real @ C @ A )
% 5.24/5.52 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI1
% 5.24/5.52 thf(fact_4236_max_Ostrict__coboundedI1,axiom,
% 5.24/5.52 ! [C: rat,A: rat,B: rat] :
% 5.24/5.52 ( ( ord_less_rat @ C @ A )
% 5.24/5.52 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI1
% 5.24/5.52 thf(fact_4237_max_Ostrict__coboundedI1,axiom,
% 5.24/5.52 ! [C: num,A: num,B: num] :
% 5.24/5.52 ( ( ord_less_num @ C @ A )
% 5.24/5.52 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI1
% 5.24/5.52 thf(fact_4238_max_Ostrict__coboundedI1,axiom,
% 5.24/5.52 ! [C: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( ord_less_nat @ C @ A )
% 5.24/5.52 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI1
% 5.24/5.52 thf(fact_4239_max_Ostrict__coboundedI1,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( ord_less_int @ C @ A )
% 5.24/5.52 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI1
% 5.24/5.52 thf(fact_4240_max_Ostrict__coboundedI2,axiom,
% 5.24/5.52 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.24/5.52 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.24/5.52 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI2
% 5.24/5.52 thf(fact_4241_max_Ostrict__coboundedI2,axiom,
% 5.24/5.52 ! [C: real,B: real,A: real] :
% 5.24/5.52 ( ( ord_less_real @ C @ B )
% 5.24/5.52 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI2
% 5.24/5.52 thf(fact_4242_max_Ostrict__coboundedI2,axiom,
% 5.24/5.52 ! [C: rat,B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ C @ B )
% 5.24/5.52 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI2
% 5.24/5.52 thf(fact_4243_max_Ostrict__coboundedI2,axiom,
% 5.24/5.52 ! [C: num,B: num,A: num] :
% 5.24/5.52 ( ( ord_less_num @ C @ B )
% 5.24/5.52 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI2
% 5.24/5.52 thf(fact_4244_max_Ostrict__coboundedI2,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_nat @ C @ B )
% 5.24/5.52 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI2
% 5.24/5.52 thf(fact_4245_max_Ostrict__coboundedI2,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( ord_less_int @ C @ B )
% 5.24/5.52 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % max.strict_coboundedI2
% 5.24/5.52 thf(fact_4246_triangle__def,axiom,
% 5.24/5.52 ( nat_triangle
% 5.24/5.52 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % triangle_def
% 5.24/5.52 thf(fact_4247_even__succ__mod__exp,axiom,
% 5.24/5.52 ! [A: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.52 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_mod_exp
% 5.24/5.52 thf(fact_4248_even__succ__mod__exp,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.52 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_mod_exp
% 5.24/5.52 thf(fact_4249_even__succ__mod__exp,axiom,
% 5.24/5.52 ! [A: code_integer,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_mod_exp
% 5.24/5.52 thf(fact_4250_option_Osize__gen_I2_J,axiom,
% 5.24/5.52 ! [X: nat > nat,X22: nat] :
% 5.24/5.52 ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 5.24/5.52 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % option.size_gen(2)
% 5.24/5.52 thf(fact_4251_option_Osize__gen_I2_J,axiom,
% 5.24/5.52 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.24/5.52 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.24/5.52 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % option.size_gen(2)
% 5.24/5.52 thf(fact_4252_option_Osize__gen_I2_J,axiom,
% 5.24/5.52 ! [X: num > nat,X22: num] :
% 5.24/5.52 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 5.24/5.52 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % option.size_gen(2)
% 5.24/5.52 thf(fact_4253_even__succ__div__exp,axiom,
% 5.24/5.52 ! [A: code_integer,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_exp
% 5.24/5.52 thf(fact_4254_even__succ__div__exp,axiom,
% 5.24/5.52 ! [A: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.52 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_exp
% 5.24/5.52 thf(fact_4255_even__succ__div__exp,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.52 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_exp
% 5.24/5.52 thf(fact_4256_signed__take__bit__Suc,axiom,
% 5.24/5.52 ! [N: nat,A: code_integer] :
% 5.24/5.52 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_Suc
% 5.24/5.52 thf(fact_4257_signed__take__bit__Suc,axiom,
% 5.24/5.52 ! [N: nat,A: int] :
% 5.24/5.52 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.24/5.52 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_Suc
% 5.24/5.52 thf(fact_4258_set__decode__Suc,axiom,
% 5.24/5.52 ! [N: nat,X: nat] :
% 5.24/5.52 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 5.24/5.52 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_decode_Suc
% 5.24/5.52 thf(fact_4259_infinite__growing,axiom,
% 5.24/5.52 ! [X7: set_real] :
% 5.24/5.52 ( ( X7 != bot_bot_set_real )
% 5.24/5.52 => ( ! [X3: real] :
% 5.24/5.52 ( ( member_real @ X3 @ X7 )
% 5.24/5.52 => ? [Xa: real] :
% 5.24/5.52 ( ( member_real @ Xa @ X7 )
% 5.24/5.52 & ( ord_less_real @ X3 @ Xa ) ) )
% 5.24/5.52 => ~ ( finite_finite_real @ X7 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % infinite_growing
% 5.24/5.52 thf(fact_4260_infinite__growing,axiom,
% 5.24/5.52 ! [X7: set_rat] :
% 5.24/5.52 ( ( X7 != bot_bot_set_rat )
% 5.24/5.52 => ( ! [X3: rat] :
% 5.24/5.52 ( ( member_rat @ X3 @ X7 )
% 5.24/5.52 => ? [Xa: rat] :
% 5.24/5.52 ( ( member_rat @ Xa @ X7 )
% 5.24/5.52 & ( ord_less_rat @ X3 @ Xa ) ) )
% 5.24/5.52 => ~ ( finite_finite_rat @ X7 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % infinite_growing
% 5.24/5.52 thf(fact_4261_infinite__growing,axiom,
% 5.24/5.52 ! [X7: set_num] :
% 5.24/5.52 ( ( X7 != bot_bot_set_num )
% 5.24/5.52 => ( ! [X3: num] :
% 5.24/5.52 ( ( member_num @ X3 @ X7 )
% 5.24/5.52 => ? [Xa: num] :
% 5.24/5.52 ( ( member_num @ Xa @ X7 )
% 5.24/5.52 & ( ord_less_num @ X3 @ Xa ) ) )
% 5.24/5.52 => ~ ( finite_finite_num @ X7 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % infinite_growing
% 5.24/5.52 thf(fact_4262_infinite__growing,axiom,
% 5.24/5.52 ! [X7: set_nat] :
% 5.24/5.52 ( ( X7 != bot_bot_set_nat )
% 5.24/5.52 => ( ! [X3: nat] :
% 5.24/5.52 ( ( member_nat @ X3 @ X7 )
% 5.24/5.52 => ? [Xa: nat] :
% 5.24/5.52 ( ( member_nat @ Xa @ X7 )
% 5.24/5.52 & ( ord_less_nat @ X3 @ Xa ) ) )
% 5.24/5.52 => ~ ( finite_finite_nat @ X7 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % infinite_growing
% 5.24/5.52 thf(fact_4263_infinite__growing,axiom,
% 5.24/5.52 ! [X7: set_int] :
% 5.24/5.52 ( ( X7 != bot_bot_set_int )
% 5.24/5.52 => ( ! [X3: int] :
% 5.24/5.52 ( ( member_int @ X3 @ X7 )
% 5.24/5.52 => ? [Xa: int] :
% 5.24/5.52 ( ( member_int @ Xa @ X7 )
% 5.24/5.52 & ( ord_less_int @ X3 @ Xa ) ) )
% 5.24/5.52 => ~ ( finite_finite_int @ X7 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % infinite_growing
% 5.24/5.52 thf(fact_4264_nat__dvd__1__iff__1,axiom,
% 5.24/5.52 ! [M: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.24/5.52 = ( M = one_one_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % nat_dvd_1_iff_1
% 5.24/5.52 thf(fact_4265_dvd__add__triv__right__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_right_iff
% 5.24/5.52 thf(fact_4266_dvd__add__triv__right__iff,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.24/5.52 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_right_iff
% 5.24/5.52 thf(fact_4267_dvd__add__triv__right__iff,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.24/5.52 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_right_iff
% 5.24/5.52 thf(fact_4268_dvd__add__triv__right__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_right_iff
% 5.24/5.52 thf(fact_4269_dvd__add__triv__right__iff,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_right_iff
% 5.24/5.52 thf(fact_4270_dvd__add__triv__left__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_left_iff
% 5.24/5.52 thf(fact_4271_dvd__add__triv__left__iff,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_left_iff
% 5.24/5.52 thf(fact_4272_dvd__add__triv__left__iff,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_left_iff
% 5.24/5.52 thf(fact_4273_dvd__add__triv__left__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_left_iff
% 5.24/5.52 thf(fact_4274_dvd__add__triv__left__iff,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_triv_left_iff
% 5.24/5.52 thf(fact_4275_dvd__1__left,axiom,
% 5.24/5.52 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_1_left
% 5.24/5.52 thf(fact_4276_dvd__1__iff__1,axiom,
% 5.24/5.52 ! [M: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.24/5.52 = ( M
% 5.24/5.52 = ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_1_iff_1
% 5.24/5.52 thf(fact_4277_div__dvd__div,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_dvd_div
% 5.24/5.52 thf(fact_4278_div__dvd__div,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.24/5.52 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_dvd_div
% 5.24/5.52 thf(fact_4279_div__dvd__div,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.24/5.52 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_dvd_div
% 5.24/5.52 thf(fact_4280_nat__mult__dvd__cancel__disj,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.24/5.52 = ( ( K = zero_zero_nat )
% 5.24/5.52 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nat_mult_dvd_cancel_disj
% 5.24/5.52 thf(fact_4281_dvd__times__right__cancel__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_times_right_cancel_iff
% 5.24/5.52 thf(fact_4282_dvd__times__right__cancel__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.24/5.52 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_times_right_cancel_iff
% 5.24/5.52 thf(fact_4283_dvd__times__right__cancel__iff,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( A != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.24/5.52 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_times_right_cancel_iff
% 5.24/5.52 thf(fact_4284_dvd__times__left__cancel__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_times_left_cancel_iff
% 5.24/5.52 thf(fact_4285_dvd__times__left__cancel__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.24/5.52 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_times_left_cancel_iff
% 5.24/5.52 thf(fact_4286_dvd__times__left__cancel__iff,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( A != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.24/5.52 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_times_left_cancel_iff
% 5.24/5.52 thf(fact_4287_dvd__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.52 = ( ( C = zero_z3403309356797280102nteger )
% 5.24/5.52 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_right
% 5.24/5.52 thf(fact_4288_dvd__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: complex,C: complex,B: complex] :
% 5.24/5.52 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.24/5.52 = ( ( C = zero_zero_complex )
% 5.24/5.52 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_right
% 5.24/5.52 thf(fact_4289_dvd__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: real,C: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.24/5.52 = ( ( C = zero_zero_real )
% 5.24/5.52 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_right
% 5.24/5.52 thf(fact_4290_dvd__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: rat,C: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.24/5.52 = ( ( C = zero_zero_rat )
% 5.24/5.52 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_right
% 5.24/5.52 thf(fact_4291_dvd__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.24/5.52 = ( ( C = zero_zero_int )
% 5.24/5.52 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_right
% 5.24/5.52 thf(fact_4292_dvd__mult__cancel__left,axiom,
% 5.24/5.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.24/5.52 = ( ( C = zero_z3403309356797280102nteger )
% 5.24/5.52 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_left
% 5.24/5.52 thf(fact_4293_dvd__mult__cancel__left,axiom,
% 5.24/5.52 ! [C: complex,A: complex,B: complex] :
% 5.24/5.52 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.24/5.52 = ( ( C = zero_zero_complex )
% 5.24/5.52 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_left
% 5.24/5.52 thf(fact_4294_dvd__mult__cancel__left,axiom,
% 5.24/5.52 ! [C: real,A: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.24/5.52 = ( ( C = zero_zero_real )
% 5.24/5.52 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_left
% 5.24/5.52 thf(fact_4295_dvd__mult__cancel__left,axiom,
% 5.24/5.52 ! [C: rat,A: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.24/5.52 = ( ( C = zero_zero_rat )
% 5.24/5.52 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_left
% 5.24/5.52 thf(fact_4296_dvd__mult__cancel__left,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.24/5.52 = ( ( C = zero_zero_int )
% 5.24/5.52 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel_left
% 5.24/5.52 thf(fact_4297_unit__prod,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_prod
% 5.24/5.52 thf(fact_4298_unit__prod,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_prod
% 5.24/5.52 thf(fact_4299_unit__prod,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_prod
% 5.24/5.52 thf(fact_4300_dvd__add__times__triv__left__iff,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_left_iff
% 5.24/5.52 thf(fact_4301_dvd__add__times__triv__left__iff,axiom,
% 5.24/5.52 ! [A: real,C: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.24/5.52 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_left_iff
% 5.24/5.52 thf(fact_4302_dvd__add__times__triv__left__iff,axiom,
% 5.24/5.52 ! [A: rat,C: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.24/5.52 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_left_iff
% 5.24/5.52 thf(fact_4303_dvd__add__times__triv__left__iff,axiom,
% 5.24/5.52 ! [A: nat,C: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_left_iff
% 5.24/5.52 thf(fact_4304_dvd__add__times__triv__left__iff,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_left_iff
% 5.24/5.52 thf(fact_4305_dvd__add__times__triv__right__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_right_iff
% 5.24/5.52 thf(fact_4306_dvd__add__times__triv__right__iff,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.24/5.52 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_right_iff
% 5.24/5.52 thf(fact_4307_dvd__add__times__triv__right__iff,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.24/5.52 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_right_iff
% 5.24/5.52 thf(fact_4308_dvd__add__times__triv__right__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_right_iff
% 5.24/5.52 thf(fact_4309_dvd__add__times__triv__right__iff,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_times_triv_right_iff
% 5.24/5.52 thf(fact_4310_dvd__div__mult__self,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult_self
% 5.24/5.52 thf(fact_4311_dvd__div__mult__self,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult_self
% 5.24/5.52 thf(fact_4312_dvd__div__mult__self,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult_self
% 5.24/5.52 thf(fact_4313_dvd__mult__div__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_div_cancel
% 5.24/5.52 thf(fact_4314_dvd__mult__div__cancel,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_div_cancel
% 5.24/5.52 thf(fact_4315_dvd__mult__div__cancel,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_div_cancel
% 5.24/5.52 thf(fact_4316_unit__div,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div
% 5.24/5.52 thf(fact_4317_unit__div,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div
% 5.24/5.52 thf(fact_4318_unit__div,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div
% 5.24/5.52 thf(fact_4319_unit__div__1__unit,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_1_unit
% 5.24/5.52 thf(fact_4320_unit__div__1__unit,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_1_unit
% 5.24/5.52 thf(fact_4321_unit__div__1__unit,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_1_unit
% 5.24/5.52 thf(fact_4322_unit__div__1__div__1,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_1_div_1
% 5.24/5.52 thf(fact_4323_unit__div__1__div__1,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_1_div_1
% 5.24/5.52 thf(fact_4324_unit__div__1__div__1,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_1_div_1
% 5.24/5.52 thf(fact_4325_div__add,axiom,
% 5.24/5.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_add
% 5.24/5.52 thf(fact_4326_div__add,axiom,
% 5.24/5.52 ! [C: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.24/5.52 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_add
% 5.24/5.52 thf(fact_4327_div__add,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.24/5.52 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_add
% 5.24/5.52 thf(fact_4328_div__diff,axiom,
% 5.24/5.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.24/5.52 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_diff
% 5.24/5.52 thf(fact_4329_div__diff,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.24/5.52 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_diff
% 5.24/5.52 thf(fact_4330_signed__take__bit__Suc__1,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.24/5.52 = one_one_int ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_Suc_1
% 5.24/5.52 thf(fact_4331_signed__take__bit__numeral__of__1,axiom,
% 5.24/5.52 ! [K: num] :
% 5.24/5.52 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.24/5.52 = one_one_int ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_numeral_of_1
% 5.24/5.52 thf(fact_4332_triangle__Suc,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( nat_triangle @ ( suc @ N ) )
% 5.24/5.52 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % triangle_Suc
% 5.24/5.52 thf(fact_4333_set__decode__zero,axiom,
% 5.24/5.52 ( ( nat_set_decode @ zero_zero_nat )
% 5.24/5.52 = bot_bot_set_nat ) ).
% 5.24/5.52
% 5.24/5.52 % set_decode_zero
% 5.24/5.52 thf(fact_4334_unit__mult__div__div,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_div_div
% 5.24/5.52 thf(fact_4335_unit__mult__div__div,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.24/5.52 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_div_div
% 5.24/5.52 thf(fact_4336_unit__mult__div__div,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.24/5.52 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_div_div
% 5.24/5.52 thf(fact_4337_unit__div__mult__self,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_mult_self
% 5.24/5.52 thf(fact_4338_unit__div__mult__self,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_mult_self
% 5.24/5.52 thf(fact_4339_unit__div__mult__self,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.24/5.52 = B ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_mult_self
% 5.24/5.52 thf(fact_4340_even__Suc,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_Suc
% 5.24/5.52 thf(fact_4341_even__Suc__Suc__iff,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.24/5.52 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_Suc_Suc_iff
% 5.24/5.52 thf(fact_4342_pow__divides__pow__iff,axiom,
% 5.24/5.52 ! [N: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pow_divides_pow_iff
% 5.24/5.52 thf(fact_4343_pow__divides__pow__iff,axiom,
% 5.24/5.52 ! [N: nat,A: int,B: int] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pow_divides_pow_iff
% 5.24/5.52 thf(fact_4344_even__mult__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mult_iff
% 5.24/5.52 thf(fact_4345_even__mult__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mult_iff
% 5.24/5.52 thf(fact_4346_even__mult__iff,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mult_iff
% 5.24/5.52 thf(fact_4347_odd__add,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.24/5.52 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.52 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_add
% 5.24/5.52 thf(fact_4348_odd__add,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.24/5.52 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.52 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_add
% 5.24/5.52 thf(fact_4349_odd__add,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.24/5.52 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.52 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_add
% 5.24/5.52 thf(fact_4350_even__add,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_add
% 5.24/5.52 thf(fact_4351_even__add,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_add
% 5.24/5.52 thf(fact_4352_even__add,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_add
% 5.24/5.52 thf(fact_4353_even__mod__2__iff,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mod_2_iff
% 5.24/5.52 thf(fact_4354_even__mod__2__iff,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mod_2_iff
% 5.24/5.52 thf(fact_4355_even__mod__2__iff,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mod_2_iff
% 5.24/5.52 thf(fact_4356_odd__Suc__div__two,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_Suc_div_two
% 5.24/5.52 thf(fact_4357_even__Suc__div__two,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_Suc_div_two
% 5.24/5.52 thf(fact_4358_signed__take__bit__Suc__bit0,axiom,
% 5.24/5.52 ! [N: nat,K: num] :
% 5.24/5.52 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.24/5.52 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_Suc_bit0
% 5.24/5.52 thf(fact_4359_set__decode__0,axiom,
% 5.24/5.52 ! [X: nat] :
% 5.24/5.52 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_decode_0
% 5.24/5.52 thf(fact_4360_zero__le__power__eq__numeral,axiom,
% 5.24/5.52 ! [A: real,W2: num] :
% 5.24/5.52 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_power_eq_numeral
% 5.24/5.52 thf(fact_4361_zero__le__power__eq__numeral,axiom,
% 5.24/5.52 ! [A: rat,W2: num] :
% 5.24/5.52 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_power_eq_numeral
% 5.24/5.52 thf(fact_4362_zero__le__power__eq__numeral,axiom,
% 5.24/5.52 ! [A: int,W2: num] :
% 5.24/5.52 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_power_eq_numeral
% 5.24/5.52 thf(fact_4363_power__less__zero__eq,axiom,
% 5.24/5.52 ! [A: real,N: nat] :
% 5.24/5.52 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_less_zero_eq
% 5.24/5.52 thf(fact_4364_power__less__zero__eq,axiom,
% 5.24/5.52 ! [A: rat,N: nat] :
% 5.24/5.52 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_less_zero_eq
% 5.24/5.52 thf(fact_4365_power__less__zero__eq,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_less_zero_eq
% 5.24/5.52 thf(fact_4366_power__less__zero__eq__numeral,axiom,
% 5.24/5.52 ! [A: real,W2: num] :
% 5.24/5.52 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_less_zero_eq_numeral
% 5.24/5.52 thf(fact_4367_power__less__zero__eq__numeral,axiom,
% 5.24/5.52 ! [A: rat,W2: num] :
% 5.24/5.52 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_less_zero_eq_numeral
% 5.24/5.52 thf(fact_4368_power__less__zero__eq__numeral,axiom,
% 5.24/5.52 ! [A: int,W2: num] :
% 5.24/5.52 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_less_zero_eq_numeral
% 5.24/5.52 thf(fact_4369_even__plus__one__iff,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_plus_one_iff
% 5.24/5.52 thf(fact_4370_even__plus__one__iff,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_plus_one_iff
% 5.24/5.52 thf(fact_4371_even__plus__one__iff,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_plus_one_iff
% 5.24/5.52 thf(fact_4372_even__diff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_diff
% 5.24/5.52 thf(fact_4373_even__diff,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.24/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_diff
% 5.24/5.52 thf(fact_4374_odd__Suc__minus__one,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.24/5.52 = N ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_Suc_minus_one
% 5.24/5.52 thf(fact_4375_even__diff__nat,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.52 = ( ( ord_less_nat @ M @ N )
% 5.24/5.52 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_diff_nat
% 5.24/5.52 thf(fact_4376_zero__less__power__eq__numeral,axiom,
% 5.24/5.52 ! [A: real,W2: num] :
% 5.24/5.52 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.24/5.52 = ( ( ( numeral_numeral_nat @ W2 )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( A != zero_zero_real ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_power_eq_numeral
% 5.24/5.52 thf(fact_4377_zero__less__power__eq__numeral,axiom,
% 5.24/5.52 ! [A: rat,W2: num] :
% 5.24/5.52 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.24/5.52 = ( ( ( numeral_numeral_nat @ W2 )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( A != zero_zero_rat ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_power_eq_numeral
% 5.24/5.52 thf(fact_4378_zero__less__power__eq__numeral,axiom,
% 5.24/5.52 ! [A: int,W2: num] :
% 5.24/5.52 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.24/5.52 = ( ( ( numeral_numeral_nat @ W2 )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( A != zero_zero_int ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_power_eq_numeral
% 5.24/5.52 thf(fact_4379_even__succ__div__2,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_2
% 5.24/5.52 thf(fact_4380_even__succ__div__2,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_2
% 5.24/5.52 thf(fact_4381_even__succ__div__2,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_2
% 5.24/5.52 thf(fact_4382_odd__succ__div__two,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_succ_div_two
% 5.24/5.52 thf(fact_4383_odd__succ__div__two,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_succ_div_two
% 5.24/5.52 thf(fact_4384_odd__succ__div__two,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_succ_div_two
% 5.24/5.52 thf(fact_4385_even__succ__div__two,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_two
% 5.24/5.52 thf(fact_4386_even__succ__div__two,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_two
% 5.24/5.52 thf(fact_4387_even__succ__div__two,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_succ_div_two
% 5.24/5.52 thf(fact_4388_even__power,axiom,
% 5.24/5.52 ! [A: code_integer,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_power
% 5.24/5.52 thf(fact_4389_even__power,axiom,
% 5.24/5.52 ! [A: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_power
% 5.24/5.52 thf(fact_4390_even__power,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_power
% 5.24/5.52 thf(fact_4391_odd__two__times__div__two__nat,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_two_times_div_two_nat
% 5.24/5.52 thf(fact_4392_odd__two__times__div__two__succ,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_two_times_div_two_succ
% 5.24/5.52 thf(fact_4393_odd__two__times__div__two__succ,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_two_times_div_two_succ
% 5.24/5.52 thf(fact_4394_odd__two__times__div__two__succ,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_two_times_div_two_succ
% 5.24/5.52 thf(fact_4395_power__le__zero__eq__numeral,axiom,
% 5.24/5.52 ! [A: real,W2: num] :
% 5.24/5.52 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 5.24/5.52 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_zero_eq_numeral
% 5.24/5.52 thf(fact_4396_power__le__zero__eq__numeral,axiom,
% 5.24/5.52 ! [A: rat,W2: num] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 5.24/5.52 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_zero_eq_numeral
% 5.24/5.52 thf(fact_4397_power__le__zero__eq__numeral,axiom,
% 5.24/5.52 ! [A: int,W2: num] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 5.24/5.52 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.52 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_zero_eq_numeral
% 5.24/5.52 thf(fact_4398_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.24/5.52 = ( N = zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % semiring_parity_class.even_mask_iff
% 5.24/5.52 thf(fact_4399_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.24/5.52 = ( N = zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % semiring_parity_class.even_mask_iff
% 5.24/5.52 thf(fact_4400_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.24/5.52 = ( N = zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % semiring_parity_class.even_mask_iff
% 5.24/5.52 thf(fact_4401_division__decomp,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.52 => ? [B6: nat,C4: nat] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_times_nat @ B6 @ C4 ) )
% 5.24/5.52 & ( dvd_dvd_nat @ B6 @ B )
% 5.24/5.52 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % division_decomp
% 5.24/5.52 thf(fact_4402_division__decomp,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.52 => ? [B6: int,C4: int] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_times_int @ B6 @ C4 ) )
% 5.24/5.52 & ( dvd_dvd_int @ B6 @ B )
% 5.24/5.52 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % division_decomp
% 5.24/5.52 thf(fact_4403_dvd__productE,axiom,
% 5.24/5.52 ! [P6: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ P6 @ ( times_times_nat @ A @ B ) )
% 5.24/5.52 => ~ ! [X3: nat,Y3: nat] :
% 5.24/5.52 ( ( P6
% 5.24/5.52 = ( times_times_nat @ X3 @ Y3 ) )
% 5.24/5.52 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.24/5.52 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_productE
% 5.24/5.52 thf(fact_4404_dvd__productE,axiom,
% 5.24/5.52 ! [P6: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ P6 @ ( times_times_int @ A @ B ) )
% 5.24/5.52 => ~ ! [X3: int,Y3: int] :
% 5.24/5.52 ( ( P6
% 5.24/5.52 = ( times_times_int @ X3 @ Y3 ) )
% 5.24/5.52 => ( ( dvd_dvd_int @ X3 @ A )
% 5.24/5.52 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_productE
% 5.24/5.52 thf(fact_4405_dvd__triv__right,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_right
% 5.24/5.52 thf(fact_4406_dvd__triv__right,axiom,
% 5.24/5.52 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_right
% 5.24/5.52 thf(fact_4407_dvd__triv__right,axiom,
% 5.24/5.52 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_right
% 5.24/5.52 thf(fact_4408_dvd__triv__right,axiom,
% 5.24/5.52 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_right
% 5.24/5.52 thf(fact_4409_dvd__triv__right,axiom,
% 5.24/5.52 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_right
% 5.24/5.52 thf(fact_4410_dvd__mult__right,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_right
% 5.24/5.52 thf(fact_4411_dvd__mult__right,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_right
% 5.24/5.52 thf(fact_4412_dvd__mult__right,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_right
% 5.24/5.52 thf(fact_4413_dvd__mult__right,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_right
% 5.24/5.52 thf(fact_4414_dvd__mult__right,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_right
% 5.24/5.52 thf(fact_4415_mult__dvd__mono,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_dvd_mono
% 5.24/5.52 thf(fact_4416_mult__dvd__mono,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_real @ C @ D )
% 5.24/5.52 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_dvd_mono
% 5.24/5.52 thf(fact_4417_mult__dvd__mono,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_rat @ C @ D )
% 5.24/5.52 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_dvd_mono
% 5.24/5.52 thf(fact_4418_mult__dvd__mono,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ D )
% 5.24/5.52 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_dvd_mono
% 5.24/5.52 thf(fact_4419_mult__dvd__mono,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ D )
% 5.24/5.52 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_dvd_mono
% 5.24/5.52 thf(fact_4420_dvd__triv__left,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_left
% 5.24/5.52 thf(fact_4421_dvd__triv__left,axiom,
% 5.24/5.52 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_left
% 5.24/5.52 thf(fact_4422_dvd__triv__left,axiom,
% 5.24/5.52 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_left
% 5.24/5.52 thf(fact_4423_dvd__triv__left,axiom,
% 5.24/5.52 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_left
% 5.24/5.52 thf(fact_4424_dvd__triv__left,axiom,
% 5.24/5.52 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_triv_left
% 5.24/5.52 thf(fact_4425_dvd__mult__left,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_left
% 5.24/5.52 thf(fact_4426_dvd__mult__left,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_left
% 5.24/5.52 thf(fact_4427_dvd__mult__left,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_left
% 5.24/5.52 thf(fact_4428_dvd__mult__left,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_left
% 5.24/5.52 thf(fact_4429_dvd__mult__left,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.24/5.52 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_left
% 5.24/5.52 thf(fact_4430_dvd__mult2,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult2
% 5.24/5.52 thf(fact_4431_dvd__mult2,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ B )
% 5.24/5.52 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult2
% 5.24/5.52 thf(fact_4432_dvd__mult2,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ B )
% 5.24/5.52 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult2
% 5.24/5.52 thf(fact_4433_dvd__mult2,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult2
% 5.24/5.52 thf(fact_4434_dvd__mult2,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult2
% 5.24/5.52 thf(fact_4435_dvd__mult,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult
% 5.24/5.52 thf(fact_4436_dvd__mult,axiom,
% 5.24/5.52 ! [A: real,C: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ C )
% 5.24/5.52 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult
% 5.24/5.52 thf(fact_4437_dvd__mult,axiom,
% 5.24/5.52 ! [A: rat,C: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ C )
% 5.24/5.52 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult
% 5.24/5.52 thf(fact_4438_dvd__mult,axiom,
% 5.24/5.52 ! [A: nat,C: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ C )
% 5.24/5.52 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult
% 5.24/5.52 thf(fact_4439_dvd__mult,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ C )
% 5.24/5.52 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult
% 5.24/5.52 thf(fact_4440_dvd__def,axiom,
% 5.24/5.52 ( dvd_dvd_Code_integer
% 5.24/5.52 = ( ^ [B3: code_integer,A4: code_integer] :
% 5.24/5.52 ? [K3: code_integer] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( times_3573771949741848930nteger @ B3 @ K3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_def
% 5.24/5.52 thf(fact_4441_dvd__def,axiom,
% 5.24/5.52 ( dvd_dvd_real
% 5.24/5.52 = ( ^ [B3: real,A4: real] :
% 5.24/5.52 ? [K3: real] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( times_times_real @ B3 @ K3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_def
% 5.24/5.52 thf(fact_4442_dvd__def,axiom,
% 5.24/5.52 ( dvd_dvd_rat
% 5.24/5.52 = ( ^ [B3: rat,A4: rat] :
% 5.24/5.52 ? [K3: rat] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( times_times_rat @ B3 @ K3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_def
% 5.24/5.52 thf(fact_4443_dvd__def,axiom,
% 5.24/5.52 ( dvd_dvd_nat
% 5.24/5.52 = ( ^ [B3: nat,A4: nat] :
% 5.24/5.52 ? [K3: nat] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( times_times_nat @ B3 @ K3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_def
% 5.24/5.52 thf(fact_4444_dvd__def,axiom,
% 5.24/5.52 ( dvd_dvd_int
% 5.24/5.52 = ( ^ [B3: int,A4: int] :
% 5.24/5.52 ? [K3: int] :
% 5.24/5.52 ( A4
% 5.24/5.52 = ( times_times_int @ B3 @ K3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_def
% 5.24/5.52 thf(fact_4445_dvdI,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdI
% 5.24/5.52 thf(fact_4446_dvdI,axiom,
% 5.24/5.52 ! [A: real,B: real,K: real] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_times_real @ B @ K ) )
% 5.24/5.52 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdI
% 5.24/5.52 thf(fact_4447_dvdI,axiom,
% 5.24/5.52 ! [A: rat,B: rat,K: rat] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_times_rat @ B @ K ) )
% 5.24/5.52 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdI
% 5.24/5.52 thf(fact_4448_dvdI,axiom,
% 5.24/5.52 ! [A: nat,B: nat,K: nat] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_times_nat @ B @ K ) )
% 5.24/5.52 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdI
% 5.24/5.52 thf(fact_4449_dvdI,axiom,
% 5.24/5.52 ! [A: int,B: int,K: int] :
% 5.24/5.52 ( ( A
% 5.24/5.52 = ( times_times_int @ B @ K ) )
% 5.24/5.52 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdI
% 5.24/5.52 thf(fact_4450_dvdE,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ~ ! [K2: code_integer] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdE
% 5.24/5.52 thf(fact_4451_dvdE,axiom,
% 5.24/5.52 ! [B: real,A: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ B @ A )
% 5.24/5.52 => ~ ! [K2: real] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdE
% 5.24/5.52 thf(fact_4452_dvdE,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ B @ A )
% 5.24/5.52 => ~ ! [K2: rat] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdE
% 5.24/5.52 thf(fact_4453_dvdE,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ~ ! [K2: nat] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdE
% 5.24/5.52 thf(fact_4454_dvdE,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ~ ! [K2: int] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvdE
% 5.24/5.52 thf(fact_4455_dvd__unit__imp__unit,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_unit_imp_unit
% 5.24/5.52 thf(fact_4456_dvd__unit__imp__unit,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_unit_imp_unit
% 5.24/5.52 thf(fact_4457_dvd__unit__imp__unit,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_unit_imp_unit
% 5.24/5.52 thf(fact_4458_unit__imp__dvd,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_imp_dvd
% 5.24/5.52 thf(fact_4459_unit__imp__dvd,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_imp_dvd
% 5.24/5.52 thf(fact_4460_unit__imp__dvd,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_imp_dvd
% 5.24/5.52 thf(fact_4461_one__dvd,axiom,
% 5.24/5.52 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.24/5.52
% 5.24/5.52 % one_dvd
% 5.24/5.52 thf(fact_4462_one__dvd,axiom,
% 5.24/5.52 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.24/5.52
% 5.24/5.52 % one_dvd
% 5.24/5.52 thf(fact_4463_one__dvd,axiom,
% 5.24/5.52 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.24/5.52
% 5.24/5.52 % one_dvd
% 5.24/5.52 thf(fact_4464_one__dvd,axiom,
% 5.24/5.52 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.24/5.52
% 5.24/5.52 % one_dvd
% 5.24/5.52 thf(fact_4465_one__dvd,axiom,
% 5.24/5.52 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.24/5.52
% 5.24/5.52 % one_dvd
% 5.24/5.52 thf(fact_4466_one__dvd,axiom,
% 5.24/5.52 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.24/5.52
% 5.24/5.52 % one_dvd
% 5.24/5.52 thf(fact_4467_dvd__add__right__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_right_iff
% 5.24/5.52 thf(fact_4468_dvd__add__right__iff,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_right_iff
% 5.24/5.52 thf(fact_4469_dvd__add__right__iff,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_right_iff
% 5.24/5.52 thf(fact_4470_dvd__add__right__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_right_iff
% 5.24/5.52 thf(fact_4471_dvd__add__right__iff,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_right_iff
% 5.24/5.52 thf(fact_4472_dvd__add__left__iff,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_left_iff
% 5.24/5.52 thf(fact_4473_dvd__add__left__iff,axiom,
% 5.24/5.52 ! [A: real,C: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_left_iff
% 5.24/5.52 thf(fact_4474_dvd__add__left__iff,axiom,
% 5.24/5.52 ! [A: rat,C: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_left_iff
% 5.24/5.52 thf(fact_4475_dvd__add__left__iff,axiom,
% 5.24/5.52 ! [A: nat,C: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_left_iff
% 5.24/5.52 thf(fact_4476_dvd__add__left__iff,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ C )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add_left_iff
% 5.24/5.52 thf(fact_4477_dvd__add,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add
% 5.24/5.52 thf(fact_4478_dvd__add,axiom,
% 5.24/5.52 ! [A: real,B: real,C: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_real @ A @ C )
% 5.24/5.52 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add
% 5.24/5.52 thf(fact_4479_dvd__add,axiom,
% 5.24/5.52 ! [A: rat,B: rat,C: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_rat @ A @ C )
% 5.24/5.52 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add
% 5.24/5.52 thf(fact_4480_dvd__add,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ C )
% 5.24/5.52 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add
% 5.24/5.52 thf(fact_4481_dvd__add,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ C )
% 5.24/5.52 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_add
% 5.24/5.52 thf(fact_4482_dvd__diff__commute,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_diff_commute
% 5.24/5.52 thf(fact_4483_dvd__diff__commute,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_diff_commute
% 5.24/5.52 thf(fact_4484_dvd__div__eq__iff,axiom,
% 5.24/5.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.24/5.52 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.24/5.52 = ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_iff
% 5.24/5.52 thf(fact_4485_dvd__div__eq__iff,axiom,
% 5.24/5.52 ! [C: complex,A: complex,B: complex] :
% 5.24/5.52 ( ( dvd_dvd_complex @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_complex @ C @ B )
% 5.24/5.52 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.24/5.52 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.24/5.52 = ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_iff
% 5.24/5.52 thf(fact_4486_dvd__div__eq__iff,axiom,
% 5.24/5.52 ! [C: real,A: real,B: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_real @ C @ B )
% 5.24/5.52 => ( ( ( divide_divide_real @ A @ C )
% 5.24/5.52 = ( divide_divide_real @ B @ C ) )
% 5.24/5.52 = ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_iff
% 5.24/5.52 thf(fact_4487_dvd__div__eq__iff,axiom,
% 5.24/5.52 ! [C: rat,A: rat,B: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_rat @ C @ B )
% 5.24/5.52 => ( ( ( divide_divide_rat @ A @ C )
% 5.24/5.52 = ( divide_divide_rat @ B @ C ) )
% 5.24/5.52 = ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_iff
% 5.24/5.52 thf(fact_4488_dvd__div__eq__iff,axiom,
% 5.24/5.52 ! [C: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( ( divide_divide_nat @ A @ C )
% 5.24/5.52 = ( divide_divide_nat @ B @ C ) )
% 5.24/5.52 = ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_iff
% 5.24/5.52 thf(fact_4489_dvd__div__eq__iff,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( ( divide_divide_int @ A @ C )
% 5.24/5.52 = ( divide_divide_int @ B @ C ) )
% 5.24/5.52 = ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_iff
% 5.24/5.52 thf(fact_4490_dvd__div__eq__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.24/5.52 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_cancel
% 5.24/5.52 thf(fact_4491_dvd__div__eq__cancel,axiom,
% 5.24/5.52 ! [A: complex,C: complex,B: complex] :
% 5.24/5.52 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.24/5.52 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.24/5.52 => ( ( dvd_dvd_complex @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_complex @ C @ B )
% 5.24/5.52 => ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_cancel
% 5.24/5.52 thf(fact_4492_dvd__div__eq__cancel,axiom,
% 5.24/5.52 ! [A: real,C: real,B: real] :
% 5.24/5.52 ( ( ( divide_divide_real @ A @ C )
% 5.24/5.52 = ( divide_divide_real @ B @ C ) )
% 5.24/5.52 => ( ( dvd_dvd_real @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_real @ C @ B )
% 5.24/5.52 => ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_cancel
% 5.24/5.52 thf(fact_4493_dvd__div__eq__cancel,axiom,
% 5.24/5.52 ! [A: rat,C: rat,B: rat] :
% 5.24/5.52 ( ( ( divide_divide_rat @ A @ C )
% 5.24/5.52 = ( divide_divide_rat @ B @ C ) )
% 5.24/5.52 => ( ( dvd_dvd_rat @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_rat @ C @ B )
% 5.24/5.52 => ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_cancel
% 5.24/5.52 thf(fact_4494_dvd__div__eq__cancel,axiom,
% 5.24/5.52 ! [A: nat,C: nat,B: nat] :
% 5.24/5.52 ( ( ( divide_divide_nat @ A @ C )
% 5.24/5.52 = ( divide_divide_nat @ B @ C ) )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_cancel
% 5.24/5.52 thf(fact_4495_dvd__div__eq__cancel,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( ( divide_divide_int @ A @ C )
% 5.24/5.52 = ( divide_divide_int @ B @ C ) )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ A )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( A = B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_cancel
% 5.24/5.52 thf(fact_4496_div__div__div__same,axiom,
% 5.24/5.52 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_div_div_same
% 5.24/5.52 thf(fact_4497_div__div__div__same,axiom,
% 5.24/5.52 ! [D: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ D @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.24/5.52 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_div_div_same
% 5.24/5.52 thf(fact_4498_div__div__div__same,axiom,
% 5.24/5.52 ! [D: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.24/5.52 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_div_div_same
% 5.24/5.52 thf(fact_4499_dvd__power__same,axiom,
% 5.24/5.52 ! [X: code_integer,Y4: code_integer,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ X @ Y4 )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y4 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_same
% 5.24/5.52 thf(fact_4500_dvd__power__same,axiom,
% 5.24/5.52 ! [X: nat,Y4: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ X @ Y4 )
% 5.24/5.52 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y4 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_same
% 5.24/5.52 thf(fact_4501_dvd__power__same,axiom,
% 5.24/5.52 ! [X: real,Y4: real,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_real @ X @ Y4 )
% 5.24/5.52 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_same
% 5.24/5.52 thf(fact_4502_dvd__power__same,axiom,
% 5.24/5.52 ! [X: int,Y4: int,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ X @ Y4 )
% 5.24/5.52 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_same
% 5.24/5.52 thf(fact_4503_dvd__power__same,axiom,
% 5.24/5.52 ! [X: complex,Y4: complex,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_complex @ X @ Y4 )
% 5.24/5.52 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_same
% 5.24/5.52 thf(fact_4504_dvd__mod,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ K @ M )
% 5.24/5.52 => ( ( dvd_dvd_nat @ K @ N )
% 5.24/5.52 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mod
% 5.24/5.52 thf(fact_4505_dvd__mod,axiom,
% 5.24/5.52 ! [K: int,M: int,N: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ K @ M )
% 5.24/5.52 => ( ( dvd_dvd_int @ K @ N )
% 5.24/5.52 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mod
% 5.24/5.52 thf(fact_4506_dvd__mod,axiom,
% 5.24/5.52 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mod
% 5.24/5.52 thf(fact_4507_mod__mod__cancel,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.24/5.52 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_mod_cancel
% 5.24/5.52 thf(fact_4508_mod__mod__cancel,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.24/5.52 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_mod_cancel
% 5.24/5.52 thf(fact_4509_mod__mod__cancel,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.24/5.52 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_mod_cancel
% 5.24/5.52 thf(fact_4510_signed__take__bit__mult,axiom,
% 5.24/5.52 ! [N: nat,K: int,L2: int] :
% 5.24/5.52 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.24/5.52 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_mult
% 5.24/5.52 thf(fact_4511_signed__take__bit__add,axiom,
% 5.24/5.52 ! [N: nat,K: int,L2: int] :
% 5.24/5.52 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.24/5.52 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_add
% 5.24/5.52 thf(fact_4512_even__signed__take__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_signed_take_bit_iff
% 5.24/5.52 thf(fact_4513_even__signed__take__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.24/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_signed_take_bit_iff
% 5.24/5.52 thf(fact_4514_not__is__unit__0,axiom,
% 5.24/5.52 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.24/5.52
% 5.24/5.52 % not_is_unit_0
% 5.24/5.52 thf(fact_4515_not__is__unit__0,axiom,
% 5.24/5.52 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.24/5.52
% 5.24/5.52 % not_is_unit_0
% 5.24/5.52 thf(fact_4516_not__is__unit__0,axiom,
% 5.24/5.52 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.24/5.52
% 5.24/5.52 % not_is_unit_0
% 5.24/5.52 thf(fact_4517_minf_I10_J,axiom,
% 5.24/5.52 ! [D: code_integer,S2: code_integer] :
% 5.24/5.52 ? [Z: code_integer] :
% 5.24/5.52 ! [X5: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ X5 @ Z )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(10)
% 5.24/5.52 thf(fact_4518_minf_I10_J,axiom,
% 5.24/5.52 ! [D: real,S2: real] :
% 5.24/5.52 ? [Z: real] :
% 5.24/5.52 ! [X5: real] :
% 5.24/5.52 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(10)
% 5.24/5.52 thf(fact_4519_minf_I10_J,axiom,
% 5.24/5.52 ! [D: rat,S2: rat] :
% 5.24/5.52 ? [Z: rat] :
% 5.24/5.52 ! [X5: rat] :
% 5.24/5.52 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(10)
% 5.24/5.52 thf(fact_4520_minf_I10_J,axiom,
% 5.24/5.52 ! [D: nat,S2: nat] :
% 5.24/5.52 ? [Z: nat] :
% 5.24/5.52 ! [X5: nat] :
% 5.24/5.52 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(10)
% 5.24/5.52 thf(fact_4521_minf_I10_J,axiom,
% 5.24/5.52 ! [D: int,S2: int] :
% 5.24/5.52 ? [Z: int] :
% 5.24/5.52 ! [X5: int] :
% 5.24/5.52 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(10)
% 5.24/5.52 thf(fact_4522_minf_I9_J,axiom,
% 5.24/5.52 ! [D: code_integer,S2: code_integer] :
% 5.24/5.52 ? [Z: code_integer] :
% 5.24/5.52 ! [X5: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ X5 @ Z )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(9)
% 5.24/5.52 thf(fact_4523_minf_I9_J,axiom,
% 5.24/5.52 ! [D: real,S2: real] :
% 5.24/5.52 ? [Z: real] :
% 5.24/5.52 ! [X5: real] :
% 5.24/5.52 ( ( ord_less_real @ X5 @ Z )
% 5.24/5.52 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(9)
% 5.24/5.52 thf(fact_4524_minf_I9_J,axiom,
% 5.24/5.52 ! [D: rat,S2: rat] :
% 5.24/5.52 ? [Z: rat] :
% 5.24/5.52 ! [X5: rat] :
% 5.24/5.52 ( ( ord_less_rat @ X5 @ Z )
% 5.24/5.52 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(9)
% 5.24/5.52 thf(fact_4525_minf_I9_J,axiom,
% 5.24/5.52 ! [D: nat,S2: nat] :
% 5.24/5.52 ? [Z: nat] :
% 5.24/5.52 ! [X5: nat] :
% 5.24/5.52 ( ( ord_less_nat @ X5 @ Z )
% 5.24/5.52 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(9)
% 5.24/5.52 thf(fact_4526_minf_I9_J,axiom,
% 5.24/5.52 ! [D: int,S2: int] :
% 5.24/5.52 ? [Z: int] :
% 5.24/5.52 ! [X5: int] :
% 5.24/5.52 ( ( ord_less_int @ X5 @ Z )
% 5.24/5.52 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minf(9)
% 5.24/5.52 thf(fact_4527_pinf_I10_J,axiom,
% 5.24/5.52 ! [D: code_integer,S2: code_integer] :
% 5.24/5.52 ? [Z: code_integer] :
% 5.24/5.52 ! [X5: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ Z @ X5 )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(10)
% 5.24/5.52 thf(fact_4528_pinf_I10_J,axiom,
% 5.24/5.52 ! [D: real,S2: real] :
% 5.24/5.52 ? [Z: real] :
% 5.24/5.52 ! [X5: real] :
% 5.24/5.52 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(10)
% 5.24/5.52 thf(fact_4529_pinf_I10_J,axiom,
% 5.24/5.52 ! [D: rat,S2: rat] :
% 5.24/5.52 ? [Z: rat] :
% 5.24/5.52 ! [X5: rat] :
% 5.24/5.52 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(10)
% 5.24/5.52 thf(fact_4530_pinf_I10_J,axiom,
% 5.24/5.52 ! [D: nat,S2: nat] :
% 5.24/5.52 ? [Z: nat] :
% 5.24/5.52 ! [X5: nat] :
% 5.24/5.52 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(10)
% 5.24/5.52 thf(fact_4531_pinf_I10_J,axiom,
% 5.24/5.52 ! [D: int,S2: int] :
% 5.24/5.52 ? [Z: int] :
% 5.24/5.52 ! [X5: int] :
% 5.24/5.52 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.52 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(10)
% 5.24/5.52 thf(fact_4532_pinf_I9_J,axiom,
% 5.24/5.52 ! [D: code_integer,S2: code_integer] :
% 5.24/5.52 ? [Z: code_integer] :
% 5.24/5.52 ! [X5: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ Z @ X5 )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(9)
% 5.24/5.52 thf(fact_4533_pinf_I9_J,axiom,
% 5.24/5.52 ! [D: real,S2: real] :
% 5.24/5.52 ? [Z: real] :
% 5.24/5.52 ! [X5: real] :
% 5.24/5.52 ( ( ord_less_real @ Z @ X5 )
% 5.24/5.52 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(9)
% 5.24/5.52 thf(fact_4534_pinf_I9_J,axiom,
% 5.24/5.52 ! [D: rat,S2: rat] :
% 5.24/5.52 ? [Z: rat] :
% 5.24/5.52 ! [X5: rat] :
% 5.24/5.52 ( ( ord_less_rat @ Z @ X5 )
% 5.24/5.52 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(9)
% 5.24/5.52 thf(fact_4535_pinf_I9_J,axiom,
% 5.24/5.52 ! [D: nat,S2: nat] :
% 5.24/5.52 ? [Z: nat] :
% 5.24/5.52 ! [X5: nat] :
% 5.24/5.52 ( ( ord_less_nat @ Z @ X5 )
% 5.24/5.52 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(9)
% 5.24/5.52 thf(fact_4536_pinf_I9_J,axiom,
% 5.24/5.52 ! [D: int,S2: int] :
% 5.24/5.52 ? [Z: int] :
% 5.24/5.52 ! [X5: int] :
% 5.24/5.52 ( ( ord_less_int @ Z @ X5 )
% 5.24/5.52 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.24/5.52 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % pinf(9)
% 5.24/5.52 thf(fact_4537_dvd__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.24/5.52 = zero_z3403309356797280102nteger )
% 5.24/5.52 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_0_iff
% 5.24/5.52 thf(fact_4538_dvd__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: complex,A: complex] :
% 5.24/5.52 ( ( dvd_dvd_complex @ B @ A )
% 5.24/5.52 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.24/5.52 = zero_zero_complex )
% 5.24/5.52 = ( A = zero_zero_complex ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_0_iff
% 5.24/5.52 thf(fact_4539_dvd__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: real,A: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ B @ A )
% 5.24/5.52 => ( ( ( divide_divide_real @ A @ B )
% 5.24/5.52 = zero_zero_real )
% 5.24/5.52 = ( A = zero_zero_real ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_0_iff
% 5.24/5.52 thf(fact_4540_dvd__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ B @ A )
% 5.24/5.52 => ( ( ( divide_divide_rat @ A @ B )
% 5.24/5.52 = zero_zero_rat )
% 5.24/5.52 = ( A = zero_zero_rat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_0_iff
% 5.24/5.52 thf(fact_4541_dvd__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( ( divide_divide_nat @ A @ B )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 = ( A = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_0_iff
% 5.24/5.52 thf(fact_4542_dvd__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( ( divide_divide_int @ A @ B )
% 5.24/5.52 = zero_zero_int )
% 5.24/5.52 = ( A = zero_zero_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_0_iff
% 5.24/5.52 thf(fact_4543_unit__mult__right__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.24/5.52 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_right_cancel
% 5.24/5.52 thf(fact_4544_unit__mult__right__cancel,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( ( times_times_nat @ B @ A )
% 5.24/5.52 = ( times_times_nat @ C @ A ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_right_cancel
% 5.24/5.52 thf(fact_4545_unit__mult__right__cancel,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( ( times_times_int @ B @ A )
% 5.24/5.52 = ( times_times_int @ C @ A ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_right_cancel
% 5.24/5.52 thf(fact_4546_unit__mult__left__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.24/5.52 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_left_cancel
% 5.24/5.52 thf(fact_4547_unit__mult__left__cancel,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( ( times_times_nat @ A @ B )
% 5.24/5.52 = ( times_times_nat @ A @ C ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_left_cancel
% 5.24/5.52 thf(fact_4548_unit__mult__left__cancel,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( ( times_times_int @ A @ B )
% 5.24/5.52 = ( times_times_int @ A @ C ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_mult_left_cancel
% 5.24/5.52 thf(fact_4549_mult__unit__dvd__iff_H,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_unit_dvd_iff'
% 5.24/5.52 thf(fact_4550_mult__unit__dvd__iff_H,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_unit_dvd_iff'
% 5.24/5.52 thf(fact_4551_mult__unit__dvd__iff_H,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_unit_dvd_iff'
% 5.24/5.52 thf(fact_4552_dvd__mult__unit__iff_H,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_unit_iff'
% 5.24/5.52 thf(fact_4553_dvd__mult__unit__iff_H,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_unit_iff'
% 5.24/5.52 thf(fact_4554_dvd__mult__unit__iff_H,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_unit_iff'
% 5.24/5.52 thf(fact_4555_mult__unit__dvd__iff,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_unit_dvd_iff
% 5.24/5.52 thf(fact_4556_mult__unit__dvd__iff,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_unit_dvd_iff
% 5.24/5.52 thf(fact_4557_mult__unit__dvd__iff,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_unit_dvd_iff
% 5.24/5.52 thf(fact_4558_dvd__mult__unit__iff,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_unit_iff
% 5.24/5.52 thf(fact_4559_dvd__mult__unit__iff,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_unit_iff
% 5.24/5.52 thf(fact_4560_dvd__mult__unit__iff,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_unit_iff
% 5.24/5.52 thf(fact_4561_is__unit__mult__iff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_mult_iff
% 5.24/5.52 thf(fact_4562_is__unit__mult__iff,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.24/5.52 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_mult_iff
% 5.24/5.52 thf(fact_4563_is__unit__mult__iff,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.24/5.52 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_mult_iff
% 5.24/5.52 thf(fact_4564_dvd__div__mult,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult
% 5.24/5.52 thf(fact_4565_dvd__div__mult,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.24/5.52 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult
% 5.24/5.52 thf(fact_4566_dvd__div__mult,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.24/5.52 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult
% 5.24/5.52 thf(fact_4567_div__mult__swap,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_swap
% 5.24/5.52 thf(fact_4568_div__mult__swap,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.24/5.52 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_swap
% 5.24/5.52 thf(fact_4569_div__mult__swap,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.24/5.52 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_swap
% 5.24/5.52 thf(fact_4570_div__div__eq__right,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.24/5.52 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_div_eq_right
% 5.24/5.52 thf(fact_4571_div__div__eq__right,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.24/5.52 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_div_eq_right
% 5.24/5.52 thf(fact_4572_div__div__eq__right,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.24/5.52 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_div_eq_right
% 5.24/5.52 thf(fact_4573_dvd__div__mult2__eq,axiom,
% 5.24/5.52 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult2_eq
% 5.24/5.52 thf(fact_4574_dvd__div__mult2__eq,axiom,
% 5.24/5.52 ! [B: nat,C: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.52 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult2_eq
% 5.24/5.52 thf(fact_4575_dvd__div__mult2__eq,axiom,
% 5.24/5.52 ! [B: int,C: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.24/5.52 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.52 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_mult2_eq
% 5.24/5.52 thf(fact_4576_dvd__mult__imp__div,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_imp_div
% 5.24/5.52 thf(fact_4577_dvd__mult__imp__div,axiom,
% 5.24/5.52 ! [A: nat,C: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.24/5.52 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_imp_div
% 5.24/5.52 thf(fact_4578_dvd__mult__imp__div,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.24/5.52 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_imp_div
% 5.24/5.52 thf(fact_4579_div__mult__div__if__dvd,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_div_if_dvd
% 5.24/5.52 thf(fact_4580_div__mult__div__if__dvd,axiom,
% 5.24/5.52 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( dvd_dvd_nat @ D @ C )
% 5.24/5.52 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.24/5.52 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_div_if_dvd
% 5.24/5.52 thf(fact_4581_div__mult__div__if__dvd,axiom,
% 5.24/5.52 ! [B: int,A: int,D: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( dvd_dvd_int @ D @ C )
% 5.24/5.52 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.24/5.52 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_div_if_dvd
% 5.24/5.52 thf(fact_4582_unit__div__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.24/5.52 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_cancel
% 5.24/5.52 thf(fact_4583_unit__div__cancel,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ( ( ( divide_divide_nat @ B @ A )
% 5.24/5.52 = ( divide_divide_nat @ C @ A ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_cancel
% 5.24/5.52 thf(fact_4584_unit__div__cancel,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ( ( ( divide_divide_int @ B @ A )
% 5.24/5.52 = ( divide_divide_int @ C @ A ) )
% 5.24/5.52 = ( B = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_cancel
% 5.24/5.52 thf(fact_4585_div__unit__dvd__iff,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_unit_dvd_iff
% 5.24/5.52 thf(fact_4586_div__unit__dvd__iff,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_unit_dvd_iff
% 5.24/5.52 thf(fact_4587_div__unit__dvd__iff,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_unit_dvd_iff
% 5.24/5.52 thf(fact_4588_dvd__div__unit__iff,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_unit_iff
% 5.24/5.52 thf(fact_4589_dvd__div__unit__iff,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_unit_iff
% 5.24/5.52 thf(fact_4590_dvd__div__unit__iff,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_unit_iff
% 5.24/5.52 thf(fact_4591_div__plus__div__distrib__dvd__right,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_plus_div_distrib_dvd_right
% 5.24/5.52 thf(fact_4592_div__plus__div__distrib__dvd__right,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.24/5.52 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_plus_div_distrib_dvd_right
% 5.24/5.52 thf(fact_4593_div__plus__div__distrib__dvd__right,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.24/5.52 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_plus_div_distrib_dvd_right
% 5.24/5.52 thf(fact_4594_div__plus__div__distrib__dvd__left,axiom,
% 5.24/5.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_plus_div_distrib_dvd_left
% 5.24/5.52 thf(fact_4595_div__plus__div__distrib__dvd__left,axiom,
% 5.24/5.52 ! [C: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.24/5.52 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_plus_div_distrib_dvd_left
% 5.24/5.52 thf(fact_4596_div__plus__div__distrib__dvd__left,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ A )
% 5.24/5.52 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.24/5.52 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_plus_div_distrib_dvd_left
% 5.24/5.52 thf(fact_4597_div__power,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_power
% 5.24/5.52 thf(fact_4598_div__power,axiom,
% 5.24/5.52 ! [B: nat,A: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.24/5.52 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_power
% 5.24/5.52 thf(fact_4599_div__power,axiom,
% 5.24/5.52 ! [B: int,A: int,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.24/5.52 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_power
% 5.24/5.52 thf(fact_4600_dvd__power__le,axiom,
% 5.24/5.52 ! [X: code_integer,Y4: code_integer,N: nat,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ X @ Y4 )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y4 @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_le
% 5.24/5.52 thf(fact_4601_dvd__power__le,axiom,
% 5.24/5.52 ! [X: nat,Y4: nat,N: nat,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ X @ Y4 )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y4 @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_le
% 5.24/5.52 thf(fact_4602_dvd__power__le,axiom,
% 5.24/5.52 ! [X: real,Y4: real,N: nat,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_real @ X @ Y4 )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_le
% 5.24/5.52 thf(fact_4603_dvd__power__le,axiom,
% 5.24/5.52 ! [X: int,Y4: int,N: nat,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ X @ Y4 )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_le
% 5.24/5.52 thf(fact_4604_dvd__power__le,axiom,
% 5.24/5.52 ! [X: complex,Y4: complex,N: nat,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_complex @ X @ Y4 )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_le
% 5.24/5.52 thf(fact_4605_power__le__dvd,axiom,
% 5.24/5.52 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.24/5.52 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_dvd
% 5.24/5.52 thf(fact_4606_power__le__dvd,axiom,
% 5.24/5.52 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.24/5.52 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_dvd
% 5.24/5.52 thf(fact_4607_power__le__dvd,axiom,
% 5.24/5.52 ! [A: real,N: nat,B: real,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.24/5.52 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_dvd
% 5.24/5.52 thf(fact_4608_power__le__dvd,axiom,
% 5.24/5.52 ! [A: int,N: nat,B: int,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.24/5.52 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_dvd
% 5.24/5.52 thf(fact_4609_power__le__dvd,axiom,
% 5.24/5.52 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.24/5.52 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.24/5.52 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_dvd
% 5.24/5.52 thf(fact_4610_le__imp__power__dvd,axiom,
% 5.24/5.52 ! [M: nat,N: nat,A: code_integer] :
% 5.24/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_imp_power_dvd
% 5.24/5.52 thf(fact_4611_le__imp__power__dvd,axiom,
% 5.24/5.52 ! [M: nat,N: nat,A: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_imp_power_dvd
% 5.24/5.52 thf(fact_4612_le__imp__power__dvd,axiom,
% 5.24/5.52 ! [M: nat,N: nat,A: real] :
% 5.24/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_imp_power_dvd
% 5.24/5.52 thf(fact_4613_le__imp__power__dvd,axiom,
% 5.24/5.52 ! [M: nat,N: nat,A: int] :
% 5.24/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_imp_power_dvd
% 5.24/5.52 thf(fact_4614_le__imp__power__dvd,axiom,
% 5.24/5.52 ! [M: nat,N: nat,A: complex] :
% 5.24/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % le_imp_power_dvd
% 5.24/5.52 thf(fact_4615_mod__eq__dvd__iff,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int] :
% 5.24/5.52 ( ( ( modulo_modulo_int @ A @ C )
% 5.24/5.52 = ( modulo_modulo_int @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_eq_dvd_iff
% 5.24/5.52 thf(fact_4616_mod__eq__dvd__iff,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.24/5.52 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.24/5.52 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_eq_dvd_iff
% 5.24/5.52 thf(fact_4617_dvd__pos__nat,axiom,
% 5.24/5.52 ! [N: nat,M: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ( dvd_dvd_nat @ M @ N )
% 5.24/5.52 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_pos_nat
% 5.24/5.52 thf(fact_4618_nat__dvd__not__less,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.52 => ( ( ord_less_nat @ M @ N )
% 5.24/5.52 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nat_dvd_not_less
% 5.24/5.52 thf(fact_4619_dvd__minus__self,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.24/5.52 = ( ( ord_less_nat @ N @ M )
% 5.24/5.52 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_minus_self
% 5.24/5.52 thf(fact_4620_less__eq__dvd__minus,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 => ( ( dvd_dvd_nat @ M @ N )
% 5.24/5.52 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_eq_dvd_minus
% 5.24/5.52 thf(fact_4621_dvd__diffD1,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.52 => ( ( dvd_dvd_nat @ K @ M )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_diffD1
% 5.24/5.52 thf(fact_4622_dvd__diffD,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.52 => ( ( dvd_dvd_nat @ K @ N )
% 5.24/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_diffD
% 5.24/5.52 thf(fact_4623_zdvd__mult__cancel,axiom,
% 5.24/5.52 ! [K: int,M: int,N: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.24/5.52 => ( ( K != zero_zero_int )
% 5.24/5.52 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zdvd_mult_cancel
% 5.24/5.52 thf(fact_4624_zdvd__mono,axiom,
% 5.24/5.52 ! [K: int,M: int,T: int] :
% 5.24/5.52 ( ( K != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ M @ T )
% 5.24/5.52 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zdvd_mono
% 5.24/5.52 thf(fact_4625_bezout__add__nat,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ? [D3: nat,X3: nat,Y3: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ D3 @ A )
% 5.24/5.52 & ( dvd_dvd_nat @ D3 @ B )
% 5.24/5.52 & ( ( ( times_times_nat @ A @ X3 )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.24/5.52 | ( ( times_times_nat @ B @ X3 )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bezout_add_nat
% 5.24/5.52 thf(fact_4626_bezout__lemma__nat,axiom,
% 5.24/5.52 ! [D: nat,A: nat,B: nat,X: nat,Y4: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ D @ A )
% 5.24/5.52 => ( ( dvd_dvd_nat @ D @ B )
% 5.24/5.52 => ( ( ( ( times_times_nat @ A @ X )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D ) )
% 5.24/5.52 | ( ( times_times_nat @ B @ X )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) )
% 5.24/5.52 => ? [X3: nat,Y3: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ D @ A )
% 5.24/5.52 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.24/5.52 & ( ( ( times_times_nat @ A @ X3 )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.24/5.52 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bezout_lemma_nat
% 5.24/5.52 thf(fact_4627_bezout1__nat,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ? [D3: nat,X3: nat,Y3: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ D3 @ A )
% 5.24/5.52 & ( dvd_dvd_nat @ D3 @ B )
% 5.24/5.52 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.24/5.52 = D3 )
% 5.24/5.52 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.24/5.52 = D3 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bezout1_nat
% 5.24/5.52 thf(fact_4628_zdvd__period,axiom,
% 5.24/5.52 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ D )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.24/5.52 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zdvd_period
% 5.24/5.52 thf(fact_4629_zdvd__reduce,axiom,
% 5.24/5.52 ! [K: int,N: int,M: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.24/5.52 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % zdvd_reduce
% 5.24/5.52 thf(fact_4630_unit__dvdE,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ! [C3: code_integer] :
% 5.24/5.52 ( B
% 5.24/5.52 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_dvdE
% 5.24/5.52 thf(fact_4631_unit__dvdE,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ~ ( ( A != zero_zero_nat )
% 5.24/5.52 => ! [C3: nat] :
% 5.24/5.52 ( B
% 5.24/5.52 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_dvdE
% 5.24/5.52 thf(fact_4632_unit__dvdE,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ~ ( ( A != zero_zero_int )
% 5.24/5.52 => ! [C3: int] :
% 5.24/5.52 ( B
% 5.24/5.52 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_dvdE
% 5.24/5.52 thf(fact_4633_unity__coeff__ex,axiom,
% 5.24/5.52 ! [P: code_integer > $o,L2: code_integer] :
% 5.24/5.52 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 5.24/5.52 = ( ? [X2: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.24/5.52 & ( P @ X2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unity_coeff_ex
% 5.24/5.52 thf(fact_4634_unity__coeff__ex,axiom,
% 5.24/5.52 ! [P: complex > $o,L2: complex] :
% 5.24/5.52 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 5.24/5.52 = ( ? [X2: complex] :
% 5.24/5.52 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 5.24/5.52 & ( P @ X2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unity_coeff_ex
% 5.24/5.52 thf(fact_4635_unity__coeff__ex,axiom,
% 5.24/5.52 ! [P: real > $o,L2: real] :
% 5.24/5.52 ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 5.24/5.52 = ( ? [X2: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.24/5.52 & ( P @ X2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unity_coeff_ex
% 5.24/5.52 thf(fact_4636_unity__coeff__ex,axiom,
% 5.24/5.52 ! [P: rat > $o,L2: rat] :
% 5.24/5.52 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L2 @ X2 ) ) )
% 5.24/5.52 = ( ? [X2: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 5.24/5.52 & ( P @ X2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unity_coeff_ex
% 5.24/5.52 thf(fact_4637_unity__coeff__ex,axiom,
% 5.24/5.52 ! [P: nat > $o,L2: nat] :
% 5.24/5.52 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 5.24/5.52 = ( ? [X2: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.24/5.52 & ( P @ X2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unity_coeff_ex
% 5.24/5.52 thf(fact_4638_unity__coeff__ex,axiom,
% 5.24/5.52 ! [P: int > $o,L2: int] :
% 5.24/5.52 ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 5.24/5.52 = ( ? [X2: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.24/5.52 & ( P @ X2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unity_coeff_ex
% 5.24/5.52 thf(fact_4639_dvd__div__eq__mult,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.24/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.24/5.52 = C )
% 5.24/5.52 = ( B
% 5.24/5.52 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_mult
% 5.24/5.52 thf(fact_4640_dvd__div__eq__mult,axiom,
% 5.24/5.52 ! [A: nat,B: nat,C: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( ( divide_divide_nat @ B @ A )
% 5.24/5.52 = C )
% 5.24/5.52 = ( B
% 5.24/5.52 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_mult
% 5.24/5.52 thf(fact_4641_dvd__div__eq__mult,axiom,
% 5.24/5.52 ! [A: int,B: int,C: int] :
% 5.24/5.52 ( ( A != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( ( divide_divide_int @ B @ A )
% 5.24/5.52 = C )
% 5.24/5.52 = ( B
% 5.24/5.52 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_eq_mult
% 5.24/5.52 thf(fact_4642_div__dvd__iff__mult,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( B != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_dvd_iff_mult
% 5.24/5.52 thf(fact_4643_div__dvd__iff__mult,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( B != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_dvd_iff_mult
% 5.24/5.52 thf(fact_4644_div__dvd__iff__mult,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( B != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.24/5.52 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_dvd_iff_mult
% 5.24/5.52 thf(fact_4645_dvd__div__iff__mult,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( C != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_iff_mult
% 5.24/5.52 thf(fact_4646_dvd__div__iff__mult,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( C != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_iff_mult
% 5.24/5.52 thf(fact_4647_dvd__div__iff__mult,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( C != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.24/5.52 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_iff_mult
% 5.24/5.52 thf(fact_4648_dvd__div__div__eq__mult,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.24/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( C != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.24/5.52 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.24/5.52 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.24/5.52 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_div_eq_mult
% 5.24/5.52 thf(fact_4649_dvd__div__div__eq__mult,axiom,
% 5.24/5.52 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ( ( C != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ D )
% 5.24/5.52 => ( ( ( divide_divide_nat @ B @ A )
% 5.24/5.52 = ( divide_divide_nat @ D @ C ) )
% 5.24/5.52 = ( ( times_times_nat @ B @ C )
% 5.24/5.52 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_div_eq_mult
% 5.24/5.52 thf(fact_4650_dvd__div__div__eq__mult,axiom,
% 5.24/5.52 ! [A: int,C: int,B: int,D: int] :
% 5.24/5.52 ( ( A != zero_zero_int )
% 5.24/5.52 => ( ( C != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ A @ B )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ D )
% 5.24/5.52 => ( ( ( divide_divide_int @ B @ A )
% 5.24/5.52 = ( divide_divide_int @ D @ C ) )
% 5.24/5.52 = ( ( times_times_int @ B @ C )
% 5.24/5.52 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_div_div_eq_mult
% 5.24/5.52 thf(fact_4651_unit__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.24/5.52 = zero_z3403309356797280102nteger )
% 5.24/5.52 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_eq_0_iff
% 5.24/5.52 thf(fact_4652_unit__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( ( divide_divide_nat @ A @ B )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 = ( A = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_eq_0_iff
% 5.24/5.52 thf(fact_4653_unit__div__eq__0__iff,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( ( divide_divide_int @ A @ B )
% 5.24/5.52 = zero_zero_int )
% 5.24/5.52 = ( A = zero_zero_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_eq_0_iff
% 5.24/5.52 thf(fact_4654_even__numeral,axiom,
% 5.24/5.52 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_numeral
% 5.24/5.52 thf(fact_4655_even__numeral,axiom,
% 5.24/5.52 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_numeral
% 5.24/5.52 thf(fact_4656_even__numeral,axiom,
% 5.24/5.52 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_numeral
% 5.24/5.52 thf(fact_4657_inf__period_I4_J,axiom,
% 5.24/5.52 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.24/5.52 => ! [X5: code_integer,K4: code_integer] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(4)
% 5.24/5.52 thf(fact_4658_inf__period_I4_J,axiom,
% 5.24/5.52 ! [D: real,D4: real,T: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ D @ D4 )
% 5.24/5.52 => ! [X5: real,K4: real] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(4)
% 5.24/5.52 thf(fact_4659_inf__period_I4_J,axiom,
% 5.24/5.52 ! [D: rat,D4: rat,T: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ D @ D4 )
% 5.24/5.52 => ! [X5: rat,K4: rat] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(4)
% 5.24/5.52 thf(fact_4660_inf__period_I4_J,axiom,
% 5.24/5.52 ! [D: int,D4: int,T: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.24/5.52 => ! [X5: int,K4: int] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(4)
% 5.24/5.52 thf(fact_4661_inf__period_I3_J,axiom,
% 5.24/5.52 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.24/5.52 => ! [X5: code_integer,K4: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(3)
% 5.24/5.52 thf(fact_4662_inf__period_I3_J,axiom,
% 5.24/5.52 ! [D: real,D4: real,T: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ D @ D4 )
% 5.24/5.52 => ! [X5: real,K4: real] :
% 5.24/5.52 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.24/5.52 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(3)
% 5.24/5.52 thf(fact_4663_inf__period_I3_J,axiom,
% 5.24/5.52 ! [D: rat,D4: rat,T: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ D @ D4 )
% 5.24/5.52 => ! [X5: rat,K4: rat] :
% 5.24/5.52 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.24/5.52 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(3)
% 5.24/5.52 thf(fact_4664_inf__period_I3_J,axiom,
% 5.24/5.52 ! [D: int,D4: int,T: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.24/5.52 => ! [X5: int,K4: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.24/5.52 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % inf_period(3)
% 5.24/5.52 thf(fact_4665_unit__eq__div1,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.24/5.52 = C )
% 5.24/5.52 = ( A
% 5.24/5.52 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_eq_div1
% 5.24/5.52 thf(fact_4666_unit__eq__div1,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( ( divide_divide_nat @ A @ B )
% 5.24/5.52 = C )
% 5.24/5.52 = ( A
% 5.24/5.52 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_eq_div1
% 5.24/5.52 thf(fact_4667_unit__eq__div1,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( ( divide_divide_int @ A @ B )
% 5.24/5.52 = C )
% 5.24/5.52 = ( A
% 5.24/5.52 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_eq_div1
% 5.24/5.52 thf(fact_4668_unit__eq__div2,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( A
% 5.24/5.52 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.24/5.52 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.24/5.52 = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_eq_div2
% 5.24/5.52 thf(fact_4669_unit__eq__div2,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( A
% 5.24/5.52 = ( divide_divide_nat @ C @ B ) )
% 5.24/5.52 = ( ( times_times_nat @ A @ B )
% 5.24/5.52 = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_eq_div2
% 5.24/5.52 thf(fact_4670_unit__eq__div2,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( A
% 5.24/5.52 = ( divide_divide_int @ C @ B ) )
% 5.24/5.52 = ( ( times_times_int @ A @ B )
% 5.24/5.52 = C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_eq_div2
% 5.24/5.52 thf(fact_4671_div__mult__unit2,axiom,
% 5.24/5.52 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_unit2
% 5.24/5.52 thf(fact_4672_div__mult__unit2,axiom,
% 5.24/5.52 ! [C: nat,B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ A )
% 5.24/5.52 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.52 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_unit2
% 5.24/5.52 thf(fact_4673_div__mult__unit2,axiom,
% 5.24/5.52 ! [C: int,B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ A )
% 5.24/5.52 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.52 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_mult_unit2
% 5.24/5.52 thf(fact_4674_unit__div__commute,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_commute
% 5.24/5.52 thf(fact_4675_unit__div__commute,axiom,
% 5.24/5.52 ! [B: nat,A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.24/5.52 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_commute
% 5.24/5.52 thf(fact_4676_unit__div__commute,axiom,
% 5.24/5.52 ! [B: int,A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.24/5.52 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_commute
% 5.24/5.52 thf(fact_4677_unit__div__mult__swap,axiom,
% 5.24/5.52 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_mult_swap
% 5.24/5.52 thf(fact_4678_unit__div__mult__swap,axiom,
% 5.24/5.52 ! [C: nat,A: nat,B: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.24/5.52 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.24/5.52 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_mult_swap
% 5.24/5.52 thf(fact_4679_unit__div__mult__swap,axiom,
% 5.24/5.52 ! [C: int,A: int,B: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.24/5.52 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.24/5.52 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_div_mult_swap
% 5.24/5.52 thf(fact_4680_is__unit__div__mult2__eq,axiom,
% 5.24/5.52 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult2_eq
% 5.24/5.52 thf(fact_4681_is__unit__div__mult2__eq,axiom,
% 5.24/5.52 ! [B: nat,C: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.24/5.52 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.24/5.52 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult2_eq
% 5.24/5.52 thf(fact_4682_is__unit__div__mult2__eq,axiom,
% 5.24/5.52 ! [B: int,C: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.24/5.52 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.24/5.52 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult2_eq
% 5.24/5.52 thf(fact_4683_unit__imp__mod__eq__0,axiom,
% 5.24/5.52 ! [B: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( modulo_modulo_nat @ A @ B )
% 5.24/5.52 = zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_imp_mod_eq_0
% 5.24/5.52 thf(fact_4684_unit__imp__mod__eq__0,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( modulo_modulo_int @ A @ B )
% 5.24/5.52 = zero_zero_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_imp_mod_eq_0
% 5.24/5.52 thf(fact_4685_unit__imp__mod__eq__0,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.24/5.52 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.52
% 5.24/5.52 % unit_imp_mod_eq_0
% 5.24/5.52 thf(fact_4686_is__unit__power__iff,axiom,
% 5.24/5.52 ! [A: code_integer,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_power_iff
% 5.24/5.52 thf(fact_4687_is__unit__power__iff,axiom,
% 5.24/5.52 ! [A: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.24/5.52 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_power_iff
% 5.24/5.52 thf(fact_4688_is__unit__power__iff,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.24/5.52 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_power_iff
% 5.24/5.52 thf(fact_4689_dvd__imp__le,axiom,
% 5.24/5.52 ! [K: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ K @ N )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_imp_le
% 5.24/5.52 thf(fact_4690_dvd__mult__cancel,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.24/5.52 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.52 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel
% 5.24/5.52 thf(fact_4691_nat__mult__dvd__cancel1,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.24/5.52 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % nat_mult_dvd_cancel1
% 5.24/5.52 thf(fact_4692_bezout__add__strong__nat,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ? [D3: nat,X3: nat,Y3: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ D3 @ A )
% 5.24/5.52 & ( dvd_dvd_nat @ D3 @ B )
% 5.24/5.52 & ( ( times_times_nat @ A @ X3 )
% 5.24/5.52 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bezout_add_strong_nat
% 5.24/5.52 thf(fact_4693_mod__greater__zero__iff__not__dvd,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.52 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_greater_zero_iff_not_dvd
% 5.24/5.52 thf(fact_4694_set__decode__def,axiom,
% 5.24/5.52 ( nat_set_decode
% 5.24/5.52 = ( ^ [X2: nat] :
% 5.24/5.52 ( collect_nat
% 5.24/5.52 @ ^ [N2: nat] :
% 5.24/5.52 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % set_decode_def
% 5.24/5.52 thf(fact_4695_mod__eq__dvd__iff__nat,axiom,
% 5.24/5.52 ! [N: nat,M: nat,Q2: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.52 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.24/5.52 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.24/5.52 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_eq_dvd_iff_nat
% 5.24/5.52 thf(fact_4696_finite__divisors__nat,axiom,
% 5.24/5.52 ! [M: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.52 => ( finite_finite_nat
% 5.24/5.52 @ ( collect_nat
% 5.24/5.52 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % finite_divisors_nat
% 5.24/5.52 thf(fact_4697_even__zero,axiom,
% 5.24/5.52 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.24/5.52
% 5.24/5.52 % even_zero
% 5.24/5.52 thf(fact_4698_even__zero,axiom,
% 5.24/5.52 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.24/5.52
% 5.24/5.52 % even_zero
% 5.24/5.52 thf(fact_4699_even__zero,axiom,
% 5.24/5.52 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.24/5.52
% 5.24/5.52 % even_zero
% 5.24/5.52 thf(fact_4700_is__unitE,axiom,
% 5.24/5.52 ! [A: code_integer,C: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.24/5.52 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ! [B2: code_integer] :
% 5.24/5.52 ( ( B2 != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.24/5.52 = B2 )
% 5.24/5.52 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 5.24/5.52 = A )
% 5.24/5.52 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.24/5.52 = one_one_Code_integer )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.24/5.52 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unitE
% 5.24/5.52 thf(fact_4701_is__unitE,axiom,
% 5.24/5.52 ! [A: nat,C: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.24/5.52 => ~ ( ( A != zero_zero_nat )
% 5.24/5.52 => ! [B2: nat] :
% 5.24/5.52 ( ( B2 != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.24/5.52 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.24/5.52 = B2 )
% 5.24/5.52 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 5.24/5.52 = A )
% 5.24/5.52 => ( ( ( times_times_nat @ A @ B2 )
% 5.24/5.52 = one_one_nat )
% 5.24/5.52 => ( ( divide_divide_nat @ C @ A )
% 5.24/5.52 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unitE
% 5.24/5.52 thf(fact_4702_is__unitE,axiom,
% 5.24/5.52 ! [A: int,C: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.24/5.52 => ~ ( ( A != zero_zero_int )
% 5.24/5.52 => ! [B2: int] :
% 5.24/5.52 ( ( B2 != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.24/5.52 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.24/5.52 = B2 )
% 5.24/5.52 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 5.24/5.52 = A )
% 5.24/5.52 => ( ( ( times_times_int @ A @ B2 )
% 5.24/5.52 = one_one_int )
% 5.24/5.52 => ( ( divide_divide_int @ C @ A )
% 5.24/5.52 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unitE
% 5.24/5.52 thf(fact_4703_is__unit__div__mult__cancel__left,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult_cancel_left
% 5.24/5.52 thf(fact_4704_is__unit__div__mult__cancel__left,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.24/5.52 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult_cancel_left
% 5.24/5.52 thf(fact_4705_is__unit__div__mult__cancel__left,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( A != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.24/5.52 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult_cancel_left
% 5.24/5.52 thf(fact_4706_is__unit__div__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.24/5.52 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult_cancel_right
% 5.24/5.52 thf(fact_4707_is__unit__div__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ( A != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.24/5.52 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.24/5.52 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult_cancel_right
% 5.24/5.52 thf(fact_4708_is__unit__div__mult__cancel__right,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( A != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.24/5.52 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.24/5.52 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % is_unit_div_mult_cancel_right
% 5.24/5.52 thf(fact_4709_evenE,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ~ ! [B2: code_integer] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % evenE
% 5.24/5.52 thf(fact_4710_evenE,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ~ ! [B2: nat] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % evenE
% 5.24/5.52 thf(fact_4711_evenE,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ~ ! [B2: int] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % evenE
% 5.24/5.52 thf(fact_4712_odd__one,axiom,
% 5.24/5.52 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.24/5.52
% 5.24/5.52 % odd_one
% 5.24/5.52 thf(fact_4713_odd__one,axiom,
% 5.24/5.52 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.24/5.52
% 5.24/5.52 % odd_one
% 5.24/5.52 thf(fact_4714_odd__one,axiom,
% 5.24/5.52 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.24/5.52
% 5.24/5.52 % odd_one
% 5.24/5.52 thf(fact_4715_odd__even__add,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_even_add
% 5.24/5.52 thf(fact_4716_odd__even__add,axiom,
% 5.24/5.52 ! [A: nat,B: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.24/5.52 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_even_add
% 5.24/5.52 thf(fact_4717_odd__even__add,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.24/5.52 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_even_add
% 5.24/5.52 thf(fact_4718_bit__eq__rec,axiom,
% 5.24/5.52 ( ( ^ [Y6: code_integer,Z3: code_integer] : ( Y6 = Z3 ) )
% 5.24/5.52 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.24/5.52 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.24/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.24/5.52 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bit_eq_rec
% 5.24/5.52 thf(fact_4719_bit__eq__rec,axiom,
% 5.24/5.52 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.24/5.52 = ( ^ [A4: nat,B3: nat] :
% 5.24/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.24/5.52 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.24/5.52 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bit_eq_rec
% 5.24/5.52 thf(fact_4720_bit__eq__rec,axiom,
% 5.24/5.52 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.24/5.52 = ( ^ [A4: int,B3: int] :
% 5.24/5.52 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.24/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.24/5.52 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bit_eq_rec
% 5.24/5.52 thf(fact_4721_dvd__power__iff,axiom,
% 5.24/5.52 ! [X: code_integer,M: nat,N: nat] :
% 5.24/5.52 ( ( X != zero_z3403309356797280102nteger )
% 5.24/5.52 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.24/5.52 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_iff
% 5.24/5.52 thf(fact_4722_dvd__power__iff,axiom,
% 5.24/5.52 ! [X: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( X != zero_zero_nat )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.24/5.52 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_iff
% 5.24/5.52 thf(fact_4723_dvd__power__iff,axiom,
% 5.24/5.52 ! [X: int,M: nat,N: nat] :
% 5.24/5.52 ( ( X != zero_zero_int )
% 5.24/5.52 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.24/5.52 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_iff
% 5.24/5.52 thf(fact_4724_subset__decode__imp__le,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.24/5.52 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % subset_decode_imp_le
% 5.24/5.52 thf(fact_4725_dvd__power,axiom,
% 5.24/5.52 ! [N: nat,X: code_integer] :
% 5.24/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 | ( X = one_one_Code_integer ) )
% 5.24/5.52 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power
% 5.24/5.52 thf(fact_4726_dvd__power,axiom,
% 5.24/5.52 ! [N: nat,X: rat] :
% 5.24/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 | ( X = one_one_rat ) )
% 5.24/5.52 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power
% 5.24/5.52 thf(fact_4727_dvd__power,axiom,
% 5.24/5.52 ! [N: nat,X: nat] :
% 5.24/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 | ( X = one_one_nat ) )
% 5.24/5.52 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power
% 5.24/5.52 thf(fact_4728_dvd__power,axiom,
% 5.24/5.52 ! [N: nat,X: real] :
% 5.24/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 | ( X = one_one_real ) )
% 5.24/5.52 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power
% 5.24/5.52 thf(fact_4729_dvd__power,axiom,
% 5.24/5.52 ! [N: nat,X: int] :
% 5.24/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 | ( X = one_one_int ) )
% 5.24/5.52 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power
% 5.24/5.52 thf(fact_4730_dvd__power,axiom,
% 5.24/5.52 ! [N: nat,X: complex] :
% 5.24/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 | ( X = one_one_complex ) )
% 5.24/5.52 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power
% 5.24/5.52 thf(fact_4731_div2__even__ext__nat,axiom,
% 5.24/5.52 ! [X: nat,Y4: nat] :
% 5.24/5.52 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = ( divide_divide_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.52 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.24/5.52 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y4 ) )
% 5.24/5.52 => ( X = Y4 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % div2_even_ext_nat
% 5.24/5.52 thf(fact_4732_even__even__mod__4__iff,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_even_mod_4_iff
% 5.24/5.52 thf(fact_4733_dvd__mult__cancel1,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.24/5.52 = ( N = one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel1
% 5.24/5.52 thf(fact_4734_dvd__mult__cancel2,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.24/5.52 = ( N = one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_mult_cancel2
% 5.24/5.52 thf(fact_4735_dvd__minus__add,axiom,
% 5.24/5.52 ! [Q2: nat,N: nat,R2: nat,M: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.24/5.52 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.24/5.52 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.24/5.52 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_minus_add
% 5.24/5.52 thf(fact_4736_power__dvd__imp__le,axiom,
% 5.24/5.52 ! [I2: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 5.24/5.52 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.24/5.52 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_dvd_imp_le
% 5.24/5.52 thf(fact_4737_mod__nat__eqI,axiom,
% 5.24/5.52 ! [R2: nat,N: nat,M: nat] :
% 5.24/5.52 ( ( ord_less_nat @ R2 @ N )
% 5.24/5.52 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.24/5.52 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.24/5.52 => ( ( modulo_modulo_nat @ M @ N )
% 5.24/5.52 = R2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_nat_eqI
% 5.24/5.52 thf(fact_4738_bset_I9_J,axiom,
% 5.24/5.52 ! [D: int,D4: int,B5: set_int,T: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.24/5.52 => ! [X5: int] :
% 5.24/5.52 ( ! [Xa3: int] :
% 5.24/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.52 => ! [Xb3: int] :
% 5.24/5.52 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.52 => ( X5
% 5.24/5.52 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.52 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.24/5.52 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bset(9)
% 5.24/5.52 thf(fact_4739_bset_I10_J,axiom,
% 5.24/5.52 ! [D: int,D4: int,B5: set_int,T: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.24/5.52 => ! [X5: int] :
% 5.24/5.52 ( ! [Xa3: int] :
% 5.24/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.52 => ! [Xb3: int] :
% 5.24/5.52 ( ( member_int @ Xb3 @ B5 )
% 5.24/5.52 => ( X5
% 5.24/5.52 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.52 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.24/5.52 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % bset(10)
% 5.24/5.52 thf(fact_4740_aset_I9_J,axiom,
% 5.24/5.52 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.24/5.52 => ! [X5: int] :
% 5.24/5.52 ( ! [Xa3: int] :
% 5.24/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.52 => ! [Xb3: int] :
% 5.24/5.52 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.52 => ( X5
% 5.24/5.52 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.52 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.24/5.52 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % aset(9)
% 5.24/5.52 thf(fact_4741_aset_I10_J,axiom,
% 5.24/5.52 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.24/5.52 => ! [X5: int] :
% 5.24/5.52 ( ! [Xa3: int] :
% 5.24/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.24/5.52 => ! [Xb3: int] :
% 5.24/5.52 ( ( member_int @ Xb3 @ A2 )
% 5.24/5.52 => ( X5
% 5.24/5.52 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.24/5.52 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.24/5.52 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % aset(10)
% 5.24/5.52 thf(fact_4742_even__two__times__div__two,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_two_times_div_two
% 5.24/5.52 thf(fact_4743_even__two__times__div__two,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_two_times_div_two
% 5.24/5.52 thf(fact_4744_even__two__times__div__two,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_two_times_div_two
% 5.24/5.52 thf(fact_4745_even__iff__mod__2__eq__zero,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_iff_mod_2_eq_zero
% 5.24/5.52 thf(fact_4746_even__iff__mod__2__eq__zero,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = zero_zero_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_iff_mod_2_eq_zero
% 5.24/5.52 thf(fact_4747_even__iff__mod__2__eq__zero,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_iff_mod_2_eq_zero
% 5.24/5.52 thf(fact_4748_odd__iff__mod__2__eq__one,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.52 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = one_one_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_iff_mod_2_eq_one
% 5.24/5.52 thf(fact_4749_odd__iff__mod__2__eq__one,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.52 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = one_one_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_iff_mod_2_eq_one
% 5.24/5.52 thf(fact_4750_odd__iff__mod__2__eq__one,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.52 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = one_one_Code_integer ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_iff_mod_2_eq_one
% 5.24/5.52 thf(fact_4751_power__mono__odd,axiom,
% 5.24/5.52 ! [N: nat,A: real,B: real] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( ord_less_eq_real @ A @ B )
% 5.24/5.52 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_mono_odd
% 5.24/5.52 thf(fact_4752_power__mono__odd,axiom,
% 5.24/5.52 ! [N: nat,A: rat,B: rat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.52 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_mono_odd
% 5.24/5.52 thf(fact_4753_power__mono__odd,axiom,
% 5.24/5.52 ! [N: nat,A: int,B: int] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( ord_less_eq_int @ A @ B )
% 5.24/5.52 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_mono_odd
% 5.24/5.52 thf(fact_4754_odd__pos,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % odd_pos
% 5.24/5.52 thf(fact_4755_dvd__power__iff__le,axiom,
% 5.24/5.52 ! [K: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.24/5.52 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.24/5.52 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % dvd_power_iff_le
% 5.24/5.52 thf(fact_4756_signed__take__bit__int__less__exp,axiom,
% 5.24/5.52 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_int_less_exp
% 5.24/5.52 thf(fact_4757_even__unset__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 | ( M = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_unset_bit_iff
% 5.24/5.52 thf(fact_4758_even__unset__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 | ( M = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_unset_bit_iff
% 5.24/5.52 thf(fact_4759_even__unset__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 | ( M = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_unset_bit_iff
% 5.24/5.52 thf(fact_4760_even__set__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 & ( M != zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_set_bit_iff
% 5.24/5.52 thf(fact_4761_even__set__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 & ( M != zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_set_bit_iff
% 5.24/5.52 thf(fact_4762_even__set__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 & ( M != zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_set_bit_iff
% 5.24/5.52 thf(fact_4763_even__flip__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: code_integer] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 != ( M = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_flip_bit_iff
% 5.24/5.52 thf(fact_4764_even__flip__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 != ( M = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_flip_bit_iff
% 5.24/5.52 thf(fact_4765_even__flip__bit__iff,axiom,
% 5.24/5.52 ! [M: nat,A: nat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 != ( M = zero_zero_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_flip_bit_iff
% 5.24/5.52 thf(fact_4766_even__diff__iff,axiom,
% 5.24/5.52 ! [K: int,L2: int] :
% 5.24/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.24/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_diff_iff
% 5.24/5.52 thf(fact_4767_oddE,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ~ ! [B2: code_integer] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % oddE
% 5.24/5.52 thf(fact_4768_oddE,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ~ ! [B2: nat] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % oddE
% 5.24/5.52 thf(fact_4769_oddE,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ~ ! [B2: int] :
% 5.24/5.52 ( A
% 5.24/5.52 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % oddE
% 5.24/5.52 thf(fact_4770_mod2__eq__if,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = zero_zero_nat ) )
% 5.24/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 = one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod2_eq_if
% 5.24/5.52 thf(fact_4771_mod2__eq__if,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = zero_zero_int ) )
% 5.24/5.52 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 = one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod2_eq_if
% 5.24/5.52 thf(fact_4772_mod2__eq__if,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = zero_z3403309356797280102nteger ) )
% 5.24/5.52 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 = one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod2_eq_if
% 5.24/5.52 thf(fact_4773_parity__cases,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 != zero_zero_nat ) )
% 5.24/5.52 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.52 != one_one_nat ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % parity_cases
% 5.24/5.52 thf(fact_4774_parity__cases,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 != zero_zero_int ) )
% 5.24/5.52 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.52 != one_one_int ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % parity_cases
% 5.24/5.52 thf(fact_4775_parity__cases,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 != zero_z3403309356797280102nteger ) )
% 5.24/5.52 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.24/5.52 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.52 != one_one_Code_integer ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % parity_cases
% 5.24/5.52 thf(fact_4776_zero__le__power__eq,axiom,
% 5.24/5.52 ! [A: real,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_power_eq
% 5.24/5.52 thf(fact_4777_zero__le__power__eq,axiom,
% 5.24/5.52 ! [A: rat,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_power_eq
% 5.24/5.52 thf(fact_4778_zero__le__power__eq,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.24/5.52 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_power_eq
% 5.24/5.52 thf(fact_4779_zero__le__odd__power,axiom,
% 5.24/5.52 ! [N: nat,A: real] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.24/5.52 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_odd_power
% 5.24/5.52 thf(fact_4780_zero__le__odd__power,axiom,
% 5.24/5.52 ! [N: nat,A: rat] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.24/5.52 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_odd_power
% 5.24/5.52 thf(fact_4781_zero__le__odd__power,axiom,
% 5.24/5.52 ! [N: nat,A: int] :
% 5.24/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.24/5.52 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_odd_power
% 5.24/5.52 thf(fact_4782_zero__le__even__power,axiom,
% 5.24/5.52 ! [N: nat,A: real] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_even_power
% 5.24/5.52 thf(fact_4783_zero__le__even__power,axiom,
% 5.24/5.52 ! [N: nat,A: rat] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_even_power
% 5.24/5.52 thf(fact_4784_zero__le__even__power,axiom,
% 5.24/5.52 ! [N: nat,A: int] :
% 5.24/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_le_even_power
% 5.24/5.52 thf(fact_4785_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.24/5.52 ! [K: int,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.24/5.52 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_int_greater_eq_self_iff
% 5.24/5.52 thf(fact_4786_signed__take__bit__int__less__self__iff,axiom,
% 5.24/5.52 ! [N: nat,K: int] :
% 5.24/5.52 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.24/5.52 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_int_less_self_iff
% 5.24/5.52 thf(fact_4787_zero__less__power__eq,axiom,
% 5.24/5.52 ! [A: real,N: nat] :
% 5.24/5.52 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.24/5.52 = ( ( N = zero_zero_nat )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( A != zero_zero_real ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_power_eq
% 5.24/5.52 thf(fact_4788_zero__less__power__eq,axiom,
% 5.24/5.52 ! [A: rat,N: nat] :
% 5.24/5.52 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.24/5.52 = ( ( N = zero_zero_nat )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( A != zero_zero_rat ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_power_eq
% 5.24/5.52 thf(fact_4789_zero__less__power__eq,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.24/5.52 = ( ( N = zero_zero_nat )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( A != zero_zero_int ) )
% 5.24/5.52 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_power_eq
% 5.24/5.52 thf(fact_4790_signed__take__bit__int__less__eq,axiom,
% 5.24/5.52 ! [N: nat,K: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.24/5.52 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_int_less_eq
% 5.24/5.52 thf(fact_4791_even__mask__div__iff_H,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mask_div_iff'
% 5.24/5.52 thf(fact_4792_even__mask__div__iff_H,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mask_div_iff'
% 5.24/5.52 thf(fact_4793_even__mask__div__iff_H,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mask_div_iff'
% 5.24/5.52 thf(fact_4794_power__le__zero__eq,axiom,
% 5.24/5.52 ! [A: real,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.24/5.52 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_zero_eq
% 5.24/5.52 thf(fact_4795_power__le__zero__eq,axiom,
% 5.24/5.52 ! [A: rat,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.24/5.52 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_zero_eq
% 5.24/5.52 thf(fact_4796_power__le__zero__eq,axiom,
% 5.24/5.52 ! [A: int,N: nat] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.24/5.52 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.52 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.24/5.52 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % power_le_zero_eq
% 5.24/5.52 thf(fact_4797_option_Osize__gen_I1_J,axiom,
% 5.24/5.52 ! [X: nat > nat] :
% 5.24/5.52 ( ( size_option_nat @ X @ none_nat )
% 5.24/5.52 = ( suc @ zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % option.size_gen(1)
% 5.24/5.52 thf(fact_4798_option_Osize__gen_I1_J,axiom,
% 5.24/5.52 ! [X: product_prod_nat_nat > nat] :
% 5.24/5.52 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.24/5.52 = ( suc @ zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % option.size_gen(1)
% 5.24/5.52 thf(fact_4799_option_Osize__gen_I1_J,axiom,
% 5.24/5.52 ! [X: num > nat] :
% 5.24/5.52 ( ( size_option_num @ X @ none_num )
% 5.24/5.52 = ( suc @ zero_zero_nat ) ) ).
% 5.24/5.52
% 5.24/5.52 % option.size_gen(1)
% 5.24/5.52 thf(fact_4800_even__mod__4__div__2,axiom,
% 5.24/5.52 ! [N: nat] :
% 5.24/5.52 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.52 = ( suc @ zero_zero_nat ) )
% 5.24/5.52 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mod_4_div_2
% 5.24/5.52 thf(fact_4801_even__mask__div__iff,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = zero_z3403309356797280102nteger )
% 5.24/5.52 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mask_div_iff
% 5.24/5.52 thf(fact_4802_even__mask__div__iff,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mask_div_iff
% 5.24/5.52 thf(fact_4803_even__mask__div__iff,axiom,
% 5.24/5.52 ! [M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = zero_zero_int )
% 5.24/5.52 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mask_div_iff
% 5.24/5.52 thf(fact_4804_even__mult__exp__div__exp__iff,axiom,
% 5.24/5.52 ! [A: code_integer,M: nat,N: nat] :
% 5.24/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.52 = ( ( ord_less_nat @ N @ M )
% 5.24/5.52 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = zero_z3403309356797280102nteger )
% 5.24/5.52 | ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mult_exp_div_exp_iff
% 5.24/5.52 thf(fact_4805_even__mult__exp__div__exp__iff,axiom,
% 5.24/5.52 ! [A: nat,M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ( ord_less_nat @ N @ M )
% 5.24/5.52 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = zero_zero_nat )
% 5.24/5.52 | ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 & ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mult_exp_div_exp_iff
% 5.24/5.52 thf(fact_4806_even__mult__exp__div__exp__iff,axiom,
% 5.24/5.52 ! [A: int,M: nat,N: nat] :
% 5.24/5.52 ( ( 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 ) ) )
% 5.24/5.52 = ( ( ord_less_nat @ N @ M )
% 5.24/5.52 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.24/5.52 = zero_zero_int )
% 5.24/5.52 | ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.52 & ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % even_mult_exp_div_exp_iff
% 5.24/5.52 thf(fact_4807_ex__min__if__finite,axiom,
% 5.24/5.52 ! [S3: set_real] :
% 5.24/5.52 ( ( finite_finite_real @ S3 )
% 5.24/5.52 => ( ( S3 != bot_bot_set_real )
% 5.24/5.52 => ? [X3: real] :
% 5.24/5.52 ( ( member_real @ X3 @ S3 )
% 5.24/5.52 & ~ ? [Xa: real] :
% 5.24/5.52 ( ( member_real @ Xa @ S3 )
% 5.24/5.52 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % ex_min_if_finite
% 5.24/5.52 thf(fact_4808_ex__min__if__finite,axiom,
% 5.24/5.52 ! [S3: set_rat] :
% 5.24/5.52 ( ( finite_finite_rat @ S3 )
% 5.24/5.52 => ( ( S3 != bot_bot_set_rat )
% 5.24/5.52 => ? [X3: rat] :
% 5.24/5.52 ( ( member_rat @ X3 @ S3 )
% 5.24/5.52 & ~ ? [Xa: rat] :
% 5.24/5.52 ( ( member_rat @ Xa @ S3 )
% 5.24/5.52 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % ex_min_if_finite
% 5.24/5.52 thf(fact_4809_ex__min__if__finite,axiom,
% 5.24/5.52 ! [S3: set_num] :
% 5.24/5.52 ( ( finite_finite_num @ S3 )
% 5.24/5.52 => ( ( S3 != bot_bot_set_num )
% 5.24/5.52 => ? [X3: num] :
% 5.24/5.52 ( ( member_num @ X3 @ S3 )
% 5.24/5.52 & ~ ? [Xa: num] :
% 5.24/5.52 ( ( member_num @ Xa @ S3 )
% 5.24/5.52 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % ex_min_if_finite
% 5.24/5.52 thf(fact_4810_ex__min__if__finite,axiom,
% 5.24/5.52 ! [S3: set_nat] :
% 5.24/5.52 ( ( finite_finite_nat @ S3 )
% 5.24/5.52 => ( ( S3 != bot_bot_set_nat )
% 5.24/5.52 => ? [X3: nat] :
% 5.24/5.52 ( ( member_nat @ X3 @ S3 )
% 5.24/5.52 & ~ ? [Xa: nat] :
% 5.24/5.52 ( ( member_nat @ Xa @ S3 )
% 5.24/5.52 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % ex_min_if_finite
% 5.24/5.52 thf(fact_4811_ex__min__if__finite,axiom,
% 5.24/5.52 ! [S3: set_int] :
% 5.24/5.52 ( ( finite_finite_int @ S3 )
% 5.24/5.52 => ( ( S3 != bot_bot_set_int )
% 5.24/5.52 => ? [X3: int] :
% 5.24/5.52 ( ( member_int @ X3 @ S3 )
% 5.24/5.52 & ~ ? [Xa: int] :
% 5.24/5.52 ( ( member_int @ Xa @ S3 )
% 5.24/5.52 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % ex_min_if_finite
% 5.24/5.52 thf(fact_4812_vebt__buildup_Oelims,axiom,
% 5.24/5.52 ! [X: nat,Y4: vEBT_VEBT] :
% 5.24/5.52 ( ( ( vEBT_vebt_buildup @ X )
% 5.24/5.52 = Y4 )
% 5.24/5.52 => ( ( ( X = zero_zero_nat )
% 5.24/5.52 => ( Y4
% 5.24/5.52 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.24/5.52 => ( ( ( X
% 5.24/5.52 = ( suc @ zero_zero_nat ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.24/5.52 => ~ ! [Va3: nat] :
% 5.24/5.52 ( ( X
% 5.24/5.52 = ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.52 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( 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 ) ) ) ) ) ) )
% 5.24/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.52 => ( Y4
% 5.24/5.52 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % vebt_buildup.elims
% 5.24/5.52 thf(fact_4813_signed__take__bit__rec,axiom,
% 5.24/5.52 ( bit_ri6519982836138164636nteger
% 5.24/5.52 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_rec
% 5.24/5.52 thf(fact_4814_signed__take__bit__rec,axiom,
% 5.24/5.52 ( bit_ri631733984087533419it_int
% 5.24/5.52 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % signed_take_bit_rec
% 5.24/5.52 thf(fact_4815_flip__bit__0,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % flip_bit_0
% 5.24/5.52 thf(fact_4816_flip__bit__0,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.24/5.52 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % flip_bit_0
% 5.24/5.52 thf(fact_4817_flip__bit__0,axiom,
% 5.24/5.52 ! [A: nat] :
% 5.24/5.52 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.24/5.52 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % flip_bit_0
% 5.24/5.52 thf(fact_4818_diff__shunt__var,axiom,
% 5.24/5.52 ! [X: set_int,Y4: set_int] :
% 5.24/5.52 ( ( ( minus_minus_set_int @ X @ Y4 )
% 5.24/5.52 = bot_bot_set_int )
% 5.24/5.52 = ( ord_less_eq_set_int @ X @ Y4 ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_shunt_var
% 5.24/5.52 thf(fact_4819_diff__shunt__var,axiom,
% 5.24/5.52 ! [X: set_real,Y4: set_real] :
% 5.24/5.52 ( ( ( minus_minus_set_real @ X @ Y4 )
% 5.24/5.52 = bot_bot_set_real )
% 5.24/5.52 = ( ord_less_eq_set_real @ X @ Y4 ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_shunt_var
% 5.24/5.52 thf(fact_4820_diff__shunt__var,axiom,
% 5.24/5.52 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.52 ( ( ( minus_minus_set_nat @ X @ Y4 )
% 5.24/5.52 = bot_bot_set_nat )
% 5.24/5.52 = ( ord_less_eq_set_nat @ X @ Y4 ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_shunt_var
% 5.24/5.52 thf(fact_4821_add__scale__eq__noteq,axiom,
% 5.24/5.52 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.24/5.52 ( ( R2 != zero_zero_complex )
% 5.24/5.52 => ( ( ( A = B )
% 5.24/5.52 & ( C != D ) )
% 5.24/5.52 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.24/5.52 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_scale_eq_noteq
% 5.24/5.52 thf(fact_4822_add__scale__eq__noteq,axiom,
% 5.24/5.52 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.24/5.52 ( ( R2 != zero_zero_real )
% 5.24/5.52 => ( ( ( A = B )
% 5.24/5.52 & ( C != D ) )
% 5.24/5.52 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.24/5.52 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_scale_eq_noteq
% 5.24/5.52 thf(fact_4823_add__scale__eq__noteq,axiom,
% 5.24/5.52 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.24/5.52 ( ( R2 != zero_zero_rat )
% 5.24/5.52 => ( ( ( A = B )
% 5.24/5.52 & ( C != D ) )
% 5.24/5.52 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.24/5.52 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_scale_eq_noteq
% 5.24/5.52 thf(fact_4824_add__scale__eq__noteq,axiom,
% 5.24/5.52 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.24/5.52 ( ( R2 != zero_zero_nat )
% 5.24/5.52 => ( ( ( A = B )
% 5.24/5.52 & ( C != D ) )
% 5.24/5.52 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.24/5.52 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_scale_eq_noteq
% 5.24/5.52 thf(fact_4825_add__scale__eq__noteq,axiom,
% 5.24/5.52 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.24/5.52 ( ( R2 != zero_zero_int )
% 5.24/5.52 => ( ( ( A = B )
% 5.24/5.52 & ( C != D ) )
% 5.24/5.52 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.24/5.52 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_scale_eq_noteq
% 5.24/5.52 thf(fact_4826_artanh__def,axiom,
% 5.24/5.52 ( artanh_real
% 5.24/5.52 = ( ^ [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 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % artanh_def
% 5.24/5.52 thf(fact_4827_Sum__Icc__int,axiom,
% 5.24/5.52 ! [M: int,N: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ M @ N )
% 5.24/5.52 => ( ( groups4538972089207619220nt_int
% 5.24/5.52 @ ^ [X2: int] : X2
% 5.24/5.52 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.24/5.52 = ( 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 ) ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % Sum_Icc_int
% 5.24/5.52 thf(fact_4828_intind,axiom,
% 5.24/5.52 ! [I2: nat,N: nat,P: nat > $o,X: nat] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ N )
% 5.24/5.52 => ( ( P @ X )
% 5.24/5.52 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % intind
% 5.24/5.52 thf(fact_4829_intind,axiom,
% 5.24/5.52 ! [I2: nat,N: nat,P: int > $o,X: int] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ N )
% 5.24/5.52 => ( ( P @ X )
% 5.24/5.52 => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % intind
% 5.24/5.52 thf(fact_4830_intind,axiom,
% 5.24/5.52 ! [I2: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.24/5.52 ( ( ord_less_nat @ I2 @ N )
% 5.24/5.52 => ( ( P @ X )
% 5.24/5.52 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % intind
% 5.24/5.52 thf(fact_4831_verit__minus__simplify_I4_J,axiom,
% 5.24/5.52 ! [B: real] :
% 5.24/5.52 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(4)
% 5.24/5.52 thf(fact_4832_verit__minus__simplify_I4_J,axiom,
% 5.24/5.52 ! [B: int] :
% 5.24/5.52 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(4)
% 5.24/5.52 thf(fact_4833_verit__minus__simplify_I4_J,axiom,
% 5.24/5.52 ! [B: complex] :
% 5.24/5.52 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(4)
% 5.24/5.52 thf(fact_4834_verit__minus__simplify_I4_J,axiom,
% 5.24/5.52 ! [B: rat] :
% 5.24/5.52 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(4)
% 5.24/5.52 thf(fact_4835_verit__minus__simplify_I4_J,axiom,
% 5.24/5.52 ! [B: code_integer] :
% 5.24/5.52 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(4)
% 5.24/5.52 thf(fact_4836_compl__le__compl__iff,axiom,
% 5.24/5.52 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.52 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y4 ) )
% 5.24/5.52 = ( ord_less_eq_set_nat @ Y4 @ X ) ) ).
% 5.24/5.52
% 5.24/5.52 % compl_le_compl_iff
% 5.24/5.52 thf(fact_4837_neg__le__iff__le,axiom,
% 5.24/5.52 ! [B: real,A: real] :
% 5.24/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_iff_le
% 5.24/5.52 thf(fact_4838_neg__le__iff__le,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_iff_le
% 5.24/5.52 thf(fact_4839_neg__le__iff__le,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_iff_le
% 5.24/5.52 thf(fact_4840_neg__le__iff__le,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_iff_le
% 5.24/5.52 thf(fact_4841_neg__less__iff__less,axiom,
% 5.24/5.52 ! [B: real,A: real] :
% 5.24/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = ( ord_less_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_iff_less
% 5.24/5.52 thf(fact_4842_neg__less__iff__less,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = ( ord_less_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_iff_less
% 5.24/5.52 thf(fact_4843_neg__less__iff__less,axiom,
% 5.24/5.52 ! [B: rat,A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = ( ord_less_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_iff_less
% 5.24/5.52 thf(fact_4844_neg__less__iff__less,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_iff_less
% 5.24/5.52 thf(fact_4845_neg__numeral__eq__iff,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.24/5.52 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.52 = ( M = N ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_numeral_eq_iff
% 5.24/5.52 thf(fact_4846_neg__numeral__eq__iff,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.24/5.52 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.52 = ( M = N ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_numeral_eq_iff
% 5.24/5.52 thf(fact_4847_neg__numeral__eq__iff,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.52 = ( M = N ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_numeral_eq_iff
% 5.24/5.52 thf(fact_4848_neg__numeral__eq__iff,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.24/5.52 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.52 = ( M = N ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_numeral_eq_iff
% 5.24/5.52 thf(fact_4849_neg__numeral__eq__iff,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.52 = ( M = N ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_numeral_eq_iff
% 5.24/5.52 thf(fact_4850_mult__minus__left,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.52 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_left
% 5.24/5.52 thf(fact_4851_mult__minus__left,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.52 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_left
% 5.24/5.52 thf(fact_4852_mult__minus__left,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_left
% 5.24/5.52 thf(fact_4853_mult__minus__left,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.52 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_left
% 5.24/5.52 thf(fact_4854_mult__minus__left,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_left
% 5.24/5.52 thf(fact_4855_minus__mult__minus,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.24/5.52 = ( times_times_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mult_minus
% 5.24/5.52 thf(fact_4856_minus__mult__minus,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.24/5.52 = ( times_times_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mult_minus
% 5.24/5.52 thf(fact_4857_minus__mult__minus,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.52 = ( times_times_complex @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mult_minus
% 5.24/5.52 thf(fact_4858_minus__mult__minus,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.24/5.52 = ( times_times_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mult_minus
% 5.24/5.52 thf(fact_4859_minus__mult__minus,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.52 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mult_minus
% 5.24/5.52 thf(fact_4860_mult__minus__right,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.24/5.52 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_right
% 5.24/5.52 thf(fact_4861_mult__minus__right,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.52 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_right
% 5.24/5.52 thf(fact_4862_mult__minus__right,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_right
% 5.24/5.52 thf(fact_4863_mult__minus__right,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.24/5.52 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_right
% 5.24/5.52 thf(fact_4864_mult__minus__right,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus_right
% 5.24/5.52 thf(fact_4865_add__minus__cancel,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % add_minus_cancel
% 5.24/5.52 thf(fact_4866_add__minus__cancel,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % add_minus_cancel
% 5.24/5.52 thf(fact_4867_add__minus__cancel,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % add_minus_cancel
% 5.24/5.52 thf(fact_4868_add__minus__cancel,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % add_minus_cancel
% 5.24/5.52 thf(fact_4869_add__minus__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % add_minus_cancel
% 5.24/5.52 thf(fact_4870_minus__add__cancel,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_cancel
% 5.24/5.52 thf(fact_4871_minus__add__cancel,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_cancel
% 5.24/5.52 thf(fact_4872_minus__add__cancel,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_cancel
% 5.24/5.52 thf(fact_4873_minus__add__cancel,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_cancel
% 5.24/5.52 thf(fact_4874_minus__add__cancel,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.24/5.52 = B ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_cancel
% 5.24/5.52 thf(fact_4875_minus__add__distrib,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.24/5.52 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_distrib
% 5.24/5.52 thf(fact_4876_minus__add__distrib,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.24/5.52 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_distrib
% 5.24/5.52 thf(fact_4877_minus__add__distrib,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.24/5.52 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_distrib
% 5.24/5.52 thf(fact_4878_minus__add__distrib,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.24/5.52 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_distrib
% 5.24/5.52 thf(fact_4879_minus__add__distrib,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_add_distrib
% 5.24/5.52 thf(fact_4880_div__minus__minus,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.24/5.52 = ( divide_divide_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_minus_minus
% 5.24/5.52 thf(fact_4881_div__minus__minus,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.52 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_minus_minus
% 5.24/5.52 thf(fact_4882_mod__minus__minus,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.24/5.52 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_minus_minus
% 5.24/5.52 thf(fact_4883_mod__minus__minus,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % mod_minus_minus
% 5.24/5.52 thf(fact_4884_of__bool__less__eq__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.24/5.52 = ( P
% 5.24/5.52 => Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_eq_iff
% 5.24/5.52 thf(fact_4885_of__bool__less__eq__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.24/5.52 = ( P
% 5.24/5.52 => Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_eq_iff
% 5.24/5.52 thf(fact_4886_of__bool__less__eq__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.24/5.52 = ( P
% 5.24/5.52 => Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_eq_iff
% 5.24/5.52 thf(fact_4887_of__bool__less__eq__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.24/5.52 = ( P
% 5.24/5.52 => Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_eq_iff
% 5.24/5.52 thf(fact_4888_real__add__minus__iff,axiom,
% 5.24/5.52 ! [X: real,A: real] :
% 5.24/5.52 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = zero_zero_real )
% 5.24/5.52 = ( X = A ) ) ).
% 5.24/5.52
% 5.24/5.52 % real_add_minus_iff
% 5.24/5.52 thf(fact_4889_of__bool__less__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.24/5.52 = ( ~ P
% 5.24/5.52 & Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_iff
% 5.24/5.52 thf(fact_4890_of__bool__less__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.24/5.52 = ( ~ P
% 5.24/5.52 & Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_iff
% 5.24/5.52 thf(fact_4891_of__bool__less__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.24/5.52 = ( ~ P
% 5.24/5.52 & Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_iff
% 5.24/5.52 thf(fact_4892_of__bool__less__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.24/5.52 = ( ~ P
% 5.24/5.52 & Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_iff
% 5.24/5.52 thf(fact_4893_of__bool__less__iff,axiom,
% 5.24/5.52 ! [P: $o,Q: $o] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.24/5.52 = ( ~ P
% 5.24/5.52 & Q ) ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_less_iff
% 5.24/5.52 thf(fact_4894_of__bool__eq_I2_J,axiom,
% 5.24/5.52 ( ( zero_n1201886186963655149omplex @ $true )
% 5.24/5.52 = one_one_complex ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq(2)
% 5.24/5.52 thf(fact_4895_of__bool__eq_I2_J,axiom,
% 5.24/5.52 ( ( zero_n3304061248610475627l_real @ $true )
% 5.24/5.52 = one_one_real ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq(2)
% 5.24/5.52 thf(fact_4896_of__bool__eq_I2_J,axiom,
% 5.24/5.52 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.24/5.52 = one_one_rat ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq(2)
% 5.24/5.52 thf(fact_4897_of__bool__eq_I2_J,axiom,
% 5.24/5.52 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.24/5.52 = one_one_nat ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq(2)
% 5.24/5.52 thf(fact_4898_of__bool__eq_I2_J,axiom,
% 5.24/5.52 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.24/5.52 = one_one_int ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq(2)
% 5.24/5.52 thf(fact_4899_of__bool__eq_I2_J,axiom,
% 5.24/5.52 ( ( zero_n356916108424825756nteger @ $true )
% 5.24/5.52 = one_one_Code_integer ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq(2)
% 5.24/5.52 thf(fact_4900_of__bool__eq__1__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.24/5.52 = one_one_complex )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq_1_iff
% 5.24/5.52 thf(fact_4901_of__bool__eq__1__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.24/5.52 = one_one_real )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq_1_iff
% 5.24/5.52 thf(fact_4902_of__bool__eq__1__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.24/5.52 = one_one_rat )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq_1_iff
% 5.24/5.52 thf(fact_4903_of__bool__eq__1__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.24/5.52 = one_one_nat )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq_1_iff
% 5.24/5.52 thf(fact_4904_of__bool__eq__1__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.24/5.52 = one_one_int )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq_1_iff
% 5.24/5.52 thf(fact_4905_of__bool__eq__1__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ( zero_n356916108424825756nteger @ P )
% 5.24/5.52 = one_one_Code_integer )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % of_bool_eq_1_iff
% 5.24/5.52 thf(fact_4906_length__replicate,axiom,
% 5.24/5.52 ! [N: nat,X: vEBT_VEBT] :
% 5.24/5.52 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.24/5.52 = N ) ).
% 5.24/5.52
% 5.24/5.52 % length_replicate
% 5.24/5.52 thf(fact_4907_length__replicate,axiom,
% 5.24/5.52 ! [N: nat,X: $o] :
% 5.24/5.52 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 5.24/5.52 = N ) ).
% 5.24/5.52
% 5.24/5.52 % length_replicate
% 5.24/5.52 thf(fact_4908_length__replicate,axiom,
% 5.24/5.52 ! [N: nat,X: nat] :
% 5.24/5.52 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 5.24/5.52 = N ) ).
% 5.24/5.52
% 5.24/5.52 % length_replicate
% 5.24/5.52 thf(fact_4909_length__replicate,axiom,
% 5.24/5.52 ! [N: nat,X: int] :
% 5.24/5.52 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 5.24/5.52 = N ) ).
% 5.24/5.52
% 5.24/5.52 % length_replicate
% 5.24/5.52 thf(fact_4910_neg__0__le__iff__le,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_le_iff_le
% 5.24/5.52 thf(fact_4911_neg__0__le__iff__le,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_le_iff_le
% 5.24/5.52 thf(fact_4912_neg__0__le__iff__le,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_le_iff_le
% 5.24/5.52 thf(fact_4913_neg__0__le__iff__le,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_le_iff_le
% 5.24/5.52 thf(fact_4914_neg__le__0__iff__le,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.24/5.52 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_0_iff_le
% 5.24/5.52 thf(fact_4915_neg__le__0__iff__le,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.24/5.52 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_0_iff_le
% 5.24/5.52 thf(fact_4916_neg__le__0__iff__le,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.24/5.52 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_0_iff_le
% 5.24/5.52 thf(fact_4917_neg__le__0__iff__le,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.24/5.52 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_le_0_iff_le
% 5.24/5.52 thf(fact_4918_less__eq__neg__nonpos,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_eq_neg_nonpos
% 5.24/5.52 thf(fact_4919_less__eq__neg__nonpos,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_eq_neg_nonpos
% 5.24/5.52 thf(fact_4920_less__eq__neg__nonpos,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_eq_neg_nonpos
% 5.24/5.52 thf(fact_4921_less__eq__neg__nonpos,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_eq_neg_nonpos
% 5.24/5.52 thf(fact_4922_neg__less__eq__nonneg,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.24/5.52 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_eq_nonneg
% 5.24/5.52 thf(fact_4923_neg__less__eq__nonneg,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.24/5.52 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_eq_nonneg
% 5.24/5.52 thf(fact_4924_neg__less__eq__nonneg,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.24/5.52 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_eq_nonneg
% 5.24/5.52 thf(fact_4925_neg__less__eq__nonneg,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.24/5.52 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_eq_nonneg
% 5.24/5.52 thf(fact_4926_neg__less__0__iff__less,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.24/5.52 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_0_iff_less
% 5.24/5.52 thf(fact_4927_neg__less__0__iff__less,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.24/5.52 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_0_iff_less
% 5.24/5.52 thf(fact_4928_neg__less__0__iff__less,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.24/5.52 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_0_iff_less
% 5.24/5.52 thf(fact_4929_neg__less__0__iff__less,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.24/5.52 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_0_iff_less
% 5.24/5.52 thf(fact_4930_neg__0__less__iff__less,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_less_iff_less
% 5.24/5.52 thf(fact_4931_neg__0__less__iff__less,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_less_iff_less
% 5.24/5.52 thf(fact_4932_neg__0__less__iff__less,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_less_iff_less
% 5.24/5.52 thf(fact_4933_neg__0__less__iff__less,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_0_less_iff_less
% 5.24/5.52 thf(fact_4934_neg__less__pos,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.24/5.52 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_pos
% 5.24/5.52 thf(fact_4935_neg__less__pos,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.24/5.52 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_pos
% 5.24/5.52 thf(fact_4936_neg__less__pos,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.24/5.52 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_pos
% 5.24/5.52 thf(fact_4937_neg__less__pos,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.24/5.52 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % neg_less_pos
% 5.24/5.52 thf(fact_4938_less__neg__neg,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_neg_neg
% 5.24/5.52 thf(fact_4939_less__neg__neg,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_neg_neg
% 5.24/5.52 thf(fact_4940_less__neg__neg,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_neg_neg
% 5.24/5.52 thf(fact_4941_less__neg__neg,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.24/5.52
% 5.24/5.52 % less_neg_neg
% 5.24/5.52 thf(fact_4942_add_Oright__inverse,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.24/5.52 = zero_zero_real ) ).
% 5.24/5.52
% 5.24/5.52 % add.right_inverse
% 5.24/5.52 thf(fact_4943_add_Oright__inverse,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.24/5.52 = zero_zero_int ) ).
% 5.24/5.52
% 5.24/5.52 % add.right_inverse
% 5.24/5.52 thf(fact_4944_add_Oright__inverse,axiom,
% 5.24/5.52 ! [A: complex] :
% 5.24/5.52 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.24/5.52 = zero_zero_complex ) ).
% 5.24/5.52
% 5.24/5.52 % add.right_inverse
% 5.24/5.52 thf(fact_4945_add_Oright__inverse,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.24/5.52 = zero_zero_rat ) ).
% 5.24/5.52
% 5.24/5.52 % add.right_inverse
% 5.24/5.52 thf(fact_4946_add_Oright__inverse,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.52 = zero_z3403309356797280102nteger ) ).
% 5.24/5.52
% 5.24/5.52 % add.right_inverse
% 5.24/5.52 thf(fact_4947_ab__left__minus,axiom,
% 5.24/5.52 ! [A: real] :
% 5.24/5.52 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.24/5.52 = zero_zero_real ) ).
% 5.24/5.52
% 5.24/5.52 % ab_left_minus
% 5.24/5.52 thf(fact_4948_ab__left__minus,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.24/5.52 = zero_zero_int ) ).
% 5.24/5.52
% 5.24/5.52 % ab_left_minus
% 5.24/5.52 thf(fact_4949_ab__left__minus,axiom,
% 5.24/5.52 ! [A: complex] :
% 5.24/5.52 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.24/5.52 = zero_zero_complex ) ).
% 5.24/5.52
% 5.24/5.52 % ab_left_minus
% 5.24/5.52 thf(fact_4950_ab__left__minus,axiom,
% 5.24/5.52 ! [A: rat] :
% 5.24/5.52 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.24/5.52 = zero_zero_rat ) ).
% 5.24/5.52
% 5.24/5.52 % ab_left_minus
% 5.24/5.52 thf(fact_4951_ab__left__minus,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.24/5.52 = zero_z3403309356797280102nteger ) ).
% 5.24/5.52
% 5.24/5.52 % ab_left_minus
% 5.24/5.52 thf(fact_4952_verit__minus__simplify_I3_J,axiom,
% 5.24/5.52 ! [B: real] :
% 5.24/5.52 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.24/5.52 = ( uminus_uminus_real @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(3)
% 5.24/5.52 thf(fact_4953_verit__minus__simplify_I3_J,axiom,
% 5.24/5.52 ! [B: int] :
% 5.24/5.52 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.24/5.52 = ( uminus_uminus_int @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(3)
% 5.24/5.52 thf(fact_4954_verit__minus__simplify_I3_J,axiom,
% 5.24/5.52 ! [B: complex] :
% 5.24/5.52 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(3)
% 5.24/5.52 thf(fact_4955_verit__minus__simplify_I3_J,axiom,
% 5.24/5.52 ! [B: rat] :
% 5.24/5.52 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.24/5.52 = ( uminus_uminus_rat @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(3)
% 5.24/5.52 thf(fact_4956_verit__minus__simplify_I3_J,axiom,
% 5.24/5.52 ! [B: code_integer] :
% 5.24/5.52 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % verit_minus_simplify(3)
% 5.24/5.52 thf(fact_4957_add__neg__numeral__simps_I3_J,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.52 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_neg_numeral_simps(3)
% 5.24/5.52 thf(fact_4958_add__neg__numeral__simps_I3_J,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.52 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_neg_numeral_simps(3)
% 5.24/5.52 thf(fact_4959_add__neg__numeral__simps_I3_J,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_neg_numeral_simps(3)
% 5.24/5.52 thf(fact_4960_add__neg__numeral__simps_I3_J,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.52 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_neg_numeral_simps(3)
% 5.24/5.52 thf(fact_4961_add__neg__numeral__simps_I3_J,axiom,
% 5.24/5.52 ! [M: num,N: num] :
% 5.24/5.52 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.24/5.52
% 5.24/5.52 % add_neg_numeral_simps(3)
% 5.24/5.52 thf(fact_4962_mult__minus1__right,axiom,
% 5.24/5.52 ! [Z2: real] :
% 5.24/5.52 ( ( times_times_real @ Z2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.52 = ( uminus_uminus_real @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1_right
% 5.24/5.52 thf(fact_4963_mult__minus1__right,axiom,
% 5.24/5.52 ! [Z2: int] :
% 5.24/5.52 ( ( times_times_int @ Z2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.52 = ( uminus_uminus_int @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1_right
% 5.24/5.52 thf(fact_4964_mult__minus1__right,axiom,
% 5.24/5.52 ! [Z2: complex] :
% 5.24/5.52 ( ( times_times_complex @ Z2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1_right
% 5.24/5.52 thf(fact_4965_mult__minus1__right,axiom,
% 5.24/5.52 ! [Z2: rat] :
% 5.24/5.52 ( ( times_times_rat @ Z2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.52 = ( uminus_uminus_rat @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1_right
% 5.24/5.52 thf(fact_4966_mult__minus1__right,axiom,
% 5.24/5.52 ! [Z2: code_integer] :
% 5.24/5.52 ( ( times_3573771949741848930nteger @ Z2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1_right
% 5.24/5.52 thf(fact_4967_mult__minus1,axiom,
% 5.24/5.52 ! [Z2: real] :
% 5.24/5.52 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z2 )
% 5.24/5.52 = ( uminus_uminus_real @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1
% 5.24/5.52 thf(fact_4968_mult__minus1,axiom,
% 5.24/5.52 ! [Z2: int] :
% 5.24/5.52 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z2 )
% 5.24/5.52 = ( uminus_uminus_int @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1
% 5.24/5.52 thf(fact_4969_mult__minus1,axiom,
% 5.24/5.52 ! [Z2: complex] :
% 5.24/5.52 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z2 )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1
% 5.24/5.52 thf(fact_4970_mult__minus1,axiom,
% 5.24/5.52 ! [Z2: rat] :
% 5.24/5.52 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z2 )
% 5.24/5.52 = ( uminus_uminus_rat @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1
% 5.24/5.52 thf(fact_4971_mult__minus1,axiom,
% 5.24/5.52 ! [Z2: code_integer] :
% 5.24/5.52 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z2 )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 5.24/5.52
% 5.24/5.52 % mult_minus1
% 5.24/5.52 thf(fact_4972_diff__minus__eq__add,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.24/5.52 = ( plus_plus_real @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_minus_eq_add
% 5.24/5.52 thf(fact_4973_diff__minus__eq__add,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.52 = ( plus_plus_int @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_minus_eq_add
% 5.24/5.52 thf(fact_4974_diff__minus__eq__add,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.52 = ( plus_plus_complex @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_minus_eq_add
% 5.24/5.52 thf(fact_4975_diff__minus__eq__add,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.24/5.52 = ( plus_plus_rat @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_minus_eq_add
% 5.24/5.52 thf(fact_4976_diff__minus__eq__add,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.52 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % diff_minus_eq_add
% 5.24/5.52 thf(fact_4977_uminus__add__conv__diff,axiom,
% 5.24/5.52 ! [A: real,B: real] :
% 5.24/5.52 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.52 = ( minus_minus_real @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % uminus_add_conv_diff
% 5.24/5.52 thf(fact_4978_uminus__add__conv__diff,axiom,
% 5.24/5.52 ! [A: int,B: int] :
% 5.24/5.52 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.52 = ( minus_minus_int @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % uminus_add_conv_diff
% 5.24/5.52 thf(fact_4979_uminus__add__conv__diff,axiom,
% 5.24/5.52 ! [A: complex,B: complex] :
% 5.24/5.52 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.24/5.52 = ( minus_minus_complex @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % uminus_add_conv_diff
% 5.24/5.52 thf(fact_4980_uminus__add__conv__diff,axiom,
% 5.24/5.52 ! [A: rat,B: rat] :
% 5.24/5.52 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.52 = ( minus_minus_rat @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % uminus_add_conv_diff
% 5.24/5.52 thf(fact_4981_uminus__add__conv__diff,axiom,
% 5.24/5.52 ! [A: code_integer,B: code_integer] :
% 5.24/5.52 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.52 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % uminus_add_conv_diff
% 5.24/5.52 thf(fact_4982_div__minus1__right,axiom,
% 5.24/5.52 ! [A: int] :
% 5.24/5.52 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.52 = ( uminus_uminus_int @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_minus1_right
% 5.24/5.52 thf(fact_4983_div__minus1__right,axiom,
% 5.24/5.52 ! [A: code_integer] :
% 5.24/5.52 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.52 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.24/5.52
% 5.24/5.52 % div_minus1_right
% 5.24/5.52 thf(fact_4984_divide__minus1,axiom,
% 5.24/5.52 ! [X: real] :
% 5.24/5.52 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.52 = ( uminus_uminus_real @ X ) ) ).
% 5.24/5.52
% 5.24/5.52 % divide_minus1
% 5.24/5.52 thf(fact_4985_divide__minus1,axiom,
% 5.24/5.52 ! [X: complex] :
% 5.24/5.52 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.52 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.24/5.52
% 5.24/5.52 % divide_minus1
% 5.24/5.52 thf(fact_4986_divide__minus1,axiom,
% 5.24/5.52 ! [X: rat] :
% 5.24/5.52 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.52 = ( uminus_uminus_rat @ X ) ) ).
% 5.24/5.52
% 5.24/5.52 % divide_minus1
% 5.24/5.52 thf(fact_4987_sum_Oempty,axiom,
% 5.24/5.52 ! [G: nat > complex] :
% 5.24/5.52 ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 5.24/5.52 = zero_zero_complex ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4988_sum_Oempty,axiom,
% 5.24/5.52 ! [G: nat > rat] :
% 5.24/5.52 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 5.24/5.52 = zero_zero_rat ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4989_sum_Oempty,axiom,
% 5.24/5.52 ! [G: nat > int] :
% 5.24/5.52 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 5.24/5.52 = zero_zero_int ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4990_sum_Oempty,axiom,
% 5.24/5.52 ! [G: int > complex] :
% 5.24/5.52 ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 5.24/5.52 = zero_zero_complex ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4991_sum_Oempty,axiom,
% 5.24/5.52 ! [G: int > real] :
% 5.24/5.52 ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 5.24/5.52 = zero_zero_real ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4992_sum_Oempty,axiom,
% 5.24/5.52 ! [G: int > rat] :
% 5.24/5.52 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 5.24/5.52 = zero_zero_rat ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4993_sum_Oempty,axiom,
% 5.24/5.52 ! [G: int > nat] :
% 5.24/5.52 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 5.24/5.52 = zero_zero_nat ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4994_sum_Oempty,axiom,
% 5.24/5.52 ! [G: real > complex] :
% 5.24/5.52 ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 5.24/5.52 = zero_zero_complex ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4995_sum_Oempty,axiom,
% 5.24/5.52 ! [G: real > real] :
% 5.24/5.52 ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 5.24/5.52 = zero_zero_real ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4996_sum_Oempty,axiom,
% 5.24/5.52 ! [G: real > rat] :
% 5.24/5.52 ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 5.24/5.52 = zero_zero_rat ) ).
% 5.24/5.52
% 5.24/5.52 % sum.empty
% 5.24/5.52 thf(fact_4997_minus__mod__self1,axiom,
% 5.24/5.52 ! [B: int,A: int] :
% 5.24/5.52 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.24/5.52 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mod_self1
% 5.24/5.52 thf(fact_4998_minus__mod__self1,axiom,
% 5.24/5.52 ! [B: code_integer,A: code_integer] :
% 5.24/5.52 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.24/5.52 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.24/5.52
% 5.24/5.52 % minus_mod_self1
% 5.24/5.52 thf(fact_4999_zero__less__of__bool__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_of_bool_iff
% 5.24/5.52 thf(fact_5000_zero__less__of__bool__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_of_bool_iff
% 5.24/5.52 thf(fact_5001_zero__less__of__bool__iff,axiom,
% 5.24/5.52 ! [P: $o] :
% 5.24/5.52 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.24/5.52 = P ) ).
% 5.24/5.52
% 5.24/5.52 % zero_less_of_bool_iff
% 5.24/5.52 thf(fact_5002_zero__less__of__bool__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.24/5.53 = P ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_of_bool_iff
% 5.24/5.53 thf(fact_5003_zero__less__of__bool__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.24/5.53 = P ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_of_bool_iff
% 5.24/5.53 thf(fact_5004_ln__eq__zero__iff,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ( ln_ln_real @ X )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 = ( X = one_one_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_eq_zero_iff
% 5.24/5.53 thf(fact_5005_ln__gt__zero__iff,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.24/5.53 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_gt_zero_iff
% 5.24/5.53 thf(fact_5006_ln__less__zero__iff,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.24/5.53 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_less_zero_iff
% 5.24/5.53 thf(fact_5007_of__bool__less__one__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.24/5.53 = ~ P ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_one_iff
% 5.24/5.53 thf(fact_5008_of__bool__less__one__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.24/5.53 = ~ P ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_one_iff
% 5.24/5.53 thf(fact_5009_of__bool__less__one__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.24/5.53 = ~ P ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_one_iff
% 5.24/5.53 thf(fact_5010_of__bool__less__one__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.24/5.53 = ~ P ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_one_iff
% 5.24/5.53 thf(fact_5011_of__bool__less__one__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.24/5.53 = ~ P ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_one_iff
% 5.24/5.53 thf(fact_5012_ln__one,axiom,
% 5.24/5.53 ( ( ln_ln_real @ one_one_real )
% 5.24/5.53 = zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % ln_one
% 5.24/5.53 thf(fact_5013_of__bool__not__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.24/5.53 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_not_iff
% 5.24/5.53 thf(fact_5014_of__bool__not__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.24/5.53 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_not_iff
% 5.24/5.53 thf(fact_5015_of__bool__not__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.24/5.53 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_not_iff
% 5.24/5.53 thf(fact_5016_of__bool__not__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.24/5.53 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_not_iff
% 5.24/5.53 thf(fact_5017_of__bool__not__iff,axiom,
% 5.24/5.53 ! [P: $o] :
% 5.24/5.53 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.24/5.53 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_not_iff
% 5.24/5.53 thf(fact_5018_Suc__0__mod__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.53 = ( zero_n2687167440665602831ol_nat
% 5.24/5.53 @ ( N
% 5.24/5.53 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Suc_0_mod_eq
% 5.24/5.53 thf(fact_5019_signed__take__bit__of__minus__1,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % signed_take_bit_of_minus_1
% 5.24/5.53 thf(fact_5020_signed__take__bit__of__minus__1,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % signed_take_bit_of_minus_1
% 5.24/5.53 thf(fact_5021_in__set__replicate,axiom,
% 5.24/5.53 ! [X: real,N: nat,Y4: real] :
% 5.24/5.53 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y4 ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % in_set_replicate
% 5.24/5.53 thf(fact_5022_in__set__replicate,axiom,
% 5.24/5.53 ! [X: complex,N: nat,Y4: complex] :
% 5.24/5.53 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y4 ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % in_set_replicate
% 5.24/5.53 thf(fact_5023_in__set__replicate,axiom,
% 5.24/5.53 ! [X: product_prod_nat_nat,N: nat,Y4: product_prod_nat_nat] :
% 5.24/5.53 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y4 ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % in_set_replicate
% 5.24/5.53 thf(fact_5024_in__set__replicate,axiom,
% 5.24/5.53 ! [X: int,N: nat,Y4: int] :
% 5.24/5.53 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y4 ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % in_set_replicate
% 5.24/5.53 thf(fact_5025_in__set__replicate,axiom,
% 5.24/5.53 ! [X: nat,N: nat,Y4: nat] :
% 5.24/5.53 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y4 ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % in_set_replicate
% 5.24/5.53 thf(fact_5026_in__set__replicate,axiom,
% 5.24/5.53 ! [X: vEBT_VEBT,N: nat,Y4: vEBT_VEBT] :
% 5.24/5.53 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y4 ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % in_set_replicate
% 5.24/5.53 thf(fact_5027_Bex__set__replicate,axiom,
% 5.24/5.53 ! [N: nat,A: int,P: int > $o] :
% 5.24/5.53 ( ( ? [X2: int] :
% 5.24/5.53 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.24/5.53 & ( P @ X2 ) ) )
% 5.24/5.53 = ( ( P @ A )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Bex_set_replicate
% 5.24/5.53 thf(fact_5028_Bex__set__replicate,axiom,
% 5.24/5.53 ! [N: nat,A: nat,P: nat > $o] :
% 5.24/5.53 ( ( ? [X2: nat] :
% 5.24/5.53 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.24/5.53 & ( P @ X2 ) ) )
% 5.24/5.53 = ( ( P @ A )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Bex_set_replicate
% 5.24/5.53 thf(fact_5029_Bex__set__replicate,axiom,
% 5.24/5.53 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.24/5.53 ( ( ? [X2: vEBT_VEBT] :
% 5.24/5.53 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.24/5.53 & ( P @ X2 ) ) )
% 5.24/5.53 = ( ( P @ A )
% 5.24/5.53 & ( N != zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Bex_set_replicate
% 5.24/5.53 thf(fact_5030_Ball__set__replicate,axiom,
% 5.24/5.53 ! [N: nat,A: int,P: int > $o] :
% 5.24/5.53 ( ( ! [X2: int] :
% 5.24/5.53 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.24/5.53 => ( P @ X2 ) ) )
% 5.24/5.53 = ( ( P @ A )
% 5.24/5.53 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Ball_set_replicate
% 5.24/5.53 thf(fact_5031_Ball__set__replicate,axiom,
% 5.24/5.53 ! [N: nat,A: nat,P: nat > $o] :
% 5.24/5.53 ( ( ! [X2: nat] :
% 5.24/5.53 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.24/5.53 => ( P @ X2 ) ) )
% 5.24/5.53 = ( ( P @ A )
% 5.24/5.53 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Ball_set_replicate
% 5.24/5.53 thf(fact_5032_Ball__set__replicate,axiom,
% 5.24/5.53 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.24/5.53 ( ( ! [X2: vEBT_VEBT] :
% 5.24/5.53 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.24/5.53 => ( P @ X2 ) ) )
% 5.24/5.53 = ( ( P @ A )
% 5.24/5.53 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Ball_set_replicate
% 5.24/5.53 thf(fact_5033_nth__replicate,axiom,
% 5.24/5.53 ! [I2: nat,N: nat,X: nat] :
% 5.24/5.53 ( ( ord_less_nat @ I2 @ N )
% 5.24/5.53 => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 )
% 5.24/5.53 = X ) ) ).
% 5.24/5.53
% 5.24/5.53 % nth_replicate
% 5.24/5.53 thf(fact_5034_nth__replicate,axiom,
% 5.24/5.53 ! [I2: nat,N: nat,X: int] :
% 5.24/5.53 ( ( ord_less_nat @ I2 @ N )
% 5.24/5.53 => ( ( nth_int @ ( replicate_int @ N @ X ) @ I2 )
% 5.24/5.53 = X ) ) ).
% 5.24/5.53
% 5.24/5.53 % nth_replicate
% 5.24/5.53 thf(fact_5035_nth__replicate,axiom,
% 5.24/5.53 ! [I2: nat,N: nat,X: vEBT_VEBT] :
% 5.24/5.53 ( ( ord_less_nat @ I2 @ N )
% 5.24/5.53 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 )
% 5.24/5.53 = X ) ) ).
% 5.24/5.53
% 5.24/5.53 % nth_replicate
% 5.24/5.53 thf(fact_5036_dbl__simps_I1_J,axiom,
% 5.24/5.53 ! [K: num] :
% 5.24/5.53 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(1)
% 5.24/5.53 thf(fact_5037_dbl__simps_I1_J,axiom,
% 5.24/5.53 ! [K: num] :
% 5.24/5.53 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(1)
% 5.24/5.53 thf(fact_5038_dbl__simps_I1_J,axiom,
% 5.24/5.53 ! [K: num] :
% 5.24/5.53 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(1)
% 5.24/5.53 thf(fact_5039_dbl__simps_I1_J,axiom,
% 5.24/5.53 ! [K: num] :
% 5.24/5.53 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(1)
% 5.24/5.53 thf(fact_5040_dbl__simps_I1_J,axiom,
% 5.24/5.53 ! [K: num] :
% 5.24/5.53 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(1)
% 5.24/5.53 thf(fact_5041_add__neg__numeral__special_I8_J,axiom,
% 5.24/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.24/5.53 = zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(8)
% 5.24/5.53 thf(fact_5042_add__neg__numeral__special_I8_J,axiom,
% 5.24/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.24/5.53 = zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(8)
% 5.24/5.53 thf(fact_5043_add__neg__numeral__special_I8_J,axiom,
% 5.24/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.24/5.53 = zero_zero_complex ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(8)
% 5.24/5.53 thf(fact_5044_add__neg__numeral__special_I8_J,axiom,
% 5.24/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.24/5.53 = zero_zero_rat ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(8)
% 5.24/5.53 thf(fact_5045_add__neg__numeral__special_I8_J,axiom,
% 5.24/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(8)
% 5.24/5.53 thf(fact_5046_add__neg__numeral__special_I7_J,axiom,
% 5.24/5.53 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(7)
% 5.24/5.53 thf(fact_5047_add__neg__numeral__special_I7_J,axiom,
% 5.24/5.53 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(7)
% 5.24/5.53 thf(fact_5048_add__neg__numeral__special_I7_J,axiom,
% 5.24/5.53 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = zero_zero_complex ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(7)
% 5.24/5.53 thf(fact_5049_add__neg__numeral__special_I7_J,axiom,
% 5.24/5.53 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = zero_zero_rat ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(7)
% 5.24/5.53 thf(fact_5050_add__neg__numeral__special_I7_J,axiom,
% 5.24/5.53 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(7)
% 5.24/5.53 thf(fact_5051_diff__numeral__special_I12_J,axiom,
% 5.24/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(12)
% 5.24/5.53 thf(fact_5052_diff__numeral__special_I12_J,axiom,
% 5.24/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(12)
% 5.24/5.53 thf(fact_5053_diff__numeral__special_I12_J,axiom,
% 5.24/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = zero_zero_complex ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(12)
% 5.24/5.53 thf(fact_5054_diff__numeral__special_I12_J,axiom,
% 5.24/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = zero_zero_rat ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(12)
% 5.24/5.53 thf(fact_5055_diff__numeral__special_I12_J,axiom,
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(12)
% 5.24/5.53 thf(fact_5056_numeral__eq__neg__one__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.24/5.53 = ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_eq_neg_one_iff
% 5.24/5.53 thf(fact_5057_numeral__eq__neg__one__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_eq_neg_one_iff
% 5.24/5.53 thf(fact_5058_numeral__eq__neg__one__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_eq_neg_one_iff
% 5.24/5.53 thf(fact_5059_numeral__eq__neg__one__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.24/5.53 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_eq_neg_one_iff
% 5.24/5.53 thf(fact_5060_numeral__eq__neg__one__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_eq_neg_one_iff
% 5.24/5.53 thf(fact_5061_neg__one__eq__numeral__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus_uminus_real @ one_one_real )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_eq_numeral_iff
% 5.24/5.53 thf(fact_5062_neg__one__eq__numeral__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus_uminus_int @ one_one_int )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_eq_numeral_iff
% 5.24/5.53 thf(fact_5063_neg__one__eq__numeral__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_eq_numeral_iff
% 5.24/5.53 thf(fact_5064_neg__one__eq__numeral__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_eq_numeral_iff
% 5.24/5.53 thf(fact_5065_neg__one__eq__numeral__iff,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( N = one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_eq_numeral_iff
% 5.24/5.53 thf(fact_5066_left__minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat,A: real] :
% 5.24/5.53 ( ( 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 ) )
% 5.24/5.53 = A ) ).
% 5.24/5.53
% 5.24/5.53 % left_minus_one_mult_self
% 5.24/5.53 thf(fact_5067_left__minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat,A: int] :
% 5.24/5.53 ( ( 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 ) )
% 5.24/5.53 = A ) ).
% 5.24/5.53
% 5.24/5.53 % left_minus_one_mult_self
% 5.24/5.53 thf(fact_5068_left__minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat,A: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.24/5.53 = A ) ).
% 5.24/5.53
% 5.24/5.53 % left_minus_one_mult_self
% 5.24/5.53 thf(fact_5069_left__minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat,A: rat] :
% 5.24/5.53 ( ( 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 ) )
% 5.24/5.53 = A ) ).
% 5.24/5.53
% 5.24/5.53 % left_minus_one_mult_self
% 5.24/5.53 thf(fact_5070_left__minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat,A: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.24/5.53 = A ) ).
% 5.24/5.53
% 5.24/5.53 % left_minus_one_mult_self
% 5.24/5.53 thf(fact_5071_minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.24/5.53 = one_one_real ) ).
% 5.24/5.53
% 5.24/5.53 % minus_one_mult_self
% 5.24/5.53 thf(fact_5072_minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.24/5.53 = one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % minus_one_mult_self
% 5.24/5.53 thf(fact_5073_minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.24/5.53 = one_one_complex ) ).
% 5.24/5.53
% 5.24/5.53 % minus_one_mult_self
% 5.24/5.53 thf(fact_5074_minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.24/5.53 = one_one_rat ) ).
% 5.24/5.53
% 5.24/5.53 % minus_one_mult_self
% 5.24/5.53 thf(fact_5075_minus__one__mult__self,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.24/5.53 = one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % minus_one_mult_self
% 5.24/5.53 thf(fact_5076_mod__minus1__right,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus1_right
% 5.24/5.53 thf(fact_5077_mod__minus1__right,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus1_right
% 5.24/5.53 thf(fact_5078_max__number__of_I2_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 => ( ( ord_max_real @ ( numeral_numeral_real @ U2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 => ( ( ord_max_real @ ( numeral_numeral_real @ U2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 = ( numeral_numeral_real @ U2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(2)
% 5.24/5.53 thf(fact_5079_max__number__of_I2_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 = ( numera6620942414471956472nteger @ U2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(2)
% 5.24/5.53 thf(fact_5080_max__number__of_I2_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 = ( numeral_numeral_rat @ U2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(2)
% 5.24/5.53 thf(fact_5081_max__number__of_I2_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 => ( ( ord_max_int @ ( numeral_numeral_int @ U2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 => ( ( ord_max_int @ ( numeral_numeral_int @ U2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 = ( numeral_numeral_int @ U2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(2)
% 5.24/5.53 thf(fact_5082_max__number__of_I3_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.53 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.53 = ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.53 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( numeral_numeral_real @ V ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(3)
% 5.24/5.53 thf(fact_5083_max__number__of_I3_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.24/5.53 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.24/5.53 = ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.24/5.53 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(3)
% 5.24/5.53 thf(fact_5084_max__number__of_I3_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.53 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.53 = ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.53 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( numeral_numeral_rat @ V ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(3)
% 5.24/5.53 thf(fact_5085_max__number__of_I3_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.53 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.53 = ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.53 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(3)
% 5.24/5.53 thf(fact_5086_max__number__of_I4_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(4)
% 5.24/5.53 thf(fact_5087_max__number__of_I4_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(4)
% 5.24/5.53 thf(fact_5088_max__number__of_I4_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(4)
% 5.24/5.53 thf(fact_5089_max__number__of_I4_J,axiom,
% 5.24/5.53 ! [U2: num,V: num] :
% 5.24/5.53 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.24/5.53 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ U2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % max_number_of(4)
% 5.24/5.53 thf(fact_5090_ln__le__zero__iff,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.24/5.53 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_le_zero_iff
% 5.24/5.53 thf(fact_5091_ln__ge__zero__iff,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.24/5.53 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_ge_zero_iff
% 5.24/5.53 thf(fact_5092_semiring__norm_I168_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: real] :
% 5.24/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(168)
% 5.24/5.53 thf(fact_5093_semiring__norm_I168_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: int] :
% 5.24/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(168)
% 5.24/5.53 thf(fact_5094_semiring__norm_I168_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: complex] :
% 5.24/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(168)
% 5.24/5.53 thf(fact_5095_semiring__norm_I168_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: rat] :
% 5.24/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(168)
% 5.24/5.53 thf(fact_5096_semiring__norm_I168_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: code_integer] :
% 5.24/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(168)
% 5.24/5.53 thf(fact_5097_diff__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(2)
% 5.24/5.53 thf(fact_5098_diff__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(2)
% 5.24/5.53 thf(fact_5099_diff__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.53 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(2)
% 5.24/5.53 thf(fact_5100_diff__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(2)
% 5.24/5.53 thf(fact_5101_diff__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(2)
% 5.24/5.53 thf(fact_5102_diff__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(3)
% 5.24/5.53 thf(fact_5103_diff__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(3)
% 5.24/5.53 thf(fact_5104_diff__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(3)
% 5.24/5.53 thf(fact_5105_diff__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(3)
% 5.24/5.53 thf(fact_5106_diff__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_simps(3)
% 5.24/5.53 thf(fact_5107_semiring__norm_I172_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: real] :
% 5.24/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(172)
% 5.24/5.53 thf(fact_5108_semiring__norm_I172_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: int] :
% 5.24/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(172)
% 5.24/5.53 thf(fact_5109_semiring__norm_I172_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W2 ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(172)
% 5.24/5.53 thf(fact_5110_semiring__norm_I172_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: rat] :
% 5.24/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(172)
% 5.24/5.53 thf(fact_5111_semiring__norm_I172_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(172)
% 5.24/5.53 thf(fact_5112_semiring__norm_I171_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: real] :
% 5.24/5.53 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(171)
% 5.24/5.53 thf(fact_5113_semiring__norm_I171_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: int] :
% 5.24/5.53 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(171)
% 5.24/5.53 thf(fact_5114_semiring__norm_I171_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(171)
% 5.24/5.53 thf(fact_5115_semiring__norm_I171_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: rat] :
% 5.24/5.53 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(171)
% 5.24/5.53 thf(fact_5116_semiring__norm_I171_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y4 ) )
% 5.24/5.53 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(171)
% 5.24/5.53 thf(fact_5117_semiring__norm_I170_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: real] :
% 5.24/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Y4 ) )
% 5.24/5.53 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(170)
% 5.24/5.53 thf(fact_5118_semiring__norm_I170_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: int] :
% 5.24/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Y4 ) )
% 5.24/5.53 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(170)
% 5.24/5.53 thf(fact_5119_semiring__norm_I170_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Y4 ) )
% 5.24/5.53 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(170)
% 5.24/5.53 thf(fact_5120_semiring__norm_I170_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: rat] :
% 5.24/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y4 ) )
% 5.24/5.53 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(170)
% 5.24/5.53 thf(fact_5121_semiring__norm_I170_J,axiom,
% 5.24/5.53 ! [V: num,W2: num,Y4: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Y4 ) )
% 5.24/5.53 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % semiring_norm(170)
% 5.24/5.53 thf(fact_5122_mult__neg__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(3)
% 5.24/5.53 thf(fact_5123_mult__neg__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(3)
% 5.24/5.53 thf(fact_5124_mult__neg__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(3)
% 5.24/5.53 thf(fact_5125_mult__neg__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(3)
% 5.24/5.53 thf(fact_5126_mult__neg__numeral__simps_I3_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(3)
% 5.24/5.53 thf(fact_5127_mult__neg__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(2)
% 5.24/5.53 thf(fact_5128_mult__neg__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(2)
% 5.24/5.53 thf(fact_5129_mult__neg__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(2)
% 5.24/5.53 thf(fact_5130_mult__neg__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(2)
% 5.24/5.53 thf(fact_5131_mult__neg__numeral__simps_I2_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(2)
% 5.24/5.53 thf(fact_5132_mult__neg__numeral__simps_I1_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(1)
% 5.24/5.53 thf(fact_5133_mult__neg__numeral__simps_I1_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(1)
% 5.24/5.53 thf(fact_5134_mult__neg__numeral__simps_I1_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.53 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(1)
% 5.24/5.53 thf(fact_5135_mult__neg__numeral__simps_I1_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(1)
% 5.24/5.53 thf(fact_5136_mult__neg__numeral__simps_I1_J,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_neg_numeral_simps(1)
% 5.24/5.53 thf(fact_5137_neg__numeral__le__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_iff
% 5.24/5.53 thf(fact_5138_neg__numeral__le__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_iff
% 5.24/5.53 thf(fact_5139_neg__numeral__le__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_iff
% 5.24/5.53 thf(fact_5140_neg__numeral__le__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_iff
% 5.24/5.53 thf(fact_5141_neg__numeral__less__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( ord_less_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_iff
% 5.24/5.53 thf(fact_5142_neg__numeral__less__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( ord_less_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_iff
% 5.24/5.53 thf(fact_5143_neg__numeral__less__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( ord_less_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_iff
% 5.24/5.53 thf(fact_5144_neg__numeral__less__iff,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( ord_less_num @ N @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_iff
% 5.24/5.53 thf(fact_5145_not__neg__one__le__neg__numeral__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_le_neg_numeral_iff
% 5.24/5.53 thf(fact_5146_not__neg__one__le__neg__numeral__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_le_neg_numeral_iff
% 5.24/5.53 thf(fact_5147_not__neg__one__le__neg__numeral__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_le_neg_numeral_iff
% 5.24/5.53 thf(fact_5148_not__neg__one__le__neg__numeral__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_le_neg_numeral_iff
% 5.24/5.53 thf(fact_5149_le__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: real,B: real,W2: num] :
% 5.24/5.53 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.24/5.53 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5150_le__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: rat,B: rat,W2: num] :
% 5.24/5.53 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.24/5.53 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5151_divide__le__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: real,W2: num,A: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 5.24/5.53 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_le_eq_numeral1(2)
% 5.24/5.53 thf(fact_5152_divide__le__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: rat,W2: num,A: rat] :
% 5.24/5.53 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 5.24/5.53 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_le_eq_numeral1(2)
% 5.24/5.53 thf(fact_5153_eq__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: real,B: real,W2: num] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.24/5.53 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 != zero_zero_real )
% 5.24/5.53 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 => ( A = zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5154_eq__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: complex,B: complex,W2: num] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 5.24/5.53 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 != zero_zero_complex )
% 5.24/5.53 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 = zero_zero_complex )
% 5.24/5.53 => ( A = zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5155_eq__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: rat,B: rat,W2: num] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.24/5.53 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 != zero_zero_rat )
% 5.24/5.53 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( A = zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5156_divide__eq__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: real,W2: num,A: real] :
% 5.24/5.53 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.53 = A )
% 5.24/5.53 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 != zero_zero_real )
% 5.24/5.53 => ( B
% 5.24/5.53 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 5.24/5.53 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 => ( A = zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_eq_numeral1(2)
% 5.24/5.53 thf(fact_5157_divide__eq__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: complex,W2: num,A: complex] :
% 5.24/5.53 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.53 = A )
% 5.24/5.53 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 != zero_zero_complex )
% 5.24/5.53 => ( B
% 5.24/5.53 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 5.24/5.53 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 = zero_zero_complex )
% 5.24/5.53 => ( A = zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_eq_numeral1(2)
% 5.24/5.53 thf(fact_5158_divide__eq__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: rat,W2: num,A: rat] :
% 5.24/5.53 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.24/5.53 = A )
% 5.24/5.53 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 != zero_zero_rat )
% 5.24/5.53 => ( B
% 5.24/5.53 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 5.24/5.53 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( A = zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_eq_numeral1(2)
% 5.24/5.53 thf(fact_5159_neg__numeral__less__neg__one__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_neg_one_iff
% 5.24/5.53 thf(fact_5160_neg__numeral__less__neg__one__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_neg_one_iff
% 5.24/5.53 thf(fact_5161_neg__numeral__less__neg__one__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_neg_one_iff
% 5.24/5.53 thf(fact_5162_neg__numeral__less__neg__one__iff,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = ( M != one ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_neg_one_iff
% 5.24/5.53 thf(fact_5163_less__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: real,B: real,W2: num] :
% 5.24/5.53 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.24/5.53 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5164_less__divide__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [A: rat,B: rat,W2: num] :
% 5.24/5.53 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.24/5.53 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_divide_eq_numeral1(2)
% 5.24/5.53 thf(fact_5165_divide__less__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: real,W2: num,A: real] :
% 5.24/5.53 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 5.24/5.53 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_less_eq_numeral1(2)
% 5.24/5.53 thf(fact_5166_divide__less__eq__numeral1_I2_J,axiom,
% 5.24/5.53 ! [B: rat,W2: num,A: rat] :
% 5.24/5.53 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 5.24/5.53 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_less_eq_numeral1(2)
% 5.24/5.53 thf(fact_5167_power2__minus,axiom,
% 5.24/5.53 ! [A: real] :
% 5.24/5.53 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_minus
% 5.24/5.53 thf(fact_5168_power2__minus,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_minus
% 5.24/5.53 thf(fact_5169_power2__minus,axiom,
% 5.24/5.53 ! [A: complex] :
% 5.24/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_minus
% 5.24/5.53 thf(fact_5170_power2__minus,axiom,
% 5.24/5.53 ! [A: rat] :
% 5.24/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_minus
% 5.24/5.53 thf(fact_5171_power2__minus,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_minus
% 5.24/5.53 thf(fact_5172_odd__of__bool__self,axiom,
% 5.24/5.53 ! [P6: $o] :
% 5.24/5.53 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P6 ) ) )
% 5.24/5.53 = P6 ) ).
% 5.24/5.53
% 5.24/5.53 % odd_of_bool_self
% 5.24/5.53 thf(fact_5173_odd__of__bool__self,axiom,
% 5.24/5.53 ! [P6: $o] :
% 5.24/5.53 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P6 ) ) )
% 5.24/5.53 = P6 ) ).
% 5.24/5.53
% 5.24/5.53 % odd_of_bool_self
% 5.24/5.53 thf(fact_5174_odd__of__bool__self,axiom,
% 5.24/5.53 ! [P6: $o] :
% 5.24/5.53 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P6 ) ) )
% 5.24/5.53 = P6 ) ).
% 5.24/5.53
% 5.24/5.53 % odd_of_bool_self
% 5.24/5.53 thf(fact_5175_add__neg__numeral__special_I9_J,axiom,
% 5.24/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(9)
% 5.24/5.53 thf(fact_5176_add__neg__numeral__special_I9_J,axiom,
% 5.24/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(9)
% 5.24/5.53 thf(fact_5177_add__neg__numeral__special_I9_J,axiom,
% 5.24/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(9)
% 5.24/5.53 thf(fact_5178_add__neg__numeral__special_I9_J,axiom,
% 5.24/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(9)
% 5.24/5.53 thf(fact_5179_add__neg__numeral__special_I9_J,axiom,
% 5.24/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_neg_numeral_special(9)
% 5.24/5.53 thf(fact_5180_diff__numeral__special_I10_J,axiom,
% 5.24/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(10)
% 5.24/5.53 thf(fact_5181_diff__numeral__special_I10_J,axiom,
% 5.24/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(10)
% 5.24/5.53 thf(fact_5182_diff__numeral__special_I10_J,axiom,
% 5.24/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(10)
% 5.24/5.53 thf(fact_5183_diff__numeral__special_I10_J,axiom,
% 5.24/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(10)
% 5.24/5.53 thf(fact_5184_diff__numeral__special_I10_J,axiom,
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(10)
% 5.24/5.53 thf(fact_5185_diff__numeral__special_I11_J,axiom,
% 5.24/5.53 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(11)
% 5.24/5.53 thf(fact_5186_diff__numeral__special_I11_J,axiom,
% 5.24/5.53 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(11)
% 5.24/5.53 thf(fact_5187_diff__numeral__special_I11_J,axiom,
% 5.24/5.53 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(11)
% 5.24/5.53 thf(fact_5188_diff__numeral__special_I11_J,axiom,
% 5.24/5.53 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(11)
% 5.24/5.53 thf(fact_5189_diff__numeral__special_I11_J,axiom,
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(11)
% 5.24/5.53 thf(fact_5190_minus__1__div__2__eq,axiom,
% 5.24/5.53 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_1_div_2_eq
% 5.24/5.53 thf(fact_5191_minus__1__div__2__eq,axiom,
% 5.24/5.53 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_1_div_2_eq
% 5.24/5.53 thf(fact_5192_minus__1__mod__2__eq,axiom,
% 5.24/5.53 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % minus_1_mod_2_eq
% 5.24/5.53 thf(fact_5193_minus__1__mod__2__eq,axiom,
% 5.24/5.53 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % minus_1_mod_2_eq
% 5.24/5.53 thf(fact_5194_bits__minus__1__mod__2__eq,axiom,
% 5.24/5.53 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % bits_minus_1_mod_2_eq
% 5.24/5.53 thf(fact_5195_bits__minus__1__mod__2__eq,axiom,
% 5.24/5.53 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % bits_minus_1_mod_2_eq
% 5.24/5.53 thf(fact_5196_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [A: real,N: nat] :
% 5.24/5.53 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Power.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5197_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [A: int,N: nat] :
% 5.24/5.53 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Power.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5198_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [A: complex,N: nat] :
% 5.24/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Power.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5199_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [A: rat,N: nat] :
% 5.24/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Power.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5200_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [A: code_integer,N: nat] :
% 5.24/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Power.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5201_of__bool__half__eq__0,axiom,
% 5.24/5.53 ! [B: $o] :
% 5.24/5.53 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = zero_zero_nat ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_half_eq_0
% 5.24/5.53 thf(fact_5202_of__bool__half__eq__0,axiom,
% 5.24/5.53 ! [B: $o] :
% 5.24/5.53 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.53 = zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_half_eq_0
% 5.24/5.53 thf(fact_5203_of__bool__half__eq__0,axiom,
% 5.24/5.53 ! [B: $o] :
% 5.24/5.53 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_half_eq_0
% 5.24/5.53 thf(fact_5204_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [N: nat,A: real] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.24/5.53 = ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Parity.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5205_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [N: nat,A: int] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.24/5.53 = ( power_power_int @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Parity.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5206_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [N: nat,A: complex] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.24/5.53 = ( power_power_complex @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Parity.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5207_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [N: nat,A: rat] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.24/5.53 = ( power_power_rat @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Parity.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5208_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.24/5.53 ! [N: nat,A: code_integer] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.24/5.53 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % Parity.ring_1_class.power_minus_even
% 5.24/5.53 thf(fact_5209_power__minus__odd,axiom,
% 5.24/5.53 ! [N: nat,A: real] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.24/5.53 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_odd
% 5.24/5.53 thf(fact_5210_power__minus__odd,axiom,
% 5.24/5.53 ! [N: nat,A: int] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.24/5.53 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_odd
% 5.24/5.53 thf(fact_5211_power__minus__odd,axiom,
% 5.24/5.53 ! [N: nat,A: complex] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_odd
% 5.24/5.53 thf(fact_5212_power__minus__odd,axiom,
% 5.24/5.53 ! [N: nat,A: rat] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.24/5.53 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_odd
% 5.24/5.53 thf(fact_5213_power__minus__odd,axiom,
% 5.24/5.53 ! [N: nat,A: code_integer] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_odd
% 5.24/5.53 thf(fact_5214_diff__numeral__special_I3_J,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(3)
% 5.24/5.53 thf(fact_5215_diff__numeral__special_I3_J,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(3)
% 5.24/5.53 thf(fact_5216_diff__numeral__special_I3_J,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.24/5.53 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(3)
% 5.24/5.53 thf(fact_5217_diff__numeral__special_I3_J,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.53 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(3)
% 5.24/5.53 thf(fact_5218_diff__numeral__special_I3_J,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.53 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(3)
% 5.24/5.53 thf(fact_5219_diff__numeral__special_I4_J,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(4)
% 5.24/5.53 thf(fact_5220_diff__numeral__special_I4_J,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(4)
% 5.24/5.53 thf(fact_5221_diff__numeral__special_I4_J,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(4)
% 5.24/5.53 thf(fact_5222_diff__numeral__special_I4_J,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(4)
% 5.24/5.53 thf(fact_5223_diff__numeral__special_I4_J,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_numeral_special(4)
% 5.24/5.53 thf(fact_5224_signed__take__bit__Suc__minus__bit0,axiom,
% 5.24/5.53 ! [N: nat,K: num] :
% 5.24/5.53 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.24/5.53 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % signed_take_bit_Suc_minus_bit0
% 5.24/5.53 thf(fact_5225_dbl__simps_I4_J,axiom,
% 5.24/5.53 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(4)
% 5.24/5.53 thf(fact_5226_dbl__simps_I4_J,axiom,
% 5.24/5.53 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(4)
% 5.24/5.53 thf(fact_5227_dbl__simps_I4_J,axiom,
% 5.24/5.53 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(4)
% 5.24/5.53 thf(fact_5228_dbl__simps_I4_J,axiom,
% 5.24/5.53 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(4)
% 5.24/5.53 thf(fact_5229_dbl__simps_I4_J,axiom,
% 5.24/5.53 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dbl_simps(4)
% 5.24/5.53 thf(fact_5230_power__minus1__even,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = one_one_real ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus1_even
% 5.24/5.53 thf(fact_5231_power__minus1__even,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus1_even
% 5.24/5.53 thf(fact_5232_power__minus1__even,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = one_one_complex ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus1_even
% 5.24/5.53 thf(fact_5233_power__minus1__even,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = one_one_rat ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus1_even
% 5.24/5.53 thf(fact_5234_power__minus1__even,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus1_even
% 5.24/5.53 thf(fact_5235_neg__one__even__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.24/5.53 = one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_even_power
% 5.24/5.53 thf(fact_5236_neg__one__even__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.24/5.53 = one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_even_power
% 5.24/5.53 thf(fact_5237_neg__one__even__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.24/5.53 = one_one_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_even_power
% 5.24/5.53 thf(fact_5238_neg__one__even__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.24/5.53 = one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_even_power
% 5.24/5.53 thf(fact_5239_neg__one__even__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.24/5.53 = one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_even_power
% 5.24/5.53 thf(fact_5240_neg__one__odd__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.24/5.53 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_odd_power
% 5.24/5.53 thf(fact_5241_neg__one__odd__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_odd_power
% 5.24/5.53 thf(fact_5242_neg__one__odd__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_odd_power
% 5.24/5.53 thf(fact_5243_neg__one__odd__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.24/5.53 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_odd_power
% 5.24/5.53 thf(fact_5244_neg__one__odd__power,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_odd_power
% 5.24/5.53 thf(fact_5245_signed__take__bit__0,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % signed_take_bit_0
% 5.24/5.53 thf(fact_5246_signed__take__bit__0,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.24/5.53 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % signed_take_bit_0
% 5.24/5.53 thf(fact_5247_one__div__2__pow__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_div_2_pow_eq
% 5.24/5.53 thf(fact_5248_one__div__2__pow__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_div_2_pow_eq
% 5.24/5.53 thf(fact_5249_one__div__2__pow__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_div_2_pow_eq
% 5.24/5.53 thf(fact_5250_bits__1__div__exp,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % bits_1_div_exp
% 5.24/5.53 thf(fact_5251_bits__1__div__exp,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % bits_1_div_exp
% 5.24/5.53 thf(fact_5252_bits__1__div__exp,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % bits_1_div_exp
% 5.24/5.53 thf(fact_5253_one__mod__2__pow__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_mod_2_pow_eq
% 5.24/5.53 thf(fact_5254_one__mod__2__pow__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_mod_2_pow_eq
% 5.24/5.53 thf(fact_5255_one__mod__2__pow__eq,axiom,
% 5.24/5.53 ! [N: nat] :
% 5.24/5.53 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.53 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_mod_2_pow_eq
% 5.24/5.53 thf(fact_5256_compl__le__swap2,axiom,
% 5.24/5.53 ! [Y4: set_nat,X: set_nat] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y4 ) @ X )
% 5.24/5.53 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % compl_le_swap2
% 5.24/5.53 thf(fact_5257_compl__le__swap1,axiom,
% 5.24/5.53 ! [Y4: set_nat,X: set_nat] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ Y4 @ ( uminus5710092332889474511et_nat @ X ) )
% 5.24/5.53 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y4 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % compl_le_swap1
% 5.24/5.53 thf(fact_5258_compl__mono,axiom,
% 5.24/5.53 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 5.24/5.53 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y4 ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % compl_mono
% 5.24/5.53 thf(fact_5259_verit__negate__coefficient_I3_J,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( A = B )
% 5.24/5.53 => ( ( uminus_uminus_real @ A )
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(3)
% 5.24/5.53 thf(fact_5260_verit__negate__coefficient_I3_J,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( A = B )
% 5.24/5.53 => ( ( uminus_uminus_int @ A )
% 5.24/5.53 = ( uminus_uminus_int @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(3)
% 5.24/5.53 thf(fact_5261_verit__negate__coefficient_I3_J,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( A = B )
% 5.24/5.53 => ( ( uminus_uminus_rat @ A )
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(3)
% 5.24/5.53 thf(fact_5262_verit__negate__coefficient_I3_J,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( A = B )
% 5.24/5.53 => ( ( uminus1351360451143612070nteger @ A )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(3)
% 5.24/5.53 thf(fact_5263_of__bool__conj,axiom,
% 5.24/5.53 ! [P: $o,Q: $o] :
% 5.24/5.53 ( ( zero_n3304061248610475627l_real
% 5.24/5.53 @ ( P
% 5.24/5.53 & Q ) )
% 5.24/5.53 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_conj
% 5.24/5.53 thf(fact_5264_of__bool__conj,axiom,
% 5.24/5.53 ! [P: $o,Q: $o] :
% 5.24/5.53 ( ( zero_n2052037380579107095ol_rat
% 5.24/5.53 @ ( P
% 5.24/5.53 & Q ) )
% 5.24/5.53 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_conj
% 5.24/5.53 thf(fact_5265_of__bool__conj,axiom,
% 5.24/5.53 ! [P: $o,Q: $o] :
% 5.24/5.53 ( ( zero_n2687167440665602831ol_nat
% 5.24/5.53 @ ( P
% 5.24/5.53 & Q ) )
% 5.24/5.53 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_conj
% 5.24/5.53 thf(fact_5266_of__bool__conj,axiom,
% 5.24/5.53 ! [P: $o,Q: $o] :
% 5.24/5.53 ( ( zero_n2684676970156552555ol_int
% 5.24/5.53 @ ( P
% 5.24/5.53 & Q ) )
% 5.24/5.53 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_conj
% 5.24/5.53 thf(fact_5267_of__bool__conj,axiom,
% 5.24/5.53 ! [P: $o,Q: $o] :
% 5.24/5.53 ( ( zero_n356916108424825756nteger
% 5.24/5.53 @ ( P
% 5.24/5.53 & Q ) )
% 5.24/5.53 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_conj
% 5.24/5.53 thf(fact_5268_le__imp__neg__le,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.53 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_imp_neg_le
% 5.24/5.53 thf(fact_5269_le__imp__neg__le,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.24/5.53 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_imp_neg_le
% 5.24/5.53 thf(fact_5270_le__imp__neg__le,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.53 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_imp_neg_le
% 5.24/5.53 thf(fact_5271_le__imp__neg__le,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.24/5.53 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_imp_neg_le
% 5.24/5.53 thf(fact_5272_minus__le__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.53 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_le_iff
% 5.24/5.53 thf(fact_5273_minus__le__iff,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.53 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_le_iff
% 5.24/5.53 thf(fact_5274_minus__le__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.53 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_le_iff
% 5.24/5.53 thf(fact_5275_minus__le__iff,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.53 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_le_iff
% 5.24/5.53 thf(fact_5276_le__minus__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.24/5.53 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_iff
% 5.24/5.53 thf(fact_5277_le__minus__iff,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.53 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_iff
% 5.24/5.53 thf(fact_5278_le__minus__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.24/5.53 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_iff
% 5.24/5.53 thf(fact_5279_le__minus__iff,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.53 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_iff
% 5.24/5.53 thf(fact_5280_less__minus__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.24/5.53 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_iff
% 5.24/5.53 thf(fact_5281_less__minus__iff,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.53 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_iff
% 5.24/5.53 thf(fact_5282_less__minus__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.24/5.53 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_iff
% 5.24/5.53 thf(fact_5283_less__minus__iff,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.53 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_iff
% 5.24/5.53 thf(fact_5284_minus__less__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.53 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_less_iff
% 5.24/5.53 thf(fact_5285_minus__less__iff,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.53 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_less_iff
% 5.24/5.53 thf(fact_5286_minus__less__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.53 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_less_iff
% 5.24/5.53 thf(fact_5287_minus__less__iff,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.53 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_less_iff
% 5.24/5.53 thf(fact_5288_verit__negate__coefficient_I2_J,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ A @ B )
% 5.24/5.53 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(2)
% 5.24/5.53 thf(fact_5289_verit__negate__coefficient_I2_J,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ord_less_int @ A @ B )
% 5.24/5.53 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(2)
% 5.24/5.53 thf(fact_5290_verit__negate__coefficient_I2_J,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ A @ B )
% 5.24/5.53 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(2)
% 5.24/5.53 thf(fact_5291_verit__negate__coefficient_I2_J,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.24/5.53 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_negate_coefficient(2)
% 5.24/5.53 thf(fact_5292_numeral__neq__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( numeral_numeral_real @ M )
% 5.24/5.53 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_numeral
% 5.24/5.53 thf(fact_5293_numeral__neq__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( numeral_numeral_int @ M )
% 5.24/5.53 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_numeral
% 5.24/5.53 thf(fact_5294_numeral__neq__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( numera6690914467698888265omplex @ M )
% 5.24/5.53 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_numeral
% 5.24/5.53 thf(fact_5295_numeral__neq__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( numeral_numeral_rat @ M )
% 5.24/5.53 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_numeral
% 5.24/5.53 thf(fact_5296_numeral__neq__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( numera6620942414471956472nteger @ M )
% 5.24/5.53 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_numeral
% 5.24/5.53 thf(fact_5297_neg__numeral__neq__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.24/5.53 != ( numeral_numeral_real @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_neq_numeral
% 5.24/5.53 thf(fact_5298_neg__numeral__neq__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.24/5.53 != ( numeral_numeral_int @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_neq_numeral
% 5.24/5.53 thf(fact_5299_neg__numeral__neq__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.24/5.53 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_neq_numeral
% 5.24/5.53 thf(fact_5300_neg__numeral__neq__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.24/5.53 != ( numeral_numeral_rat @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_neq_numeral
% 5.24/5.53 thf(fact_5301_neg__numeral__neq__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.24/5.53 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_neq_numeral
% 5.24/5.53 thf(fact_5302_square__eq__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ( times_times_real @ A @ A )
% 5.24/5.53 = ( times_times_real @ B @ B ) )
% 5.24/5.53 = ( ( A = B )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_iff
% 5.24/5.53 thf(fact_5303_square__eq__iff,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ( times_times_int @ A @ A )
% 5.24/5.53 = ( times_times_int @ B @ B ) )
% 5.24/5.53 = ( ( A = B )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_iff
% 5.24/5.53 thf(fact_5304_square__eq__iff,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( ( times_times_complex @ A @ A )
% 5.24/5.53 = ( times_times_complex @ B @ B ) )
% 5.24/5.53 = ( ( A = B )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_iff
% 5.24/5.53 thf(fact_5305_square__eq__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ( times_times_rat @ A @ A )
% 5.24/5.53 = ( times_times_rat @ B @ B ) )
% 5.24/5.53 = ( ( A = B )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_iff
% 5.24/5.53 thf(fact_5306_square__eq__iff,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.24/5.53 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.24/5.53 = ( ( A = B )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_iff
% 5.24/5.53 thf(fact_5307_minus__mult__commute,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.53 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_mult_commute
% 5.24/5.53 thf(fact_5308_minus__mult__commute,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.53 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_mult_commute
% 5.24/5.53 thf(fact_5309_minus__mult__commute,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.24/5.53 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_mult_commute
% 5.24/5.53 thf(fact_5310_minus__mult__commute,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.53 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_mult_commute
% 5.24/5.53 thf(fact_5311_minus__mult__commute,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.53 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_mult_commute
% 5.24/5.53 thf(fact_5312_one__neq__neg__one,axiom,
% 5.24/5.53 ( one_one_real
% 5.24/5.53 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_one
% 5.24/5.53 thf(fact_5313_one__neq__neg__one,axiom,
% 5.24/5.53 ( one_one_int
% 5.24/5.53 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_one
% 5.24/5.53 thf(fact_5314_one__neq__neg__one,axiom,
% 5.24/5.53 ( one_one_complex
% 5.24/5.53 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_one
% 5.24/5.53 thf(fact_5315_one__neq__neg__one,axiom,
% 5.24/5.53 ( one_one_rat
% 5.24/5.53 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_one
% 5.24/5.53 thf(fact_5316_one__neq__neg__one,axiom,
% 5.24/5.53 ( one_one_Code_integer
% 5.24/5.53 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_one
% 5.24/5.53 thf(fact_5317_group__cancel_Oneg1,axiom,
% 5.24/5.53 ! [A2: real,K: real,A: real] :
% 5.24/5.53 ( ( A2
% 5.24/5.53 = ( plus_plus_real @ K @ A ) )
% 5.24/5.53 => ( ( uminus_uminus_real @ A2 )
% 5.24/5.53 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.neg1
% 5.24/5.53 thf(fact_5318_group__cancel_Oneg1,axiom,
% 5.24/5.53 ! [A2: int,K: int,A: int] :
% 5.24/5.53 ( ( A2
% 5.24/5.53 = ( plus_plus_int @ K @ A ) )
% 5.24/5.53 => ( ( uminus_uminus_int @ A2 )
% 5.24/5.53 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.neg1
% 5.24/5.53 thf(fact_5319_group__cancel_Oneg1,axiom,
% 5.24/5.53 ! [A2: complex,K: complex,A: complex] :
% 5.24/5.53 ( ( A2
% 5.24/5.53 = ( plus_plus_complex @ K @ A ) )
% 5.24/5.53 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.24/5.53 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.neg1
% 5.24/5.53 thf(fact_5320_group__cancel_Oneg1,axiom,
% 5.24/5.53 ! [A2: rat,K: rat,A: rat] :
% 5.24/5.53 ( ( A2
% 5.24/5.53 = ( plus_plus_rat @ K @ A ) )
% 5.24/5.53 => ( ( uminus_uminus_rat @ A2 )
% 5.24/5.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.neg1
% 5.24/5.53 thf(fact_5321_group__cancel_Oneg1,axiom,
% 5.24/5.53 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.24/5.53 ( ( A2
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.24/5.53 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.neg1
% 5.24/5.53 thf(fact_5322_add_Oinverse__distrib__swap,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.24/5.53 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_distrib_swap
% 5.24/5.53 thf(fact_5323_add_Oinverse__distrib__swap,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.24/5.53 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_distrib_swap
% 5.24/5.53 thf(fact_5324_add_Oinverse__distrib__swap,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.24/5.53 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_distrib_swap
% 5.24/5.53 thf(fact_5325_add_Oinverse__distrib__swap,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.24/5.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_distrib_swap
% 5.24/5.53 thf(fact_5326_add_Oinverse__distrib__swap,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_distrib_swap
% 5.24/5.53 thf(fact_5327_is__num__normalize_I8_J,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.24/5.53 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % is_num_normalize(8)
% 5.24/5.53 thf(fact_5328_is__num__normalize_I8_J,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.24/5.53 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % is_num_normalize(8)
% 5.24/5.53 thf(fact_5329_is__num__normalize_I8_J,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.24/5.53 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % is_num_normalize(8)
% 5.24/5.53 thf(fact_5330_is__num__normalize_I8_J,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.24/5.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % is_num_normalize(8)
% 5.24/5.53 thf(fact_5331_is__num__normalize_I8_J,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % is_num_normalize(8)
% 5.24/5.53 thf(fact_5332_div__minus__right,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.53 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % div_minus_right
% 5.24/5.53 thf(fact_5333_div__minus__right,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.53 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % div_minus_right
% 5.24/5.53 thf(fact_5334_minus__divide__left,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.53 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_left
% 5.24/5.53 thf(fact_5335_minus__divide__left,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.53 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_left
% 5.24/5.53 thf(fact_5336_minus__divide__left,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.53 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_left
% 5.24/5.53 thf(fact_5337_minus__divide__divide,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.24/5.53 = ( divide_divide_real @ A @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_divide
% 5.24/5.53 thf(fact_5338_minus__divide__divide,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.53 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_divide
% 5.24/5.53 thf(fact_5339_minus__divide__divide,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.24/5.53 = ( divide_divide_rat @ A @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_divide
% 5.24/5.53 thf(fact_5340_minus__divide__right,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.53 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_right
% 5.24/5.53 thf(fact_5341_minus__divide__right,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.53 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_right
% 5.24/5.53 thf(fact_5342_minus__divide__right,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.53 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_right
% 5.24/5.53 thf(fact_5343_mod__minus__right,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus_right
% 5.24/5.53 thf(fact_5344_mod__minus__right,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus_right
% 5.24/5.53 thf(fact_5345_mod__minus__cong,axiom,
% 5.24/5.53 ! [A: int,B: int,A5: int] :
% 5.24/5.53 ( ( ( modulo_modulo_int @ A @ B )
% 5.24/5.53 = ( modulo_modulo_int @ A5 @ B ) )
% 5.24/5.53 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.53 = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus_cong
% 5.24/5.53 thf(fact_5346_mod__minus__cong,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer,A5: code_integer] :
% 5.24/5.53 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.24/5.53 = ( modulo364778990260209775nteger @ A5 @ B ) )
% 5.24/5.53 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.53 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus_cong
% 5.24/5.53 thf(fact_5347_mod__minus__eq,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.24/5.53 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus_eq
% 5.24/5.53 thf(fact_5348_mod__minus__eq,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.24/5.53 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_minus_eq
% 5.24/5.53 thf(fact_5349_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.24/5.53 ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5350_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.24/5.53 ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5351_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.24/5.53 ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5352_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.24/5.53 ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5353_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.24/5.53 ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5354_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.24/5.53 ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5355_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.24/5.53 ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5356_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.24/5.53 ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5357_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_real,F: real > int,G: real > int] :
% 5.24/5.53 ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5358_sum__mono,axiom,
% 5.24/5.53 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.24/5.53 ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ K5 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono
% 5.24/5.53 thf(fact_5359_sum__product,axiom,
% 5.24/5.53 ! [F: int > int,A2: set_int,G: int > int,B5: set_int] :
% 5.24/5.53 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B5 ) )
% 5.24/5.53 = ( groups4538972089207619220nt_int
% 5.24/5.53 @ ^ [I4: int] :
% 5.24/5.53 ( groups4538972089207619220nt_int
% 5.24/5.53 @ ^ [J3: int] : ( times_times_int @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.24/5.53 @ B5 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_product
% 5.24/5.53 thf(fact_5360_sum__product,axiom,
% 5.24/5.53 ! [F: complex > complex,A2: set_complex,G: complex > complex,B5: set_complex] :
% 5.24/5.53 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B5 ) )
% 5.24/5.53 = ( groups7754918857620584856omplex
% 5.24/5.53 @ ^ [I4: complex] :
% 5.24/5.53 ( groups7754918857620584856omplex
% 5.24/5.53 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.24/5.53 @ B5 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_product
% 5.24/5.53 thf(fact_5361_sum__product,axiom,
% 5.24/5.53 ! [F: nat > nat,A2: set_nat,G: nat > nat,B5: set_nat] :
% 5.24/5.53 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B5 ) )
% 5.24/5.53 = ( groups3542108847815614940at_nat
% 5.24/5.53 @ ^ [I4: nat] :
% 5.24/5.53 ( groups3542108847815614940at_nat
% 5.24/5.53 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.24/5.53 @ B5 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_product
% 5.24/5.53 thf(fact_5362_sum__product,axiom,
% 5.24/5.53 ! [F: nat > real,A2: set_nat,G: nat > real,B5: set_nat] :
% 5.24/5.53 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B5 ) )
% 5.24/5.53 = ( groups6591440286371151544t_real
% 5.24/5.53 @ ^ [I4: nat] :
% 5.24/5.53 ( groups6591440286371151544t_real
% 5.24/5.53 @ ^ [J3: nat] : ( times_times_real @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.24/5.53 @ B5 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_product
% 5.24/5.53 thf(fact_5363_sum__distrib__right,axiom,
% 5.24/5.53 ! [F: int > int,A2: set_int,R2: int] :
% 5.24/5.53 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R2 )
% 5.24/5.53 = ( groups4538972089207619220nt_int
% 5.24/5.53 @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R2 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_right
% 5.24/5.53 thf(fact_5364_sum__distrib__right,axiom,
% 5.24/5.53 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.24/5.53 = ( groups7754918857620584856omplex
% 5.24/5.53 @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R2 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_right
% 5.24/5.53 thf(fact_5365_sum__distrib__right,axiom,
% 5.24/5.53 ! [F: nat > nat,A2: set_nat,R2: nat] :
% 5.24/5.53 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R2 )
% 5.24/5.53 = ( groups3542108847815614940at_nat
% 5.24/5.53 @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R2 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_right
% 5.24/5.53 thf(fact_5366_sum__distrib__right,axiom,
% 5.24/5.53 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.24/5.53 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.24/5.53 = ( groups6591440286371151544t_real
% 5.24/5.53 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R2 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_right
% 5.24/5.53 thf(fact_5367_sum__distrib__left,axiom,
% 5.24/5.53 ! [R2: int,F: int > int,A2: set_int] :
% 5.24/5.53 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.24/5.53 = ( groups4538972089207619220nt_int
% 5.24/5.53 @ ^ [N2: int] : ( times_times_int @ R2 @ ( F @ N2 ) )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_left
% 5.24/5.53 thf(fact_5368_sum__distrib__left,axiom,
% 5.24/5.53 ! [R2: complex,F: complex > complex,A2: set_complex] :
% 5.24/5.53 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.24/5.53 = ( groups7754918857620584856omplex
% 5.24/5.53 @ ^ [N2: complex] : ( times_times_complex @ R2 @ ( F @ N2 ) )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_left
% 5.24/5.53 thf(fact_5369_sum__distrib__left,axiom,
% 5.24/5.53 ! [R2: nat,F: nat > nat,A2: set_nat] :
% 5.24/5.53 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.24/5.53 = ( groups3542108847815614940at_nat
% 5.24/5.53 @ ^ [N2: nat] : ( times_times_nat @ R2 @ ( F @ N2 ) )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_left
% 5.24/5.53 thf(fact_5370_sum__distrib__left,axiom,
% 5.24/5.53 ! [R2: real,F: nat > real,A2: set_nat] :
% 5.24/5.53 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.24/5.53 = ( groups6591440286371151544t_real
% 5.24/5.53 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( F @ N2 ) )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_distrib_left
% 5.24/5.53 thf(fact_5371_sum_Odistrib,axiom,
% 5.24/5.53 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.24/5.53 ( ( groups4538972089207619220nt_int
% 5.24/5.53 @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.53 @ A2 )
% 5.24/5.53 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.distrib
% 5.24/5.53 thf(fact_5372_sum_Odistrib,axiom,
% 5.24/5.53 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.24/5.53 ( ( groups7754918857620584856omplex
% 5.24/5.53 @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.53 @ A2 )
% 5.24/5.53 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.distrib
% 5.24/5.53 thf(fact_5373_sum_Odistrib,axiom,
% 5.24/5.53 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.24/5.53 ( ( groups3542108847815614940at_nat
% 5.24/5.53 @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.53 @ A2 )
% 5.24/5.53 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.distrib
% 5.24/5.53 thf(fact_5374_sum_Odistrib,axiom,
% 5.24/5.53 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.24/5.53 ( ( groups6591440286371151544t_real
% 5.24/5.53 @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.53 @ A2 )
% 5.24/5.53 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.distrib
% 5.24/5.53 thf(fact_5375_sum__divide__distrib,axiom,
% 5.24/5.53 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.24/5.53 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.24/5.53 = ( groups7754918857620584856omplex
% 5.24/5.53 @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R2 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_divide_distrib
% 5.24/5.53 thf(fact_5376_sum__divide__distrib,axiom,
% 5.24/5.53 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.24/5.53 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.24/5.53 = ( groups6591440286371151544t_real
% 5.24/5.53 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R2 )
% 5.24/5.53 @ A2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_divide_distrib
% 5.24/5.53 thf(fact_5377_mod__sum__eq,axiom,
% 5.24/5.53 ! [F: int > int,A: int,A2: set_int] :
% 5.24/5.53 ( ( modulo_modulo_int
% 5.24/5.53 @ ( groups4538972089207619220nt_int
% 5.24/5.53 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.24/5.53 @ A2 )
% 5.24/5.53 @ A )
% 5.24/5.53 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_sum_eq
% 5.24/5.53 thf(fact_5378_mod__sum__eq,axiom,
% 5.24/5.53 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.24/5.53 ( ( modulo_modulo_nat
% 5.24/5.53 @ ( groups3542108847815614940at_nat
% 5.24/5.53 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.24/5.53 @ A2 )
% 5.24/5.53 @ A )
% 5.24/5.53 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % mod_sum_eq
% 5.24/5.53 thf(fact_5379_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > real] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5380_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > real] :
% 5.24/5.53 ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5381_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > real] :
% 5.24/5.53 ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5382_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > rat] :
% 5.24/5.53 ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5383_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > rat] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5384_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > rat] :
% 5.24/5.53 ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5385_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > rat] :
% 5.24/5.53 ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5386_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > nat] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5387_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > nat] :
% 5.24/5.53 ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5388_sum__nonpos,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.53 ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonpos
% 5.24/5.53 thf(fact_5389_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > real] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5390_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > real] :
% 5.24/5.53 ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5391_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > real] :
% 5.24/5.53 ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5392_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > rat] :
% 5.24/5.53 ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5393_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > rat] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5394_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > rat] :
% 5.24/5.53 ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5395_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > rat] :
% 5.24/5.53 ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5396_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > nat] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5397_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > nat] :
% 5.24/5.53 ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5398_sum__nonneg,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.53 ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg
% 5.24/5.53 thf(fact_5399_ln__add__one__self__le__self2,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.53 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_add_one_self_le_self2
% 5.24/5.53 thf(fact_5400_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: int > rat,I5: set_int,G: int > rat,I2: int] :
% 5.24/5.53 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.24/5.53 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_int @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5401_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: real > rat,I5: set_real,G: real > rat,I2: real] :
% 5.24/5.53 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.24/5.53 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_real @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5402_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: nat > rat,I5: set_nat,G: nat > rat,I2: nat] :
% 5.24/5.53 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.24/5.53 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_nat @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_nat @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5403_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: complex > rat,I5: set_complex,G: complex > rat,I2: complex] :
% 5.24/5.53 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.24/5.53 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5404_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: int > nat,I5: set_int,G: int > nat,I2: int] :
% 5.24/5.53 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.24/5.53 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_int @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5405_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: real > nat,I5: set_real,G: real > nat,I2: real] :
% 5.24/5.53 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.24/5.53 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_real @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5406_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: complex > nat,I5: set_complex,G: complex > nat,I2: complex] :
% 5.24/5.53 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.24/5.53 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5407_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: real > int,I5: set_real,G: real > int,I2: real] :
% 5.24/5.53 ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 5.24/5.53 = ( groups1932886352136224148al_int @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_real @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5408_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: nat > int,I5: set_nat,G: nat > int,I2: nat] :
% 5.24/5.53 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 5.24/5.53 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_nat @ I2 @ I5 )
% 5.24/5.53 => ( ( finite_finite_nat @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5409_sum__mono__inv,axiom,
% 5.24/5.53 ! [F: complex > int,I5: set_complex,G: complex > int,I2: complex] :
% 5.24/5.53 ( ( ( groups5690904116761175830ex_int @ F @ I5 )
% 5.24/5.53 = ( groups5690904116761175830ex_int @ G @ I5 ) )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.24/5.53 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = ( G @ I2 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono_inv
% 5.24/5.53 thf(fact_5410_zero__less__eq__of__bool,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_eq_of_bool
% 5.24/5.53 thf(fact_5411_zero__less__eq__of__bool,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_eq_of_bool
% 5.24/5.53 thf(fact_5412_zero__less__eq__of__bool,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_eq_of_bool
% 5.24/5.53 thf(fact_5413_zero__less__eq__of__bool,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_eq_of_bool
% 5.24/5.53 thf(fact_5414_zero__less__eq__of__bool,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_less_eq_of_bool
% 5.24/5.53 thf(fact_5415_of__bool__less__eq__one,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_eq_one
% 5.24/5.53 thf(fact_5416_of__bool__less__eq__one,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_eq_one
% 5.24/5.53 thf(fact_5417_of__bool__less__eq__one,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_eq_one
% 5.24/5.53 thf(fact_5418_of__bool__less__eq__one,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_eq_one
% 5.24/5.53 thf(fact_5419_of__bool__less__eq__one,axiom,
% 5.24/5.53 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_less_eq_one
% 5.24/5.53 thf(fact_5420_split__of__bool__asm,axiom,
% 5.24/5.53 ! [P: complex > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 5.24/5.53 = ( ~ ( ( P6
% 5.24/5.53 & ~ ( P @ one_one_complex ) )
% 5.24/5.53 | ( ~ P6
% 5.24/5.53 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool_asm
% 5.24/5.53 thf(fact_5421_split__of__bool__asm,axiom,
% 5.24/5.53 ! [P: real > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 5.24/5.53 = ( ~ ( ( P6
% 5.24/5.53 & ~ ( P @ one_one_real ) )
% 5.24/5.53 | ( ~ P6
% 5.24/5.53 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool_asm
% 5.24/5.53 thf(fact_5422_split__of__bool__asm,axiom,
% 5.24/5.53 ! [P: rat > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 5.24/5.53 = ( ~ ( ( P6
% 5.24/5.53 & ~ ( P @ one_one_rat ) )
% 5.24/5.53 | ( ~ P6
% 5.24/5.53 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool_asm
% 5.24/5.53 thf(fact_5423_split__of__bool__asm,axiom,
% 5.24/5.53 ! [P: nat > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 5.24/5.53 = ( ~ ( ( P6
% 5.24/5.53 & ~ ( P @ one_one_nat ) )
% 5.24/5.53 | ( ~ P6
% 5.24/5.53 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool_asm
% 5.24/5.53 thf(fact_5424_split__of__bool__asm,axiom,
% 5.24/5.53 ! [P: int > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 5.24/5.53 = ( ~ ( ( P6
% 5.24/5.53 & ~ ( P @ one_one_int ) )
% 5.24/5.53 | ( ~ P6
% 5.24/5.53 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool_asm
% 5.24/5.53 thf(fact_5425_split__of__bool__asm,axiom,
% 5.24/5.53 ! [P: code_integer > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 5.24/5.53 = ( ~ ( ( P6
% 5.24/5.53 & ~ ( P @ one_one_Code_integer ) )
% 5.24/5.53 | ( ~ P6
% 5.24/5.53 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool_asm
% 5.24/5.53 thf(fact_5426_split__of__bool,axiom,
% 5.24/5.53 ! [P: complex > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n1201886186963655149omplex @ P6 ) )
% 5.24/5.53 = ( ( P6
% 5.24/5.53 => ( P @ one_one_complex ) )
% 5.24/5.53 & ( ~ P6
% 5.24/5.53 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool
% 5.24/5.53 thf(fact_5427_split__of__bool,axiom,
% 5.24/5.53 ! [P: real > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n3304061248610475627l_real @ P6 ) )
% 5.24/5.53 = ( ( P6
% 5.24/5.53 => ( P @ one_one_real ) )
% 5.24/5.53 & ( ~ P6
% 5.24/5.53 => ( P @ zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool
% 5.24/5.53 thf(fact_5428_split__of__bool,axiom,
% 5.24/5.53 ! [P: rat > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n2052037380579107095ol_rat @ P6 ) )
% 5.24/5.53 = ( ( P6
% 5.24/5.53 => ( P @ one_one_rat ) )
% 5.24/5.53 & ( ~ P6
% 5.24/5.53 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool
% 5.24/5.53 thf(fact_5429_split__of__bool,axiom,
% 5.24/5.53 ! [P: nat > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n2687167440665602831ol_nat @ P6 ) )
% 5.24/5.53 = ( ( P6
% 5.24/5.53 => ( P @ one_one_nat ) )
% 5.24/5.53 & ( ~ P6
% 5.24/5.53 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool
% 5.24/5.53 thf(fact_5430_split__of__bool,axiom,
% 5.24/5.53 ! [P: int > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n2684676970156552555ol_int @ P6 ) )
% 5.24/5.53 = ( ( P6
% 5.24/5.53 => ( P @ one_one_int ) )
% 5.24/5.53 & ( ~ P6
% 5.24/5.53 => ( P @ zero_zero_int ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool
% 5.24/5.53 thf(fact_5431_split__of__bool,axiom,
% 5.24/5.53 ! [P: code_integer > $o,P6: $o] :
% 5.24/5.53 ( ( P @ ( zero_n356916108424825756nteger @ P6 ) )
% 5.24/5.53 = ( ( P6
% 5.24/5.53 => ( P @ one_one_Code_integer ) )
% 5.24/5.53 & ( ~ P6
% 5.24/5.53 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % split_of_bool
% 5.24/5.53 thf(fact_5432_of__bool__def,axiom,
% 5.24/5.53 ( zero_n1201886186963655149omplex
% 5.24/5.53 = ( ^ [P4: $o] : ( if_complex @ P4 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_def
% 5.24/5.53 thf(fact_5433_of__bool__def,axiom,
% 5.24/5.53 ( zero_n3304061248610475627l_real
% 5.24/5.53 = ( ^ [P4: $o] : ( if_real @ P4 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_def
% 5.24/5.53 thf(fact_5434_of__bool__def,axiom,
% 5.24/5.53 ( zero_n2052037380579107095ol_rat
% 5.24/5.53 = ( ^ [P4: $o] : ( if_rat @ P4 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_def
% 5.24/5.53 thf(fact_5435_of__bool__def,axiom,
% 5.24/5.53 ( zero_n2687167440665602831ol_nat
% 5.24/5.53 = ( ^ [P4: $o] : ( if_nat @ P4 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_def
% 5.24/5.53 thf(fact_5436_of__bool__def,axiom,
% 5.24/5.53 ( zero_n2684676970156552555ol_int
% 5.24/5.53 = ( ^ [P4: $o] : ( if_int @ P4 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_def
% 5.24/5.53 thf(fact_5437_of__bool__def,axiom,
% 5.24/5.53 ( zero_n356916108424825756nteger
% 5.24/5.53 = ( ^ [P4: $o] : ( if_Code_integer @ P4 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_def
% 5.24/5.53 thf(fact_5438_not__numeral__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_numeral
% 5.24/5.53 thf(fact_5439_not__numeral__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_numeral
% 5.24/5.53 thf(fact_5440_not__numeral__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_numeral
% 5.24/5.53 thf(fact_5441_not__numeral__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_numeral
% 5.24/5.53 thf(fact_5442_neg__numeral__le__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_numeral
% 5.24/5.53 thf(fact_5443_neg__numeral__le__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_numeral
% 5.24/5.53 thf(fact_5444_neg__numeral__le__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_numeral
% 5.24/5.53 thf(fact_5445_neg__numeral__le__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_numeral
% 5.24/5.53 thf(fact_5446_zero__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( zero_zero_real
% 5.24/5.53 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_numeral
% 5.24/5.53 thf(fact_5447_zero__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( zero_zero_int
% 5.24/5.53 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_numeral
% 5.24/5.53 thf(fact_5448_zero__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( zero_zero_complex
% 5.24/5.53 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_numeral
% 5.24/5.53 thf(fact_5449_zero__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( zero_zero_rat
% 5.24/5.53 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_numeral
% 5.24/5.53 thf(fact_5450_zero__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( zero_z3403309356797280102nteger
% 5.24/5.53 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_numeral
% 5.24/5.53 thf(fact_5451_neg__numeral__less__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_numeral
% 5.24/5.53 thf(fact_5452_neg__numeral__less__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_numeral
% 5.24/5.53 thf(fact_5453_neg__numeral__less__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_numeral
% 5.24/5.53 thf(fact_5454_neg__numeral__less__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_numeral
% 5.24/5.53 thf(fact_5455_not__numeral__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_numeral
% 5.24/5.53 thf(fact_5456_not__numeral__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_numeral
% 5.24/5.53 thf(fact_5457_not__numeral__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_numeral
% 5.24/5.53 thf(fact_5458_not__numeral__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num,N: num] :
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_numeral
% 5.24/5.53 thf(fact_5459_le__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(4)
% 5.24/5.53 thf(fact_5460_le__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(4)
% 5.24/5.53 thf(fact_5461_le__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(4)
% 5.24/5.53 thf(fact_5462_le__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(4)
% 5.24/5.53 thf(fact_5463_le__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(2)
% 5.24/5.53 thf(fact_5464_le__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(2)
% 5.24/5.53 thf(fact_5465_le__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(2)
% 5.24/5.53 thf(fact_5466_le__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(2)
% 5.24/5.53 thf(fact_5467_zero__neq__neg__one,axiom,
% 5.24/5.53 ( zero_zero_real
% 5.24/5.53 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_one
% 5.24/5.53 thf(fact_5468_zero__neq__neg__one,axiom,
% 5.24/5.53 ( zero_zero_int
% 5.24/5.53 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_one
% 5.24/5.53 thf(fact_5469_zero__neq__neg__one,axiom,
% 5.24/5.53 ( zero_zero_complex
% 5.24/5.53 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_one
% 5.24/5.53 thf(fact_5470_zero__neq__neg__one,axiom,
% 5.24/5.53 ( zero_zero_rat
% 5.24/5.53 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_one
% 5.24/5.53 thf(fact_5471_zero__neq__neg__one,axiom,
% 5.24/5.53 ( zero_z3403309356797280102nteger
% 5.24/5.53 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % zero_neq_neg_one
% 5.24/5.53 thf(fact_5472_add__eq__0__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ( plus_plus_real @ A @ B )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 = ( B
% 5.24/5.53 = ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_eq_0_iff
% 5.24/5.53 thf(fact_5473_add__eq__0__iff,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ( plus_plus_int @ A @ B )
% 5.24/5.53 = zero_zero_int )
% 5.24/5.53 = ( B
% 5.24/5.53 = ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_eq_0_iff
% 5.24/5.53 thf(fact_5474_add__eq__0__iff,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( ( plus_plus_complex @ A @ B )
% 5.24/5.53 = zero_zero_complex )
% 5.24/5.53 = ( B
% 5.24/5.53 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_eq_0_iff
% 5.24/5.53 thf(fact_5475_add__eq__0__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ( plus_plus_rat @ A @ B )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 = ( B
% 5.24/5.53 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_eq_0_iff
% 5.24/5.53 thf(fact_5476_add__eq__0__iff,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.24/5.53 = zero_z3403309356797280102nteger )
% 5.24/5.53 = ( B
% 5.24/5.53 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_eq_0_iff
% 5.24/5.53 thf(fact_5477_ab__group__add__class_Oab__left__minus,axiom,
% 5.24/5.53 ! [A: real] :
% 5.24/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.24/5.53 = zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_left_minus
% 5.24/5.53 thf(fact_5478_ab__group__add__class_Oab__left__minus,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.24/5.53 = zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_left_minus
% 5.24/5.53 thf(fact_5479_ab__group__add__class_Oab__left__minus,axiom,
% 5.24/5.53 ! [A: complex] :
% 5.24/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.24/5.53 = zero_zero_complex ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_left_minus
% 5.24/5.53 thf(fact_5480_ab__group__add__class_Oab__left__minus,axiom,
% 5.24/5.53 ! [A: rat] :
% 5.24/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.24/5.53 = zero_zero_rat ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_left_minus
% 5.24/5.53 thf(fact_5481_ab__group__add__class_Oab__left__minus,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_left_minus
% 5.24/5.53 thf(fact_5482_add_Oinverse__unique,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ( plus_plus_real @ A @ B )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 => ( ( uminus_uminus_real @ A )
% 5.24/5.53 = B ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_unique
% 5.24/5.53 thf(fact_5483_add_Oinverse__unique,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ( plus_plus_int @ A @ B )
% 5.24/5.53 = zero_zero_int )
% 5.24/5.53 => ( ( uminus_uminus_int @ A )
% 5.24/5.53 = B ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_unique
% 5.24/5.53 thf(fact_5484_add_Oinverse__unique,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( ( plus_plus_complex @ A @ B )
% 5.24/5.53 = zero_zero_complex )
% 5.24/5.53 => ( ( uminus1482373934393186551omplex @ A )
% 5.24/5.53 = B ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_unique
% 5.24/5.53 thf(fact_5485_add_Oinverse__unique,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ( plus_plus_rat @ A @ B )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( ( uminus_uminus_rat @ A )
% 5.24/5.53 = B ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_unique
% 5.24/5.53 thf(fact_5486_add_Oinverse__unique,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.24/5.53 = zero_z3403309356797280102nteger )
% 5.24/5.53 => ( ( uminus1351360451143612070nteger @ A )
% 5.24/5.53 = B ) ) ).
% 5.24/5.53
% 5.24/5.53 % add.inverse_unique
% 5.24/5.53 thf(fact_5487_eq__neg__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus_uminus_real @ B ) )
% 5.24/5.53 = ( ( plus_plus_real @ A @ B )
% 5.24/5.53 = zero_zero_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_neg_iff_add_eq_0
% 5.24/5.53 thf(fact_5488_eq__neg__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus_uminus_int @ B ) )
% 5.24/5.53 = ( ( plus_plus_int @ A @ B )
% 5.24/5.53 = zero_zero_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_neg_iff_add_eq_0
% 5.24/5.53 thf(fact_5489_eq__neg__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.53 = ( ( plus_plus_complex @ A @ B )
% 5.24/5.53 = zero_zero_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_neg_iff_add_eq_0
% 5.24/5.53 thf(fact_5490_eq__neg__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus_uminus_rat @ B ) )
% 5.24/5.53 = ( ( plus_plus_rat @ A @ B )
% 5.24/5.53 = zero_zero_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_neg_iff_add_eq_0
% 5.24/5.53 thf(fact_5491_eq__neg__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.53 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_neg_iff_add_eq_0
% 5.24/5.53 thf(fact_5492_neg__eq__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ( uminus_uminus_real @ A )
% 5.24/5.53 = B )
% 5.24/5.53 = ( ( plus_plus_real @ A @ B )
% 5.24/5.53 = zero_zero_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_eq_iff_add_eq_0
% 5.24/5.53 thf(fact_5493_neg__eq__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: int,B: int] :
% 5.24/5.53 ( ( ( uminus_uminus_int @ A )
% 5.24/5.53 = B )
% 5.24/5.53 = ( ( plus_plus_int @ A @ B )
% 5.24/5.53 = zero_zero_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_eq_iff_add_eq_0
% 5.24/5.53 thf(fact_5494_neg__eq__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( ( uminus1482373934393186551omplex @ A )
% 5.24/5.53 = B )
% 5.24/5.53 = ( ( plus_plus_complex @ A @ B )
% 5.24/5.53 = zero_zero_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_eq_iff_add_eq_0
% 5.24/5.53 thf(fact_5495_neg__eq__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ( uminus_uminus_rat @ A )
% 5.24/5.53 = B )
% 5.24/5.53 = ( ( plus_plus_rat @ A @ B )
% 5.24/5.53 = zero_zero_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_eq_iff_add_eq_0
% 5.24/5.53 thf(fact_5496_neg__eq__iff__add__eq__0,axiom,
% 5.24/5.53 ! [A: code_integer,B: code_integer] :
% 5.24/5.53 ( ( ( uminus1351360451143612070nteger @ A )
% 5.24/5.53 = B )
% 5.24/5.53 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.24/5.53 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_eq_iff_add_eq_0
% 5.24/5.53 thf(fact_5497_less__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(4)
% 5.24/5.53 thf(fact_5498_less__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(4)
% 5.24/5.53 thf(fact_5499_less__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(4)
% 5.24/5.53 thf(fact_5500_less__minus__one__simps_I4_J,axiom,
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(4)
% 5.24/5.53 thf(fact_5501_less__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(2)
% 5.24/5.53 thf(fact_5502_less__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(2)
% 5.24/5.53 thf(fact_5503_less__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(2)
% 5.24/5.53 thf(fact_5504_less__minus__one__simps_I2_J,axiom,
% 5.24/5.53 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(2)
% 5.24/5.53 thf(fact_5505_numeral__times__minus__swap,axiom,
% 5.24/5.53 ! [W2: num,X: real] :
% 5.24/5.53 ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( uminus_uminus_real @ X ) )
% 5.24/5.53 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_times_minus_swap
% 5.24/5.53 thf(fact_5506_numeral__times__minus__swap,axiom,
% 5.24/5.53 ! [W2: num,X: int] :
% 5.24/5.53 ( ( times_times_int @ ( numeral_numeral_int @ W2 ) @ ( uminus_uminus_int @ X ) )
% 5.24/5.53 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_times_minus_swap
% 5.24/5.53 thf(fact_5507_numeral__times__minus__swap,axiom,
% 5.24/5.53 ! [W2: num,X: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.24/5.53 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_times_minus_swap
% 5.24/5.53 thf(fact_5508_numeral__times__minus__swap,axiom,
% 5.24/5.53 ! [W2: num,X: rat] :
% 5.24/5.53 ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ ( uminus_uminus_rat @ X ) )
% 5.24/5.53 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_times_minus_swap
% 5.24/5.53 thf(fact_5509_numeral__times__minus__swap,axiom,
% 5.24/5.53 ! [W2: num,X: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.24/5.53 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_times_minus_swap
% 5.24/5.53 thf(fact_5510_nonzero__minus__divide__divide,axiom,
% 5.24/5.53 ! [B: real,A: real] :
% 5.24/5.53 ( ( B != zero_zero_real )
% 5.24/5.53 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.24/5.53 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_minus_divide_divide
% 5.24/5.53 thf(fact_5511_nonzero__minus__divide__divide,axiom,
% 5.24/5.53 ! [B: complex,A: complex] :
% 5.24/5.53 ( ( B != zero_zero_complex )
% 5.24/5.53 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.53 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_minus_divide_divide
% 5.24/5.53 thf(fact_5512_nonzero__minus__divide__divide,axiom,
% 5.24/5.53 ! [B: rat,A: rat] :
% 5.24/5.53 ( ( B != zero_zero_rat )
% 5.24/5.53 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.24/5.53 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_minus_divide_divide
% 5.24/5.53 thf(fact_5513_nonzero__minus__divide__right,axiom,
% 5.24/5.53 ! [B: real,A: real] :
% 5.24/5.53 ( ( B != zero_zero_real )
% 5.24/5.53 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.53 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_minus_divide_right
% 5.24/5.53 thf(fact_5514_nonzero__minus__divide__right,axiom,
% 5.24/5.53 ! [B: complex,A: complex] :
% 5.24/5.53 ( ( B != zero_zero_complex )
% 5.24/5.53 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.53 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_minus_divide_right
% 5.24/5.53 thf(fact_5515_nonzero__minus__divide__right,axiom,
% 5.24/5.53 ! [B: rat,A: rat] :
% 5.24/5.53 ( ( B != zero_zero_rat )
% 5.24/5.53 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.53 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_minus_divide_right
% 5.24/5.53 thf(fact_5516_numeral__neq__neg__one,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( numeral_numeral_real @ N )
% 5.24/5.53 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_one
% 5.24/5.53 thf(fact_5517_numeral__neq__neg__one,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( numeral_numeral_int @ N )
% 5.24/5.53 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_one
% 5.24/5.53 thf(fact_5518_numeral__neq__neg__one,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( numera6690914467698888265omplex @ N )
% 5.24/5.53 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_one
% 5.24/5.53 thf(fact_5519_numeral__neq__neg__one,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( numeral_numeral_rat @ N )
% 5.24/5.53 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_one
% 5.24/5.53 thf(fact_5520_numeral__neq__neg__one,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( ( numera6620942414471956472nteger @ N )
% 5.24/5.53 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % numeral_neq_neg_one
% 5.24/5.53 thf(fact_5521_one__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( one_one_real
% 5.24/5.53 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_numeral
% 5.24/5.53 thf(fact_5522_one__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( one_one_int
% 5.24/5.53 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_numeral
% 5.24/5.53 thf(fact_5523_one__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( one_one_complex
% 5.24/5.53 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_numeral
% 5.24/5.53 thf(fact_5524_one__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( one_one_rat
% 5.24/5.53 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_numeral
% 5.24/5.53 thf(fact_5525_one__neq__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ( one_one_Code_integer
% 5.24/5.53 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % one_neq_neg_numeral
% 5.24/5.53 thf(fact_5526_square__eq__1__iff,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ( times_times_real @ X @ X )
% 5.24/5.53 = one_one_real )
% 5.24/5.53 = ( ( X = one_one_real )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_1_iff
% 5.24/5.53 thf(fact_5527_square__eq__1__iff,axiom,
% 5.24/5.53 ! [X: int] :
% 5.24/5.53 ( ( ( times_times_int @ X @ X )
% 5.24/5.53 = one_one_int )
% 5.24/5.53 = ( ( X = one_one_int )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_1_iff
% 5.24/5.53 thf(fact_5528_square__eq__1__iff,axiom,
% 5.24/5.53 ! [X: complex] :
% 5.24/5.53 ( ( ( times_times_complex @ X @ X )
% 5.24/5.53 = one_one_complex )
% 5.24/5.53 = ( ( X = one_one_complex )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_1_iff
% 5.24/5.53 thf(fact_5529_square__eq__1__iff,axiom,
% 5.24/5.53 ! [X: rat] :
% 5.24/5.53 ( ( ( times_times_rat @ X @ X )
% 5.24/5.53 = one_one_rat )
% 5.24/5.53 = ( ( X = one_one_rat )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_1_iff
% 5.24/5.53 thf(fact_5530_square__eq__1__iff,axiom,
% 5.24/5.53 ! [X: code_integer] :
% 5.24/5.53 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.24/5.53 = one_one_Code_integer )
% 5.24/5.53 = ( ( X = one_one_Code_integer )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % square_eq_1_iff
% 5.24/5.53 thf(fact_5531_group__cancel_Osub2,axiom,
% 5.24/5.53 ! [B5: real,K: real,B: real,A: real] :
% 5.24/5.53 ( ( B5
% 5.24/5.53 = ( plus_plus_real @ K @ B ) )
% 5.24/5.53 => ( ( minus_minus_real @ A @ B5 )
% 5.24/5.53 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.sub2
% 5.24/5.53 thf(fact_5532_group__cancel_Osub2,axiom,
% 5.24/5.53 ! [B5: int,K: int,B: int,A: int] :
% 5.24/5.53 ( ( B5
% 5.24/5.53 = ( plus_plus_int @ K @ B ) )
% 5.24/5.53 => ( ( minus_minus_int @ A @ B5 )
% 5.24/5.53 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.sub2
% 5.24/5.53 thf(fact_5533_group__cancel_Osub2,axiom,
% 5.24/5.53 ! [B5: complex,K: complex,B: complex,A: complex] :
% 5.24/5.53 ( ( B5
% 5.24/5.53 = ( plus_plus_complex @ K @ B ) )
% 5.24/5.53 => ( ( minus_minus_complex @ A @ B5 )
% 5.24/5.53 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.sub2
% 5.24/5.53 thf(fact_5534_group__cancel_Osub2,axiom,
% 5.24/5.53 ! [B5: rat,K: rat,B: rat,A: rat] :
% 5.24/5.53 ( ( B5
% 5.24/5.53 = ( plus_plus_rat @ K @ B ) )
% 5.24/5.53 => ( ( minus_minus_rat @ A @ B5 )
% 5.24/5.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.sub2
% 5.24/5.53 thf(fact_5535_group__cancel_Osub2,axiom,
% 5.24/5.53 ! [B5: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.24/5.53 ( ( B5
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.24/5.53 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 5.24/5.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % group_cancel.sub2
% 5.24/5.53 thf(fact_5536_diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_real
% 5.24/5.53 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_conv_add_uminus
% 5.24/5.53 thf(fact_5537_diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_int
% 5.24/5.53 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_conv_add_uminus
% 5.24/5.53 thf(fact_5538_diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_complex
% 5.24/5.53 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_conv_add_uminus
% 5.24/5.53 thf(fact_5539_diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_rat
% 5.24/5.53 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_conv_add_uminus
% 5.24/5.53 thf(fact_5540_diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_8373710615458151222nteger
% 5.24/5.53 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % diff_conv_add_uminus
% 5.24/5.53 thf(fact_5541_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_real
% 5.24/5.53 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.24/5.53 thf(fact_5542_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_int
% 5.24/5.53 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.24/5.53 thf(fact_5543_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_complex
% 5.24/5.53 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.24/5.53 thf(fact_5544_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_minus_rat
% 5.24/5.53 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.24/5.53 thf(fact_5545_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.24/5.53 ( minus_8373710615458151222nteger
% 5.24/5.53 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.24/5.53 thf(fact_5546_replicate__length__same,axiom,
% 5.24/5.53 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.24/5.53 ( ! [X3: vEBT_VEBT] :
% 5.24/5.53 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.24/5.53 => ( X3 = X ) )
% 5.24/5.53 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 5.24/5.53 = Xs2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_length_same
% 5.24/5.53 thf(fact_5547_replicate__length__same,axiom,
% 5.24/5.53 ! [Xs2: list_o,X: $o] :
% 5.24/5.53 ( ! [X3: $o] :
% 5.24/5.53 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.24/5.53 => ( X3 = X ) )
% 5.24/5.53 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 5.24/5.53 = Xs2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_length_same
% 5.24/5.53 thf(fact_5548_replicate__length__same,axiom,
% 5.24/5.53 ! [Xs2: list_nat,X: nat] :
% 5.24/5.53 ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.24/5.53 => ( X3 = X ) )
% 5.24/5.53 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 5.24/5.53 = Xs2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_length_same
% 5.24/5.53 thf(fact_5549_replicate__length__same,axiom,
% 5.24/5.53 ! [Xs2: list_int,X: int] :
% 5.24/5.53 ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.24/5.53 => ( X3 = X ) )
% 5.24/5.53 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 5.24/5.53 = Xs2 ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_length_same
% 5.24/5.53 thf(fact_5550_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_real,N: nat,X: real] :
% 5.24/5.53 ( ( ( size_size_list_real @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: real] :
% 5.24/5.53 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replicate_real @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5551_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_complex,N: nat,X: complex] :
% 5.24/5.53 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: complex] :
% 5.24/5.53 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replicate_complex @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5552_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 5.24/5.53 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: product_prod_nat_nat] :
% 5.24/5.53 ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replic4235873036481779905at_nat @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5553_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 5.24/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: vEBT_VEBT] :
% 5.24/5.53 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5554_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_o,N: nat,X: $o] :
% 5.24/5.53 ( ( ( size_size_list_o @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: $o] :
% 5.24/5.53 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replicate_o @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5555_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_nat,N: nat,X: nat] :
% 5.24/5.53 ( ( ( size_size_list_nat @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: nat] :
% 5.24/5.53 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replicate_nat @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5556_replicate__eqI,axiom,
% 5.24/5.53 ! [Xs2: list_int,N: nat,X: int] :
% 5.24/5.53 ( ( ( size_size_list_int @ Xs2 )
% 5.24/5.53 = N )
% 5.24/5.53 => ( ! [Y3: int] :
% 5.24/5.53 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.24/5.53 => ( Y3 = X ) )
% 5.24/5.53 => ( Xs2
% 5.24/5.53 = ( replicate_int @ N @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % replicate_eqI
% 5.24/5.53 thf(fact_5557_dvd__div__neg,axiom,
% 5.24/5.53 ! [B: real,A: real] :
% 5.24/5.53 ( ( dvd_dvd_real @ B @ A )
% 5.24/5.53 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.24/5.53 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_div_neg
% 5.24/5.53 thf(fact_5558_dvd__div__neg,axiom,
% 5.24/5.53 ! [B: int,A: int] :
% 5.24/5.53 ( ( dvd_dvd_int @ B @ A )
% 5.24/5.53 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.53 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_div_neg
% 5.24/5.53 thf(fact_5559_dvd__div__neg,axiom,
% 5.24/5.53 ! [B: complex,A: complex] :
% 5.24/5.53 ( ( dvd_dvd_complex @ B @ A )
% 5.24/5.53 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_div_neg
% 5.24/5.53 thf(fact_5560_dvd__div__neg,axiom,
% 5.24/5.53 ! [B: rat,A: rat] :
% 5.24/5.53 ( ( dvd_dvd_rat @ B @ A )
% 5.24/5.53 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.24/5.53 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_div_neg
% 5.24/5.53 thf(fact_5561_dvd__div__neg,axiom,
% 5.24/5.53 ! [B: code_integer,A: code_integer] :
% 5.24/5.53 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.53 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_div_neg
% 5.24/5.53 thf(fact_5562_dvd__neg__div,axiom,
% 5.24/5.53 ! [B: real,A: real] :
% 5.24/5.53 ( ( dvd_dvd_real @ B @ A )
% 5.24/5.53 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.53 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_neg_div
% 5.24/5.53 thf(fact_5563_dvd__neg__div,axiom,
% 5.24/5.53 ! [B: int,A: int] :
% 5.24/5.53 ( ( dvd_dvd_int @ B @ A )
% 5.24/5.53 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.53 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_neg_div
% 5.24/5.53 thf(fact_5564_dvd__neg__div,axiom,
% 5.24/5.53 ! [B: complex,A: complex] :
% 5.24/5.53 ( ( dvd_dvd_complex @ B @ A )
% 5.24/5.53 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_neg_div
% 5.24/5.53 thf(fact_5565_dvd__neg__div,axiom,
% 5.24/5.53 ! [B: rat,A: rat] :
% 5.24/5.53 ( ( dvd_dvd_rat @ B @ A )
% 5.24/5.53 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.53 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_neg_div
% 5.24/5.53 thf(fact_5566_dvd__neg__div,axiom,
% 5.24/5.53 ! [B: code_integer,A: code_integer] :
% 5.24/5.53 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.24/5.53 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % dvd_neg_div
% 5.24/5.53 thf(fact_5567_subset__Compl__self__eq,axiom,
% 5.24/5.53 ! [A2: set_int] :
% 5.24/5.53 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.24/5.53 = ( A2 = bot_bot_set_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % subset_Compl_self_eq
% 5.24/5.53 thf(fact_5568_subset__Compl__self__eq,axiom,
% 5.24/5.53 ! [A2: set_real] :
% 5.24/5.53 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 5.24/5.53 = ( A2 = bot_bot_set_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % subset_Compl_self_eq
% 5.24/5.53 thf(fact_5569_subset__Compl__self__eq,axiom,
% 5.24/5.53 ! [A2: set_nat] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.24/5.53 = ( A2 = bot_bot_set_nat ) ) ).
% 5.24/5.53
% 5.24/5.53 % subset_Compl_self_eq
% 5.24/5.53 thf(fact_5570_real__minus__mult__self__le,axiom,
% 5.24/5.53 ! [U2: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U2 @ U2 ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.24/5.53
% 5.24/5.53 % real_minus_mult_self_le
% 5.24/5.53 thf(fact_5571_pos__zmult__eq__1__iff__lemma,axiom,
% 5.24/5.53 ! [M: int,N: int] :
% 5.24/5.53 ( ( ( times_times_int @ M @ N )
% 5.24/5.53 = one_one_int )
% 5.24/5.53 => ( ( M = one_one_int )
% 5.24/5.53 | ( M
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_zmult_eq_1_iff_lemma
% 5.24/5.53 thf(fact_5572_zmult__eq__1__iff,axiom,
% 5.24/5.53 ! [M: int,N: int] :
% 5.24/5.53 ( ( ( times_times_int @ M @ N )
% 5.24/5.53 = one_one_int )
% 5.24/5.53 = ( ( ( M = one_one_int )
% 5.24/5.53 & ( N = one_one_int ) )
% 5.24/5.53 | ( ( M
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.53 & ( N
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % zmult_eq_1_iff
% 5.24/5.53 thf(fact_5573_minus__real__def,axiom,
% 5.24/5.53 ( minus_minus_real
% 5.24/5.53 = ( ^ [X2: real,Y: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_real_def
% 5.24/5.53 thf(fact_5574_ln__one__minus__pos__upper__bound,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.53 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_one_minus_pos_upper_bound
% 5.24/5.53 thf(fact_5575_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > real] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 = ( ! [X2: int] :
% 5.24/5.53 ( ( member_int @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5576_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > real] :
% 5.24/5.53 ( ( finite_finite_real @ A2 )
% 5.24/5.53 => ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 = ( ! [X2: real] :
% 5.24/5.53 ( ( member_real @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5577_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 = ( ! [X2: complex] :
% 5.24/5.53 ( ( member_complex @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5578_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > rat] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 = ( ! [X2: int] :
% 5.24/5.53 ( ( member_int @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5579_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > rat] :
% 5.24/5.53 ( ( finite_finite_real @ A2 )
% 5.24/5.53 => ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 = ( ! [X2: real] :
% 5.24/5.53 ( ( member_real @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5580_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 = ( ! [X2: nat] :
% 5.24/5.53 ( ( member_nat @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5581_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 = ( ! [X2: complex] :
% 5.24/5.53 ( ( member_complex @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5582_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > nat] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.24/5.53 = zero_zero_nat )
% 5.24/5.53 = ( ! [X2: int] :
% 5.24/5.53 ( ( member_int @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_nat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5583_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > nat] :
% 5.24/5.53 ( ( finite_finite_real @ A2 )
% 5.24/5.53 => ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.24/5.53 = zero_zero_nat )
% 5.24/5.53 = ( ! [X2: real] :
% 5.24/5.53 ( ( member_real @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_nat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5584_sum__nonneg__eq__0__iff,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.53 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.24/5.53 = zero_zero_nat )
% 5.24/5.53 = ( ! [X2: complex] :
% 5.24/5.53 ( ( member_complex @ X2 @ A2 )
% 5.24/5.53 => ( ( F @ X2 )
% 5.24/5.53 = zero_zero_nat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_eq_0_iff
% 5.24/5.53 thf(fact_5585_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_complex,T: set_complex,G: complex > real,I2: complex > complex,F: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ T )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: complex] :
% 5.24/5.53 ( ( member_complex @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5586_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_nat,T: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ S2 )
% 5.24/5.53 => ( ( finite_finite_nat @ T )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: nat] :
% 5.24/5.53 ( ( member_nat @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5587_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_nat,T: set_complex,G: complex > rat,I2: complex > nat,F: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ S2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ T )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: complex] :
% 5.24/5.53 ( ( member_complex @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5588_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_complex,T: set_nat,G: nat > rat,I2: nat > complex,F: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ( finite_finite_nat @ T )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: nat] :
% 5.24/5.53 ( ( member_nat @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5589_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_complex,T: set_complex,G: complex > rat,I2: complex > complex,F: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ T )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: complex] :
% 5.24/5.53 ( ( member_complex @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5590_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_complex,T: set_complex,G: complex > nat,I2: complex > complex,F: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ T )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: complex] :
% 5.24/5.53 ( ( member_complex @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5591_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_nat,T: set_nat,G: nat > int,I2: nat > nat,F: nat > int] :
% 5.24/5.53 ( ( finite_finite_nat @ S2 )
% 5.24/5.53 => ( ( finite_finite_nat @ T )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: nat] :
% 5.24/5.53 ( ( member_nat @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S2 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5592_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_nat,T: set_complex,G: complex > int,I2: complex > nat,F: nat > int] :
% 5.24/5.53 ( ( finite_finite_nat @ S2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ T )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: complex] :
% 5.24/5.53 ( ( member_complex @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S2 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5593_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_complex,T: set_nat,G: nat > int,I2: nat > complex,F: complex > int] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ( finite_finite_nat @ T )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: nat] :
% 5.24/5.53 ( ( member_nat @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S2 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5594_sum__le__included,axiom,
% 5.24/5.53 ! [S2: set_complex,T: set_complex,G: complex > int,I2: complex > complex,F: complex > int] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ T )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ T )
% 5.24/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S2 )
% 5.24/5.53 => ? [Xa: complex] :
% 5.24/5.53 ( ( member_complex @ Xa @ T )
% 5.24/5.53 & ( ( I2 @ Xa )
% 5.24/5.53 = X3 )
% 5.24/5.53 & ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S2 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_le_included
% 5.24/5.53 thf(fact_5595_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: complex] :
% 5.24/5.53 ( ( member_complex @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5596_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: nat] :
% 5.24/5.53 ( ( member_nat @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5597_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: complex] :
% 5.24/5.53 ( ( member_complex @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5598_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: complex] :
% 5.24/5.53 ( ( member_complex @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5599_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.24/5.53 ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: nat] :
% 5.24/5.53 ( ( member_nat @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5600_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: complex] :
% 5.24/5.53 ( ( member_complex @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5601_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > int,G: int > int] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: int] :
% 5.24/5.53 ( ( member_int @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5602_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.24/5.53 ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: nat] :
% 5.24/5.53 ( ( member_nat @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5603_sum__strict__mono__ex1,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.24/5.53 ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ? [X5: nat] :
% 5.24/5.53 ( ( member_nat @ X5 @ A2 )
% 5.24/5.53 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.24/5.53 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono_ex1
% 5.24/5.53 thf(fact_5604_sum_Orelated,axiom,
% 5.24/5.53 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.24/5.53 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.24/5.53 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite_finite_nat @ S3 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups2073611262835488442omplex @ H2 @ S3 ) @ ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5605_sum_Orelated,axiom,
% 5.24/5.53 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.24/5.53 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.24/5.53 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5606_sum_Orelated,axiom,
% 5.24/5.53 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.24/5.53 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.24/5.53 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite_finite_nat @ S3 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5607_sum_Orelated,axiom,
% 5.24/5.53 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.24/5.53 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.24/5.53 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5608_sum_Orelated,axiom,
% 5.24/5.53 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.24/5.53 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.24/5.53 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5609_sum_Orelated,axiom,
% 5.24/5.53 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.24/5.53 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.24/5.53 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite_finite_nat @ S3 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups3539618377306564664at_int @ H2 @ S3 ) @ ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5610_sum_Orelated,axiom,
% 5.24/5.53 ! [R: int > int > $o,S3: set_complex,H2: complex > int,G: complex > int] :
% 5.24/5.53 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.24/5.53 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups5690904116761175830ex_int @ H2 @ S3 ) @ ( groups5690904116761175830ex_int @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5611_sum_Orelated,axiom,
% 5.24/5.53 ! [R: int > int > $o,S3: set_int,H2: int > int,G: int > int] :
% 5.24/5.53 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.24/5.53 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite_finite_int @ S3 )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups4538972089207619220nt_int @ H2 @ S3 ) @ ( groups4538972089207619220nt_int @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5612_sum_Orelated,axiom,
% 5.24/5.53 ! [R: complex > complex > $o,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.24/5.53 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.24/5.53 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups7754918857620584856omplex @ H2 @ S3 ) @ ( groups7754918857620584856omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5613_sum_Orelated,axiom,
% 5.24/5.53 ! [R: nat > nat > $o,S3: set_nat,H2: nat > nat,G: nat > nat] :
% 5.24/5.53 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.24/5.53 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.24/5.53 ( ( ( R @ X15 @ X23 )
% 5.24/5.53 & ( R @ Y15 @ Y23 ) )
% 5.24/5.53 => ( R @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.24/5.53 => ( ( finite_finite_nat @ S3 )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ S3 )
% 5.24/5.53 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( R @ ( groups3542108847815614940at_nat @ H2 @ S3 ) @ ( groups3542108847815614940at_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.related
% 5.24/5.53 thf(fact_5614_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_complex )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5615_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > real,G: int > real] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_int )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5616_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > real,G: real > real] :
% 5.24/5.53 ( ( finite_finite_real @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_real )
% 5.24/5.53 => ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5617_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_complex )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5618_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_nat )
% 5.24/5.53 => ( ! [X3: nat] :
% 5.24/5.53 ( ( member_nat @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5619_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_int )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5620_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.24/5.53 ( ( finite_finite_real @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_real )
% 5.24/5.53 => ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5621_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_complex )
% 5.24/5.53 => ( ! [X3: complex] :
% 5.24/5.53 ( ( member_complex @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5622_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.24/5.53 ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_int )
% 5.24/5.53 => ( ! [X3: int] :
% 5.24/5.53 ( ( member_int @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5623_sum__strict__mono,axiom,
% 5.24/5.53 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.24/5.53 ( ( finite_finite_real @ A2 )
% 5.24/5.53 => ( ( A2 != bot_bot_set_real )
% 5.24/5.53 => ( ! [X3: real] :
% 5.24/5.53 ( ( member_real @ X3 @ A2 )
% 5.24/5.53 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_strict_mono
% 5.24/5.53 thf(fact_5624_ln__gt__zero,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_gt_zero
% 5.24/5.53 thf(fact_5625_ln__less__zero,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.53 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_less_zero
% 5.24/5.53 thf(fact_5626_ln__gt__zero__imp__gt__one,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_gt_zero_imp_gt_one
% 5.24/5.53 thf(fact_5627_ln__ge__zero,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_ge_zero
% 5.24/5.53 thf(fact_5628_not__zero__le__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_le_neg_numeral
% 5.24/5.53 thf(fact_5629_not__zero__le__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_le_neg_numeral
% 5.24/5.53 thf(fact_5630_not__zero__le__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_le_neg_numeral
% 5.24/5.53 thf(fact_5631_not__zero__le__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_le_neg_numeral
% 5.24/5.53 thf(fact_5632_neg__numeral__le__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_zero
% 5.24/5.53 thf(fact_5633_neg__numeral__le__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_zero
% 5.24/5.53 thf(fact_5634_neg__numeral__le__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_zero
% 5.24/5.53 thf(fact_5635_neg__numeral__le__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_zero
% 5.24/5.53 thf(fact_5636_neg__numeral__less__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_zero
% 5.24/5.53 thf(fact_5637_neg__numeral__less__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_zero
% 5.24/5.53 thf(fact_5638_neg__numeral__less__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_zero
% 5.24/5.53 thf(fact_5639_neg__numeral__less__zero,axiom,
% 5.24/5.53 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_zero
% 5.24/5.53 thf(fact_5640_not__zero__less__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_less_neg_numeral
% 5.24/5.53 thf(fact_5641_not__zero__less__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_less_neg_numeral
% 5.24/5.53 thf(fact_5642_not__zero__less__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_less_neg_numeral
% 5.24/5.53 thf(fact_5643_not__zero__less__neg__numeral,axiom,
% 5.24/5.53 ! [N: num] :
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_zero_less_neg_numeral
% 5.24/5.53 thf(fact_5644_le__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(3)
% 5.24/5.53 thf(fact_5645_le__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(3)
% 5.24/5.53 thf(fact_5646_le__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(3)
% 5.24/5.53 thf(fact_5647_le__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(3)
% 5.24/5.53 thf(fact_5648_le__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(1)
% 5.24/5.53 thf(fact_5649_le__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(1)
% 5.24/5.53 thf(fact_5650_le__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(1)
% 5.24/5.53 thf(fact_5651_le__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.24/5.53
% 5.24/5.53 % le_minus_one_simps(1)
% 5.24/5.53 thf(fact_5652_less__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(1)
% 5.24/5.53 thf(fact_5653_less__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(1)
% 5.24/5.53 thf(fact_5654_less__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(1)
% 5.24/5.53 thf(fact_5655_less__minus__one__simps_I1_J,axiom,
% 5.24/5.53 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(1)
% 5.24/5.53 thf(fact_5656_less__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(3)
% 5.24/5.53 thf(fact_5657_less__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(3)
% 5.24/5.53 thf(fact_5658_less__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(3)
% 5.24/5.53 thf(fact_5659_less__minus__one__simps_I3_J,axiom,
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_one_simps(3)
% 5.24/5.53 thf(fact_5660_not__one__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_le_neg_numeral
% 5.24/5.53 thf(fact_5661_not__one__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_le_neg_numeral
% 5.24/5.53 thf(fact_5662_not__one__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_le_neg_numeral
% 5.24/5.53 thf(fact_5663_not__one__le__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_le_neg_numeral
% 5.24/5.53 thf(fact_5664_not__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_one
% 5.24/5.53 thf(fact_5665_not__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_one
% 5.24/5.53 thf(fact_5666_not__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_one
% 5.24/5.53 thf(fact_5667_not__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_le_neg_one
% 5.24/5.53 thf(fact_5668_neg__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_neg_one
% 5.24/5.53 thf(fact_5669_neg__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_neg_one
% 5.24/5.53 thf(fact_5670_neg__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_neg_one
% 5.24/5.53 thf(fact_5671_neg__numeral__le__neg__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_neg_one
% 5.24/5.53 thf(fact_5672_neg__one__le__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_le_numeral
% 5.24/5.53 thf(fact_5673_neg__one__le__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_le_numeral
% 5.24/5.53 thf(fact_5674_neg__one__le__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_le_numeral
% 5.24/5.53 thf(fact_5675_neg__one__le__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_le_numeral
% 5.24/5.53 thf(fact_5676_neg__numeral__le__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_one
% 5.24/5.53 thf(fact_5677_neg__numeral__le__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_one
% 5.24/5.53 thf(fact_5678_neg__numeral__le__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_one
% 5.24/5.53 thf(fact_5679_neg__numeral__le__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_le_one
% 5.24/5.53 thf(fact_5680_neg__numeral__less__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_one
% 5.24/5.53 thf(fact_5681_neg__numeral__less__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_one
% 5.24/5.53 thf(fact_5682_neg__numeral__less__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_one
% 5.24/5.53 thf(fact_5683_neg__numeral__less__one,axiom,
% 5.24/5.53 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.24/5.53
% 5.24/5.53 % neg_numeral_less_one
% 5.24/5.53 thf(fact_5684_neg__one__less__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_less_numeral
% 5.24/5.53 thf(fact_5685_neg__one__less__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_less_numeral
% 5.24/5.53 thf(fact_5686_neg__one__less__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_less_numeral
% 5.24/5.53 thf(fact_5687_neg__one__less__numeral,axiom,
% 5.24/5.53 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_one_less_numeral
% 5.24/5.53 thf(fact_5688_not__numeral__less__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_one
% 5.24/5.53 thf(fact_5689_not__numeral__less__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_one
% 5.24/5.53 thf(fact_5690_not__numeral__less__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_one
% 5.24/5.53 thf(fact_5691_not__numeral__less__neg__one,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_numeral_less_neg_one
% 5.24/5.53 thf(fact_5692_not__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_less_neg_numeral
% 5.24/5.53 thf(fact_5693_not__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_less_neg_numeral
% 5.24/5.53 thf(fact_5694_not__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_less_neg_numeral
% 5.24/5.53 thf(fact_5695_not__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_one_less_neg_numeral
% 5.24/5.53 thf(fact_5696_not__neg__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_less_neg_numeral
% 5.24/5.53 thf(fact_5697_not__neg__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_less_neg_numeral
% 5.24/5.53 thf(fact_5698_not__neg__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_less_neg_numeral
% 5.24/5.53 thf(fact_5699_not__neg__one__less__neg__numeral,axiom,
% 5.24/5.53 ! [M: num] :
% 5.24/5.53 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % not_neg_one_less_neg_numeral
% 5.24/5.53 thf(fact_5700_nonzero__neg__divide__eq__eq2,axiom,
% 5.24/5.53 ! [B: real,C: real,A: real] :
% 5.24/5.53 ( ( B != zero_zero_real )
% 5.24/5.53 => ( ( C
% 5.24/5.53 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.24/5.53 = ( ( times_times_real @ C @ B )
% 5.24/5.53 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_neg_divide_eq_eq2
% 5.24/5.53 thf(fact_5701_nonzero__neg__divide__eq__eq2,axiom,
% 5.24/5.53 ! [B: complex,C: complex,A: complex] :
% 5.24/5.53 ( ( B != zero_zero_complex )
% 5.24/5.53 => ( ( C
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.53 = ( ( times_times_complex @ C @ B )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_neg_divide_eq_eq2
% 5.24/5.53 thf(fact_5702_nonzero__neg__divide__eq__eq2,axiom,
% 5.24/5.53 ! [B: rat,C: rat,A: rat] :
% 5.24/5.53 ( ( B != zero_zero_rat )
% 5.24/5.53 => ( ( C
% 5.24/5.53 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.24/5.53 = ( ( times_times_rat @ C @ B )
% 5.24/5.53 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_neg_divide_eq_eq2
% 5.24/5.53 thf(fact_5703_nonzero__neg__divide__eq__eq,axiom,
% 5.24/5.53 ! [B: real,A: real,C: real] :
% 5.24/5.53 ( ( B != zero_zero_real )
% 5.24/5.53 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.53 = C )
% 5.24/5.53 = ( ( uminus_uminus_real @ A )
% 5.24/5.53 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_neg_divide_eq_eq
% 5.24/5.53 thf(fact_5704_nonzero__neg__divide__eq__eq,axiom,
% 5.24/5.53 ! [B: complex,A: complex,C: complex] :
% 5.24/5.53 ( ( B != zero_zero_complex )
% 5.24/5.53 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.53 = C )
% 5.24/5.53 = ( ( uminus1482373934393186551omplex @ A )
% 5.24/5.53 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_neg_divide_eq_eq
% 5.24/5.53 thf(fact_5705_nonzero__neg__divide__eq__eq,axiom,
% 5.24/5.53 ! [B: rat,A: rat,C: rat] :
% 5.24/5.53 ( ( B != zero_zero_rat )
% 5.24/5.53 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.53 = C )
% 5.24/5.53 = ( ( uminus_uminus_rat @ A )
% 5.24/5.53 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % nonzero_neg_divide_eq_eq
% 5.24/5.53 thf(fact_5706_minus__divide__eq__eq,axiom,
% 5.24/5.53 ! [B: real,C: real,A: real] :
% 5.24/5.53 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.24/5.53 = A )
% 5.24/5.53 = ( ( ( C != zero_zero_real )
% 5.24/5.53 => ( ( uminus_uminus_real @ B )
% 5.24/5.53 = ( times_times_real @ A @ C ) ) )
% 5.24/5.53 & ( ( C = zero_zero_real )
% 5.24/5.53 => ( A = zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_eq_eq
% 5.24/5.53 thf(fact_5707_minus__divide__eq__eq,axiom,
% 5.24/5.53 ! [B: complex,C: complex,A: complex] :
% 5.24/5.53 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.24/5.53 = A )
% 5.24/5.53 = ( ( ( C != zero_zero_complex )
% 5.24/5.53 => ( ( uminus1482373934393186551omplex @ B )
% 5.24/5.53 = ( times_times_complex @ A @ C ) ) )
% 5.24/5.53 & ( ( C = zero_zero_complex )
% 5.24/5.53 => ( A = zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_eq_eq
% 5.24/5.53 thf(fact_5708_minus__divide__eq__eq,axiom,
% 5.24/5.53 ! [B: rat,C: rat,A: rat] :
% 5.24/5.53 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.24/5.53 = A )
% 5.24/5.53 = ( ( ( C != zero_zero_rat )
% 5.24/5.53 => ( ( uminus_uminus_rat @ B )
% 5.24/5.53 = ( times_times_rat @ A @ C ) ) )
% 5.24/5.53 & ( ( C = zero_zero_rat )
% 5.24/5.53 => ( A = zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_eq_eq
% 5.24/5.53 thf(fact_5709_eq__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: real,B: real,C: real] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ( ( C != zero_zero_real )
% 5.24/5.53 => ( ( times_times_real @ A @ C )
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ( C = zero_zero_real )
% 5.24/5.53 => ( A = zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_minus_divide_eq
% 5.24/5.53 thf(fact_5710_eq__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: complex,B: complex,C: complex] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.24/5.53 = ( ( ( C != zero_zero_complex )
% 5.24/5.53 => ( ( times_times_complex @ A @ C )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.24/5.53 & ( ( C = zero_zero_complex )
% 5.24/5.53 => ( A = zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_minus_divide_eq
% 5.24/5.53 thf(fact_5711_eq__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: rat,B: rat,C: rat] :
% 5.24/5.53 ( ( A
% 5.24/5.53 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ( ( C != zero_zero_rat )
% 5.24/5.53 => ( ( times_times_rat @ A @ C )
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ( C = zero_zero_rat )
% 5.24/5.53 => ( A = zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_minus_divide_eq
% 5.24/5.53 thf(fact_5712_mult__1s__ring__1_I1_J,axiom,
% 5.24/5.53 ! [B: real] :
% 5.24/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(1)
% 5.24/5.53 thf(fact_5713_mult__1s__ring__1_I1_J,axiom,
% 5.24/5.53 ! [B: int] :
% 5.24/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.24/5.53 = ( uminus_uminus_int @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(1)
% 5.24/5.53 thf(fact_5714_mult__1s__ring__1_I1_J,axiom,
% 5.24/5.53 ! [B: complex] :
% 5.24/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(1)
% 5.24/5.53 thf(fact_5715_mult__1s__ring__1_I1_J,axiom,
% 5.24/5.53 ! [B: rat] :
% 5.24/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(1)
% 5.24/5.53 thf(fact_5716_mult__1s__ring__1_I1_J,axiom,
% 5.24/5.53 ! [B: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(1)
% 5.24/5.53 thf(fact_5717_mult__1s__ring__1_I2_J,axiom,
% 5.24/5.53 ! [B: real] :
% 5.24/5.53 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(2)
% 5.24/5.53 thf(fact_5718_mult__1s__ring__1_I2_J,axiom,
% 5.24/5.53 ! [B: int] :
% 5.24/5.53 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.24/5.53 = ( uminus_uminus_int @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(2)
% 5.24/5.53 thf(fact_5719_mult__1s__ring__1_I2_J,axiom,
% 5.24/5.53 ! [B: complex] :
% 5.24/5.53 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(2)
% 5.24/5.53 thf(fact_5720_mult__1s__ring__1_I2_J,axiom,
% 5.24/5.53 ! [B: rat] :
% 5.24/5.53 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(2)
% 5.24/5.53 thf(fact_5721_mult__1s__ring__1_I2_J,axiom,
% 5.24/5.53 ! [B: code_integer] :
% 5.24/5.53 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.24/5.53
% 5.24/5.53 % mult_1s_ring_1(2)
% 5.24/5.53 thf(fact_5722_divide__eq__minus__1__iff,axiom,
% 5.24/5.53 ! [A: real,B: real] :
% 5.24/5.53 ( ( ( divide_divide_real @ A @ B )
% 5.24/5.53 = ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.53 = ( ( B != zero_zero_real )
% 5.24/5.53 & ( A
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_minus_1_iff
% 5.24/5.53 thf(fact_5723_divide__eq__minus__1__iff,axiom,
% 5.24/5.53 ! [A: complex,B: complex] :
% 5.24/5.53 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.53 = ( ( B != zero_zero_complex )
% 5.24/5.53 & ( A
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_minus_1_iff
% 5.24/5.53 thf(fact_5724_divide__eq__minus__1__iff,axiom,
% 5.24/5.53 ! [A: rat,B: rat] :
% 5.24/5.53 ( ( ( divide_divide_rat @ A @ B )
% 5.24/5.53 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.53 = ( ( B != zero_zero_rat )
% 5.24/5.53 & ( A
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_minus_1_iff
% 5.24/5.53 thf(fact_5725_uminus__numeral__One,axiom,
% 5.24/5.53 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.24/5.53 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_numeral_One
% 5.24/5.53 thf(fact_5726_uminus__numeral__One,axiom,
% 5.24/5.53 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_numeral_One
% 5.24/5.53 thf(fact_5727_uminus__numeral__One,axiom,
% 5.24/5.53 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_numeral_One
% 5.24/5.53 thf(fact_5728_uminus__numeral__One,axiom,
% 5.24/5.53 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.24/5.53 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_numeral_One
% 5.24/5.53 thf(fact_5729_uminus__numeral__One,axiom,
% 5.24/5.53 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_numeral_One
% 5.24/5.53 thf(fact_5730_power__minus,axiom,
% 5.24/5.53 ! [A: real,N: nat] :
% 5.24/5.53 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.24/5.53 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus
% 5.24/5.53 thf(fact_5731_power__minus,axiom,
% 5.24/5.53 ! [A: int,N: nat] :
% 5.24/5.53 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.24/5.53 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus
% 5.24/5.53 thf(fact_5732_power__minus,axiom,
% 5.24/5.53 ! [A: complex,N: nat] :
% 5.24/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.24/5.53 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus
% 5.24/5.53 thf(fact_5733_power__minus,axiom,
% 5.24/5.53 ! [A: rat,N: nat] :
% 5.24/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.24/5.53 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus
% 5.24/5.53 thf(fact_5734_power__minus,axiom,
% 5.24/5.53 ! [A: code_integer,N: nat] :
% 5.24/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.24/5.53 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus
% 5.24/5.53 thf(fact_5735_power__minus__Bit0,axiom,
% 5.24/5.53 ! [X: real,K: num] :
% 5.24/5.53 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.24/5.53 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_Bit0
% 5.24/5.53 thf(fact_5736_power__minus__Bit0,axiom,
% 5.24/5.53 ! [X: int,K: num] :
% 5.24/5.53 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.24/5.53 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_Bit0
% 5.24/5.53 thf(fact_5737_power__minus__Bit0,axiom,
% 5.24/5.53 ! [X: complex,K: num] :
% 5.24/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.24/5.53 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_Bit0
% 5.24/5.53 thf(fact_5738_power__minus__Bit0,axiom,
% 5.24/5.53 ! [X: rat,K: num] :
% 5.24/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.24/5.53 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_Bit0
% 5.24/5.53 thf(fact_5739_power__minus__Bit0,axiom,
% 5.24/5.53 ! [X: code_integer,K: num] :
% 5.24/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.24/5.53 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power_minus_Bit0
% 5.24/5.53 thf(fact_5740_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_int,F: int > real,I2: int] :
% 5.24/5.53 ( ( finite_finite_int @ S2 )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 => ( ( member_int @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_real ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5741_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_real,F: real > real,I2: real] :
% 5.24/5.53 ( ( finite_finite_real @ S2 )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 => ( ( member_real @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_real ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5742_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_complex,F: complex > real,I2: complex] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.24/5.53 = zero_zero_real )
% 5.24/5.53 => ( ( member_complex @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_real ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5743_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_int,F: int > rat,I2: int] :
% 5.24/5.53 ( ( finite_finite_int @ S2 )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( ( member_int @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5744_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_real,F: real > rat,I2: real] :
% 5.24/5.53 ( ( finite_finite_real @ S2 )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( ( member_real @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5745_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_nat,F: nat > rat,I2: nat] :
% 5.24/5.53 ( ( finite_finite_nat @ S2 )
% 5.24/5.53 => ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( ( member_nat @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5746_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_complex,F: complex > rat,I2: complex] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.24/5.53 = zero_zero_rat )
% 5.24/5.53 => ( ( member_complex @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5747_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_int,F: int > nat,I2: int] :
% 5.24/5.53 ( ( finite_finite_int @ S2 )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.24/5.53 = zero_zero_nat )
% 5.24/5.53 => ( ( member_int @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_nat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5748_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_real,F: real > nat,I2: real] :
% 5.24/5.53 ( ( finite_finite_real @ S2 )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.24/5.53 = zero_zero_nat )
% 5.24/5.53 => ( ( member_real @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_nat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5749_sum__nonneg__0,axiom,
% 5.24/5.53 ! [S2: set_complex,F: complex > nat,I2: complex] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.24/5.53 = zero_zero_nat )
% 5.24/5.53 => ( ( member_complex @ I2 @ S2 )
% 5.24/5.53 => ( ( F @ I2 )
% 5.24/5.53 = zero_zero_nat ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_0
% 5.24/5.53 thf(fact_5750_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_int,F: int > real,B5: real,I2: int] :
% 5.24/5.53 ( ( finite_finite_int @ S2 )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_int @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5751_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_real,F: real > real,B5: real,I2: real] :
% 5.24/5.53 ( ( finite_finite_real @ S2 )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_real @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5752_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_complex,F: complex > real,B5: real,I2: complex] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_complex @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_real @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5753_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_int,F: int > rat,B5: rat,I2: int] :
% 5.24/5.53 ( ( finite_finite_int @ S2 )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_int @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5754_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_real,F: real > rat,B5: rat,I2: real] :
% 5.24/5.53 ( ( finite_finite_real @ S2 )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_real @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5755_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_nat,F: nat > rat,B5: rat,I2: nat] :
% 5.24/5.53 ( ( finite_finite_nat @ S2 )
% 5.24/5.53 => ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_nat @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5756_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_complex,F: complex > rat,B5: rat,I2: complex] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_complex @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5757_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_int,F: int > nat,B5: nat,I2: int] :
% 5.24/5.53 ( ( finite_finite_int @ S2 )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_int @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5758_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_real,F: real > nat,B5: nat,I2: real] :
% 5.24/5.53 ( ( finite_finite_real @ S2 )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_real @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5759_sum__nonneg__leq__bound,axiom,
% 5.24/5.53 ! [S2: set_complex,F: complex > nat,B5: nat,I2: complex] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ S2 )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.24/5.53 = B5 )
% 5.24/5.53 => ( ( member_complex @ I2 @ S2 )
% 5.24/5.53 => ( ord_less_eq_nat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_nonneg_leq_bound
% 5.24/5.53 thf(fact_5760_real__0__less__add__iff,axiom,
% 5.24/5.53 ! [X: real,Y4: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.53 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % real_0_less_add_iff
% 5.24/5.53 thf(fact_5761_real__add__less__0__iff,axiom,
% 5.24/5.53 ! [X: real,Y4: real] :
% 5.24/5.53 ( ( ord_less_real @ ( plus_plus_real @ X @ Y4 ) @ zero_zero_real )
% 5.24/5.53 = ( ord_less_real @ Y4 @ ( uminus_uminus_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % real_add_less_0_iff
% 5.24/5.53 thf(fact_5762_real__add__le__0__iff,axiom,
% 5.24/5.53 ! [X: real,Y4: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y4 ) @ zero_zero_real )
% 5.24/5.53 = ( ord_less_eq_real @ Y4 @ ( uminus_uminus_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % real_add_le_0_iff
% 5.24/5.53 thf(fact_5763_real__0__le__add__iff,axiom,
% 5.24/5.53 ! [X: real,Y4: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.53 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y4 ) ) ).
% 5.24/5.53
% 5.24/5.53 % real_0_le_add_iff
% 5.24/5.53 thf(fact_5764_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_int,I2: int,F: int > real] :
% 5.24/5.53 ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( member_int @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5765_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_real,I2: real,F: real > real] :
% 5.24/5.53 ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( member_real @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5766_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_complex,I2: complex,F: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5767_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_int,I2: int,F: int > rat] :
% 5.24/5.53 ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( member_int @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5768_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_real,I2: real,F: real > rat] :
% 5.24/5.53 ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( member_real @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5769_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ I5 )
% 5.24/5.53 => ( ( member_nat @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5770_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_complex,I2: complex,F: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5771_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_int,I2: int,F: int > nat] :
% 5.24/5.53 ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( member_int @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5772_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_real,I2: real,F: real > nat] :
% 5.24/5.53 ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( member_real @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5773_sum__pos2,axiom,
% 5.24/5.53 ! [I5: set_complex,I2: complex,F: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.53 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos2
% 5.24/5.53 thf(fact_5774_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_complex,F: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_complex )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5775_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_int,F: int > real] :
% 5.24/5.53 ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_int )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5776_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_real,F: real > real] :
% 5.24/5.53 ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_real )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5777_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_complex,F: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_complex )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5778_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_nat,F: nat > rat] :
% 5.24/5.53 ( ( finite_finite_nat @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_nat )
% 5.24/5.53 => ( ! [I3: nat] :
% 5.24/5.53 ( ( member_nat @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5779_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_int,F: int > rat] :
% 5.24/5.53 ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_int )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5780_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_real,F: real > rat] :
% 5.24/5.53 ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_real )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5781_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_complex,F: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_complex )
% 5.24/5.53 => ( ! [I3: complex] :
% 5.24/5.53 ( ( member_complex @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5782_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_int,F: int > nat] :
% 5.24/5.53 ( ( finite_finite_int @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_int )
% 5.24/5.53 => ( ! [I3: int] :
% 5.24/5.53 ( ( member_int @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5783_sum__pos,axiom,
% 5.24/5.53 ! [I5: set_real,F: real > nat] :
% 5.24/5.53 ( ( finite_finite_real @ I5 )
% 5.24/5.53 => ( ( I5 != bot_bot_set_real )
% 5.24/5.53 => ( ! [I3: real] :
% 5.24/5.53 ( ( member_real @ I3 @ I5 )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.24/5.53 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_pos
% 5.24/5.53 thf(fact_5784_ln__ge__zero__imp__ge__one,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_ge_zero_imp_ge_one
% 5.24/5.53 thf(fact_5785_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,G: complex > real] :
% 5.24/5.53 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.24/5.53 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups5808333547571424918x_real @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5786_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,G: complex > rat] :
% 5.24/5.53 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.24/5.53 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups5058264527183730370ex_rat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5787_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,G: complex > nat] :
% 5.24/5.53 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.24/5.53 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups5693394587270226106ex_nat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5788_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,G: complex > int] :
% 5.24/5.53 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.24/5.53 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups5690904116761175830ex_int @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5789_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_nat,A2: set_nat,G: nat > rat] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.53 => ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.24/5.53 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5790_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_nat,A2: set_nat,G: nat > int] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.53 => ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.24/5.53 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5791_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_int,A2: set_int,G: int > int] :
% 5.24/5.53 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 5.24/5.53 => ( ( finite_finite_int @ A2 )
% 5.24/5.53 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.24/5.53 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5792_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,G: complex > complex] :
% 5.24/5.53 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.53 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.53 => ( ( groups7754918857620584856omplex @ G @ A2 )
% 5.24/5.53 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups7754918857620584856omplex @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5793_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_nat,A2: set_nat,G: nat > nat] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.53 => ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 5.24/5.53 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5794_sum_Osubset__diff,axiom,
% 5.24/5.53 ! [B5: set_nat,A2: set_nat,G: nat > real] :
% 5.24/5.53 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.53 => ( ( finite_finite_nat @ A2 )
% 5.24/5.53 => ( ( groups6591440286371151544t_real @ G @ A2 )
% 5.24/5.53 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups6591440286371151544t_real @ G @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum.subset_diff
% 5.24/5.53 thf(fact_5795_ln__add__one__self__le__self,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_add_one_self_le_self
% 5.24/5.53 thf(fact_5796_ln__mult,axiom,
% 5.24/5.53 ! [X: real,Y4: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.53 => ( ( ln_ln_real @ ( times_times_real @ X @ Y4 ) )
% 5.24/5.53 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y4 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_mult
% 5.24/5.53 thf(fact_5797_ln__eq__minus__one,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ( ( ln_ln_real @ X )
% 5.24/5.53 = ( minus_minus_real @ X @ one_one_real ) )
% 5.24/5.53 => ( X = one_one_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_eq_minus_one
% 5.24/5.53 thf(fact_5798_pos__minus__divide__less__eq,axiom,
% 5.24/5.53 ! [C: real,B: real,A: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_minus_divide_less_eq
% 5.24/5.53 thf(fact_5799_pos__minus__divide__less__eq,axiom,
% 5.24/5.53 ! [C: rat,B: rat,A: rat] :
% 5.24/5.53 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_minus_divide_less_eq
% 5.24/5.53 thf(fact_5800_pos__less__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: real,A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_less_minus_divide_eq
% 5.24/5.53 thf(fact_5801_pos__less__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_less_minus_divide_eq
% 5.24/5.53 thf(fact_5802_neg__minus__divide__less__eq,axiom,
% 5.24/5.53 ! [C: real,B: real,A: real] :
% 5.24/5.53 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_minus_divide_less_eq
% 5.24/5.53 thf(fact_5803_neg__minus__divide__less__eq,axiom,
% 5.24/5.53 ! [C: rat,B: rat,A: rat] :
% 5.24/5.53 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_minus_divide_less_eq
% 5.24/5.53 thf(fact_5804_neg__less__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: real,A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_less_minus_divide_eq
% 5.24/5.53 thf(fact_5805_neg__less__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_less_minus_divide_eq
% 5.24/5.53 thf(fact_5806_minus__divide__less__eq,axiom,
% 5.24/5.53 ! [B: real,C: real,A: real] :
% 5.24/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.24/5.53 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_less_eq
% 5.24/5.53 thf(fact_5807_minus__divide__less__eq,axiom,
% 5.24/5.53 ! [B: rat,C: rat,A: rat] :
% 5.24/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.24/5.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_less_eq
% 5.24/5.53 thf(fact_5808_less__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: real,B: real,C: real] :
% 5.24/5.53 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_divide_eq
% 5.24/5.53 thf(fact_5809_less__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: rat,B: rat,C: rat] :
% 5.24/5.53 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_minus_divide_eq
% 5.24/5.53 thf(fact_5810_eq__divide__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [W2: num,B: real,C: real] :
% 5.24/5.53 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 = ( divide_divide_real @ B @ C ) )
% 5.24/5.53 = ( ( ( C != zero_zero_real )
% 5.24/5.53 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( C = zero_zero_real )
% 5.24/5.53 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 = zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_divide_eq_numeral(2)
% 5.24/5.53 thf(fact_5811_eq__divide__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [W2: num,B: complex,C: complex] :
% 5.24/5.53 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.24/5.53 = ( ( ( C != zero_zero_complex )
% 5.24/5.53 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( C = zero_zero_complex )
% 5.24/5.53 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 = zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_divide_eq_numeral(2)
% 5.24/5.53 thf(fact_5812_eq__divide__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [W2: num,B: rat,C: rat] :
% 5.24/5.53 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 = ( divide_divide_rat @ B @ C ) )
% 5.24/5.53 = ( ( ( C != zero_zero_rat )
% 5.24/5.53 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( C = zero_zero_rat )
% 5.24/5.53 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % eq_divide_eq_numeral(2)
% 5.24/5.53 thf(fact_5813_divide__eq__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [B: real,C: real,W2: num] :
% 5.24/5.53 ( ( ( divide_divide_real @ B @ C )
% 5.24/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.53 = ( ( ( C != zero_zero_real )
% 5.24/5.53 => ( B
% 5.24/5.53 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ( C = zero_zero_real )
% 5.24/5.53 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.53 = zero_zero_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_eq_numeral(2)
% 5.24/5.53 thf(fact_5814_divide__eq__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [B: complex,C: complex,W2: num] :
% 5.24/5.53 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.53 = ( ( ( C != zero_zero_complex )
% 5.24/5.53 => ( B
% 5.24/5.53 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ( C = zero_zero_complex )
% 5.24/5.53 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.53 = zero_zero_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_eq_numeral(2)
% 5.24/5.53 thf(fact_5815_divide__eq__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [B: rat,C: rat,W2: num] :
% 5.24/5.53 ( ( ( divide_divide_rat @ B @ C )
% 5.24/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.24/5.53 = ( ( ( C != zero_zero_rat )
% 5.24/5.53 => ( B
% 5.24/5.53 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ( C = zero_zero_rat )
% 5.24/5.53 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.53 = zero_zero_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_eq_eq_numeral(2)
% 5.24/5.53 thf(fact_5816_add__divide__eq__if__simps_I3_J,axiom,
% 5.24/5.53 ! [Z2: real,A: real,B: real] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_real )
% 5.24/5.53 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_real )
% 5.24/5.53 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(3)
% 5.24/5.53 thf(fact_5817_add__divide__eq__if__simps_I3_J,axiom,
% 5.24/5.53 ! [Z2: complex,A: complex,B: complex] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_complex )
% 5.24/5.53 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_complex )
% 5.24/5.53 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(3)
% 5.24/5.53 thf(fact_5818_add__divide__eq__if__simps_I3_J,axiom,
% 5.24/5.53 ! [Z2: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_rat )
% 5.24/5.53 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.24/5.53 = B ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_rat )
% 5.24/5.53 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(3)
% 5.24/5.53 thf(fact_5819_minus__divide__add__eq__iff,axiom,
% 5.24/5.53 ! [Z2: real,X: real,Y4: real] :
% 5.24/5.53 ( ( Z2 != zero_zero_real )
% 5.24/5.53 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z2 ) ) @ Y4 )
% 5.24/5.53 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_add_eq_iff
% 5.24/5.53 thf(fact_5820_minus__divide__add__eq__iff,axiom,
% 5.24/5.53 ! [Z2: complex,X: complex,Y4: complex] :
% 5.24/5.53 ( ( Z2 != zero_zero_complex )
% 5.24/5.53 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z2 ) ) @ Y4 )
% 5.24/5.53 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_add_eq_iff
% 5.24/5.53 thf(fact_5821_minus__divide__add__eq__iff,axiom,
% 5.24/5.53 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.53 ( ( Z2 != zero_zero_rat )
% 5.24/5.53 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z2 ) ) @ Y4 )
% 5.24/5.53 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_add_eq_iff
% 5.24/5.53 thf(fact_5822_add__divide__eq__if__simps_I6_J,axiom,
% 5.24/5.53 ! [Z2: real,A: real,B: real] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_real )
% 5.24/5.53 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_real )
% 5.24/5.53 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(6)
% 5.24/5.53 thf(fact_5823_add__divide__eq__if__simps_I6_J,axiom,
% 5.24/5.53 ! [Z2: complex,A: complex,B: complex] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_complex )
% 5.24/5.53 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_complex )
% 5.24/5.53 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(6)
% 5.24/5.53 thf(fact_5824_add__divide__eq__if__simps_I6_J,axiom,
% 5.24/5.53 ! [Z2: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_rat )
% 5.24/5.53 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_rat )
% 5.24/5.53 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.24/5.53 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(6)
% 5.24/5.53 thf(fact_5825_add__divide__eq__if__simps_I5_J,axiom,
% 5.24/5.53 ! [Z2: real,A: real,B: real] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_real )
% 5.24/5.53 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.24/5.53 = ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_real )
% 5.24/5.53 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.24/5.53 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(5)
% 5.24/5.53 thf(fact_5826_add__divide__eq__if__simps_I5_J,axiom,
% 5.24/5.53 ! [Z2: complex,A: complex,B: complex] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_complex )
% 5.24/5.53 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_complex )
% 5.24/5.53 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.24/5.53 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(5)
% 5.24/5.53 thf(fact_5827_add__divide__eq__if__simps_I5_J,axiom,
% 5.24/5.53 ! [Z2: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ( Z2 = zero_zero_rat )
% 5.24/5.53 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.24/5.53 = ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ( Z2 != zero_zero_rat )
% 5.24/5.53 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.24/5.53 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % add_divide_eq_if_simps(5)
% 5.24/5.53 thf(fact_5828_minus__divide__diff__eq__iff,axiom,
% 5.24/5.53 ! [Z2: real,X: real,Y4: real] :
% 5.24/5.53 ( ( Z2 != zero_zero_real )
% 5.24/5.53 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z2 ) ) @ Y4 )
% 5.24/5.53 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_diff_eq_iff
% 5.24/5.53 thf(fact_5829_minus__divide__diff__eq__iff,axiom,
% 5.24/5.53 ! [Z2: complex,X: complex,Y4: complex] :
% 5.24/5.53 ( ( Z2 != zero_zero_complex )
% 5.24/5.53 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z2 ) ) @ Y4 )
% 5.24/5.53 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_diff_eq_iff
% 5.24/5.53 thf(fact_5830_minus__divide__diff__eq__iff,axiom,
% 5.24/5.53 ! [Z2: rat,X: rat,Y4: rat] :
% 5.24/5.53 ( ( Z2 != zero_zero_rat )
% 5.24/5.53 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z2 ) ) @ Y4 )
% 5.24/5.53 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y4 @ Z2 ) ) @ Z2 ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_diff_eq_iff
% 5.24/5.53 thf(fact_5831_even__minus,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.24/5.53 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % even_minus
% 5.24/5.53 thf(fact_5832_even__minus,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.24/5.53 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.24/5.53
% 5.24/5.53 % even_minus
% 5.24/5.53 thf(fact_5833_power2__eq__iff,axiom,
% 5.24/5.53 ! [X: real,Y4: real] :
% 5.24/5.53 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus_uminus_real @ Y4 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_iff
% 5.24/5.53 thf(fact_5834_power2__eq__iff,axiom,
% 5.24/5.53 ! [X: int,Y4: int] :
% 5.24/5.53 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus_uminus_int @ Y4 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_iff
% 5.24/5.53 thf(fact_5835_power2__eq__iff,axiom,
% 5.24/5.53 ! [X: complex,Y4: complex] :
% 5.24/5.53 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus1482373934393186551omplex @ Y4 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_iff
% 5.24/5.53 thf(fact_5836_power2__eq__iff,axiom,
% 5.24/5.53 ! [X: rat,Y4: rat] :
% 5.24/5.53 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus_uminus_rat @ Y4 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_iff
% 5.24/5.53 thf(fact_5837_power2__eq__iff,axiom,
% 5.24/5.53 ! [X: code_integer,Y4: code_integer] :
% 5.24/5.53 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.53 = ( ( X = Y4 )
% 5.24/5.53 | ( X
% 5.24/5.53 = ( uminus1351360451143612070nteger @ Y4 ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_iff
% 5.24/5.53 thf(fact_5838_uminus__power__if,axiom,
% 5.24/5.53 ! [N: nat,A: real] :
% 5.24/5.53 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.24/5.53 = ( power_power_real @ A @ N ) ) )
% 5.24/5.53 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.24/5.53 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_power_if
% 5.24/5.53 thf(fact_5839_uminus__power__if,axiom,
% 5.24/5.53 ! [N: nat,A: int] :
% 5.24/5.53 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.24/5.53 = ( power_power_int @ A @ N ) ) )
% 5.24/5.53 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.24/5.53 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_power_if
% 5.24/5.53 thf(fact_5840_uminus__power__if,axiom,
% 5.24/5.53 ! [N: nat,A: complex] :
% 5.24/5.53 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.24/5.53 = ( power_power_complex @ A @ N ) ) )
% 5.24/5.53 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.24/5.53 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_power_if
% 5.24/5.53 thf(fact_5841_uminus__power__if,axiom,
% 5.24/5.53 ! [N: nat,A: rat] :
% 5.24/5.53 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.24/5.53 = ( power_power_rat @ A @ N ) ) )
% 5.24/5.53 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.24/5.53 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_power_if
% 5.24/5.53 thf(fact_5842_uminus__power__if,axiom,
% 5.24/5.53 ! [N: nat,A: code_integer] :
% 5.24/5.53 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.24/5.53 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.24/5.53 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.24/5.53 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % uminus_power_if
% 5.24/5.53 thf(fact_5843_verit__less__mono__div__int2,axiom,
% 5.24/5.53 ! [A2: int,B5: int,N: int] :
% 5.24/5.53 ( ( ord_less_eq_int @ A2 @ B5 )
% 5.24/5.53 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( divide_divide_int @ B5 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % verit_less_mono_div_int2
% 5.24/5.53 thf(fact_5844_div__eq__minus1,axiom,
% 5.24/5.53 ! [B: int] :
% 5.24/5.53 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.53 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % div_eq_minus1
% 5.24/5.53 thf(fact_5845_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_int,A2: set_int,F: int > real] :
% 5.24/5.53 ( ( finite_finite_int @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: int] :
% 5.24/5.53 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5846_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_real,A2: set_real,F: real > real] :
% 5.24/5.53 ( ( finite_finite_real @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: real] :
% 5.24/5.53 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5847_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,F: complex > real] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.53 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: complex] :
% 5.24/5.53 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5848_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_int,A2: set_int,F: int > rat] :
% 5.24/5.53 ( ( finite_finite_int @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: int] :
% 5.24/5.53 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5849_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_real,A2: set_real,F: real > rat] :
% 5.24/5.53 ( ( finite_finite_real @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: real] :
% 5.24/5.53 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5850_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,F: complex > rat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.53 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: complex] :
% 5.24/5.53 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5851_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_int,A2: set_int,F: int > nat] :
% 5.24/5.53 ( ( finite_finite_int @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: int] :
% 5.24/5.53 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5852_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_real,A2: set_real,F: real > nat] :
% 5.24/5.53 ( ( finite_finite_real @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: real] :
% 5.24/5.53 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5853_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_complex,A2: set_complex,F: complex > nat] :
% 5.24/5.53 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.53 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: complex] :
% 5.24/5.53 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5854_sum__mono2,axiom,
% 5.24/5.53 ! [B5: set_real,A2: set_real,F: real > int] :
% 5.24/5.53 ( ( finite_finite_real @ B5 )
% 5.24/5.53 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.53 => ( ! [B2: real] :
% 5.24/5.53 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.24/5.53 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B5 ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % sum_mono2
% 5.24/5.53 thf(fact_5855_ln__le__minus__one,axiom,
% 5.24/5.53 ! [X: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.53 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % ln_le_minus_one
% 5.24/5.53 thf(fact_5856_of__bool__odd__eq__mod__2,axiom,
% 5.24/5.53 ! [A: nat] :
% 5.24/5.53 ( ( zero_n2687167440665602831ol_nat
% 5.24/5.53 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.53 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_odd_eq_mod_2
% 5.24/5.53 thf(fact_5857_of__bool__odd__eq__mod__2,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( zero_n2684676970156552555ol_int
% 5.24/5.53 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.53 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_odd_eq_mod_2
% 5.24/5.53 thf(fact_5858_of__bool__odd__eq__mod__2,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( zero_n356916108424825756nteger
% 5.24/5.53 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.24/5.53 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % of_bool_odd_eq_mod_2
% 5.24/5.53 thf(fact_5859_le__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: real,B: real,C: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_divide_eq
% 5.24/5.53 thf(fact_5860_le__minus__divide__eq,axiom,
% 5.24/5.53 ! [A: rat,B: rat,C: rat] :
% 5.24/5.53 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % le_minus_divide_eq
% 5.24/5.53 thf(fact_5861_minus__divide__le__eq,axiom,
% 5.24/5.53 ! [B: real,C: real,A: real] :
% 5.24/5.53 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.24/5.53 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_le_eq
% 5.24/5.53 thf(fact_5862_minus__divide__le__eq,axiom,
% 5.24/5.53 ! [B: rat,C: rat,A: rat] :
% 5.24/5.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.24/5.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % minus_divide_le_eq
% 5.24/5.53 thf(fact_5863_neg__le__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: real,A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_le_minus_divide_eq
% 5.24/5.53 thf(fact_5864_neg__le__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_le_minus_divide_eq
% 5.24/5.53 thf(fact_5865_neg__minus__divide__le__eq,axiom,
% 5.24/5.53 ! [C: real,B: real,A: real] :
% 5.24/5.53 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_minus_divide_le_eq
% 5.24/5.53 thf(fact_5866_neg__minus__divide__le__eq,axiom,
% 5.24/5.53 ! [C: rat,B: rat,A: rat] :
% 5.24/5.53 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % neg_minus_divide_le_eq
% 5.24/5.53 thf(fact_5867_pos__le__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: real,A: real,B: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_le_minus_divide_eq
% 5.24/5.53 thf(fact_5868_pos__le__minus__divide__eq,axiom,
% 5.24/5.53 ! [C: rat,A: rat,B: rat] :
% 5.24/5.53 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.24/5.53 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_le_minus_divide_eq
% 5.24/5.53 thf(fact_5869_pos__minus__divide__le__eq,axiom,
% 5.24/5.53 ! [C: real,B: real,A: real] :
% 5.24/5.53 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_minus_divide_le_eq
% 5.24/5.53 thf(fact_5870_pos__minus__divide__le__eq,axiom,
% 5.24/5.53 ! [C: rat,B: rat,A: rat] :
% 5.24/5.53 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.24/5.53 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % pos_minus_divide_le_eq
% 5.24/5.53 thf(fact_5871_divide__less__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [B: real,C: real,W2: num] :
% 5.24/5.53 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.53 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_less_eq_numeral(2)
% 5.24/5.53 thf(fact_5872_divide__less__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [B: rat,C: rat,W2: num] :
% 5.24/5.53 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.24/5.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % divide_less_eq_numeral(2)
% 5.24/5.53 thf(fact_5873_less__divide__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [W2: num,B: real,C: real] :
% 5.24/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 5.24/5.53 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.53 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.53 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_divide_eq_numeral(2)
% 5.24/5.53 thf(fact_5874_less__divide__eq__numeral_I2_J,axiom,
% 5.24/5.53 ! [W2: num,B: rat,C: rat] :
% 5.24/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.24/5.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.53 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.24/5.53 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.53 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % less_divide_eq_numeral(2)
% 5.24/5.53 thf(fact_5875_power2__eq__1__iff,axiom,
% 5.24/5.53 ! [A: real] :
% 5.24/5.53 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_real )
% 5.24/5.53 = ( ( A = one_one_real )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_1_iff
% 5.24/5.53 thf(fact_5876_power2__eq__1__iff,axiom,
% 5.24/5.53 ! [A: int] :
% 5.24/5.53 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_int )
% 5.24/5.53 = ( ( A = one_one_int )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_1_iff
% 5.24/5.53 thf(fact_5877_power2__eq__1__iff,axiom,
% 5.24/5.53 ! [A: complex] :
% 5.24/5.53 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_complex )
% 5.24/5.53 = ( ( A = one_one_complex )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_1_iff
% 5.24/5.53 thf(fact_5878_power2__eq__1__iff,axiom,
% 5.24/5.53 ! [A: rat] :
% 5.24/5.53 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_rat )
% 5.24/5.53 = ( ( A = one_one_rat )
% 5.24/5.53 | ( A
% 5.24/5.53 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.24/5.53
% 5.24/5.53 % power2_eq_1_iff
% 5.24/5.53 thf(fact_5879_power2__eq__1__iff,axiom,
% 5.24/5.53 ! [A: code_integer] :
% 5.24/5.53 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.53 = one_one_Code_integer )
% 5.24/5.54 = ( ( A = one_one_Code_integer )
% 5.24/5.54 | ( A
% 5.24/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_eq_1_iff
% 5.24/5.54 thf(fact_5880_minus__one__power__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.24/5.54 = one_one_real ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.24/5.54 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_one_power_iff
% 5.24/5.54 thf(fact_5881_minus__one__power__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.24/5.54 = one_one_int ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.24/5.54 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_one_power_iff
% 5.24/5.54 thf(fact_5882_minus__one__power__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.24/5.54 = one_one_complex ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_one_power_iff
% 5.24/5.54 thf(fact_5883_minus__one__power__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.24/5.54 = one_one_rat ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.24/5.54 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_one_power_iff
% 5.24/5.54 thf(fact_5884_minus__one__power__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.24/5.54 = one_one_Code_integer ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_one_power_iff
% 5.24/5.54 thf(fact_5885_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.24/5.54 ! [K: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.54 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.24/5.54 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_one_power_add_eq_neg_one_power_diff
% 5.24/5.54 thf(fact_5886_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.24/5.54 ! [K: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.54 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_one_power_add_eq_neg_one_power_diff
% 5.24/5.54 thf(fact_5887_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.24/5.54 ! [K: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.54 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.24/5.54 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_one_power_add_eq_neg_one_power_diff
% 5.24/5.54 thf(fact_5888_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.24/5.54 ! [K: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.54 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.24/5.54 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_one_power_add_eq_neg_one_power_diff
% 5.24/5.54 thf(fact_5889_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.24/5.54 ! [K: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.54 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.24/5.54 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_one_power_add_eq_neg_one_power_diff
% 5.24/5.54 thf(fact_5890_realpow__square__minus__le,axiom,
% 5.24/5.54 ! [U2: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % realpow_square_minus_le
% 5.24/5.54 thf(fact_5891_ln__one__minus__pos__lower__bound,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.54 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.54 => ( 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 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % ln_one_minus_pos_lower_bound
% 5.24/5.54 thf(fact_5892_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.24/5.54 ! [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 ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_int_greater_eq_minus_exp
% 5.24/5.54 thf(fact_5893_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.24/5.54 ! [N: nat,K: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.24/5.54 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_int_less_eq_self_iff
% 5.24/5.54 thf(fact_5894_signed__take__bit__int__greater__self__iff,axiom,
% 5.24/5.54 ! [K: int,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.24/5.54 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_int_greater_self_iff
% 5.24/5.54 thf(fact_5895_minus__mod__int__eq,axiom,
% 5.24/5.54 ! [L2: int,K: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.24/5.54 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.24/5.54 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_mod_int_eq
% 5.24/5.54 thf(fact_5896_zmod__minus1,axiom,
% 5.24/5.54 ! [B: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.54 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.24/5.54 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zmod_minus1
% 5.24/5.54 thf(fact_5897_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_int,A2: set_int,B: int,F: int > real] :
% 5.24/5.54 ( ( finite_finite_int @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.54 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: int] :
% 5.24/5.54 ( ( member_int @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5898_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_real,A2: set_real,B: real,F: real > real] :
% 5.24/5.54 ( ( finite_finite_real @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.54 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: real] :
% 5.24/5.54 ( ( member_real @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5899_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.24/5.54 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.54 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.54 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: complex] :
% 5.24/5.54 ( ( member_complex @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5900_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_int,A2: set_int,B: int,F: int > rat] :
% 5.24/5.54 ( ( finite_finite_int @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.54 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: int] :
% 5.24/5.54 ( ( member_int @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5901_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_real,A2: set_real,B: real,F: real > rat] :
% 5.24/5.54 ( ( finite_finite_real @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.54 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: real] :
% 5.24/5.54 ( ( member_real @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5902_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.24/5.54 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.54 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.54 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: complex] :
% 5.24/5.54 ( ( member_complex @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5903_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_int,A2: set_int,B: int,F: int > nat] :
% 5.24/5.54 ( ( finite_finite_int @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.54 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: int] :
% 5.24/5.54 ( ( member_int @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5904_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_real,A2: set_real,B: real,F: real > nat] :
% 5.24/5.54 ( ( finite_finite_real @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.54 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: real] :
% 5.24/5.54 ( ( member_real @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5905_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.24/5.54 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.54 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.54 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: complex] :
% 5.24/5.54 ( ( member_complex @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5906_sum__strict__mono2,axiom,
% 5.24/5.54 ! [B5: set_real,A2: set_real,B: real,F: real > int] :
% 5.24/5.54 ( ( finite_finite_real @ B5 )
% 5.24/5.54 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.54 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.54 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.24/5.54 => ( ! [X3: real] :
% 5.24/5.54 ( ( member_real @ X3 @ B5 )
% 5.24/5.54 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B5 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_strict_mono2
% 5.24/5.54 thf(fact_5907_zdiv__zminus1__eq__if,axiom,
% 5.24/5.54 ! [B: int,A: int] :
% 5.24/5.54 ( ( B != zero_zero_int )
% 5.24/5.54 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.54 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.24/5.54 & ( ( ( modulo_modulo_int @ A @ B )
% 5.24/5.54 != zero_zero_int )
% 5.24/5.54 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.54 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zdiv_zminus1_eq_if
% 5.24/5.54 thf(fact_5908_zdiv__zminus2__eq__if,axiom,
% 5.24/5.54 ! [B: int,A: int] :
% 5.24/5.54 ( ( B != zero_zero_int )
% 5.24/5.54 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.24/5.54 & ( ( ( modulo_modulo_int @ A @ B )
% 5.24/5.54 != zero_zero_int )
% 5.24/5.54 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.24/5.54 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zdiv_zminus2_eq_if
% 5.24/5.54 thf(fact_5909_zminus1__lemma,axiom,
% 5.24/5.54 ! [A: int,B: int,Q2: int,R2: int] :
% 5.24/5.54 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.54 => ( ( B != zero_zero_int )
% 5.24/5.54 => ( 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 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zminus1_lemma
% 5.24/5.54 thf(fact_5910_bits__induct,axiom,
% 5.24/5.54 ! [P: nat > $o,A: nat] :
% 5.24/5.54 ( ! [A3: nat] :
% 5.24/5.54 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = A3 )
% 5.24/5.54 => ( P @ A3 ) )
% 5.24/5.54 => ( ! [A3: nat,B2: $o] :
% 5.24/5.54 ( ( P @ A3 )
% 5.24/5.54 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = A3 )
% 5.24/5.54 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.24/5.54 => ( P @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % bits_induct
% 5.24/5.54 thf(fact_5911_bits__induct,axiom,
% 5.24/5.54 ! [P: int > $o,A: int] :
% 5.24/5.54 ( ! [A3: int] :
% 5.24/5.54 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = A3 )
% 5.24/5.54 => ( P @ A3 ) )
% 5.24/5.54 => ( ! [A3: int,B2: $o] :
% 5.24/5.54 ( ( P @ A3 )
% 5.24/5.54 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = A3 )
% 5.24/5.54 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.24/5.54 => ( P @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % bits_induct
% 5.24/5.54 thf(fact_5912_bits__induct,axiom,
% 5.24/5.54 ! [P: code_integer > $o,A: code_integer] :
% 5.24/5.54 ( ! [A3: code_integer] :
% 5.24/5.54 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.54 = A3 )
% 5.24/5.54 => ( P @ A3 ) )
% 5.24/5.54 => ( ! [A3: code_integer,B2: $o] :
% 5.24/5.54 ( ( P @ A3 )
% 5.24/5.54 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.54 = A3 )
% 5.24/5.54 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.24/5.54 => ( P @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % bits_induct
% 5.24/5.54 thf(fact_5913_le__divide__eq__numeral_I2_J,axiom,
% 5.24/5.54 ! [W2: num,B: real,C: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 5.24/5.54 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.54 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 5.24/5.54 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.54 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.54 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.24/5.54 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.54 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % le_divide_eq_numeral(2)
% 5.24/5.54 thf(fact_5914_le__divide__eq__numeral_I2_J,axiom,
% 5.24/5.54 ! [W2: num,B: rat,C: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.24/5.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.54 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.24/5.54 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.54 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.54 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.24/5.54 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.54 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % le_divide_eq_numeral(2)
% 5.24/5.54 thf(fact_5915_divide__le__eq__numeral_I2_J,axiom,
% 5.24/5.54 ! [B: real,C: real,W2: num] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.54 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.54 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.24/5.54 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.54 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.54 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 5.24/5.54 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divide_le_eq_numeral(2)
% 5.24/5.54 thf(fact_5916_divide__le__eq__numeral_I2_J,axiom,
% 5.24/5.54 ! [B: rat,C: rat,W2: num] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.24/5.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.54 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.24/5.54 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.24/5.54 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.54 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.24/5.54 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divide_le_eq_numeral(2)
% 5.24/5.54 thf(fact_5917_square__le__1,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.54 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.54 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % square_le_1
% 5.24/5.54 thf(fact_5918_square__le__1,axiom,
% 5.24/5.54 ! [X: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.24/5.54 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % square_le_1
% 5.24/5.54 thf(fact_5919_square__le__1,axiom,
% 5.24/5.54 ! [X: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.24/5.54 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.24/5.54 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % square_le_1
% 5.24/5.54 thf(fact_5920_square__le__1,axiom,
% 5.24/5.54 ! [X: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.24/5.54 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.24/5.54 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % square_le_1
% 5.24/5.54 thf(fact_5921_minus__power__mult__self,axiom,
% 5.24/5.54 ! [A: real,N: nat] :
% 5.24/5.54 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.24/5.54 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_power_mult_self
% 5.24/5.54 thf(fact_5922_minus__power__mult__self,axiom,
% 5.24/5.54 ! [A: int,N: nat] :
% 5.24/5.54 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.24/5.54 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_power_mult_self
% 5.24/5.54 thf(fact_5923_minus__power__mult__self,axiom,
% 5.24/5.54 ! [A: complex,N: nat] :
% 5.24/5.54 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.24/5.54 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_power_mult_self
% 5.24/5.54 thf(fact_5924_minus__power__mult__self,axiom,
% 5.24/5.54 ! [A: rat,N: nat] :
% 5.24/5.54 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.24/5.54 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_power_mult_self
% 5.24/5.54 thf(fact_5925_minus__power__mult__self,axiom,
% 5.24/5.54 ! [A: code_integer,N: nat] :
% 5.24/5.54 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.24/5.54 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_power_mult_self
% 5.24/5.54 thf(fact_5926_signed__take__bit__int__eq__self__iff,axiom,
% 5.24/5.54 ! [N: nat,K: int] :
% 5.24/5.54 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.24/5.54 = K )
% 5.24/5.54 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.24/5.54 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_int_eq_self_iff
% 5.24/5.54 thf(fact_5927_signed__take__bit__int__eq__self,axiom,
% 5.24/5.54 ! [N: nat,K: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.24/5.54 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.24/5.54 = K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_int_eq_self
% 5.24/5.54 thf(fact_5928_minus__1__div__exp__eq__int,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_1_div_exp_eq_int
% 5.24/5.54 thf(fact_5929_div__pos__neg__trivial,axiom,
% 5.24/5.54 ! [K: int,L2: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.24/5.54 => ( ( divide_divide_int @ K @ L2 )
% 5.24/5.54 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % div_pos_neg_trivial
% 5.24/5.54 thf(fact_5930_add__0__iff,axiom,
% 5.24/5.54 ! [B: complex,A: complex] :
% 5.24/5.54 ( ( B
% 5.24/5.54 = ( plus_plus_complex @ B @ A ) )
% 5.24/5.54 = ( A = zero_zero_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % add_0_iff
% 5.24/5.54 thf(fact_5931_add__0__iff,axiom,
% 5.24/5.54 ! [B: real,A: real] :
% 5.24/5.54 ( ( B
% 5.24/5.54 = ( plus_plus_real @ B @ A ) )
% 5.24/5.54 = ( A = zero_zero_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % add_0_iff
% 5.24/5.54 thf(fact_5932_add__0__iff,axiom,
% 5.24/5.54 ! [B: rat,A: rat] :
% 5.24/5.54 ( ( B
% 5.24/5.54 = ( plus_plus_rat @ B @ A ) )
% 5.24/5.54 = ( A = zero_zero_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % add_0_iff
% 5.24/5.54 thf(fact_5933_add__0__iff,axiom,
% 5.24/5.54 ! [B: nat,A: nat] :
% 5.24/5.54 ( ( B
% 5.24/5.54 = ( plus_plus_nat @ B @ A ) )
% 5.24/5.54 = ( A = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % add_0_iff
% 5.24/5.54 thf(fact_5934_add__0__iff,axiom,
% 5.24/5.54 ! [B: int,A: int] :
% 5.24/5.54 ( ( B
% 5.24/5.54 = ( plus_plus_int @ B @ A ) )
% 5.24/5.54 = ( A = zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % add_0_iff
% 5.24/5.54 thf(fact_5935_exp__mod__exp,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % exp_mod_exp
% 5.24/5.54 thf(fact_5936_exp__mod__exp,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % exp_mod_exp
% 5.24/5.54 thf(fact_5937_exp__mod__exp,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % exp_mod_exp
% 5.24/5.54 thf(fact_5938_crossproduct__eq,axiom,
% 5.24/5.54 ! [W2: real,Y4: real,X: real,Z2: real] :
% 5.24/5.54 ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y4 ) @ ( times_times_real @ X @ Z2 ) )
% 5.24/5.54 = ( plus_plus_real @ ( times_times_real @ W2 @ Z2 ) @ ( times_times_real @ X @ Y4 ) ) )
% 5.24/5.54 = ( ( W2 = X )
% 5.24/5.54 | ( Y4 = Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_eq
% 5.24/5.54 thf(fact_5939_crossproduct__eq,axiom,
% 5.24/5.54 ! [W2: rat,Y4: rat,X: rat,Z2: rat] :
% 5.24/5.54 ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y4 ) @ ( times_times_rat @ X @ Z2 ) )
% 5.24/5.54 = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z2 ) @ ( times_times_rat @ X @ Y4 ) ) )
% 5.24/5.54 = ( ( W2 = X )
% 5.24/5.54 | ( Y4 = Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_eq
% 5.24/5.54 thf(fact_5940_crossproduct__eq,axiom,
% 5.24/5.54 ! [W2: nat,Y4: nat,X: nat,Z2: nat] :
% 5.24/5.54 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y4 ) @ ( times_times_nat @ X @ Z2 ) )
% 5.24/5.54 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z2 ) @ ( times_times_nat @ X @ Y4 ) ) )
% 5.24/5.54 = ( ( W2 = X )
% 5.24/5.54 | ( Y4 = Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_eq
% 5.24/5.54 thf(fact_5941_crossproduct__eq,axiom,
% 5.24/5.54 ! [W2: int,Y4: int,X: int,Z2: int] :
% 5.24/5.54 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y4 ) @ ( times_times_int @ X @ Z2 ) )
% 5.24/5.54 = ( plus_plus_int @ ( times_times_int @ W2 @ Z2 ) @ ( times_times_int @ X @ Y4 ) ) )
% 5.24/5.54 = ( ( W2 = X )
% 5.24/5.54 | ( Y4 = Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_eq
% 5.24/5.54 thf(fact_5942_crossproduct__noteq,axiom,
% 5.24/5.54 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.54 ( ( ( A != B )
% 5.24/5.54 & ( C != D ) )
% 5.24/5.54 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.24/5.54 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_noteq
% 5.24/5.54 thf(fact_5943_crossproduct__noteq,axiom,
% 5.24/5.54 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.24/5.54 ( ( ( A != B )
% 5.24/5.54 & ( C != D ) )
% 5.24/5.54 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.24/5.54 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_noteq
% 5.24/5.54 thf(fact_5944_crossproduct__noteq,axiom,
% 5.24/5.54 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.24/5.54 ( ( ( A != B )
% 5.24/5.54 & ( C != D ) )
% 5.24/5.54 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.24/5.54 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_noteq
% 5.24/5.54 thf(fact_5945_crossproduct__noteq,axiom,
% 5.24/5.54 ! [A: int,B: int,C: int,D: int] :
% 5.24/5.54 ( ( ( A != B )
% 5.24/5.54 & ( C != D ) )
% 5.24/5.54 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.24/5.54 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % crossproduct_noteq
% 5.24/5.54 thf(fact_5946_power__minus1__odd,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.54 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus1_odd
% 5.24/5.54 thf(fact_5947_power__minus1__odd,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.54 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus1_odd
% 5.24/5.54 thf(fact_5948_power__minus1__odd,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus1_odd
% 5.24/5.54 thf(fact_5949_power__minus1__odd,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.54 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus1_odd
% 5.24/5.54 thf(fact_5950_power__minus1__odd,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus1_odd
% 5.24/5.54 thf(fact_5951_int__bit__induct,axiom,
% 5.24/5.54 ! [P: int > $o,K: int] :
% 5.24/5.54 ( ( P @ zero_zero_int )
% 5.24/5.54 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.54 => ( ! [K2: int] :
% 5.24/5.54 ( ( P @ K2 )
% 5.24/5.54 => ( ( K2 != zero_zero_int )
% 5.24/5.54 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.54 => ( ! [K2: int] :
% 5.24/5.54 ( ( P @ K2 )
% 5.24/5.54 => ( ( K2
% 5.24/5.54 != ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.54 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.24/5.54 => ( P @ K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % int_bit_induct
% 5.24/5.54 thf(fact_5952_ln__one__plus__pos__lower__bound,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.54 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.54 => ( 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 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % ln_one_plus_pos_lower_bound
% 5.24/5.54 thf(fact_5953_signed__take__bit__int__greater__eq,axiom,
% 5.24/5.54 ! [K: int,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.54 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_int_greater_eq
% 5.24/5.54 thf(fact_5954_exp__div__exp__eq,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( times_times_nat
% 5.24/5.54 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.54 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.24/5.54 != zero_zero_nat )
% 5.24/5.54 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.24/5.54 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % exp_div_exp_eq
% 5.24/5.54 thf(fact_5955_exp__div__exp__eq,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( times_times_int
% 5.24/5.54 @ ( zero_n2684676970156552555ol_int
% 5.24/5.54 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.24/5.54 != zero_zero_int )
% 5.24/5.54 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.24/5.54 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % exp_div_exp_eq
% 5.24/5.54 thf(fact_5956_exp__div__exp__eq,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.54 = ( times_3573771949741848930nteger
% 5.24/5.54 @ ( zero_n356916108424825756nteger
% 5.24/5.54 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.24/5.54 != zero_z3403309356797280102nteger )
% 5.24/5.54 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.24/5.54 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % exp_div_exp_eq
% 5.24/5.54 thf(fact_5957_vebt__buildup_Osimps_I3_J,axiom,
% 5.24/5.54 ! [Va: nat] :
% 5.24/5.54 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.24/5.54 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.24/5.54 = ( 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 ) ) ) ) ) ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.24/5.54 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.24/5.54 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % vebt_buildup.simps(3)
% 5.24/5.54 thf(fact_5958_ln__2__less__1,axiom,
% 5.24/5.54 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.24/5.54
% 5.24/5.54 % ln_2_less_1
% 5.24/5.54 thf(fact_5959_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.54 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.24/5.54 => ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.24/5.54 thf(fact_5960_tanh__ln__real,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.54 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.24/5.54 = ( 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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % tanh_ln_real
% 5.24/5.54 thf(fact_5961_Divides_Oadjust__div__eq,axiom,
% 5.24/5.54 ! [Q2: int,R2: int] :
% 5.24/5.54 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.24/5.54 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % Divides.adjust_div_eq
% 5.24/5.54 thf(fact_5962_signed__take__bit__Suc__minus__bit1,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.24/5.54 = ( 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 ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_Suc_minus_bit1
% 5.24/5.54 thf(fact_5963_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.54 => ( 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 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ln_one_plus_x_minus_x_bound
% 5.24/5.54 thf(fact_5964_vebt__buildup_Opelims,axiom,
% 5.24/5.54 ! [X: nat,Y4: vEBT_VEBT] :
% 5.24/5.54 ( ( ( vEBT_vebt_buildup @ X )
% 5.24/5.54 = Y4 )
% 5.24/5.54 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.24/5.54 => ( ( ( X = zero_zero_nat )
% 5.24/5.54 => ( ( Y4
% 5.24/5.54 = ( vEBT_Leaf @ $false @ $false ) )
% 5.24/5.54 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.24/5.54 => ( ( ( X
% 5.24/5.54 = ( suc @ zero_zero_nat ) )
% 5.24/5.54 => ( ( Y4
% 5.24/5.54 = ( vEBT_Leaf @ $false @ $false ) )
% 5.24/5.54 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.24/5.54 => ~ ! [Va3: nat] :
% 5.24/5.54 ( ( X
% 5.24/5.54 = ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.54 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.54 => ( Y4
% 5.24/5.54 = ( 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 ) ) ) ) ) ) )
% 5.24/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.24/5.54 => ( Y4
% 5.24/5.54 = ( 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 ) ) ) ) ) ) ) ) )
% 5.24/5.54 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % vebt_buildup.pelims
% 5.24/5.54 thf(fact_5965_verit__eq__simplify_I9_J,axiom,
% 5.24/5.54 ! [X32: num,Y32: num] :
% 5.24/5.54 ( ( ( bit1 @ X32 )
% 5.24/5.54 = ( bit1 @ Y32 ) )
% 5.24/5.54 = ( X32 = Y32 ) ) ).
% 5.24/5.54
% 5.24/5.54 % verit_eq_simplify(9)
% 5.24/5.54 thf(fact_5966_semiring__norm_I90_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( bit1 @ M )
% 5.24/5.54 = ( bit1 @ N ) )
% 5.24/5.54 = ( M = N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(90)
% 5.24/5.54 thf(fact_5967_semiring__norm_I89_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( bit1 @ M )
% 5.24/5.54 != ( bit0 @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(89)
% 5.24/5.54 thf(fact_5968_semiring__norm_I88_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( bit0 @ M )
% 5.24/5.54 != ( bit1 @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(88)
% 5.24/5.54 thf(fact_5969_semiring__norm_I86_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ( ( bit1 @ M )
% 5.24/5.54 != one ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(86)
% 5.24/5.54 thf(fact_5970_semiring__norm_I84_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( one
% 5.24/5.54 != ( bit1 @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(84)
% 5.24/5.54 thf(fact_5971_abs__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.24/5.54 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_numeral
% 5.24/5.54 thf(fact_5972_abs__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.24/5.54 = ( numeral_numeral_real @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_numeral
% 5.24/5.54 thf(fact_5973_abs__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.24/5.54 = ( numeral_numeral_rat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_numeral
% 5.24/5.54 thf(fact_5974_abs__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_numeral
% 5.24/5.54 thf(fact_5975_abs__mult__self__eq,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.24/5.54 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_self_eq
% 5.24/5.54 thf(fact_5976_abs__mult__self__eq,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.24/5.54 = ( times_times_real @ A @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_self_eq
% 5.24/5.54 thf(fact_5977_abs__mult__self__eq,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.24/5.54 = ( times_times_rat @ A @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_self_eq
% 5.24/5.54 thf(fact_5978_abs__mult__self__eq,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.24/5.54 = ( times_times_int @ A @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_self_eq
% 5.24/5.54 thf(fact_5979_abs__1,axiom,
% 5.24/5.54 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.24/5.54 = one_one_Code_integer ) ).
% 5.24/5.54
% 5.24/5.54 % abs_1
% 5.24/5.54 thf(fact_5980_abs__1,axiom,
% 5.24/5.54 ( ( abs_abs_complex @ one_one_complex )
% 5.24/5.54 = one_one_complex ) ).
% 5.24/5.54
% 5.24/5.54 % abs_1
% 5.24/5.54 thf(fact_5981_abs__1,axiom,
% 5.24/5.54 ( ( abs_abs_real @ one_one_real )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % abs_1
% 5.24/5.54 thf(fact_5982_abs__1,axiom,
% 5.24/5.54 ( ( abs_abs_rat @ one_one_rat )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % abs_1
% 5.24/5.54 thf(fact_5983_abs__1,axiom,
% 5.24/5.54 ( ( abs_abs_int @ one_one_int )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % abs_1
% 5.24/5.54 thf(fact_5984_abs__add__abs,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.24/5.54 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_abs
% 5.24/5.54 thf(fact_5985_abs__add__abs,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.24/5.54 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_abs
% 5.24/5.54 thf(fact_5986_abs__add__abs,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.24/5.54 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_abs
% 5.24/5.54 thf(fact_5987_abs__add__abs,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_abs
% 5.24/5.54 thf(fact_5988_abs__divide,axiom,
% 5.24/5.54 ! [A: complex,B: complex] :
% 5.24/5.54 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.54 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_divide
% 5.24/5.54 thf(fact_5989_abs__divide,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.54 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_divide
% 5.24/5.54 thf(fact_5990_abs__divide,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.54 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_divide
% 5.24/5.54 thf(fact_5991_semiring__norm_I80_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( ord_less_num @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(80)
% 5.24/5.54 thf(fact_5992_semiring__norm_I73_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(73)
% 5.24/5.54 thf(fact_5993_abs__le__zero__iff,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.24/5.54 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_zero_iff
% 5.24/5.54 thf(fact_5994_abs__le__zero__iff,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.24/5.54 = ( A = zero_zero_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_zero_iff
% 5.24/5.54 thf(fact_5995_abs__le__zero__iff,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.24/5.54 = ( A = zero_zero_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_zero_iff
% 5.24/5.54 thf(fact_5996_abs__le__zero__iff,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.24/5.54 = ( A = zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_zero_iff
% 5.24/5.54 thf(fact_5997_abs__le__self__iff,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.24/5.54 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_self_iff
% 5.24/5.54 thf(fact_5998_abs__le__self__iff,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.24/5.54 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_self_iff
% 5.24/5.54 thf(fact_5999_abs__le__self__iff,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.24/5.54 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_self_iff
% 5.24/5.54 thf(fact_6000_abs__le__self__iff,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.24/5.54 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_self_iff
% 5.24/5.54 thf(fact_6001_abs__of__nonneg,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.54 => ( ( abs_abs_Code_integer @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonneg
% 5.24/5.54 thf(fact_6002_abs__of__nonneg,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.54 => ( ( abs_abs_real @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonneg
% 5.24/5.54 thf(fact_6003_abs__of__nonneg,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.24/5.54 => ( ( abs_abs_rat @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonneg
% 5.24/5.54 thf(fact_6004_abs__of__nonneg,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.54 => ( ( abs_abs_int @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonneg
% 5.24/5.54 thf(fact_6005_zero__less__abs__iff,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.24/5.54 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_abs_iff
% 5.24/5.54 thf(fact_6006_zero__less__abs__iff,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.24/5.54 = ( A != zero_zero_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_abs_iff
% 5.24/5.54 thf(fact_6007_zero__less__abs__iff,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.24/5.54 = ( A != zero_zero_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_abs_iff
% 5.24/5.54 thf(fact_6008_zero__less__abs__iff,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.24/5.54 = ( A != zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_abs_iff
% 5.24/5.54 thf(fact_6009_abs__neg__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.54 = ( numeral_numeral_real @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_numeral
% 5.24/5.54 thf(fact_6010_abs__neg__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_numeral
% 5.24/5.54 thf(fact_6011_abs__neg__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.54 = ( numeral_numeral_rat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_numeral
% 5.24/5.54 thf(fact_6012_abs__neg__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.24/5.54 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_numeral
% 5.24/5.54 thf(fact_6013_abs__neg__one,axiom,
% 5.24/5.54 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_one
% 5.24/5.54 thf(fact_6014_abs__neg__one,axiom,
% 5.24/5.54 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_one
% 5.24/5.54 thf(fact_6015_abs__neg__one,axiom,
% 5.24/5.54 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_one
% 5.24/5.54 thf(fact_6016_abs__neg__one,axiom,
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.54 = one_one_Code_integer ) ).
% 5.24/5.54
% 5.24/5.54 % abs_neg_one
% 5.24/5.54 thf(fact_6017_abs__power__minus,axiom,
% 5.24/5.54 ! [A: real,N: nat] :
% 5.24/5.54 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.24/5.54 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power_minus
% 5.24/5.54 thf(fact_6018_abs__power__minus,axiom,
% 5.24/5.54 ! [A: int,N: nat] :
% 5.24/5.54 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.24/5.54 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power_minus
% 5.24/5.54 thf(fact_6019_abs__power__minus,axiom,
% 5.24/5.54 ! [A: rat,N: nat] :
% 5.24/5.54 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.24/5.54 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power_minus
% 5.24/5.54 thf(fact_6020_abs__power__minus,axiom,
% 5.24/5.54 ! [A: code_integer,N: nat] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.24/5.54 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power_minus
% 5.24/5.54 thf(fact_6021_semiring__norm_I7_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(7)
% 5.24/5.54 thf(fact_6022_semiring__norm_I9_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(9)
% 5.24/5.54 thf(fact_6023_semiring__norm_I14_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(14)
% 5.24/5.54 thf(fact_6024_semiring__norm_I15_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(15)
% 5.24/5.54 thf(fact_6025_semiring__norm_I81_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( ord_less_num @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(81)
% 5.24/5.54 thf(fact_6026_semiring__norm_I72_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(72)
% 5.24/5.54 thf(fact_6027_semiring__norm_I77_J,axiom,
% 5.24/5.54 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(77)
% 5.24/5.54 thf(fact_6028_semiring__norm_I70_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(70)
% 5.24/5.54 thf(fact_6029_sum__abs,axiom,
% 5.24/5.54 ! [F: int > int,A2: set_int] :
% 5.24/5.54 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.24/5.54 @ ( groups4538972089207619220nt_int
% 5.24/5.54 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.24/5.54 @ A2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_abs
% 5.24/5.54 thf(fact_6030_sum__abs,axiom,
% 5.24/5.54 ! [F: nat > real,A2: set_nat] :
% 5.24/5.54 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.24/5.54 @ ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.24/5.54 @ A2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_abs
% 5.24/5.54 thf(fact_6031_divide__le__0__abs__iff,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.24/5.54 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.24/5.54 | ( B = zero_zero_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divide_le_0_abs_iff
% 5.24/5.54 thf(fact_6032_divide__le__0__abs__iff,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.24/5.54 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.24/5.54 | ( B = zero_zero_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divide_le_0_abs_iff
% 5.24/5.54 thf(fact_6033_zero__le__divide__abs__iff,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.24/5.54 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.54 | ( B = zero_zero_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_le_divide_abs_iff
% 5.24/5.54 thf(fact_6034_zero__le__divide__abs__iff,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.24/5.54 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.24/5.54 | ( B = zero_zero_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_le_divide_abs_iff
% 5.24/5.54 thf(fact_6035_abs__of__nonpos,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.24/5.54 => ( ( abs_abs_real @ A )
% 5.24/5.54 = ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonpos
% 5.24/5.54 thf(fact_6036_abs__of__nonpos,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.24/5.54 => ( ( abs_abs_Code_integer @ A )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonpos
% 5.24/5.54 thf(fact_6037_abs__of__nonpos,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.24/5.54 => ( ( abs_abs_rat @ A )
% 5.24/5.54 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonpos
% 5.24/5.54 thf(fact_6038_abs__of__nonpos,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.24/5.54 => ( ( abs_abs_int @ A )
% 5.24/5.54 = ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_nonpos
% 5.24/5.54 thf(fact_6039_zdiv__numeral__Bit1,axiom,
% 5.24/5.54 ! [V: num,W2: num] :
% 5.24/5.54 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.24/5.54 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zdiv_numeral_Bit1
% 5.24/5.54 thf(fact_6040_semiring__norm_I10_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(10)
% 5.24/5.54 thf(fact_6041_semiring__norm_I8_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.24/5.54 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(8)
% 5.24/5.54 thf(fact_6042_semiring__norm_I5_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.24/5.54 = ( bit1 @ M ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(5)
% 5.24/5.54 thf(fact_6043_semiring__norm_I4_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.24/5.54 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(4)
% 5.24/5.54 thf(fact_6044_semiring__norm_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.24/5.54 = ( bit1 @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(3)
% 5.24/5.54 thf(fact_6045_artanh__minus__real,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.54 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 5.24/5.54 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % artanh_minus_real
% 5.24/5.54 thf(fact_6046_sum__abs__ge__zero,axiom,
% 5.24/5.54 ! [F: int > int,A2: set_int] :
% 5.24/5.54 ( ord_less_eq_int @ zero_zero_int
% 5.24/5.54 @ ( groups4538972089207619220nt_int
% 5.24/5.54 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.24/5.54 @ A2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_abs_ge_zero
% 5.24/5.54 thf(fact_6047_sum__abs__ge__zero,axiom,
% 5.24/5.54 ! [F: nat > real,A2: set_nat] :
% 5.24/5.54 ( ord_less_eq_real @ zero_zero_real
% 5.24/5.54 @ ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.24/5.54 @ A2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_abs_ge_zero
% 5.24/5.54 thf(fact_6048_semiring__norm_I16_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(16)
% 5.24/5.54 thf(fact_6049_semiring__norm_I74_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( ord_less_num @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(74)
% 5.24/5.54 thf(fact_6050_semiring__norm_I79_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % semiring_norm(79)
% 5.24/5.54 thf(fact_6051_zero__less__power__abs__iff,axiom,
% 5.24/5.54 ! [A: code_integer,N: nat] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.24/5.54 = ( ( A != zero_z3403309356797280102nteger )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_power_abs_iff
% 5.24/5.54 thf(fact_6052_zero__less__power__abs__iff,axiom,
% 5.24/5.54 ! [A: real,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.24/5.54 = ( ( A != zero_zero_real )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_power_abs_iff
% 5.24/5.54 thf(fact_6053_zero__less__power__abs__iff,axiom,
% 5.24/5.54 ! [A: rat,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.24/5.54 = ( ( A != zero_zero_rat )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_power_abs_iff
% 5.24/5.54 thf(fact_6054_zero__less__power__abs__iff,axiom,
% 5.24/5.54 ! [A: int,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.24/5.54 = ( ( A != zero_zero_int )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_less_power_abs_iff
% 5.24/5.54 thf(fact_6055_abs__power2,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power2
% 5.24/5.54 thf(fact_6056_abs__power2,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power2
% 5.24/5.54 thf(fact_6057_abs__power2,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power2
% 5.24/5.54 thf(fact_6058_abs__power2,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_power2
% 5.24/5.54 thf(fact_6059_power2__abs,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_abs
% 5.24/5.54 thf(fact_6060_power2__abs,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_abs
% 5.24/5.54 thf(fact_6061_power2__abs,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_abs
% 5.24/5.54 thf(fact_6062_power2__abs,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_abs
% 5.24/5.54 thf(fact_6063_sum_Ocl__ivl__Suc,axiom,
% 5.24/5.54 ! [N: nat,M: nat,G: nat > complex] :
% 5.24/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = zero_zero_complex ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.cl_ivl_Suc
% 5.24/5.54 thf(fact_6064_sum_Ocl__ivl__Suc,axiom,
% 5.24/5.54 ! [N: nat,M: nat,G: nat > rat] :
% 5.24/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = zero_zero_rat ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.cl_ivl_Suc
% 5.24/5.54 thf(fact_6065_sum_Ocl__ivl__Suc,axiom,
% 5.24/5.54 ! [N: nat,M: nat,G: nat > int] :
% 5.24/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = zero_zero_int ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.cl_ivl_Suc
% 5.24/5.54 thf(fact_6066_sum_Ocl__ivl__Suc,axiom,
% 5.24/5.54 ! [N: nat,M: nat,G: nat > nat] :
% 5.24/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = zero_zero_nat ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.cl_ivl_Suc
% 5.24/5.54 thf(fact_6067_sum_Ocl__ivl__Suc,axiom,
% 5.24/5.54 ! [N: nat,M: nat,G: nat > real] :
% 5.24/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = zero_zero_real ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.cl_ivl_Suc
% 5.24/5.54 thf(fact_6068_sum__zero__power,axiom,
% 5.24/5.54 ! [A2: set_nat,C: nat > complex] :
% 5.24/5.54 ( ( ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( C @ zero_zero_nat ) ) )
% 5.24/5.54 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = zero_zero_complex ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_zero_power
% 5.24/5.54 thf(fact_6069_sum__zero__power,axiom,
% 5.24/5.54 ! [A2: set_nat,C: nat > rat] :
% 5.24/5.54 ( ( ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( C @ zero_zero_nat ) ) )
% 5.24/5.54 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = zero_zero_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_zero_power
% 5.24/5.54 thf(fact_6070_sum__zero__power,axiom,
% 5.24/5.54 ! [A2: set_nat,C: nat > real] :
% 5.24/5.54 ( ( ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( C @ zero_zero_nat ) ) )
% 5.24/5.54 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = zero_zero_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_zero_power
% 5.24/5.54 thf(fact_6071_power__even__abs__numeral,axiom,
% 5.24/5.54 ! [W2: num,A: rat] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs_numeral
% 5.24/5.54 thf(fact_6072_power__even__abs__numeral,axiom,
% 5.24/5.54 ! [W2: num,A: code_integer] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs_numeral
% 5.24/5.54 thf(fact_6073_power__even__abs__numeral,axiom,
% 5.24/5.54 ! [W2: num,A: real] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 = ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs_numeral
% 5.24/5.54 thf(fact_6074_power__even__abs__numeral,axiom,
% 5.24/5.54 ! [W2: num,A: int] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W2 ) )
% 5.24/5.54 = ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs_numeral
% 5.24/5.54 thf(fact_6075_div__Suc__eq__div__add3,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.24/5.54 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % div_Suc_eq_div_add3
% 5.24/5.54 thf(fact_6076_Suc__div__eq__add3__div__numeral,axiom,
% 5.24/5.54 ! [M: nat,V: num] :
% 5.24/5.54 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.24/5.54 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % Suc_div_eq_add3_div_numeral
% 5.24/5.54 thf(fact_6077_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.24/5.54 ! [M: nat,V: num] :
% 5.24/5.54 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.24/5.54 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % Suc_mod_eq_add3_mod_numeral
% 5.24/5.54 thf(fact_6078_mod__Suc__eq__mod__add3,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.24/5.54 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mod_Suc_eq_mod_add3
% 5.24/5.54 thf(fact_6079_sum__zero__power_H,axiom,
% 5.24/5.54 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 5.24/5.54 ( ( ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.24/5.54 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = zero_zero_complex ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_zero_power'
% 5.24/5.54 thf(fact_6080_sum__zero__power_H,axiom,
% 5.24/5.54 ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 5.24/5.54 ( ( ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.24/5.54 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = zero_zero_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_zero_power'
% 5.24/5.54 thf(fact_6081_sum__zero__power_H,axiom,
% 5.24/5.54 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 5.24/5.54 ( ( ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.24/5.54 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.24/5.54 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = zero_zero_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_zero_power'
% 5.24/5.54 thf(fact_6082_zmod__numeral__Bit1,axiom,
% 5.24/5.54 ! [V: num,W2: num] :
% 5.24/5.54 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % zmod_numeral_Bit1
% 5.24/5.54 thf(fact_6083_signed__take__bit__Suc__bit1,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_Suc_bit1
% 5.24/5.54 thf(fact_6084_abs__le__D1,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D1
% 5.24/5.54 thf(fact_6085_abs__le__D1,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D1
% 5.24/5.54 thf(fact_6086_abs__le__D1,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D1
% 5.24/5.54 thf(fact_6087_abs__le__D1,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D1
% 5.24/5.54 thf(fact_6088_abs__ge__self,axiom,
% 5.24/5.54 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_self
% 5.24/5.54 thf(fact_6089_abs__ge__self,axiom,
% 5.24/5.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_self
% 5.24/5.54 thf(fact_6090_abs__ge__self,axiom,
% 5.24/5.54 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_self
% 5.24/5.54 thf(fact_6091_abs__ge__self,axiom,
% 5.24/5.54 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_self
% 5.24/5.54 thf(fact_6092_abs__mult,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.24/5.54 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult
% 5.24/5.54 thf(fact_6093_abs__mult,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.24/5.54 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult
% 5.24/5.54 thf(fact_6094_abs__mult,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.24/5.54 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult
% 5.24/5.54 thf(fact_6095_abs__mult,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.24/5.54 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult
% 5.24/5.54 thf(fact_6096_abs__one,axiom,
% 5.24/5.54 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.24/5.54 = one_one_Code_integer ) ).
% 5.24/5.54
% 5.24/5.54 % abs_one
% 5.24/5.54 thf(fact_6097_abs__one,axiom,
% 5.24/5.54 ( ( abs_abs_real @ one_one_real )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % abs_one
% 5.24/5.54 thf(fact_6098_abs__one,axiom,
% 5.24/5.54 ( ( abs_abs_rat @ one_one_rat )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % abs_one
% 5.24/5.54 thf(fact_6099_abs__one,axiom,
% 5.24/5.54 ( ( abs_abs_int @ one_one_int )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % abs_one
% 5.24/5.54 thf(fact_6100_power__abs,axiom,
% 5.24/5.54 ! [A: rat,N: nat] :
% 5.24/5.54 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.24/5.54 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_abs
% 5.24/5.54 thf(fact_6101_power__abs,axiom,
% 5.24/5.54 ! [A: code_integer,N: nat] :
% 5.24/5.54 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.24/5.54 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_abs
% 5.24/5.54 thf(fact_6102_power__abs,axiom,
% 5.24/5.54 ! [A: real,N: nat] :
% 5.24/5.54 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.24/5.54 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_abs
% 5.24/5.54 thf(fact_6103_power__abs,axiom,
% 5.24/5.54 ! [A: int,N: nat] :
% 5.24/5.54 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.24/5.54 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_abs
% 5.24/5.54 thf(fact_6104_verit__eq__simplify_I14_J,axiom,
% 5.24/5.54 ! [X22: num,X32: num] :
% 5.24/5.54 ( ( bit0 @ X22 )
% 5.24/5.54 != ( bit1 @ X32 ) ) ).
% 5.24/5.54
% 5.24/5.54 % verit_eq_simplify(14)
% 5.24/5.54 thf(fact_6105_verit__eq__simplify_I12_J,axiom,
% 5.24/5.54 ! [X32: num] :
% 5.24/5.54 ( one
% 5.24/5.54 != ( bit1 @ X32 ) ) ).
% 5.24/5.54
% 5.24/5.54 % verit_eq_simplify(12)
% 5.24/5.54 thf(fact_6106_abs__ge__zero,axiom,
% 5.24/5.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_zero
% 5.24/5.54 thf(fact_6107_abs__ge__zero,axiom,
% 5.24/5.54 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_zero
% 5.24/5.54 thf(fact_6108_abs__ge__zero,axiom,
% 5.24/5.54 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_zero
% 5.24/5.54 thf(fact_6109_abs__ge__zero,axiom,
% 5.24/5.54 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_zero
% 5.24/5.54 thf(fact_6110_abs__not__less__zero,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.24/5.54
% 5.24/5.54 % abs_not_less_zero
% 5.24/5.54 thf(fact_6111_abs__not__less__zero,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.24/5.54
% 5.24/5.54 % abs_not_less_zero
% 5.24/5.54 thf(fact_6112_abs__not__less__zero,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.24/5.54
% 5.24/5.54 % abs_not_less_zero
% 5.24/5.54 thf(fact_6113_abs__not__less__zero,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.24/5.54
% 5.24/5.54 % abs_not_less_zero
% 5.24/5.54 thf(fact_6114_abs__of__pos,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.54 => ( ( abs_abs_Code_integer @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_pos
% 5.24/5.54 thf(fact_6115_abs__of__pos,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.54 => ( ( abs_abs_real @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_pos
% 5.24/5.54 thf(fact_6116_abs__of__pos,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.54 => ( ( abs_abs_rat @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_pos
% 5.24/5.54 thf(fact_6117_abs__of__pos,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ A )
% 5.24/5.54 => ( ( abs_abs_int @ A )
% 5.24/5.54 = A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_pos
% 5.24/5.54 thf(fact_6118_abs__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq
% 5.24/5.54 thf(fact_6119_abs__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq
% 5.24/5.54 thf(fact_6120_abs__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq
% 5.24/5.54 thf(fact_6121_abs__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq
% 5.24/5.54 thf(fact_6122_abs__mult__less,axiom,
% 5.24/5.54 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.24/5.54 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.24/5.54 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_less
% 5.24/5.54 thf(fact_6123_abs__mult__less,axiom,
% 5.24/5.54 ! [A: real,C: real,B: real,D: real] :
% 5.24/5.54 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.24/5.54 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.24/5.54 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_less
% 5.24/5.54 thf(fact_6124_abs__mult__less,axiom,
% 5.24/5.54 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.24/5.54 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.24/5.54 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.24/5.54 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_less
% 5.24/5.54 thf(fact_6125_abs__mult__less,axiom,
% 5.24/5.54 ! [A: int,C: int,B: int,D: int] :
% 5.24/5.54 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.24/5.54 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.24/5.54 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_less
% 5.24/5.54 thf(fact_6126_abs__triangle__ineq2__sym,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2_sym
% 5.24/5.54 thf(fact_6127_abs__triangle__ineq2__sym,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2_sym
% 5.24/5.54 thf(fact_6128_abs__triangle__ineq2__sym,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2_sym
% 5.24/5.54 thf(fact_6129_abs__triangle__ineq2__sym,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2_sym
% 5.24/5.54 thf(fact_6130_abs__triangle__ineq3,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq3
% 5.24/5.54 thf(fact_6131_abs__triangle__ineq3,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq3
% 5.24/5.54 thf(fact_6132_abs__triangle__ineq3,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq3
% 5.24/5.54 thf(fact_6133_abs__triangle__ineq3,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq3
% 5.24/5.54 thf(fact_6134_abs__triangle__ineq2,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2
% 5.24/5.54 thf(fact_6135_abs__triangle__ineq2,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2
% 5.24/5.54 thf(fact_6136_abs__triangle__ineq2,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2
% 5.24/5.54 thf(fact_6137_abs__triangle__ineq2,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq2
% 5.24/5.54 thf(fact_6138_nonzero__abs__divide,axiom,
% 5.24/5.54 ! [B: real,A: real] :
% 5.24/5.54 ( ( B != zero_zero_real )
% 5.24/5.54 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.54 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % nonzero_abs_divide
% 5.24/5.54 thf(fact_6139_nonzero__abs__divide,axiom,
% 5.24/5.54 ! [B: rat,A: rat] :
% 5.24/5.54 ( ( B != zero_zero_rat )
% 5.24/5.54 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.54 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % nonzero_abs_divide
% 5.24/5.54 thf(fact_6140_abs__ge__minus__self,axiom,
% 5.24/5.54 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_minus_self
% 5.24/5.54 thf(fact_6141_abs__ge__minus__self,axiom,
% 5.24/5.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_minus_self
% 5.24/5.54 thf(fact_6142_abs__ge__minus__self,axiom,
% 5.24/5.54 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_minus_self
% 5.24/5.54 thf(fact_6143_abs__ge__minus__self,axiom,
% 5.24/5.54 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ge_minus_self
% 5.24/5.54 thf(fact_6144_abs__le__iff,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.24/5.54 = ( ( ord_less_eq_real @ A @ B )
% 5.24/5.54 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_iff
% 5.24/5.54 thf(fact_6145_abs__le__iff,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.24/5.54 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.24/5.54 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_iff
% 5.24/5.54 thf(fact_6146_abs__le__iff,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.24/5.54 = ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.54 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_iff
% 5.24/5.54 thf(fact_6147_abs__le__iff,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.24/5.54 = ( ( ord_less_eq_int @ A @ B )
% 5.24/5.54 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_iff
% 5.24/5.54 thf(fact_6148_abs__le__D2,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D2
% 5.24/5.54 thf(fact_6149_abs__le__D2,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D2
% 5.24/5.54 thf(fact_6150_abs__le__D2,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D2
% 5.24/5.54 thf(fact_6151_abs__le__D2,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_D2
% 5.24/5.54 thf(fact_6152_abs__leI,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.54 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_leI
% 5.24/5.54 thf(fact_6153_abs__leI,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.24/5.54 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_leI
% 5.24/5.54 thf(fact_6154_abs__leI,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.54 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_leI
% 5.24/5.54 thf(fact_6155_abs__leI,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ A @ B )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.24/5.54 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_leI
% 5.24/5.54 thf(fact_6156_abs__less__iff,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.24/5.54 = ( ( ord_less_real @ A @ B )
% 5.24/5.54 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_less_iff
% 5.24/5.54 thf(fact_6157_abs__less__iff,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.24/5.54 = ( ( ord_less_int @ A @ B )
% 5.24/5.54 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_less_iff
% 5.24/5.54 thf(fact_6158_abs__less__iff,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.24/5.54 = ( ( ord_less_rat @ A @ B )
% 5.24/5.54 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_less_iff
% 5.24/5.54 thf(fact_6159_abs__less__iff,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.24/5.54 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.24/5.54 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_less_iff
% 5.24/5.54 thf(fact_6160_sum__cong__Suc,axiom,
% 5.24/5.54 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.24/5.54 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.24/5.54 => ( ! [X3: nat] :
% 5.24/5.54 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.24/5.54 => ( ( F @ ( suc @ X3 ) )
% 5.24/5.54 = ( G @ ( suc @ X3 ) ) ) )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.24/5.54 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_cong_Suc
% 5.24/5.54 thf(fact_6161_sum__cong__Suc,axiom,
% 5.24/5.54 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.24/5.54 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.24/5.54 => ( ! [X3: nat] :
% 5.24/5.54 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.24/5.54 => ( ( F @ ( suc @ X3 ) )
% 5.24/5.54 = ( G @ ( suc @ X3 ) ) ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.24/5.54 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_cong_Suc
% 5.24/5.54 thf(fact_6162_xor__num_Ocases,axiom,
% 5.24/5.54 ! [X: product_prod_num_num] :
% 5.24/5.54 ( ( X
% 5.24/5.54 != ( product_Pair_num_num @ one @ one ) )
% 5.24/5.54 => ( ! [N3: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.24/5.54 => ( ! [N3: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.24/5.54 => ( ! [M4: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.24/5.54 => ( ! [M4: num,N3: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.24/5.54 => ( ! [M4: num,N3: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 5.24/5.54 => ( ! [M4: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.24/5.54 => ( ! [M4: num,N3: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.24/5.54 => ~ ! [M4: num,N3: num] :
% 5.24/5.54 ( X
% 5.24/5.54 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % xor_num.cases
% 5.24/5.54 thf(fact_6163_num_Oexhaust,axiom,
% 5.24/5.54 ! [Y4: num] :
% 5.24/5.54 ( ( Y4 != one )
% 5.24/5.54 => ( ! [X23: num] :
% 5.24/5.54 ( Y4
% 5.24/5.54 != ( bit0 @ X23 ) )
% 5.24/5.54 => ~ ! [X33: num] :
% 5.24/5.54 ( Y4
% 5.24/5.54 != ( bit1 @ X33 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % num.exhaust
% 5.24/5.54 thf(fact_6164_sin__bound__lemma,axiom,
% 5.24/5.54 ! [X: real,Y4: real,U2: real,V: real] :
% 5.24/5.54 ( ( X = Y4 )
% 5.24/5.54 => ( ( ord_less_eq_real @ ( abs_abs_real @ U2 ) @ V )
% 5.24/5.54 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U2 ) @ Y4 ) ) @ V ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sin_bound_lemma
% 5.24/5.54 thf(fact_6165_sum__subtractf__nat,axiom,
% 5.24/5.54 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.24/5.54 ( ! [X3: int] :
% 5.24/5.54 ( ( member_int @ X3 @ A2 )
% 5.24/5.54 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ( groups4541462559716669496nt_nat
% 5.24/5.54 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_subtractf_nat
% 5.24/5.54 thf(fact_6166_sum__subtractf__nat,axiom,
% 5.24/5.54 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.24/5.54 ( ! [X3: real] :
% 5.24/5.54 ( ( member_real @ X3 @ A2 )
% 5.24/5.54 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ( groups1935376822645274424al_nat
% 5.24/5.54 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_subtractf_nat
% 5.24/5.54 thf(fact_6167_sum__subtractf__nat,axiom,
% 5.24/5.54 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.24/5.54 ( ! [X3: complex] :
% 5.24/5.54 ( ( member_complex @ X3 @ A2 )
% 5.24/5.54 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ( groups5693394587270226106ex_nat
% 5.24/5.54 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_subtractf_nat
% 5.24/5.54 thf(fact_6168_sum__subtractf__nat,axiom,
% 5.24/5.54 ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.24/5.54 ( ! [X3: product_prod_nat_nat] :
% 5.24/5.54 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.24/5.54 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ( groups977919841031483927at_nat
% 5.24/5.54 @ ^ [X2: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_subtractf_nat
% 5.24/5.54 thf(fact_6169_sum__subtractf__nat,axiom,
% 5.24/5.54 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.24/5.54 ( ! [X3: nat] :
% 5.24/5.54 ( ( member_nat @ X3 @ A2 )
% 5.24/5.54 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.24/5.54 @ A2 )
% 5.24/5.54 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_subtractf_nat
% 5.24/5.54 thf(fact_6170_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.24/5.54 ! [G: nat > nat,M: nat,N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.24/5.54 = ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.shift_bounds_cl_Suc_ivl
% 5.24/5.54 thf(fact_6171_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.24/5.54 ! [G: nat > real,M: nat,N: nat] :
% 5.24/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.24/5.54 = ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.shift_bounds_cl_Suc_ivl
% 5.24/5.54 thf(fact_6172_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.24/5.54 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.24/5.54 = ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.shift_bounds_cl_nat_ivl
% 5.24/5.54 thf(fact_6173_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.24/5.54 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.24/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.24/5.54 = ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.shift_bounds_cl_nat_ivl
% 5.24/5.54 thf(fact_6174_tanh__real__lt__1,axiom,
% 5.24/5.54 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % tanh_real_lt_1
% 5.24/5.54 thf(fact_6175_tanh__real__gt__neg1,axiom,
% 5.24/5.54 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % tanh_real_gt_neg1
% 5.24/5.54 thf(fact_6176_dense__eq0__I,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ! [E2: real] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.24/5.54 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.24/5.54 => ( X = zero_zero_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % dense_eq0_I
% 5.24/5.54 thf(fact_6177_dense__eq0__I,axiom,
% 5.24/5.54 ! [X: rat] :
% 5.24/5.54 ( ! [E2: rat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.24/5.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.24/5.54 => ( X = zero_zero_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % dense_eq0_I
% 5.24/5.54 thf(fact_6178_abs__eq__mult,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.54 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.24/5.54 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.54 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.24/5.54 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.24/5.54 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_mult
% 5.24/5.54 thf(fact_6179_abs__eq__mult,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.54 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.24/5.54 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.24/5.54 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.24/5.54 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.24/5.54 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_mult
% 5.24/5.54 thf(fact_6180_abs__eq__mult,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.24/5.54 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.24/5.54 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.24/5.54 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.24/5.54 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.24/5.54 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_mult
% 5.24/5.54 thf(fact_6181_abs__eq__mult,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.54 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.24/5.54 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.24/5.54 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.24/5.54 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.24/5.54 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_mult
% 5.24/5.54 thf(fact_6182_abs__mult__pos,axiom,
% 5.24/5.54 ! [X: code_integer,Y4: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.24/5.54 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y4 ) @ X )
% 5.24/5.54 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y4 @ X ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_pos
% 5.24/5.54 thf(fact_6183_abs__mult__pos,axiom,
% 5.24/5.54 ! [X: real,Y4: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.54 => ( ( times_times_real @ ( abs_abs_real @ Y4 ) @ X )
% 5.24/5.54 = ( abs_abs_real @ ( times_times_real @ Y4 @ X ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_pos
% 5.24/5.54 thf(fact_6184_abs__mult__pos,axiom,
% 5.24/5.54 ! [X: rat,Y4: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.24/5.54 => ( ( times_times_rat @ ( abs_abs_rat @ Y4 ) @ X )
% 5.24/5.54 = ( abs_abs_rat @ ( times_times_rat @ Y4 @ X ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_pos
% 5.24/5.54 thf(fact_6185_abs__mult__pos,axiom,
% 5.24/5.54 ! [X: int,Y4: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.24/5.54 => ( ( times_times_int @ ( abs_abs_int @ Y4 ) @ X )
% 5.24/5.54 = ( abs_abs_int @ ( times_times_int @ Y4 @ X ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mult_pos
% 5.24/5.54 thf(fact_6186_abs__eq__iff_H,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( ( abs_abs_real @ A )
% 5.24/5.54 = B )
% 5.24/5.54 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.24/5.54 & ( ( A = B )
% 5.24/5.54 | ( A
% 5.24/5.54 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_iff'
% 5.24/5.54 thf(fact_6187_abs__eq__iff_H,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( ( abs_abs_Code_integer @ A )
% 5.24/5.54 = B )
% 5.24/5.54 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.24/5.54 & ( ( A = B )
% 5.24/5.54 | ( A
% 5.24/5.54 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_iff'
% 5.24/5.54 thf(fact_6188_abs__eq__iff_H,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( ( abs_abs_rat @ A )
% 5.24/5.54 = B )
% 5.24/5.54 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.24/5.54 & ( ( A = B )
% 5.24/5.54 | ( A
% 5.24/5.54 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_iff'
% 5.24/5.54 thf(fact_6189_abs__eq__iff_H,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( ( abs_abs_int @ A )
% 5.24/5.54 = B )
% 5.24/5.54 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.24/5.54 & ( ( A = B )
% 5.24/5.54 | ( A
% 5.24/5.54 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_eq_iff'
% 5.24/5.54 thf(fact_6190_eq__abs__iff_H,axiom,
% 5.24/5.54 ! [A: real,B: real] :
% 5.24/5.54 ( ( A
% 5.24/5.54 = ( abs_abs_real @ B ) )
% 5.24/5.54 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.54 & ( ( B = A )
% 5.24/5.54 | ( B
% 5.24/5.54 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % eq_abs_iff'
% 5.24/5.54 thf(fact_6191_eq__abs__iff_H,axiom,
% 5.24/5.54 ! [A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( A
% 5.24/5.54 = ( abs_abs_Code_integer @ B ) )
% 5.24/5.54 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.24/5.54 & ( ( B = A )
% 5.24/5.54 | ( B
% 5.24/5.54 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % eq_abs_iff'
% 5.24/5.54 thf(fact_6192_eq__abs__iff_H,axiom,
% 5.24/5.54 ! [A: rat,B: rat] :
% 5.24/5.54 ( ( A
% 5.24/5.54 = ( abs_abs_rat @ B ) )
% 5.24/5.54 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.24/5.54 & ( ( B = A )
% 5.24/5.54 | ( B
% 5.24/5.54 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % eq_abs_iff'
% 5.24/5.54 thf(fact_6193_eq__abs__iff_H,axiom,
% 5.24/5.54 ! [A: int,B: int] :
% 5.24/5.54 ( ( A
% 5.24/5.54 = ( abs_abs_int @ B ) )
% 5.24/5.54 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.24/5.54 & ( ( B = A )
% 5.24/5.54 | ( B
% 5.24/5.54 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % eq_abs_iff'
% 5.24/5.54 thf(fact_6194_abs__minus__le__zero,axiom,
% 5.24/5.54 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.24/5.54
% 5.24/5.54 % abs_minus_le_zero
% 5.24/5.54 thf(fact_6195_abs__minus__le__zero,axiom,
% 5.24/5.54 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.24/5.54
% 5.24/5.54 % abs_minus_le_zero
% 5.24/5.54 thf(fact_6196_abs__minus__le__zero,axiom,
% 5.24/5.54 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.24/5.54
% 5.24/5.54 % abs_minus_le_zero
% 5.24/5.54 thf(fact_6197_abs__minus__le__zero,axiom,
% 5.24/5.54 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.24/5.54
% 5.24/5.54 % abs_minus_le_zero
% 5.24/5.54 thf(fact_6198_abs__div__pos,axiom,
% 5.24/5.54 ! [Y4: real,X: real] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.54 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y4 )
% 5.24/5.54 = ( abs_abs_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_div_pos
% 5.24/5.54 thf(fact_6199_abs__div__pos,axiom,
% 5.24/5.54 ! [Y4: rat,X: rat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.24/5.54 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y4 )
% 5.24/5.54 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_div_pos
% 5.24/5.54 thf(fact_6200_zero__le__power__abs,axiom,
% 5.24/5.54 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_le_power_abs
% 5.24/5.54 thf(fact_6201_zero__le__power__abs,axiom,
% 5.24/5.54 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_le_power_abs
% 5.24/5.54 thf(fact_6202_zero__le__power__abs,axiom,
% 5.24/5.54 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_le_power_abs
% 5.24/5.54 thf(fact_6203_zero__le__power__abs,axiom,
% 5.24/5.54 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % zero_le_power_abs
% 5.24/5.54 thf(fact_6204_abs__of__neg,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( ord_less_real @ A @ zero_zero_real )
% 5.24/5.54 => ( ( abs_abs_real @ A )
% 5.24/5.54 = ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_neg
% 5.24/5.54 thf(fact_6205_abs__of__neg,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( ord_less_int @ A @ zero_zero_int )
% 5.24/5.54 => ( ( abs_abs_int @ A )
% 5.24/5.54 = ( uminus_uminus_int @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_neg
% 5.24/5.54 thf(fact_6206_abs__of__neg,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.24/5.54 => ( ( abs_abs_rat @ A )
% 5.24/5.54 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_neg
% 5.24/5.54 thf(fact_6207_abs__of__neg,axiom,
% 5.24/5.54 ! [A: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.24/5.54 => ( ( abs_abs_Code_integer @ A )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_of_neg
% 5.24/5.54 thf(fact_6208_abs__if,axiom,
% 5.24/5.54 ( abs_abs_real
% 5.24/5.54 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if
% 5.24/5.54 thf(fact_6209_abs__if,axiom,
% 5.24/5.54 ( abs_abs_int
% 5.24/5.54 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if
% 5.24/5.54 thf(fact_6210_abs__if,axiom,
% 5.24/5.54 ( abs_abs_rat
% 5.24/5.54 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if
% 5.24/5.54 thf(fact_6211_abs__if,axiom,
% 5.24/5.54 ( abs_abs_Code_integer
% 5.24/5.54 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if
% 5.24/5.54 thf(fact_6212_abs__if__raw,axiom,
% 5.24/5.54 ( abs_abs_real
% 5.24/5.54 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if_raw
% 5.24/5.54 thf(fact_6213_abs__if__raw,axiom,
% 5.24/5.54 ( abs_abs_int
% 5.24/5.54 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if_raw
% 5.24/5.54 thf(fact_6214_abs__if__raw,axiom,
% 5.24/5.54 ( abs_abs_rat
% 5.24/5.54 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if_raw
% 5.24/5.54 thf(fact_6215_abs__if__raw,axiom,
% 5.24/5.54 ( abs_abs_Code_integer
% 5.24/5.54 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_if_raw
% 5.24/5.54 thf(fact_6216_abs__diff__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_triangle_ineq
% 5.24/5.54 thf(fact_6217_abs__diff__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_triangle_ineq
% 5.24/5.54 thf(fact_6218_abs__diff__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_triangle_ineq
% 5.24/5.54 thf(fact_6219_abs__diff__triangle__ineq,axiom,
% 5.24/5.54 ! [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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_triangle_ineq
% 5.24/5.54 thf(fact_6220_abs__triangle__ineq4,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq4
% 5.24/5.54 thf(fact_6221_abs__triangle__ineq4,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq4
% 5.24/5.54 thf(fact_6222_abs__triangle__ineq4,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq4
% 5.24/5.54 thf(fact_6223_abs__triangle__ineq4,axiom,
% 5.24/5.54 ! [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 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_triangle_ineq4
% 5.24/5.54 thf(fact_6224_abs__diff__le__iff,axiom,
% 5.24/5.54 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_le_iff
% 5.24/5.54 thf(fact_6225_abs__diff__le__iff,axiom,
% 5.24/5.54 ! [X: real,A: real,R2: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_le_iff
% 5.24/5.54 thf(fact_6226_abs__diff__le__iff,axiom,
% 5.24/5.54 ! [X: rat,A: rat,R2: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_le_iff
% 5.24/5.54 thf(fact_6227_abs__diff__le__iff,axiom,
% 5.24/5.54 ! [X: int,A: int,R2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_le_iff
% 5.24/5.54 thf(fact_6228_abs__diff__less__iff,axiom,
% 5.24/5.54 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_less_iff
% 5.24/5.54 thf(fact_6229_abs__diff__less__iff,axiom,
% 5.24/5.54 ! [X: real,A: real,R2: real] :
% 5.24/5.54 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_less_iff
% 5.24/5.54 thf(fact_6230_abs__diff__less__iff,axiom,
% 5.24/5.54 ! [X: rat,A: rat,R2: rat] :
% 5.24/5.54 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_less_iff
% 5.24/5.54 thf(fact_6231_abs__diff__less__iff,axiom,
% 5.24/5.54 ! [X: int,A: int,R2: int] :
% 5.24/5.54 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.24/5.54 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.24/5.54 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_diff_less_iff
% 5.24/5.54 thf(fact_6232_sum__eq__Suc0__iff,axiom,
% 5.24/5.54 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.54 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.54 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.24/5.54 = ( suc @ zero_zero_nat ) )
% 5.24/5.54 = ( ? [X2: complex] :
% 5.24/5.54 ( ( member_complex @ X2 @ A2 )
% 5.24/5.54 & ( ( F @ X2 )
% 5.24/5.54 = ( suc @ zero_zero_nat ) )
% 5.24/5.54 & ! [Y: complex] :
% 5.24/5.54 ( ( member_complex @ Y @ A2 )
% 5.24/5.54 => ( ( X2 != Y )
% 5.24/5.54 => ( ( F @ Y )
% 5.24/5.54 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_eq_Suc0_iff
% 5.24/5.54 thf(fact_6233_sum__eq__Suc0__iff,axiom,
% 5.24/5.54 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.54 ( ( finite_finite_nat @ A2 )
% 5.24/5.54 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.24/5.54 = ( suc @ zero_zero_nat ) )
% 5.24/5.54 = ( ? [X2: nat] :
% 5.24/5.54 ( ( member_nat @ X2 @ A2 )
% 5.24/5.54 & ( ( F @ X2 )
% 5.24/5.54 = ( suc @ zero_zero_nat ) )
% 5.24/5.54 & ! [Y: nat] :
% 5.24/5.54 ( ( member_nat @ Y @ A2 )
% 5.24/5.54 => ( ( X2 != Y )
% 5.24/5.54 => ( ( F @ Y )
% 5.24/5.54 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_eq_Suc0_iff
% 5.24/5.54 thf(fact_6234_sum__SucD,axiom,
% 5.24/5.54 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.24/5.54 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.24/5.54 = ( suc @ N ) )
% 5.24/5.54 => ? [X3: nat] :
% 5.24/5.54 ( ( member_nat @ X3 @ A2 )
% 5.24/5.54 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_SucD
% 5.24/5.54 thf(fact_6235_sum__eq__1__iff,axiom,
% 5.24/5.54 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.54 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.54 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.24/5.54 = one_one_nat )
% 5.24/5.54 = ( ? [X2: complex] :
% 5.24/5.54 ( ( member_complex @ X2 @ A2 )
% 5.24/5.54 & ( ( F @ X2 )
% 5.24/5.54 = one_one_nat )
% 5.24/5.54 & ! [Y: complex] :
% 5.24/5.54 ( ( member_complex @ Y @ A2 )
% 5.24/5.54 => ( ( X2 != Y )
% 5.24/5.54 => ( ( F @ Y )
% 5.24/5.54 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_eq_1_iff
% 5.24/5.54 thf(fact_6236_sum__eq__1__iff,axiom,
% 5.24/5.54 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.54 ( ( finite_finite_nat @ A2 )
% 5.24/5.54 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.24/5.54 = one_one_nat )
% 5.24/5.54 = ( ? [X2: nat] :
% 5.24/5.54 ( ( member_nat @ X2 @ A2 )
% 5.24/5.54 & ( ( F @ X2 )
% 5.24/5.54 = one_one_nat )
% 5.24/5.54 & ! [Y: nat] :
% 5.24/5.54 ( ( member_nat @ Y @ A2 )
% 5.24/5.54 => ( ( X2 != Y )
% 5.24/5.54 => ( ( F @ Y )
% 5.24/5.54 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_eq_1_iff
% 5.24/5.54 thf(fact_6237_numeral__Bit1,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1
% 5.24/5.54 thf(fact_6238_numeral__Bit1,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1
% 5.24/5.54 thf(fact_6239_numeral__Bit1,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1
% 5.24/5.54 thf(fact_6240_numeral__Bit1,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1
% 5.24/5.54 thf(fact_6241_numeral__Bit1,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1
% 5.24/5.54 thf(fact_6242_eval__nat__numeral_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.24/5.54 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % eval_nat_numeral(3)
% 5.24/5.54 thf(fact_6243_cong__exp__iff__simps_I13_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.24/5.54 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(13)
% 5.24/5.54 thf(fact_6244_cong__exp__iff__simps_I13_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.24/5.54 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(13)
% 5.24/5.54 thf(fact_6245_cong__exp__iff__simps_I13_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.24/5.54 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(13)
% 5.24/5.54 thf(fact_6246_cong__exp__iff__simps_I12_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(12)
% 5.24/5.54 thf(fact_6247_cong__exp__iff__simps_I12_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(12)
% 5.24/5.54 thf(fact_6248_cong__exp__iff__simps_I12_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(12)
% 5.24/5.54 thf(fact_6249_cong__exp__iff__simps_I10_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(10)
% 5.24/5.54 thf(fact_6250_cong__exp__iff__simps_I10_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(10)
% 5.24/5.54 thf(fact_6251_cong__exp__iff__simps_I10_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num,N: num] :
% 5.24/5.54 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(10)
% 5.24/5.54 thf(fact_6252_power__minus__Bit1,axiom,
% 5.24/5.54 ! [X: real,K: num] :
% 5.24/5.54 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus_Bit1
% 5.24/5.54 thf(fact_6253_power__minus__Bit1,axiom,
% 5.24/5.54 ! [X: int,K: num] :
% 5.24/5.54 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus_Bit1
% 5.24/5.54 thf(fact_6254_power__minus__Bit1,axiom,
% 5.24/5.54 ! [X: complex,K: num] :
% 5.24/5.54 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus_Bit1
% 5.24/5.54 thf(fact_6255_power__minus__Bit1,axiom,
% 5.24/5.54 ! [X: rat,K: num] :
% 5.24/5.54 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus_Bit1
% 5.24/5.54 thf(fact_6256_power__minus__Bit1,axiom,
% 5.24/5.54 ! [X: code_integer,K: num] :
% 5.24/5.54 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_minus_Bit1
% 5.24/5.54 thf(fact_6257_sum__power__add,axiom,
% 5.24/5.54 ! [X: complex,M: nat,I5: set_nat] :
% 5.24/5.54 ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [I4: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_power_add
% 5.24/5.54 thf(fact_6258_sum__power__add,axiom,
% 5.24/5.54 ! [X: rat,M: nat,I5: set_nat] :
% 5.24/5.54 ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_power_add
% 5.24/5.54 thf(fact_6259_sum__power__add,axiom,
% 5.24/5.54 ! [X: int,M: nat,I5: set_nat] :
% 5.24/5.54 ( ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [I4: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_power_add
% 5.24/5.54 thf(fact_6260_sum__power__add,axiom,
% 5.24/5.54 ! [X: real,M: nat,I5: set_nat] :
% 5.24/5.54 ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_power_add
% 5.24/5.54 thf(fact_6261_sum_OatLeastAtMost__rev,axiom,
% 5.24/5.54 ! [G: nat > nat,N: nat,M: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.24/5.54 = ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeastAtMost_rev
% 5.24/5.54 thf(fact_6262_sum_OatLeastAtMost__rev,axiom,
% 5.24/5.54 ! [G: nat > real,N: nat,M: nat] :
% 5.24/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.24/5.54 = ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeastAtMost_rev
% 5.24/5.54 thf(fact_6263_numeral__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_code(3)
% 5.24/5.54 thf(fact_6264_numeral__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_code(3)
% 5.24/5.54 thf(fact_6265_numeral__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_code(3)
% 5.24/5.54 thf(fact_6266_numeral__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_code(3)
% 5.24/5.54 thf(fact_6267_numeral__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.24/5.54 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_code(3)
% 5.24/5.54 thf(fact_6268_power__numeral__odd,axiom,
% 5.24/5.54 ! [Z2: complex,W2: num] :
% 5.24/5.54 ( ( power_power_complex @ Z2 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.24/5.54 = ( times_times_complex @ ( times_times_complex @ Z2 @ ( power_power_complex @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_complex @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_numeral_odd
% 5.24/5.54 thf(fact_6269_power__numeral__odd,axiom,
% 5.24/5.54 ! [Z2: real,W2: num] :
% 5.24/5.54 ( ( power_power_real @ Z2 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.24/5.54 = ( times_times_real @ ( times_times_real @ Z2 @ ( power_power_real @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_real @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_numeral_odd
% 5.24/5.54 thf(fact_6270_power__numeral__odd,axiom,
% 5.24/5.54 ! [Z2: rat,W2: num] :
% 5.24/5.54 ( ( power_power_rat @ Z2 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.24/5.54 = ( times_times_rat @ ( times_times_rat @ Z2 @ ( power_power_rat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_rat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_numeral_odd
% 5.24/5.54 thf(fact_6271_power__numeral__odd,axiom,
% 5.24/5.54 ! [Z2: nat,W2: num] :
% 5.24/5.54 ( ( power_power_nat @ Z2 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.24/5.54 = ( times_times_nat @ ( times_times_nat @ Z2 @ ( power_power_nat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_nat @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_numeral_odd
% 5.24/5.54 thf(fact_6272_power__numeral__odd,axiom,
% 5.24/5.54 ! [Z2: int,W2: num] :
% 5.24/5.54 ( ( power_power_int @ Z2 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.24/5.54 = ( times_times_int @ ( times_times_int @ Z2 @ ( power_power_int @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_int @ Z2 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_numeral_odd
% 5.24/5.54 thf(fact_6273_sum__nth__roots,axiom,
% 5.24/5.54 ! [N: nat,C: complex] :
% 5.24/5.54 ( ( ord_less_nat @ one_one_nat @ N )
% 5.24/5.54 => ( ( groups7754918857620584856omplex
% 5.24/5.54 @ ^ [X2: complex] : X2
% 5.24/5.54 @ ( collect_complex
% 5.24/5.54 @ ^ [Z4: complex] :
% 5.24/5.54 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.54 = C ) ) )
% 5.24/5.54 = zero_zero_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_nth_roots
% 5.24/5.54 thf(fact_6274_sum__roots__unity,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ one_one_nat @ N )
% 5.24/5.54 => ( ( groups7754918857620584856omplex
% 5.24/5.54 @ ^ [X2: complex] : X2
% 5.24/5.54 @ ( collect_complex
% 5.24/5.54 @ ^ [Z4: complex] :
% 5.24/5.54 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.54 = one_one_complex ) ) )
% 5.24/5.54 = zero_zero_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_roots_unity
% 5.24/5.54 thf(fact_6275_abs__add__one__gt__zero,axiom,
% 5.24/5.54 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_one_gt_zero
% 5.24/5.54 thf(fact_6276_abs__add__one__gt__zero,axiom,
% 5.24/5.54 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_one_gt_zero
% 5.24/5.54 thf(fact_6277_abs__add__one__gt__zero,axiom,
% 5.24/5.54 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_one_gt_zero
% 5.24/5.54 thf(fact_6278_abs__add__one__gt__zero,axiom,
% 5.24/5.54 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_add_one_gt_zero
% 5.24/5.54 thf(fact_6279_sum__shift__lb__Suc0__0,axiom,
% 5.24/5.54 ! [F: nat > complex,K: nat] :
% 5.24/5.54 ( ( ( F @ zero_zero_nat )
% 5.24/5.54 = zero_zero_complex )
% 5.24/5.54 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.24/5.54 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_shift_lb_Suc0_0
% 5.24/5.54 thf(fact_6280_sum__shift__lb__Suc0__0,axiom,
% 5.24/5.54 ! [F: nat > rat,K: nat] :
% 5.24/5.54 ( ( ( F @ zero_zero_nat )
% 5.24/5.54 = zero_zero_rat )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.24/5.54 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_shift_lb_Suc0_0
% 5.24/5.54 thf(fact_6281_sum__shift__lb__Suc0__0,axiom,
% 5.24/5.54 ! [F: nat > int,K: nat] :
% 5.24/5.54 ( ( ( F @ zero_zero_nat )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.24/5.54 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_shift_lb_Suc0_0
% 5.24/5.54 thf(fact_6282_sum__shift__lb__Suc0__0,axiom,
% 5.24/5.54 ! [F: nat > nat,K: nat] :
% 5.24/5.54 ( ( ( F @ zero_zero_nat )
% 5.24/5.54 = zero_zero_nat )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.24/5.54 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_shift_lb_Suc0_0
% 5.24/5.54 thf(fact_6283_sum__shift__lb__Suc0__0,axiom,
% 5.24/5.54 ! [F: nat > real,K: nat] :
% 5.24/5.54 ( ( ( F @ zero_zero_nat )
% 5.24/5.54 = zero_zero_real )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.24/5.54 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_shift_lb_Suc0_0
% 5.24/5.54 thf(fact_6284_sum_OatLeast0__atMost__Suc,axiom,
% 5.24/5.54 ! [G: nat > rat,N: nat] :
% 5.24/5.54 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast0_atMost_Suc
% 5.24/5.54 thf(fact_6285_sum_OatLeast0__atMost__Suc,axiom,
% 5.24/5.54 ! [G: nat > int,N: nat] :
% 5.24/5.54 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast0_atMost_Suc
% 5.24/5.54 thf(fact_6286_sum_OatLeast0__atMost__Suc,axiom,
% 5.24/5.54 ! [G: nat > nat,N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast0_atMost_Suc
% 5.24/5.54 thf(fact_6287_sum_OatLeast0__atMost__Suc,axiom,
% 5.24/5.54 ! [G: nat > real,N: nat] :
% 5.24/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast0_atMost_Suc
% 5.24/5.54 thf(fact_6288_sum_OatLeast__Suc__atMost,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > rat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast_Suc_atMost
% 5.24/5.54 thf(fact_6289_sum_OatLeast__Suc__atMost,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > int] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast_Suc_atMost
% 5.24/5.54 thf(fact_6290_sum_OatLeast__Suc__atMost,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast_Suc_atMost
% 5.24/5.54 thf(fact_6291_sum_OatLeast__Suc__atMost,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > real] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.atLeast_Suc_atMost
% 5.24/5.54 thf(fact_6292_sum_Onat__ivl__Suc_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > rat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.nat_ivl_Suc'
% 5.24/5.54 thf(fact_6293_sum_Onat__ivl__Suc_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > int] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.nat_ivl_Suc'
% 5.24/5.54 thf(fact_6294_sum_Onat__ivl__Suc_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.nat_ivl_Suc'
% 5.24/5.54 thf(fact_6295_sum_Onat__ivl__Suc_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > real] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.nat_ivl_Suc'
% 5.24/5.54 thf(fact_6296_numeral__Bit1__div__2,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = ( numeral_numeral_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1_div_2
% 5.24/5.54 thf(fact_6297_numeral__Bit1__div__2,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_Bit1_div_2
% 5.24/5.54 thf(fact_6298_odd__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % odd_numeral
% 5.24/5.54 thf(fact_6299_odd__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % odd_numeral
% 5.24/5.54 thf(fact_6300_odd__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % odd_numeral
% 5.24/5.54 thf(fact_6301_cong__exp__iff__simps_I3_J,axiom,
% 5.24/5.54 ! [N: num,Q2: num] :
% 5.24/5.54 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != zero_zero_nat ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(3)
% 5.24/5.54 thf(fact_6302_cong__exp__iff__simps_I3_J,axiom,
% 5.24/5.54 ! [N: num,Q2: num] :
% 5.24/5.54 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != zero_zero_int ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(3)
% 5.24/5.54 thf(fact_6303_cong__exp__iff__simps_I3_J,axiom,
% 5.24/5.54 ! [N: num,Q2: num] :
% 5.24/5.54 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 != zero_z3403309356797280102nteger ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(3)
% 5.24/5.54 thf(fact_6304_power3__eq__cube,axiom,
% 5.24/5.54 ! [A: complex] :
% 5.24/5.54 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.24/5.54 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % power3_eq_cube
% 5.24/5.54 thf(fact_6305_power3__eq__cube,axiom,
% 5.24/5.54 ! [A: real] :
% 5.24/5.54 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.24/5.54 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % power3_eq_cube
% 5.24/5.54 thf(fact_6306_power3__eq__cube,axiom,
% 5.24/5.54 ! [A: rat] :
% 5.24/5.54 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.24/5.54 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % power3_eq_cube
% 5.24/5.54 thf(fact_6307_power3__eq__cube,axiom,
% 5.24/5.54 ! [A: nat] :
% 5.24/5.54 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.24/5.54 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % power3_eq_cube
% 5.24/5.54 thf(fact_6308_power3__eq__cube,axiom,
% 5.24/5.54 ! [A: int] :
% 5.24/5.54 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.24/5.54 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % power3_eq_cube
% 5.24/5.54 thf(fact_6309_numeral__3__eq__3,axiom,
% 5.24/5.54 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.24/5.54 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_3_eq_3
% 5.24/5.54 thf(fact_6310_Suc3__eq__add__3,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % Suc3_eq_add_3
% 5.24/5.54 thf(fact_6311_sum_OSuc__reindex__ivl,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > rat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_rat @ ( G @ M )
% 5.24/5.54 @ ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.Suc_reindex_ivl
% 5.24/5.54 thf(fact_6312_sum_OSuc__reindex__ivl,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > int] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( G @ M )
% 5.24/5.54 @ ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.Suc_reindex_ivl
% 5.24/5.54 thf(fact_6313_sum_OSuc__reindex__ivl,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_nat @ ( G @ M )
% 5.24/5.54 @ ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.Suc_reindex_ivl
% 5.24/5.54 thf(fact_6314_sum_OSuc__reindex__ivl,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > real] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.54 = ( plus_plus_real @ ( G @ M )
% 5.24/5.54 @ ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.Suc_reindex_ivl
% 5.24/5.54 thf(fact_6315_sum__Suc__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > rat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_Suc_diff
% 5.24/5.54 thf(fact_6316_sum__Suc__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > int] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_Suc_diff
% 5.24/5.54 thf(fact_6317_sum__Suc__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > real] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_Suc_diff
% 5.24/5.54 thf(fact_6318_mod__exhaust__less__4,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = zero_zero_nat )
% 5.24/5.54 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = one_one_nat )
% 5.24/5.54 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mod_exhaust_less_4
% 5.24/5.54 thf(fact_6319_abs__le__square__iff,axiom,
% 5.24/5.54 ! [X: code_integer,Y4: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y4 ) )
% 5.24/5.54 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_square_iff
% 5.24/5.54 thf(fact_6320_abs__le__square__iff,axiom,
% 5.24/5.54 ! [X: real,Y4: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y4 ) )
% 5.24/5.54 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_square_iff
% 5.24/5.54 thf(fact_6321_abs__le__square__iff,axiom,
% 5.24/5.54 ! [X: rat,Y4: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y4 ) )
% 5.24/5.54 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_square_iff
% 5.24/5.54 thf(fact_6322_abs__le__square__iff,axiom,
% 5.24/5.54 ! [X: int,Y4: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y4 ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_le_square_iff
% 5.24/5.54 thf(fact_6323_abs__square__eq__1,axiom,
% 5.24/5.54 ! [X: code_integer] :
% 5.24/5.54 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = one_one_Code_integer )
% 5.24/5.54 = ( ( abs_abs_Code_integer @ X )
% 5.24/5.54 = one_one_Code_integer ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_eq_1
% 5.24/5.54 thf(fact_6324_abs__square__eq__1,axiom,
% 5.24/5.54 ! [X: rat] :
% 5.24/5.54 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = one_one_rat )
% 5.24/5.54 = ( ( abs_abs_rat @ X )
% 5.24/5.54 = one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_eq_1
% 5.24/5.54 thf(fact_6325_abs__square__eq__1,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = one_one_real )
% 5.24/5.54 = ( ( abs_abs_real @ X )
% 5.24/5.54 = one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_eq_1
% 5.24/5.54 thf(fact_6326_abs__square__eq__1,axiom,
% 5.24/5.54 ! [X: int] :
% 5.24/5.54 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 = one_one_int )
% 5.24/5.54 = ( ( abs_abs_int @ X )
% 5.24/5.54 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_eq_1
% 5.24/5.54 thf(fact_6327_num_Osize_I6_J,axiom,
% 5.24/5.54 ! [X32: num] :
% 5.24/5.54 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.24/5.54 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % num.size(6)
% 5.24/5.54 thf(fact_6328_power__even__abs,axiom,
% 5.24/5.54 ! [N: nat,A: rat] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.24/5.54 = ( power_power_rat @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs
% 5.24/5.54 thf(fact_6329_power__even__abs,axiom,
% 5.24/5.54 ! [N: nat,A: code_integer] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.24/5.54 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs
% 5.24/5.54 thf(fact_6330_power__even__abs,axiom,
% 5.24/5.54 ! [N: nat,A: real] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.24/5.54 = ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs
% 5.24/5.54 thf(fact_6331_power__even__abs,axiom,
% 5.24/5.54 ! [N: nat,A: int] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.24/5.54 = ( power_power_int @ A @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_even_abs
% 5.24/5.54 thf(fact_6332_sum_Oub__add__nat,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.54 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.ub_add_nat
% 5.24/5.54 thf(fact_6333_sum_Oub__add__nat,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.54 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.ub_add_nat
% 5.24/5.54 thf(fact_6334_sum_Oub__add__nat,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.54 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.ub_add_nat
% 5.24/5.54 thf(fact_6335_sum_Oub__add__nat,axiom,
% 5.24/5.54 ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.54 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.ub_add_nat
% 5.24/5.54 thf(fact_6336_cong__exp__iff__simps_I11_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num] :
% 5.24/5.54 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.24/5.54 = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(11)
% 5.24/5.54 thf(fact_6337_cong__exp__iff__simps_I11_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num] :
% 5.24/5.54 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.24/5.54 = zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(11)
% 5.24/5.54 thf(fact_6338_cong__exp__iff__simps_I11_J,axiom,
% 5.24/5.54 ! [M: num,Q2: num] :
% 5.24/5.54 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.24/5.54 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(11)
% 5.24/5.54 thf(fact_6339_cong__exp__iff__simps_I7_J,axiom,
% 5.24/5.54 ! [Q2: num,N: num] :
% 5.24/5.54 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.24/5.54 = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(7)
% 5.24/5.54 thf(fact_6340_cong__exp__iff__simps_I7_J,axiom,
% 5.24/5.54 ! [Q2: num,N: num] :
% 5.24/5.54 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.24/5.54 = zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(7)
% 5.24/5.54 thf(fact_6341_cong__exp__iff__simps_I7_J,axiom,
% 5.24/5.54 ! [Q2: num,N: num] :
% 5.24/5.54 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.24/5.54 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.24/5.54 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.24/5.54 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.54
% 5.24/5.54 % cong_exp_iff_simps(7)
% 5.24/5.54 thf(fact_6342_Suc__div__eq__add3__div,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.24/5.54 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % Suc_div_eq_add3_div
% 5.24/5.54 thf(fact_6343_Suc__mod__eq__add3__mod,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.24/5.54 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % Suc_mod_eq_add3_mod
% 5.24/5.54 thf(fact_6344_power2__le__iff__abs__le,axiom,
% 5.24/5.54 ! [Y4: code_integer,X: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y4 )
% 5.24/5.54 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_le_iff_abs_le
% 5.24/5.54 thf(fact_6345_power2__le__iff__abs__le,axiom,
% 5.24/5.54 ! [Y4: real,X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.54 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_le_iff_abs_le
% 5.24/5.54 thf(fact_6346_power2__le__iff__abs__le,axiom,
% 5.24/5.54 ! [Y4: rat,X: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.24/5.54 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_le_iff_abs_le
% 5.24/5.54 thf(fact_6347_power2__le__iff__abs__le,axiom,
% 5.24/5.54 ! [Y4: int,X: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y4 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power2_le_iff_abs_le
% 5.24/5.54 thf(fact_6348_abs__sqrt__wlog,axiom,
% 5.24/5.54 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.24/5.54 ( ! [X3: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.24/5.54 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_sqrt_wlog
% 5.24/5.54 thf(fact_6349_abs__sqrt__wlog,axiom,
% 5.24/5.54 ! [P: real > real > $o,X: real] :
% 5.24/5.54 ( ! [X3: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.24/5.54 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_sqrt_wlog
% 5.24/5.54 thf(fact_6350_abs__sqrt__wlog,axiom,
% 5.24/5.54 ! [P: rat > rat > $o,X: rat] :
% 5.24/5.54 ( ! [X3: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.24/5.54 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_sqrt_wlog
% 5.24/5.54 thf(fact_6351_abs__sqrt__wlog,axiom,
% 5.24/5.54 ! [P: int > int > $o,X: int] :
% 5.24/5.54 ( ! [X3: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.24/5.54 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_sqrt_wlog
% 5.24/5.54 thf(fact_6352_abs__square__le__1,axiom,
% 5.24/5.54 ! [X: code_integer] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.24/5.54 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_le_1
% 5.24/5.54 thf(fact_6353_abs__square__le__1,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.24/5.54 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_le_1
% 5.24/5.54 thf(fact_6354_abs__square__le__1,axiom,
% 5.24/5.54 ! [X: rat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.24/5.54 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_le_1
% 5.24/5.54 thf(fact_6355_abs__square__le__1,axiom,
% 5.24/5.54 ! [X: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.24/5.54 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_le_1
% 5.24/5.54 thf(fact_6356_abs__square__less__1,axiom,
% 5.24/5.54 ! [X: code_integer] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.24/5.54 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_less_1
% 5.24/5.54 thf(fact_6357_abs__square__less__1,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.24/5.54 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_less_1
% 5.24/5.54 thf(fact_6358_abs__square__less__1,axiom,
% 5.24/5.54 ! [X: rat] :
% 5.24/5.54 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.24/5.54 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_less_1
% 5.24/5.54 thf(fact_6359_abs__square__less__1,axiom,
% 5.24/5.54 ! [X: int] :
% 5.24/5.54 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.24/5.54 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_square_less_1
% 5.24/5.54 thf(fact_6360_power__mono__even,axiom,
% 5.24/5.54 ! [N: nat,A: code_integer,B: code_integer] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_mono_even
% 5.24/5.54 thf(fact_6361_power__mono__even,axiom,
% 5.24/5.54 ! [N: nat,A: real,B: real] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.24/5.54 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_mono_even
% 5.24/5.54 thf(fact_6362_power__mono__even,axiom,
% 5.24/5.54 ! [N: nat,A: rat,B: rat] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.24/5.54 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_mono_even
% 5.24/5.54 thf(fact_6363_power__mono__even,axiom,
% 5.24/5.54 ! [N: nat,A: int,B: int] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.24/5.54 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % power_mono_even
% 5.24/5.54 thf(fact_6364_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.24/5.54 ( ! [I3: nat] :
% 5.24/5.54 ( ( member_nat @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 5.24/5.54 = one_one_Code_integer )
% 5.24/5.54 => ( ! [I3: nat] :
% 5.24/5.54 ( ( member_nat @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_le3102999989581377725nteger
% 5.24/5.54 @ ( abs_abs_Code_integer
% 5.24/5.54 @ ( minus_8373710615458151222nteger
% 5.24/5.54 @ ( groups7501900531339628137nteger
% 5.24/5.54 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6365_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.24/5.54 ( ! [I3: int] :
% 5.24/5.54 ( ( member_int @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 5.24/5.54 = one_one_Code_integer )
% 5.24/5.54 => ( ! [I3: int] :
% 5.24/5.54 ( ( member_int @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_le3102999989581377725nteger
% 5.24/5.54 @ ( abs_abs_Code_integer
% 5.24/5.54 @ ( minus_8373710615458151222nteger
% 5.24/5.54 @ ( groups7873554091576472773nteger
% 5.24/5.54 @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6366_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.24/5.54 ( ! [I3: real] :
% 5.24/5.54 ( ( member_real @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 5.24/5.54 = one_one_Code_integer )
% 5.24/5.54 => ( ! [I3: real] :
% 5.24/5.54 ( ( member_real @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_le3102999989581377725nteger
% 5.24/5.54 @ ( abs_abs_Code_integer
% 5.24/5.54 @ ( minus_8373710615458151222nteger
% 5.24/5.54 @ ( groups7713935264441627589nteger
% 5.24/5.54 @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6367_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.24/5.54 ( ! [I3: complex] :
% 5.24/5.54 ( ( member_complex @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 5.24/5.54 = one_one_Code_integer )
% 5.24/5.54 => ( ! [I3: complex] :
% 5.24/5.54 ( ( member_complex @ I3 @ I5 )
% 5.24/5.54 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_le3102999989581377725nteger
% 5.24/5.54 @ ( abs_abs_Code_integer
% 5.24/5.54 @ ( minus_8373710615458151222nteger
% 5.24/5.54 @ ( groups6621422865394947399nteger
% 5.24/5.54 @ ^ [I4: complex] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6368_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.24/5.54 ( ! [I3: int] :
% 5.24/5.54 ( ( member_int @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 5.24/5.54 = one_one_real )
% 5.24/5.54 => ( ! [I3: int] :
% 5.24/5.54 ( ( member_int @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_less_eq_real
% 5.24/5.54 @ ( abs_abs_real
% 5.24/5.54 @ ( minus_minus_real
% 5.24/5.54 @ ( groups8778361861064173332t_real
% 5.24/5.54 @ ^ [I4: int] : ( times_times_real @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6369_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.24/5.54 ( ! [I3: real] :
% 5.24/5.54 ( ( member_real @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 5.24/5.54 = one_one_real )
% 5.24/5.54 => ( ! [I3: real] :
% 5.24/5.54 ( ( member_real @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_less_eq_real
% 5.24/5.54 @ ( abs_abs_real
% 5.24/5.54 @ ( minus_minus_real
% 5.24/5.54 @ ( groups8097168146408367636l_real
% 5.24/5.54 @ ^ [I4: real] : ( times_times_real @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6370_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.24/5.54 ( ! [I3: complex] :
% 5.24/5.54 ( ( member_complex @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 5.24/5.54 = one_one_real )
% 5.24/5.54 => ( ! [I3: complex] :
% 5.24/5.54 ( ( member_complex @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_less_eq_real
% 5.24/5.54 @ ( abs_abs_real
% 5.24/5.54 @ ( minus_minus_real
% 5.24/5.54 @ ( groups5808333547571424918x_real
% 5.24/5.54 @ ^ [I4: complex] : ( times_times_real @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6371_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.24/5.54 ( ! [I3: nat] :
% 5.24/5.54 ( ( member_nat @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 5.24/5.54 = one_one_rat )
% 5.24/5.54 => ( ! [I3: nat] :
% 5.24/5.54 ( ( member_nat @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_less_eq_rat
% 5.24/5.54 @ ( abs_abs_rat
% 5.24/5.54 @ ( minus_minus_rat
% 5.24/5.54 @ ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6372_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 5.24/5.54 ( ! [I3: int] :
% 5.24/5.54 ( ( member_int @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups3906332499630173760nt_rat @ X @ I5 )
% 5.24/5.54 = one_one_rat )
% 5.24/5.54 => ( ! [I3: int] :
% 5.24/5.54 ( ( member_int @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_less_eq_rat
% 5.24/5.54 @ ( abs_abs_rat
% 5.24/5.54 @ ( minus_minus_rat
% 5.24/5.54 @ ( groups3906332499630173760nt_rat
% 5.24/5.54 @ ^ [I4: int] : ( times_times_rat @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6373_convex__sum__bound__le,axiom,
% 5.24/5.54 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.24/5.54 ( ! [I3: real] :
% 5.24/5.54 ( ( member_real @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.24/5.54 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 5.24/5.54 = one_one_rat )
% 5.24/5.54 => ( ! [I3: real] :
% 5.24/5.54 ( ( member_real @ I3 @ I5 )
% 5.24/5.54 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.24/5.54 => ( ord_less_eq_rat
% 5.24/5.54 @ ( abs_abs_rat
% 5.24/5.54 @ ( minus_minus_rat
% 5.24/5.54 @ ( groups1300246762558778688al_rat
% 5.24/5.54 @ ^ [I4: real] : ( times_times_rat @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.24/5.54 @ I5 )
% 5.24/5.54 @ B ) )
% 5.24/5.54 @ Delta ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % convex_sum_bound_le
% 5.24/5.54 thf(fact_6374_sum__natinterval__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > complex] :
% 5.24/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups2073611262835488442omplex
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_complex ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_natinterval_diff
% 5.24/5.54 thf(fact_6375_sum__natinterval__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > rat] :
% 5.24/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_natinterval_diff
% 5.24/5.54 thf(fact_6376_sum__natinterval__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > int] :
% 5.24/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_int ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_natinterval_diff
% 5.24/5.54 thf(fact_6377_sum__natinterval__diff,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > real] :
% 5.24/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_natinterval_diff
% 5.24/5.54 thf(fact_6378_sum__telescope_H_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > rat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.24/5.54 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_telescope''
% 5.24/5.54 thf(fact_6379_sum__telescope_H_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > int] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.24/5.54 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_telescope''
% 5.24/5.54 thf(fact_6380_sum__telescope_H_H,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > real] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.24/5.54 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_telescope''
% 5.24/5.54 thf(fact_6381_mask__eq__sum__exp,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.24/5.54 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 @ ( collect_nat
% 5.24/5.54 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mask_eq_sum_exp
% 5.24/5.54 thf(fact_6382_mask__eq__sum__exp,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.24/5.54 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 @ ( collect_nat
% 5.24/5.54 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mask_eq_sum_exp
% 5.24/5.54 thf(fact_6383_sum__gp__multiplied,axiom,
% 5.24/5.54 ! [M: nat,N: nat,X: complex] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.24/5.54 = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp_multiplied
% 5.24/5.54 thf(fact_6384_sum__gp__multiplied,axiom,
% 5.24/5.54 ! [M: nat,N: nat,X: rat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.24/5.54 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp_multiplied
% 5.24/5.54 thf(fact_6385_sum__gp__multiplied,axiom,
% 5.24/5.54 ! [M: nat,N: nat,X: int] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.24/5.54 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp_multiplied
% 5.24/5.54 thf(fact_6386_sum__gp__multiplied,axiom,
% 5.24/5.54 ! [M: nat,N: nat,X: real] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.24/5.54 = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp_multiplied
% 5.24/5.54 thf(fact_6387_sum_Oin__pairs,axiom,
% 5.24/5.54 ! [G: nat > rat,M: nat,N: nat] :
% 5.24/5.54 ( ( 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 ) ) ) )
% 5.24/5.54 = ( groups2906978787729119204at_rat
% 5.24/5.54 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.in_pairs
% 5.24/5.54 thf(fact_6388_sum_Oin__pairs,axiom,
% 5.24/5.54 ! [G: nat > int,M: nat,N: nat] :
% 5.24/5.54 ( ( 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 ) ) ) )
% 5.24/5.54 = ( groups3539618377306564664at_int
% 5.24/5.54 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.in_pairs
% 5.24/5.54 thf(fact_6389_sum_Oin__pairs,axiom,
% 5.24/5.54 ! [G: nat > nat,M: nat,N: nat] :
% 5.24/5.54 ( ( 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 ) ) ) )
% 5.24/5.54 = ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.in_pairs
% 5.24/5.54 thf(fact_6390_sum_Oin__pairs,axiom,
% 5.24/5.54 ! [G: nat > real,M: nat,N: nat] :
% 5.24/5.54 ( ( 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 ) ) ) )
% 5.24/5.54 = ( groups6591440286371151544t_real
% 5.24/5.54 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum.in_pairs
% 5.24/5.54 thf(fact_6391_eq__diff__eq_H,axiom,
% 5.24/5.54 ! [X: real,Y4: real,Z2: real] :
% 5.24/5.54 ( ( X
% 5.24/5.54 = ( minus_minus_real @ Y4 @ Z2 ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( plus_plus_real @ X @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % eq_diff_eq'
% 5.24/5.54 thf(fact_6392_mask__eq__sum__exp__nat,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.54 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.54 @ ( collect_nat
% 5.24/5.54 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mask_eq_sum_exp_nat
% 5.24/5.54 thf(fact_6393_gauss__sum__nat,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [X2: nat] : X2
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.54 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % gauss_sum_nat
% 5.24/5.54 thf(fact_6394_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.54 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.54 => ( 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 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.24/5.54 thf(fact_6395_arith__series__nat,axiom,
% 5.24/5.54 ! [A: nat,D: nat,N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D ) )
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.54 = ( 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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % arith_series_nat
% 5.24/5.54 thf(fact_6396_Sum__Icc__nat,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat
% 5.24/5.54 @ ^ [X2: nat] : X2
% 5.24/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( 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 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % Sum_Icc_nat
% 5.24/5.54 thf(fact_6397_odd__mod__4__div__2,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.54 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.24/5.54 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % odd_mod_4_div_2
% 5.24/5.54 thf(fact_6398_signed__take__bit__numeral__minus__bit1,axiom,
% 5.24/5.54 ! [L2: num,K: num] :
% 5.24/5.54 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.24/5.54 = ( 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 ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_numeral_minus_bit1
% 5.24/5.54 thf(fact_6399_dbl__dec__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.54 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(4)
% 5.24/5.54 thf(fact_6400_dbl__dec__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(4)
% 5.24/5.54 thf(fact_6401_dbl__dec__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(4)
% 5.24/5.54 thf(fact_6402_dbl__dec__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.54 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(4)
% 5.24/5.54 thf(fact_6403_dbl__dec__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(4)
% 5.24/5.54 thf(fact_6404_divmod__algorithm__code_I8_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( ord_less_num @ M @ N )
% 5.24/5.54 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_num @ M @ N )
% 5.24/5.54 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(8)
% 5.24/5.54 thf(fact_6405_divmod__algorithm__code_I8_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( ord_less_num @ M @ N )
% 5.24/5.54 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_num @ M @ N )
% 5.24/5.54 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(8)
% 5.24/5.54 thf(fact_6406_divmod__algorithm__code_I8_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( ord_less_num @ M @ N )
% 5.24/5.54 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_num @ M @ N )
% 5.24/5.54 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(8)
% 5.24/5.54 thf(fact_6407_divmod__algorithm__code_I7_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( ord_less_eq_num @ M @ N )
% 5.24/5.54 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.24/5.54 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(7)
% 5.24/5.54 thf(fact_6408_divmod__algorithm__code_I7_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( ord_less_eq_num @ M @ N )
% 5.24/5.54 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.24/5.54 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(7)
% 5.24/5.54 thf(fact_6409_divmod__algorithm__code_I7_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( ( ord_less_eq_num @ M @ N )
% 5.24/5.54 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.24/5.54 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.24/5.54 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.54 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(7)
% 5.24/5.54 thf(fact_6410_signed__take__bit__numeral__bit1,axiom,
% 5.24/5.54 ! [L2: num,K: num] :
% 5.24/5.54 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.24/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_numeral_bit1
% 5.24/5.54 thf(fact_6411_arctan__double,axiom,
% 5.24/5.54 ! [X: real] :
% 5.24/5.54 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.54 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.24/5.54 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % arctan_double
% 5.24/5.54 thf(fact_6412_zdvd1__eq,axiom,
% 5.24/5.54 ! [X: int] :
% 5.24/5.54 ( ( dvd_dvd_int @ X @ one_one_int )
% 5.24/5.54 = ( ( abs_abs_int @ X )
% 5.24/5.54 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % zdvd1_eq
% 5.24/5.54 thf(fact_6413_dbl__dec__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.24/5.54 = one_one_complex ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(3)
% 5.24/5.54 thf(fact_6414_dbl__dec__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(3)
% 5.24/5.54 thf(fact_6415_dbl__dec__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(3)
% 5.24/5.54 thf(fact_6416_dbl__dec__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(3)
% 5.24/5.54 thf(fact_6417_zabs__less__one__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
% 5.24/5.54 = ( Z2 = zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % zabs_less_one_iff
% 5.24/5.54 thf(fact_6418_pred__numeral__simps_I1_J,axiom,
% 5.24/5.54 ( ( pred_numeral @ one )
% 5.24/5.54 = zero_zero_nat ) ).
% 5.24/5.54
% 5.24/5.54 % pred_numeral_simps(1)
% 5.24/5.54 thf(fact_6419_Suc__eq__numeral,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( ( suc @ N )
% 5.24/5.54 = ( numeral_numeral_nat @ K ) )
% 5.24/5.54 = ( N
% 5.24/5.54 = ( pred_numeral @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % Suc_eq_numeral
% 5.24/5.54 thf(fact_6420_eq__numeral__Suc,axiom,
% 5.24/5.54 ! [K: num,N: nat] :
% 5.24/5.54 ( ( ( numeral_numeral_nat @ K )
% 5.24/5.54 = ( suc @ N ) )
% 5.24/5.54 = ( ( pred_numeral @ K )
% 5.24/5.54 = N ) ) ).
% 5.24/5.54
% 5.24/5.54 % eq_numeral_Suc
% 5.24/5.54 thf(fact_6421_less__Suc__numeral,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.54 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % less_Suc_numeral
% 5.24/5.54 thf(fact_6422_less__numeral__Suc,axiom,
% 5.24/5.54 ! [K: num,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.24/5.54 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % less_numeral_Suc
% 5.24/5.54 thf(fact_6423_pred__numeral__simps_I3_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.24/5.54 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % pred_numeral_simps(3)
% 5.24/5.54 thf(fact_6424_le__numeral__Suc,axiom,
% 5.24/5.54 ! [K: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % le_numeral_Suc
% 5.24/5.54 thf(fact_6425_le__Suc__numeral,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.54 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % le_Suc_numeral
% 5.24/5.54 thf(fact_6426_diff__Suc__numeral,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.54 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % diff_Suc_numeral
% 5.24/5.54 thf(fact_6427_diff__numeral__Suc,axiom,
% 5.24/5.54 ! [K: num,N: nat] :
% 5.24/5.54 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.24/5.54 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % diff_numeral_Suc
% 5.24/5.54 thf(fact_6428_max__Suc__numeral,axiom,
% 5.24/5.54 ! [N: nat,K: num] :
% 5.24/5.54 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.54 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % max_Suc_numeral
% 5.24/5.54 thf(fact_6429_max__numeral__Suc,axiom,
% 5.24/5.54 ! [K: num,N: nat] :
% 5.24/5.54 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.24/5.54 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % max_numeral_Suc
% 5.24/5.54 thf(fact_6430_dbl__dec__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.24/5.54 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(2)
% 5.24/5.54 thf(fact_6431_dbl__dec__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.24/5.54 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(2)
% 5.24/5.54 thf(fact_6432_dbl__dec__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(2)
% 5.24/5.54 thf(fact_6433_dbl__dec__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.24/5.54 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(2)
% 5.24/5.54 thf(fact_6434_dbl__dec__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(2)
% 5.24/5.54 thf(fact_6435_dvd__numeral__simp,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.54 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dvd_numeral_simp
% 5.24/5.54 thf(fact_6436_dvd__numeral__simp,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.54 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dvd_numeral_simp
% 5.24/5.54 thf(fact_6437_dvd__numeral__simp,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.24/5.54 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dvd_numeral_simp
% 5.24/5.54 thf(fact_6438_divmod__algorithm__code_I2_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ( ( unique5052692396658037445od_int @ M @ one )
% 5.24/5.54 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(2)
% 5.24/5.54 thf(fact_6439_divmod__algorithm__code_I2_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.24/5.54 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(2)
% 5.24/5.54 thf(fact_6440_divmod__algorithm__code_I2_J,axiom,
% 5.24/5.54 ! [M: num] :
% 5.24/5.54 ( ( unique3479559517661332726nteger @ M @ one )
% 5.24/5.54 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(2)
% 5.24/5.54 thf(fact_6441_divmod__algorithm__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.24/5.54 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(3)
% 5.24/5.54 thf(fact_6442_divmod__algorithm__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.24/5.54 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(3)
% 5.24/5.54 thf(fact_6443_divmod__algorithm__code_I3_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(3)
% 5.24/5.54 thf(fact_6444_divmod__algorithm__code_I4_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.24/5.54 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(4)
% 5.24/5.54 thf(fact_6445_divmod__algorithm__code_I4_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.24/5.54 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(4)
% 5.24/5.54 thf(fact_6446_divmod__algorithm__code_I4_J,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.24/5.54 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(4)
% 5.24/5.54 thf(fact_6447_one__div__minus__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % one_div_minus_numeral
% 5.24/5.54 thf(fact_6448_minus__one__div__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % minus_one_div_numeral
% 5.24/5.54 thf(fact_6449_signed__take__bit__numeral__bit0,axiom,
% 5.24/5.54 ! [L2: num,K: num] :
% 5.24/5.54 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.24/5.54 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_numeral_bit0
% 5.24/5.54 thf(fact_6450_signed__take__bit__numeral__minus__bit0,axiom,
% 5.24/5.54 ! [L2: num,K: num] :
% 5.24/5.54 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.24/5.54 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % signed_take_bit_numeral_minus_bit0
% 5.24/5.54 thf(fact_6451_abs__zmult__eq__1,axiom,
% 5.24/5.54 ! [M: int,N: int] :
% 5.24/5.54 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.24/5.54 = one_one_int )
% 5.24/5.54 => ( ( abs_abs_int @ M )
% 5.24/5.54 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_zmult_eq_1
% 5.24/5.54 thf(fact_6452_numeral__eq__Suc,axiom,
% 5.24/5.54 ( numeral_numeral_nat
% 5.24/5.54 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_eq_Suc
% 5.24/5.54 thf(fact_6453_abs__mod__less,axiom,
% 5.24/5.54 ! [L2: int,K: int] :
% 5.24/5.54 ( ( L2 != zero_zero_int )
% 5.24/5.54 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % abs_mod_less
% 5.24/5.54 thf(fact_6454_pred__numeral__def,axiom,
% 5.24/5.54 ( pred_numeral
% 5.24/5.54 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % pred_numeral_def
% 5.24/5.54 thf(fact_6455_zdvd__mult__cancel1,axiom,
% 5.24/5.54 ! [M: int,N: int] :
% 5.24/5.54 ( ( M != zero_zero_int )
% 5.24/5.54 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.24/5.54 = ( ( abs_abs_int @ N )
% 5.24/5.54 = one_one_int ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % zdvd_mult_cancel1
% 5.24/5.54 thf(fact_6456_even__abs__add__iff,axiom,
% 5.24/5.54 ! [K: int,L2: int] :
% 5.24/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.24/5.54 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % even_abs_add_iff
% 5.24/5.54 thf(fact_6457_even__add__abs__iff,axiom,
% 5.24/5.54 ! [K: int,L2: int] :
% 5.24/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.24/5.54 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % even_add_abs_iff
% 5.24/5.54 thf(fact_6458_divmod__int__def,axiom,
% 5.24/5.54 ( unique5052692396658037445od_int
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_int_def
% 5.24/5.54 thf(fact_6459_divmod__def,axiom,
% 5.24/5.54 ( unique5052692396658037445od_int
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_def
% 5.24/5.54 thf(fact_6460_divmod__def,axiom,
% 5.24/5.54 ( unique5055182867167087721od_nat
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_def
% 5.24/5.54 thf(fact_6461_divmod__def,axiom,
% 5.24/5.54 ( unique3479559517661332726nteger
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_def
% 5.24/5.54 thf(fact_6462_divmod_H__nat__def,axiom,
% 5.24/5.54 ( unique5055182867167087721od_nat
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod'_nat_def
% 5.24/5.54 thf(fact_6463_nat__intermed__int__val,axiom,
% 5.24/5.54 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.24/5.54 ( ! [I3: nat] :
% 5.24/5.54 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.24/5.54 & ( ord_less_nat @ I3 @ N ) )
% 5.24/5.54 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.24/5.54 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.24/5.54 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.24/5.54 => ? [I3: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ M @ I3 )
% 5.24/5.54 & ( ord_less_eq_nat @ I3 @ N )
% 5.24/5.54 & ( ( F @ I3 )
% 5.24/5.54 = K ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % nat_intermed_int_val
% 5.24/5.54 thf(fact_6464_dbl__dec__def,axiom,
% 5.24/5.54 ( neg_nu6511756317524482435omplex
% 5.24/5.54 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_def
% 5.24/5.54 thf(fact_6465_dbl__dec__def,axiom,
% 5.24/5.54 ( neg_nu6075765906172075777c_real
% 5.24/5.54 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_def
% 5.24/5.54 thf(fact_6466_dbl__dec__def,axiom,
% 5.24/5.54 ( neg_nu3179335615603231917ec_rat
% 5.24/5.54 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_def
% 5.24/5.54 thf(fact_6467_dbl__dec__def,axiom,
% 5.24/5.54 ( neg_nu3811975205180677377ec_int
% 5.24/5.54 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_def
% 5.24/5.54 thf(fact_6468_incr__lemma,axiom,
% 5.24/5.54 ! [D: int,Z2: int,X: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.54 => ( ord_less_int @ Z2 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % incr_lemma
% 5.24/5.54 thf(fact_6469_decr__lemma,axiom,
% 5.24/5.54 ! [D: int,X: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ D )
% 5.24/5.54 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % decr_lemma
% 5.24/5.54 thf(fact_6470_nat__ivt__aux,axiom,
% 5.24/5.54 ! [N: nat,F: nat > int,K: int] :
% 5.24/5.54 ( ! [I3: nat] :
% 5.24/5.54 ( ( ord_less_nat @ I3 @ N )
% 5.24/5.54 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.24/5.54 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.24/5.54 => ? [I3: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ I3 @ N )
% 5.24/5.54 & ( ( F @ I3 )
% 5.24/5.54 = K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % nat_ivt_aux
% 5.24/5.54 thf(fact_6471_nat0__intermed__int__val,axiom,
% 5.24/5.54 ! [N: nat,F: nat > int,K: int] :
% 5.24/5.54 ( ! [I3: nat] :
% 5.24/5.54 ( ( ord_less_nat @ I3 @ N )
% 5.24/5.54 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.24/5.54 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.24/5.54 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.24/5.54 => ? [I3: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ I3 @ N )
% 5.24/5.54 & ( ( F @ I3 )
% 5.24/5.54 = K ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % nat0_intermed_int_val
% 5.24/5.54 thf(fact_6472_arctan__add,axiom,
% 5.24/5.54 ! [X: real,Y4: real] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.54 => ( ( ord_less_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.54 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y4 ) )
% 5.24/5.54 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % arctan_add
% 5.24/5.54 thf(fact_6473_divmod__divmod__step,axiom,
% 5.24/5.54 ( unique5055182867167087721od_nat
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M2 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_divmod_step
% 5.24/5.54 thf(fact_6474_divmod__divmod__step,axiom,
% 5.24/5.54 ( unique5052692396658037445od_int
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M2 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_divmod_step
% 5.24/5.54 thf(fact_6475_divmod__divmod__step,axiom,
% 5.24/5.54 ( unique3479559517661332726nteger
% 5.24/5.54 = ( ^ [M2: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M2 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_divmod_step
% 5.24/5.54 thf(fact_6476_sum__gp,axiom,
% 5.24/5.54 ! [N: nat,M: nat,X: complex] :
% 5.24/5.54 ( ( ( ord_less_nat @ N @ M )
% 5.24/5.54 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_complex ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ N @ M )
% 5.24/5.54 => ( ( ( X = one_one_complex )
% 5.24/5.54 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.24/5.54 & ( ( X != one_one_complex )
% 5.24/5.54 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp
% 5.24/5.54 thf(fact_6477_sum__gp,axiom,
% 5.24/5.54 ! [N: nat,M: nat,X: rat] :
% 5.24/5.54 ( ( ( ord_less_nat @ N @ M )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_rat ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ N @ M )
% 5.24/5.54 => ( ( ( X = one_one_rat )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.24/5.54 & ( ( X != one_one_rat )
% 5.24/5.54 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp
% 5.24/5.54 thf(fact_6478_sum__gp,axiom,
% 5.24/5.54 ! [N: nat,M: nat,X: real] :
% 5.24/5.54 ( ( ( ord_less_nat @ N @ M )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = zero_zero_real ) )
% 5.24/5.54 & ( ~ ( ord_less_nat @ N @ M )
% 5.24/5.54 => ( ( ( X = one_one_real )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.24/5.54 & ( ( X != one_one_real )
% 5.24/5.54 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.54 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % sum_gp
% 5.24/5.54 thf(fact_6479_dbl__inc__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.24/5.54 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(3)
% 5.24/5.54 thf(fact_6480_dbl__inc__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.24/5.54 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(3)
% 5.24/5.54 thf(fact_6481_dbl__inc__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.24/5.54 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(3)
% 5.24/5.54 thf(fact_6482_dbl__inc__simps_I3_J,axiom,
% 5.24/5.54 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.24/5.54 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(3)
% 5.24/5.54 thf(fact_6483_gauss__sum__from__Suc__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.54 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % gauss_sum_from_Suc_0
% 5.24/5.54 thf(fact_6484_gauss__sum__from__Suc__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.54 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % gauss_sum_from_Suc_0
% 5.24/5.54 thf(fact_6485_of__int__code__if,axiom,
% 5.24/5.54 ( ring_1_of_int_real
% 5.24/5.54 = ( ^ [K3: int] :
% 5.24/5.54 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.24/5.54 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.24/5.54 @ ( if_real
% 5.24/5.54 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 @ ( 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 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_code_if
% 5.24/5.54 thf(fact_6486_of__int__code__if,axiom,
% 5.24/5.54 ( ring_1_of_int_int
% 5.24/5.54 = ( ^ [K3: int] :
% 5.24/5.54 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.24/5.54 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.24/5.54 @ ( if_int
% 5.24/5.54 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 @ ( 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 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_code_if
% 5.24/5.54 thf(fact_6487_of__int__code__if,axiom,
% 5.24/5.54 ( ring_17405671764205052669omplex
% 5.24/5.54 = ( ^ [K3: int] :
% 5.24/5.54 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.24/5.54 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.24/5.54 @ ( if_complex
% 5.24/5.54 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_code_if
% 5.24/5.54 thf(fact_6488_of__int__code__if,axiom,
% 5.24/5.54 ( ring_1_of_int_rat
% 5.24/5.54 = ( ^ [K3: int] :
% 5.24/5.54 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.24/5.54 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.24/5.54 @ ( if_rat
% 5.24/5.54 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 @ ( 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 ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_code_if
% 5.24/5.54 thf(fact_6489_of__int__code__if,axiom,
% 5.24/5.54 ( ring_18347121197199848620nteger
% 5.24/5.54 = ( ^ [K3: int] :
% 5.24/5.54 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.24/5.54 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.24/5.54 @ ( if_Code_integer
% 5.24/5.54 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.54 = zero_zero_int )
% 5.24/5.54 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.54 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_code_if
% 5.24/5.54 thf(fact_6490_divmod__algorithm__code_I6_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc4245557441103728435nt_int
% 5.24/5.54 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.24/5.54 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(6)
% 5.24/5.54 thf(fact_6491_divmod__algorithm__code_I6_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc2626176000494625587at_nat
% 5.24/5.54 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.24/5.54 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(6)
% 5.24/5.54 thf(fact_6492_divmod__algorithm__code_I6_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc6916734918728496179nteger
% 5.24/5.54 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.24/5.54 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(6)
% 5.24/5.54 thf(fact_6493_dbl__dec__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(1)
% 5.24/5.54 thf(fact_6494_dbl__dec__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(1)
% 5.24/5.54 thf(fact_6495_dbl__dec__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(1)
% 5.24/5.54 thf(fact_6496_dbl__dec__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(1)
% 5.24/5.54 thf(fact_6497_dbl__dec__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_dec_simps(1)
% 5.24/5.54 thf(fact_6498_int__eq__iff__numeral,axiom,
% 5.24/5.54 ! [M: nat,V: num] :
% 5.24/5.54 ( ( ( semiri1314217659103216013at_int @ M )
% 5.24/5.54 = ( numeral_numeral_int @ V ) )
% 5.24/5.54 = ( M
% 5.24/5.54 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % int_eq_iff_numeral
% 5.24/5.54 thf(fact_6499_case__prod__conv,axiom,
% 5.24/5.54 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.24/5.54 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.24/5.54 = ( F @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_conv
% 5.24/5.54 thf(fact_6500_case__prod__conv,axiom,
% 5.24/5.54 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.24/5.54 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.24/5.54 = ( F @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_conv
% 5.24/5.54 thf(fact_6501_case__prod__conv,axiom,
% 5.24/5.54 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.24/5.54 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.24/5.54 = ( F @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_conv
% 5.24/5.54 thf(fact_6502_case__prod__conv,axiom,
% 5.24/5.54 ! [F: int > int > $o,A: int,B: int] :
% 5.24/5.54 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.24/5.54 = ( F @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_conv
% 5.24/5.54 thf(fact_6503_case__prod__conv,axiom,
% 5.24/5.54 ! [F: int > int > int,A: int,B: int] :
% 5.24/5.54 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.24/5.54 = ( F @ A @ B ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_conv
% 5.24/5.54 thf(fact_6504_of__nat__less__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_iff
% 5.24/5.54 thf(fact_6505_of__nat__less__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_iff
% 5.24/5.54 thf(fact_6506_of__nat__less__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_iff
% 5.24/5.54 thf(fact_6507_of__nat__less__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.24/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_iff
% 5.24/5.54 thf(fact_6508_of__nat__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.24/5.54 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_numeral
% 5.24/5.54 thf(fact_6509_of__nat__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_numeral
% 5.24/5.54 thf(fact_6510_of__nat__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.24/5.54 = ( numeral_numeral_real @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_numeral
% 5.24/5.54 thf(fact_6511_of__nat__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.24/5.54 = ( numeral_numeral_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_numeral
% 5.24/5.54 thf(fact_6512_of__nat__numeral,axiom,
% 5.24/5.54 ! [N: num] :
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.24/5.54 = ( numeral_numeral_rat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_numeral
% 5.24/5.54 thf(fact_6513_of__nat__le__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_iff
% 5.24/5.54 thf(fact_6514_of__nat__le__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_iff
% 5.24/5.54 thf(fact_6515_of__nat__le__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_iff
% 5.24/5.54 thf(fact_6516_of__nat__le__iff,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_iff
% 5.24/5.54 thf(fact_6517_of__nat__add,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_add
% 5.24/5.54 thf(fact_6518_of__nat__add,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_add
% 5.24/5.54 thf(fact_6519_of__nat__add,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_add
% 5.24/5.54 thf(fact_6520_of__nat__add,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.24/5.54 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_add
% 5.24/5.54 thf(fact_6521_of__nat__mult,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.24/5.54 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_mult
% 5.24/5.54 thf(fact_6522_of__nat__mult,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.24/5.54 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_mult
% 5.24/5.54 thf(fact_6523_of__nat__mult,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.24/5.54 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_mult
% 5.24/5.54 thf(fact_6524_of__nat__mult,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.24/5.54 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_mult
% 5.24/5.54 thf(fact_6525_of__nat__eq__1__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( semiri8010041392384452111omplex @ N )
% 5.24/5.54 = one_one_complex )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_1_iff
% 5.24/5.54 thf(fact_6526_of__nat__eq__1__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( semiri1314217659103216013at_int @ N )
% 5.24/5.54 = one_one_int )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_1_iff
% 5.24/5.54 thf(fact_6527_of__nat__eq__1__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( semiri5074537144036343181t_real @ N )
% 5.24/5.54 = one_one_real )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_1_iff
% 5.24/5.54 thf(fact_6528_of__nat__eq__1__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.24/5.54 = one_one_nat )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_1_iff
% 5.24/5.54 thf(fact_6529_of__nat__eq__1__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ( semiri681578069525770553at_rat @ N )
% 5.24/5.54 = one_one_rat )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_1_iff
% 5.24/5.54 thf(fact_6530_of__nat__1__eq__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( one_one_complex
% 5.24/5.54 = ( semiri8010041392384452111omplex @ N ) )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1_eq_iff
% 5.24/5.54 thf(fact_6531_of__nat__1__eq__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( one_one_int
% 5.24/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1_eq_iff
% 5.24/5.54 thf(fact_6532_of__nat__1__eq__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( one_one_real
% 5.24/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1_eq_iff
% 5.24/5.54 thf(fact_6533_of__nat__1__eq__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( one_one_nat
% 5.24/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1_eq_iff
% 5.24/5.54 thf(fact_6534_of__nat__1__eq__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( one_one_rat
% 5.24/5.54 = ( semiri681578069525770553at_rat @ N ) )
% 5.24/5.54 = ( N = one_one_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1_eq_iff
% 5.24/5.54 thf(fact_6535_of__nat__1,axiom,
% 5.24/5.54 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.24/5.54 = one_one_complex ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1
% 5.24/5.54 thf(fact_6536_of__nat__1,axiom,
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1
% 5.24/5.54 thf(fact_6537_of__nat__1,axiom,
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1
% 5.24/5.54 thf(fact_6538_of__nat__1,axiom,
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.24/5.54 = one_one_nat ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1
% 5.24/5.54 thf(fact_6539_of__nat__1,axiom,
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_1
% 5.24/5.54 thf(fact_6540_of__int__le__iff,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_iff
% 5.24/5.54 thf(fact_6541_of__int__le__iff,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_iff
% 5.24/5.54 thf(fact_6542_of__int__le__iff,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_iff
% 5.24/5.54 thf(fact_6543_of__int__eq__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ( ring_17405671764205052669omplex @ Z2 )
% 5.24/5.54 = ( numera6690914467698888265omplex @ N ) )
% 5.24/5.54 = ( Z2
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_iff
% 5.24/5.54 thf(fact_6544_of__int__eq__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ( ring_1_of_int_real @ Z2 )
% 5.24/5.54 = ( numeral_numeral_real @ N ) )
% 5.24/5.54 = ( Z2
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_iff
% 5.24/5.54 thf(fact_6545_of__int__eq__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ( ring_1_of_int_rat @ Z2 )
% 5.24/5.54 = ( numeral_numeral_rat @ N ) )
% 5.24/5.54 = ( Z2
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_iff
% 5.24/5.54 thf(fact_6546_of__int__eq__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ( ring_1_of_int_int @ Z2 )
% 5.24/5.54 = ( numeral_numeral_int @ N ) )
% 5.24/5.54 = ( Z2
% 5.24/5.54 = ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_iff
% 5.24/5.54 thf(fact_6547_of__int__numeral,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.24/5.54 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral
% 5.24/5.54 thf(fact_6548_of__int__numeral,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.24/5.54 = ( numeral_numeral_real @ K ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral
% 5.24/5.54 thf(fact_6549_of__int__numeral,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.24/5.54 = ( numeral_numeral_rat @ K ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral
% 5.24/5.54 thf(fact_6550_of__int__numeral,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.24/5.54 = ( numeral_numeral_int @ K ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral
% 5.24/5.54 thf(fact_6551_of__int__less__iff,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ W2 @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_iff
% 5.24/5.54 thf(fact_6552_of__int__less__iff,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ W2 @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_iff
% 5.24/5.54 thf(fact_6553_of__int__less__iff,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ W2 @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_iff
% 5.24/5.54 thf(fact_6554_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ( semiri8010041392384452111omplex @ X )
% 5.24/5.54 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6555_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ( semiri1314217659103216013at_int @ X )
% 5.24/5.54 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6556_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ( semiri5074537144036343181t_real @ X )
% 5.24/5.54 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6557_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.24/5.54 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6558_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ( semiri681578069525770553at_rat @ X )
% 5.24/5.54 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6559_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W2 )
% 5.24/5.54 = ( semiri8010041392384452111omplex @ X ) )
% 5.24/5.54 = ( ( power_power_nat @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6560_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 )
% 5.24/5.54 = ( semiri1314217659103216013at_int @ X ) )
% 5.24/5.54 = ( ( power_power_nat @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6561_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 )
% 5.24/5.54 = ( semiri5074537144036343181t_real @ X ) )
% 5.24/5.54 = ( ( power_power_nat @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6562_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 )
% 5.24/5.54 = ( semiri1316708129612266289at_nat @ X ) )
% 5.24/5.54 = ( ( power_power_nat @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6563_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 )
% 5.24/5.54 = ( semiri681578069525770553at_rat @ X ) )
% 5.24/5.54 = ( ( power_power_nat @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6564_of__nat__power,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.24/5.54 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power
% 5.24/5.54 thf(fact_6565_of__nat__power,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.24/5.54 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power
% 5.24/5.54 thf(fact_6566_of__nat__power,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.24/5.54 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power
% 5.24/5.54 thf(fact_6567_of__nat__power,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.24/5.54 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power
% 5.24/5.54 thf(fact_6568_of__nat__power,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.24/5.54 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power
% 5.24/5.54 thf(fact_6569_of__int__1,axiom,
% 5.24/5.54 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.24/5.54 = one_one_complex ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1
% 5.24/5.54 thf(fact_6570_of__int__1,axiom,
% 5.24/5.54 ( ( ring_1_of_int_int @ one_one_int )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1
% 5.24/5.54 thf(fact_6571_of__int__1,axiom,
% 5.24/5.54 ( ( ring_1_of_int_real @ one_one_int )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1
% 5.24/5.54 thf(fact_6572_of__int__1,axiom,
% 5.24/5.54 ( ( ring_1_of_int_rat @ one_one_int )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1
% 5.24/5.54 thf(fact_6573_of__int__eq__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ( ring_17405671764205052669omplex @ Z2 )
% 5.24/5.54 = one_one_complex )
% 5.24/5.54 = ( Z2 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_1_iff
% 5.24/5.54 thf(fact_6574_of__int__eq__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ( ring_1_of_int_int @ Z2 )
% 5.24/5.54 = one_one_int )
% 5.24/5.54 = ( Z2 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_1_iff
% 5.24/5.54 thf(fact_6575_of__int__eq__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ( ring_1_of_int_real @ Z2 )
% 5.24/5.54 = one_one_real )
% 5.24/5.54 = ( Z2 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_1_iff
% 5.24/5.54 thf(fact_6576_of__int__eq__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ( ring_1_of_int_rat @ Z2 )
% 5.24/5.54 = one_one_rat )
% 5.24/5.54 = ( Z2 = one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_1_iff
% 5.24/5.54 thf(fact_6577_of__int__mult,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ring_1_of_int_real @ ( times_times_int @ W2 @ Z2 ) )
% 5.24/5.54 = ( times_times_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_mult
% 5.24/5.54 thf(fact_6578_of__int__mult,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ring_1_of_int_rat @ ( times_times_int @ W2 @ Z2 ) )
% 5.24/5.54 = ( times_times_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_mult
% 5.24/5.54 thf(fact_6579_of__int__mult,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z2 ) )
% 5.24/5.54 = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_mult
% 5.24/5.54 thf(fact_6580_of__int__add,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z2 ) )
% 5.24/5.54 = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_add
% 5.24/5.54 thf(fact_6581_of__int__add,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ring_1_of_int_real @ ( plus_plus_int @ W2 @ Z2 ) )
% 5.24/5.54 = ( plus_plus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_add
% 5.24/5.54 thf(fact_6582_of__int__add,axiom,
% 5.24/5.54 ! [W2: int,Z2: int] :
% 5.24/5.54 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W2 @ Z2 ) )
% 5.24/5.54 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_add
% 5.24/5.54 thf(fact_6583_negative__zless,axiom,
% 5.24/5.54 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.24/5.54
% 5.24/5.54 % negative_zless
% 5.24/5.54 thf(fact_6584_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_rat @ X )
% 5.24/5.54 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6585_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_real @ X )
% 5.24/5.54 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6586_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_int @ X )
% 5.24/5.54 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6587_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ( ring_17405671764205052669omplex @ X )
% 5.24/5.54 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W2 ) )
% 5.24/5.54 = ( X
% 5.24/5.54 = ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6588_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 )
% 5.24/5.54 = ( ring_1_of_int_rat @ X ) )
% 5.24/5.54 = ( ( power_power_int @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6589_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 )
% 5.24/5.54 = ( ring_1_of_int_real @ X ) )
% 5.24/5.54 = ( ( power_power_int @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6590_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 )
% 5.24/5.54 = ( ring_1_of_int_int @ X ) )
% 5.24/5.54 = ( ( power_power_int @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6591_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W2 )
% 5.24/5.54 = ( ring_17405671764205052669omplex @ X ) )
% 5.24/5.54 = ( ( power_power_int @ B @ W2 )
% 5.24/5.54 = X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6592_of__int__power,axiom,
% 5.24/5.54 ! [Z2: int,N: nat] :
% 5.24/5.54 ( ( ring_1_of_int_rat @ ( power_power_int @ Z2 @ N ) )
% 5.24/5.54 = ( power_power_rat @ ( ring_1_of_int_rat @ Z2 ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power
% 5.24/5.54 thf(fact_6593_of__int__power,axiom,
% 5.24/5.54 ! [Z2: int,N: nat] :
% 5.24/5.54 ( ( ring_1_of_int_real @ ( power_power_int @ Z2 @ N ) )
% 5.24/5.54 = ( power_power_real @ ( ring_1_of_int_real @ Z2 ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power
% 5.24/5.54 thf(fact_6594_of__int__power,axiom,
% 5.24/5.54 ! [Z2: int,N: nat] :
% 5.24/5.54 ( ( ring_1_of_int_int @ ( power_power_int @ Z2 @ N ) )
% 5.24/5.54 = ( power_power_int @ ( ring_1_of_int_int @ Z2 ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power
% 5.24/5.54 thf(fact_6595_of__int__power,axiom,
% 5.24/5.54 ! [Z2: int,N: nat] :
% 5.24/5.54 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z2 @ N ) )
% 5.24/5.54 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z2 ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power
% 5.24/5.54 thf(fact_6596_dbl__inc__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.24/5.54 = one_one_complex ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(2)
% 5.24/5.54 thf(fact_6597_dbl__inc__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.24/5.54 = one_one_real ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(2)
% 5.24/5.54 thf(fact_6598_dbl__inc__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.24/5.54 = one_one_rat ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(2)
% 5.24/5.54 thf(fact_6599_dbl__inc__simps_I2_J,axiom,
% 5.24/5.54 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.24/5.54 = one_one_int ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(2)
% 5.24/5.54 thf(fact_6600_dbl__inc__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.54 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(4)
% 5.24/5.54 thf(fact_6601_dbl__inc__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.54 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(4)
% 5.24/5.54 thf(fact_6602_dbl__inc__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(4)
% 5.24/5.54 thf(fact_6603_dbl__inc__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.54 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(4)
% 5.24/5.54 thf(fact_6604_dbl__inc__simps_I4_J,axiom,
% 5.24/5.54 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(4)
% 5.24/5.54 thf(fact_6605_dbl__inc__simps_I5_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.24/5.54 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(5)
% 5.24/5.54 thf(fact_6606_dbl__inc__simps_I5_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.24/5.54 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(5)
% 5.24/5.54 thf(fact_6607_dbl__inc__simps_I5_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.24/5.54 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(5)
% 5.24/5.54 thf(fact_6608_dbl__inc__simps_I5_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.24/5.54 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(5)
% 5.24/5.54 thf(fact_6609_of__nat__le__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.24/5.54 = ( M = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_0_iff
% 5.24/5.54 thf(fact_6610_of__nat__le__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.24/5.54 = ( M = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_0_iff
% 5.24/5.54 thf(fact_6611_of__nat__le__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.24/5.54 = ( M = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_0_iff
% 5.24/5.54 thf(fact_6612_of__nat__le__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.24/5.54 = ( M = zero_zero_nat ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_0_iff
% 5.24/5.54 thf(fact_6613_of__nat__Suc,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.24/5.54 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_Suc
% 5.24/5.54 thf(fact_6614_of__nat__Suc,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.24/5.54 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_Suc
% 5.24/5.54 thf(fact_6615_of__nat__Suc,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.24/5.54 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_Suc
% 5.24/5.54 thf(fact_6616_of__nat__Suc,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.24/5.54 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_Suc
% 5.24/5.54 thf(fact_6617_of__nat__Suc,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.24/5.54 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_Suc
% 5.24/5.54 thf(fact_6618_real__of__nat__less__numeral__iff,axiom,
% 5.24/5.54 ! [N: nat,W2: num] :
% 5.24/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.54 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % real_of_nat_less_numeral_iff
% 5.24/5.54 thf(fact_6619_numeral__less__real__of__nat__iff,axiom,
% 5.24/5.54 ! [W2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.54 = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_less_real_of_nat_iff
% 5.24/5.54 thf(fact_6620_numeral__le__real__of__nat__iff,axiom,
% 5.24/5.54 ! [N: num,M: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_le_real_of_nat_iff
% 5.24/5.54 thf(fact_6621_of__nat__0__less__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_less_iff
% 5.24/5.54 thf(fact_6622_of__nat__0__less__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_less_iff
% 5.24/5.54 thf(fact_6623_of__nat__0__less__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_less_iff
% 5.24/5.54 thf(fact_6624_of__nat__0__less__iff,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.24/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_less_iff
% 5.24/5.54 thf(fact_6625_dbl__inc__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(1)
% 5.24/5.54 thf(fact_6626_dbl__inc__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(1)
% 5.24/5.54 thf(fact_6627_dbl__inc__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.24/5.54 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(1)
% 5.24/5.54 thf(fact_6628_dbl__inc__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.24/5.54 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(1)
% 5.24/5.54 thf(fact_6629_dbl__inc__simps_I1_J,axiom,
% 5.24/5.54 ! [K: num] :
% 5.24/5.54 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.24/5.54 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % dbl_inc_simps(1)
% 5.24/5.54 thf(fact_6630_of__int__0__le__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_0_le_iff
% 5.24/5.54 thf(fact_6631_of__int__0__le__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_0_le_iff
% 5.24/5.54 thf(fact_6632_of__int__0__le__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_0_le_iff
% 5.24/5.54 thf(fact_6633_of__int__le__0__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_0_iff
% 5.24/5.54 thf(fact_6634_of__int__le__0__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_0_iff
% 5.24/5.54 thf(fact_6635_of__int__le__0__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_0_iff
% 5.24/5.54 thf(fact_6636_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6637_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6638_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6639_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6640_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6641_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6642_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6643_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6644_of__int__0__less__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_0_less_iff
% 5.24/5.54 thf(fact_6645_of__int__0__less__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_0_less_iff
% 5.24/5.54 thf(fact_6646_of__int__0__less__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_0_less_iff
% 5.24/5.54 thf(fact_6647_of__int__less__0__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 5.24/5.54 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_0_iff
% 5.24/5.54 thf(fact_6648_of__int__less__0__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 5.24/5.54 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_0_iff
% 5.24/5.54 thf(fact_6649_of__int__less__0__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 5.24/5.54 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_0_iff
% 5.24/5.54 thf(fact_6650_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: nat] :
% 5.24/5.54 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.24/5.54 = ( semiri8010041392384452111omplex @ Y4 ) )
% 5.24/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6651_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: nat] :
% 5.24/5.54 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.54 = ( semiri1314217659103216013at_int @ Y4 ) )
% 5.24/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6652_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: nat] :
% 5.24/5.54 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.24/5.54 = ( semiri5074537144036343181t_real @ Y4 ) )
% 5.24/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6653_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: nat] :
% 5.24/5.54 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.54 = ( semiri1316708129612266289at_nat @ Y4 ) )
% 5.24/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6654_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: nat] :
% 5.24/5.54 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.24/5.54 = ( semiri681578069525770553at_rat @ Y4 ) )
% 5.24/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6655_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: nat,X: num,N: nat] :
% 5.24/5.54 ( ( ( semiri8010041392384452111omplex @ Y4 )
% 5.24/5.54 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6656_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: nat,X: num,N: nat] :
% 5.24/5.54 ( ( ( semiri1314217659103216013at_int @ Y4 )
% 5.24/5.54 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6657_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: nat,X: num,N: nat] :
% 5.24/5.54 ( ( ( semiri5074537144036343181t_real @ Y4 )
% 5.24/5.54 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6658_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: nat,X: num,N: nat] :
% 5.24/5.54 ( ( ( semiri1316708129612266289at_nat @ Y4 )
% 5.24/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6659_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: nat,X: num,N: nat] :
% 5.24/5.54 ( ( ( semiri681578069525770553at_rat @ Y4 )
% 5.24/5.54 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6660_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6661_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6662_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6663_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: nat,W2: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.24/5.54 thf(fact_6664_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6665_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6666_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6667_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,B: nat,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6668_of__int__le__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_numeral_iff
% 5.24/5.54 thf(fact_6669_of__int__le__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_numeral_iff
% 5.24/5.54 thf(fact_6670_of__int__le__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_numeral_iff
% 5.24/5.54 thf(fact_6671_of__int__numeral__le__iff,axiom,
% 5.24/5.54 ! [N: num,Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral_le_iff
% 5.24/5.54 thf(fact_6672_of__int__numeral__le__iff,axiom,
% 5.24/5.54 ! [N: num,Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral_le_iff
% 5.24/5.54 thf(fact_6673_of__int__numeral__le__iff,axiom,
% 5.24/5.54 ! [N: num,Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral_le_iff
% 5.24/5.54 thf(fact_6674_of__int__numeral__less__iff,axiom,
% 5.24/5.54 ! [N: num,Z2: int] :
% 5.24/5.54 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral_less_iff
% 5.24/5.54 thf(fact_6675_of__int__numeral__less__iff,axiom,
% 5.24/5.54 ! [N: num,Z2: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral_less_iff
% 5.24/5.54 thf(fact_6676_of__int__numeral__less__iff,axiom,
% 5.24/5.54 ! [N: num,Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_numeral_less_iff
% 5.24/5.54 thf(fact_6677_of__int__less__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N ) )
% 5.24/5.54 = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_numeral_iff
% 5.24/5.54 thf(fact_6678_of__int__less__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 5.24/5.54 = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_numeral_iff
% 5.24/5.54 thf(fact_6679_of__int__less__numeral__iff,axiom,
% 5.24/5.54 ! [Z2: int,N: num] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.54 = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_numeral_iff
% 5.24/5.54 thf(fact_6680_of__int__le__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_1_iff
% 5.24/5.54 thf(fact_6681_of__int__le__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_1_iff
% 5.24/5.54 thf(fact_6682_of__int__le__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 5.24/5.54 = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_1_iff
% 5.24/5.54 thf(fact_6683_of__int__1__le__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1_le_iff
% 5.24/5.54 thf(fact_6684_of__int__1__le__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1_le_iff
% 5.24/5.54 thf(fact_6685_of__int__1__le__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1_le_iff
% 5.24/5.54 thf(fact_6686_of__int__1__less__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1_less_iff
% 5.24/5.54 thf(fact_6687_of__int__1__less__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1_less_iff
% 5.24/5.54 thf(fact_6688_of__int__1__less__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.24/5.54 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_1_less_iff
% 5.24/5.54 thf(fact_6689_of__int__less__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 5.24/5.54 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_1_iff
% 5.24/5.54 thf(fact_6690_of__int__less__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 5.24/5.54 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_1_iff
% 5.24/5.54 thf(fact_6691_of__int__less__1__iff,axiom,
% 5.24/5.54 ! [Z2: int] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 5.24/5.54 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_1_iff
% 5.24/5.54 thf(fact_6692_of__int__le__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6693_of__int__le__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6694_of__int__le__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6695_of__int__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6696_of__int__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6697_of__int__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6698_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.24/5.54 = ( ring_17405671764205052669omplex @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6699_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.24/5.54 = ( ring_1_of_int_real @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6700_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.24/5.54 = ( ring_1_of_int_rat @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6701_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.54 = ( ring_1_of_int_int @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6702_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_17405671764205052669omplex @ Y4 )
% 5.24/5.54 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6703_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_real @ Y4 )
% 5.24/5.54 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6704_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_rat @ Y4 )
% 5.24/5.54 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6705_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_int @ Y4 )
% 5.24/5.54 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6706_of__int__less__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6707_of__int__less__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6708_of__int__less__of__int__power__cancel__iff,axiom,
% 5.24/5.54 ! [B: int,W2: nat,X: int] :
% 5.24/5.54 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_of_int_power_cancel_iff
% 5.24/5.54 thf(fact_6709_of__int__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6710_of__int__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6711_of__int__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: int,B: int,W2: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 5.24/5.54 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6712_of__nat__zero__less__power__iff,axiom,
% 5.24/5.54 ! [X: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 5.24/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_zero_less_power_iff
% 5.24/5.54 thf(fact_6713_of__nat__zero__less__power__iff,axiom,
% 5.24/5.54 ! [X: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 5.24/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_zero_less_power_iff
% 5.24/5.54 thf(fact_6714_of__nat__zero__less__power__iff,axiom,
% 5.24/5.54 ! [X: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 5.24/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_zero_less_power_iff
% 5.24/5.54 thf(fact_6715_of__nat__zero__less__power__iff,axiom,
% 5.24/5.54 ! [X: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 5.24/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.24/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_zero_less_power_iff
% 5.24/5.54 thf(fact_6716_even__of__nat,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.24/5.54 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % even_of_nat
% 5.24/5.54 thf(fact_6717_even__of__nat,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.54 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % even_of_nat
% 5.24/5.54 thf(fact_6718_even__of__nat,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.54 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % even_of_nat
% 5.24/5.54 thf(fact_6719_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6720_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6721_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6722_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6723_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6724_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6725_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6726_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.24/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6727_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6728_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6729_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6730_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.24/5.54 ! [I2: num,N: nat,X: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.24/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.24/5.54 thf(fact_6731_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6732_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6733_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6734_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [X: nat,I2: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6735_numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6736_numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6737_numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6738_of__int__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6739_of__int__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6740_of__int__le__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6741_of__int__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6742_of__int__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6743_of__int__less__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6744_numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6745_numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6746_numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6747_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 5.24/5.54 = ( ring_1_of_int_real @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6748_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.24/5.54 = ( ring_1_of_int_int @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6749_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 5.24/5.54 = ( ring_17405671764205052669omplex @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6750_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 5.24/5.54 = ( ring_1_of_int_rat @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6751_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,Y4: int] :
% 5.24/5.54 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 5.24/5.54 = ( ring_18347121197199848620nteger @ Y4 ) )
% 5.24/5.54 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.24/5.54 = Y4 ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_eq_of_int_cancel_iff
% 5.24/5.54 thf(fact_6752_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_real @ Y4 )
% 5.24/5.54 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6753_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_int @ Y4 )
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6754_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_17405671764205052669omplex @ Y4 )
% 5.24/5.54 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6755_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_1_of_int_rat @ Y4 )
% 5.24/5.54 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6756_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [Y4: int,X: num,N: nat] :
% 5.24/5.54 ( ( ( ring_18347121197199848620nteger @ Y4 )
% 5.24/5.54 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.24/5.54 = ( Y4
% 5.24/5.54 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_eq_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6757_divmod__algorithm__code_I5_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc4245557441103728435nt_int
% 5.24/5.54 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.24/5.54 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(5)
% 5.24/5.54 thf(fact_6758_divmod__algorithm__code_I5_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc2626176000494625587at_nat
% 5.24/5.54 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.24/5.54 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(5)
% 5.24/5.54 thf(fact_6759_divmod__algorithm__code_I5_J,axiom,
% 5.24/5.54 ! [M: num,N: num] :
% 5.24/5.54 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.24/5.54 = ( produc6916734918728496179nteger
% 5.24/5.54 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.24/5.54 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % divmod_algorithm_code(5)
% 5.24/5.54 thf(fact_6760_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6761_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6762_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6763_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.24/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_le_of_int_cancel_iff
% 5.24/5.54 thf(fact_6764_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6765_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6766_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6767_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_le_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6768_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6769_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6770_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6771_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.24/5.54 ! [X: num,N: nat,A: int] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.24/5.54 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.24/5.54
% 5.24/5.54 % neg_numeral_power_less_of_int_cancel_iff
% 5.24/5.54 thf(fact_6772_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6773_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6774_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6775_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.24/5.54 ! [A: int,X: num,N: nat] :
% 5.24/5.54 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.24/5.54 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_int_less_neg_numeral_power_cancel_iff
% 5.24/5.54 thf(fact_6776_of__nat__less__of__int__iff,axiom,
% 5.24/5.54 ! [N: nat,X: int] :
% 5.24/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 5.24/5.54 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_int_iff
% 5.24/5.54 thf(fact_6777_of__nat__less__of__int__iff,axiom,
% 5.24/5.54 ! [N: nat,X: int] :
% 5.24/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 5.24/5.54 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_int_iff
% 5.24/5.54 thf(fact_6778_of__nat__less__of__int__iff,axiom,
% 5.24/5.54 ! [N: nat,X: int] :
% 5.24/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 5.24/5.54 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_of_int_iff
% 5.24/5.54 thf(fact_6779_mult__of__int__commute,axiom,
% 5.24/5.54 ! [X: int,Y4: real] :
% 5.24/5.54 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_real @ Y4 @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_int_commute
% 5.24/5.54 thf(fact_6780_mult__of__int__commute,axiom,
% 5.24/5.54 ! [X: int,Y4: rat] :
% 5.24/5.54 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_rat @ Y4 @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_int_commute
% 5.24/5.54 thf(fact_6781_mult__of__int__commute,axiom,
% 5.24/5.54 ! [X: int,Y4: int] :
% 5.24/5.54 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_int @ Y4 @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_int_commute
% 5.24/5.54 thf(fact_6782_mult__of__nat__commute,axiom,
% 5.24/5.54 ! [X: nat,Y4: int] :
% 5.24/5.54 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_int @ Y4 @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_nat_commute
% 5.24/5.54 thf(fact_6783_mult__of__nat__commute,axiom,
% 5.24/5.54 ! [X: nat,Y4: real] :
% 5.24/5.54 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_real @ Y4 @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_nat_commute
% 5.24/5.54 thf(fact_6784_mult__of__nat__commute,axiom,
% 5.24/5.54 ! [X: nat,Y4: nat] :
% 5.24/5.54 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_nat @ Y4 @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_nat_commute
% 5.24/5.54 thf(fact_6785_mult__of__nat__commute,axiom,
% 5.24/5.54 ! [X: nat,Y4: rat] :
% 5.24/5.54 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y4 )
% 5.24/5.54 = ( times_times_rat @ Y4 @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % mult_of_nat_commute
% 5.24/5.54 thf(fact_6786_old_Oprod_Ocase,axiom,
% 5.24/5.54 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.24/5.54 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.24/5.54 = ( F @ X1 @ X22 ) ) ).
% 5.24/5.54
% 5.24/5.54 % old.prod.case
% 5.24/5.54 thf(fact_6787_old_Oprod_Ocase,axiom,
% 5.24/5.54 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.24/5.54 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.24/5.54 = ( F @ X1 @ X22 ) ) ).
% 5.24/5.54
% 5.24/5.54 % old.prod.case
% 5.24/5.54 thf(fact_6788_old_Oprod_Ocase,axiom,
% 5.24/5.54 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.24/5.54 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.24/5.54 = ( F @ X1 @ X22 ) ) ).
% 5.24/5.54
% 5.24/5.54 % old.prod.case
% 5.24/5.54 thf(fact_6789_old_Oprod_Ocase,axiom,
% 5.24/5.54 ! [F: int > int > $o,X1: int,X22: int] :
% 5.24/5.54 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.24/5.54 = ( F @ X1 @ X22 ) ) ).
% 5.24/5.54
% 5.24/5.54 % old.prod.case
% 5.24/5.54 thf(fact_6790_old_Oprod_Ocase,axiom,
% 5.24/5.54 ! [F: int > int > int,X1: int,X22: int] :
% 5.24/5.54 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.24/5.54 = ( F @ X1 @ X22 ) ) ).
% 5.24/5.54
% 5.24/5.54 % old.prod.case
% 5.24/5.54 thf(fact_6791_case__prodE2,axiom,
% 5.24/5.54 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 5.24/5.54 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z2 ) )
% 5.24/5.54 => ~ ! [X3: nat,Y3: nat] :
% 5.24/5.54 ( ( Z2
% 5.24/5.54 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.24/5.54 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prodE2
% 5.24/5.54 thf(fact_6792_case__prodE2,axiom,
% 5.24/5.54 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z2: product_prod_nat_nat] :
% 5.24/5.54 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z2 ) )
% 5.24/5.54 => ~ ! [X3: nat,Y3: nat] :
% 5.24/5.54 ( ( Z2
% 5.24/5.54 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.24/5.54 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prodE2
% 5.24/5.54 thf(fact_6793_case__prodE2,axiom,
% 5.24/5.54 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z2: product_prod_int_int] :
% 5.24/5.54 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z2 ) )
% 5.24/5.54 => ~ ! [X3: int,Y3: int] :
% 5.24/5.54 ( ( Z2
% 5.24/5.54 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.54 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prodE2
% 5.24/5.54 thf(fact_6794_case__prodE2,axiom,
% 5.24/5.54 ! [Q: $o > $o,P: int > int > $o,Z2: product_prod_int_int] :
% 5.24/5.54 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z2 ) )
% 5.24/5.54 => ~ ! [X3: int,Y3: int] :
% 5.24/5.54 ( ( Z2
% 5.24/5.54 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.54 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prodE2
% 5.24/5.54 thf(fact_6795_case__prodE2,axiom,
% 5.24/5.54 ! [Q: int > $o,P: int > int > int,Z2: product_prod_int_int] :
% 5.24/5.54 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z2 ) )
% 5.24/5.54 => ~ ! [X3: int,Y3: int] :
% 5.24/5.54 ( ( Z2
% 5.24/5.54 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.54 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % case_prodE2
% 5.24/5.54 thf(fact_6796_case__prod__eta,axiom,
% 5.24/5.54 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.24/5.54 ( ( produc27273713700761075at_nat
% 5.24/5.54 @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 5.24/5.54 = F ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_eta
% 5.24/5.54 thf(fact_6797_case__prod__eta,axiom,
% 5.24/5.54 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.24/5.54 ( ( produc8739625826339149834_nat_o
% 5.24/5.54 @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 5.24/5.54 = F ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_eta
% 5.24/5.54 thf(fact_6798_case__prod__eta,axiom,
% 5.24/5.54 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.24/5.54 ( ( produc4245557441103728435nt_int
% 5.24/5.54 @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 5.24/5.54 = F ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_eta
% 5.24/5.54 thf(fact_6799_case__prod__eta,axiom,
% 5.24/5.54 ! [F: product_prod_int_int > $o] :
% 5.24/5.54 ( ( produc4947309494688390418_int_o
% 5.24/5.54 @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 5.24/5.54 = F ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_eta
% 5.24/5.54 thf(fact_6800_case__prod__eta,axiom,
% 5.24/5.54 ! [F: product_prod_int_int > int] :
% 5.24/5.54 ( ( produc8211389475949308722nt_int
% 5.24/5.54 @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 5.24/5.54 = F ) ).
% 5.24/5.54
% 5.24/5.54 % case_prod_eta
% 5.24/5.54 thf(fact_6801_cond__case__prod__eta,axiom,
% 5.24/5.54 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.24/5.54 ( ! [X3: nat,Y3: nat] :
% 5.24/5.54 ( ( F @ X3 @ Y3 )
% 5.24/5.54 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.24/5.54 => ( ( produc27273713700761075at_nat @ F )
% 5.24/5.54 = G ) ) ).
% 5.24/5.54
% 5.24/5.54 % cond_case_prod_eta
% 5.24/5.54 thf(fact_6802_cond__case__prod__eta,axiom,
% 5.24/5.54 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.24/5.54 ( ! [X3: nat,Y3: nat] :
% 5.24/5.54 ( ( F @ X3 @ Y3 )
% 5.24/5.54 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.24/5.54 => ( ( produc8739625826339149834_nat_o @ F )
% 5.24/5.54 = G ) ) ).
% 5.24/5.54
% 5.24/5.54 % cond_case_prod_eta
% 5.24/5.54 thf(fact_6803_cond__case__prod__eta,axiom,
% 5.24/5.54 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.24/5.54 ( ! [X3: int,Y3: int] :
% 5.24/5.54 ( ( F @ X3 @ Y3 )
% 5.24/5.54 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.24/5.54 => ( ( produc4245557441103728435nt_int @ F )
% 5.24/5.54 = G ) ) ).
% 5.24/5.54
% 5.24/5.54 % cond_case_prod_eta
% 5.24/5.54 thf(fact_6804_cond__case__prod__eta,axiom,
% 5.24/5.54 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.24/5.54 ( ! [X3: int,Y3: int] :
% 5.24/5.54 ( ( F @ X3 @ Y3 )
% 5.24/5.54 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.24/5.54 => ( ( produc4947309494688390418_int_o @ F )
% 5.24/5.54 = G ) ) ).
% 5.24/5.54
% 5.24/5.54 % cond_case_prod_eta
% 5.24/5.54 thf(fact_6805_cond__case__prod__eta,axiom,
% 5.24/5.54 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.24/5.54 ( ! [X3: int,Y3: int] :
% 5.24/5.54 ( ( F @ X3 @ Y3 )
% 5.24/5.54 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.24/5.54 => ( ( produc8211389475949308722nt_int @ F )
% 5.24/5.54 = G ) ) ).
% 5.24/5.54
% 5.24/5.54 % cond_case_prod_eta
% 5.24/5.54 thf(fact_6806_of__nat__0__le__iff,axiom,
% 5.24/5.54 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_le_iff
% 5.24/5.54 thf(fact_6807_of__nat__0__le__iff,axiom,
% 5.24/5.54 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_le_iff
% 5.24/5.54 thf(fact_6808_of__nat__0__le__iff,axiom,
% 5.24/5.54 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_le_iff
% 5.24/5.54 thf(fact_6809_of__nat__0__le__iff,axiom,
% 5.24/5.54 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_0_le_iff
% 5.24/5.54 thf(fact_6810_of__nat__less__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_0_iff
% 5.24/5.54 thf(fact_6811_of__nat__less__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_0_iff
% 5.24/5.54 thf(fact_6812_of__nat__less__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_0_iff
% 5.24/5.54 thf(fact_6813_of__nat__less__0__iff,axiom,
% 5.24/5.54 ! [M: nat] :
% 5.24/5.54 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_0_iff
% 5.24/5.54 thf(fact_6814_of__nat__neq__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.24/5.54 != zero_zero_complex ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_neq_0
% 5.24/5.54 thf(fact_6815_of__nat__neq__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.24/5.54 != zero_zero_int ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_neq_0
% 5.24/5.54 thf(fact_6816_of__nat__neq__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.24/5.54 != zero_zero_real ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_neq_0
% 5.24/5.54 thf(fact_6817_of__nat__neq__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.24/5.54 != zero_zero_nat ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_neq_0
% 5.24/5.54 thf(fact_6818_of__nat__neq__0,axiom,
% 5.24/5.54 ! [N: nat] :
% 5.24/5.54 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.24/5.54 != zero_zero_rat ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_neq_0
% 5.24/5.54 thf(fact_6819_div__mult2__eq_H,axiom,
% 5.24/5.54 ! [A: int,M: nat,N: nat] :
% 5.24/5.54 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.54 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % div_mult2_eq'
% 5.24/5.54 thf(fact_6820_div__mult2__eq_H,axiom,
% 5.24/5.54 ! [A: nat,M: nat,N: nat] :
% 5.24/5.54 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.24/5.54 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % div_mult2_eq'
% 5.24/5.54 thf(fact_6821_of__nat__less__imp__less,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_imp_less
% 5.24/5.54 thf(fact_6822_of__nat__less__imp__less,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_imp_less
% 5.24/5.54 thf(fact_6823_of__nat__less__imp__less,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_imp_less
% 5.24/5.54 thf(fact_6824_of__nat__less__imp__less,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.24/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.54
% 5.24/5.54 % of_nat_less_imp_less
% 5.24/5.54 thf(fact_6825_less__imp__of__nat__less,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ M @ N )
% 5.24/5.54 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.54
% 5.24/5.54 % less_imp_of_nat_less
% 5.24/5.54 thf(fact_6826_less__imp__of__nat__less,axiom,
% 5.24/5.54 ! [M: nat,N: nat] :
% 5.24/5.54 ( ( ord_less_nat @ M @ N )
% 5.24/5.54 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % less_imp_of_nat_less
% 5.24/5.55 thf(fact_6827_less__imp__of__nat__less,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % less_imp_of_nat_less
% 5.24/5.55 thf(fact_6828_less__imp__of__nat__less,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % less_imp_of_nat_less
% 5.24/5.55 thf(fact_6829_of__nat__mono,axiom,
% 5.24/5.55 ! [I2: nat,J: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.55 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mono
% 5.24/5.55 thf(fact_6830_of__nat__mono,axiom,
% 5.24/5.55 ! [I2: nat,J: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.55 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mono
% 5.24/5.55 thf(fact_6831_of__nat__mono,axiom,
% 5.24/5.55 ! [I2: nat,J: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.55 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mono
% 5.24/5.55 thf(fact_6832_of__nat__mono,axiom,
% 5.24/5.55 ! [I2: nat,J: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.55 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mono
% 5.24/5.55 thf(fact_6833_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.24/5.55 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.24/5.55 thf(fact_6834_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.24/5.55 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.24/5.55 thf(fact_6835_of__nat__dvd__iff,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.24/5.55 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_dvd_iff
% 5.24/5.55 thf(fact_6836_of__nat__dvd__iff,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.55 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_dvd_iff
% 5.24/5.55 thf(fact_6837_of__nat__dvd__iff,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.24/5.55 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_dvd_iff
% 5.24/5.55 thf(fact_6838_int__ops_I1_J,axiom,
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.24/5.55 = zero_zero_int ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(1)
% 5.24/5.55 thf(fact_6839_int__ops_I3_J,axiom,
% 5.24/5.55 ! [N: num] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.24/5.55 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(3)
% 5.24/5.55 thf(fact_6840_nat__int__comparison_I2_J,axiom,
% 5.24/5.55 ( ord_less_nat
% 5.24/5.55 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_int_comparison(2)
% 5.24/5.55 thf(fact_6841_int__of__nat__induct,axiom,
% 5.24/5.55 ! [P: int > $o,Z2: int] :
% 5.24/5.55 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.24/5.55 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.24/5.55 => ( P @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_of_nat_induct
% 5.24/5.55 thf(fact_6842_int__cases,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ! [N3: nat] :
% 5.24/5.55 ( Z2
% 5.24/5.55 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ( Z2
% 5.24/5.55 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_cases
% 5.24/5.55 thf(fact_6843_zle__int,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.55 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % zle_int
% 5.24/5.55 thf(fact_6844_nat__int__comparison_I3_J,axiom,
% 5.24/5.55 ( ord_less_eq_nat
% 5.24/5.55 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_int_comparison(3)
% 5.24/5.55 thf(fact_6845_of__nat__mod,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.55 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mod
% 5.24/5.55 thf(fact_6846_of__nat__mod,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.55 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mod
% 5.24/5.55 thf(fact_6847_of__nat__mod,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.24/5.55 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_mod
% 5.24/5.55 thf(fact_6848_zadd__int__left,axiom,
% 5.24/5.55 ! [M: nat,N: nat,Z2: int] :
% 5.24/5.55 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z2 ) )
% 5.24/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z2 ) ) ).
% 5.24/5.55
% 5.24/5.55 % zadd_int_left
% 5.24/5.55 thf(fact_6849_int__ops_I5_J,axiom,
% 5.24/5.55 ! [A: nat,B: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.24/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(5)
% 5.24/5.55 thf(fact_6850_int__plus,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.24/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_plus
% 5.24/5.55 thf(fact_6851_int__ops_I2_J,axiom,
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(2)
% 5.24/5.55 thf(fact_6852_int__ops_I7_J,axiom,
% 5.24/5.55 ! [A: nat,B: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.24/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(7)
% 5.24/5.55 thf(fact_6853_zle__iff__zadd,axiom,
% 5.24/5.55 ( ord_less_eq_int
% 5.24/5.55 = ( ^ [W3: int,Z4: int] :
% 5.24/5.55 ? [N2: nat] :
% 5.24/5.55 ( Z4
% 5.24/5.55 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % zle_iff_zadd
% 5.24/5.55 thf(fact_6854_zdiv__int,axiom,
% 5.24/5.55 ! [A: nat,B: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.24/5.55 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % zdiv_int
% 5.24/5.55 thf(fact_6855_nat__less__as__int,axiom,
% 5.24/5.55 ( ord_less_nat
% 5.24/5.55 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_less_as_int
% 5.24/5.55 thf(fact_6856_nat__leq__as__int,axiom,
% 5.24/5.55 ( ord_less_eq_nat
% 5.24/5.55 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_leq_as_int
% 5.24/5.55 thf(fact_6857_of__nat__diff,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.55 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_diff
% 5.24/5.55 thf(fact_6858_of__nat__diff,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.55 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_diff
% 5.24/5.55 thf(fact_6859_of__nat__diff,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.55 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_diff
% 5.24/5.55 thf(fact_6860_of__nat__diff,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.24/5.55 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_diff
% 5.24/5.55 thf(fact_6861_reals__Archimedean3,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ! [Y5: real] :
% 5.24/5.55 ? [N3: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % reals_Archimedean3
% 5.24/5.55 thf(fact_6862_int__cases4,axiom,
% 5.24/5.55 ! [M: int] :
% 5.24/5.55 ( ! [N3: nat] :
% 5.24/5.55 ( M
% 5.24/5.55 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.24/5.55 => ( M
% 5.24/5.55 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_cases4
% 5.24/5.55 thf(fact_6863_real__of__nat__div4,axiom,
% 5.24/5.55 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_nat_div4
% 5.24/5.55 thf(fact_6864_int__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.24/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_Suc
% 5.24/5.55 thf(fact_6865_int__ops_I4_J,axiom,
% 5.24/5.55 ! [A: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.24/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(4)
% 5.24/5.55 thf(fact_6866_zless__iff__Suc__zadd,axiom,
% 5.24/5.55 ( ord_less_int
% 5.24/5.55 = ( ^ [W3: int,Z4: int] :
% 5.24/5.55 ? [N2: nat] :
% 5.24/5.55 ( Z4
% 5.24/5.55 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % zless_iff_Suc_zadd
% 5.24/5.55 thf(fact_6867_real__of__nat__div,axiom,
% 5.24/5.55 ! [D: nat,N: nat] :
% 5.24/5.55 ( ( dvd_dvd_nat @ D @ N )
% 5.24/5.55 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.24/5.55 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_nat_div
% 5.24/5.55 thf(fact_6868_of__int__nonneg,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_nonneg
% 5.24/5.55 thf(fact_6869_of__int__nonneg,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.55 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_nonneg
% 5.24/5.55 thf(fact_6870_of__int__nonneg,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_nonneg
% 5.24/5.55 thf(fact_6871_of__int__leD,axiom,
% 5.24/5.55 ! [N: int,X: code_integer] :
% 5.24/5.55 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_leD
% 5.24/5.55 thf(fact_6872_of__int__leD,axiom,
% 5.24/5.55 ! [N: int,X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_leD
% 5.24/5.55 thf(fact_6873_of__int__leD,axiom,
% 5.24/5.55 ! [N: int,X: rat] :
% 5.24/5.55 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_leD
% 5.24/5.55 thf(fact_6874_of__int__leD,axiom,
% 5.24/5.55 ! [N: int,X: int] :
% 5.24/5.55 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_leD
% 5.24/5.55 thf(fact_6875_of__int__pos,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_pos
% 5.24/5.55 thf(fact_6876_of__int__pos,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.55 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_pos
% 5.24/5.55 thf(fact_6877_of__int__pos,axiom,
% 5.24/5.55 ! [Z2: int] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.55 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_pos
% 5.24/5.55 thf(fact_6878_of__int__lessD,axiom,
% 5.24/5.55 ! [N: int,X: code_integer] :
% 5.24/5.55 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_lessD
% 5.24/5.55 thf(fact_6879_of__int__lessD,axiom,
% 5.24/5.55 ! [N: int,X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_lessD
% 5.24/5.55 thf(fact_6880_of__int__lessD,axiom,
% 5.24/5.55 ! [N: int,X: rat] :
% 5.24/5.55 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_lessD
% 5.24/5.55 thf(fact_6881_of__int__lessD,axiom,
% 5.24/5.55 ! [N: int,X: int] :
% 5.24/5.55 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.24/5.55 => ( ( N = zero_zero_int )
% 5.24/5.55 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_lessD
% 5.24/5.55 thf(fact_6882_mod__mult2__eq_H,axiom,
% 5.24/5.55 ! [A: code_integer,M: nat,N: nat] :
% 5.24/5.55 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.24/5.55 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mod_mult2_eq'
% 5.24/5.55 thf(fact_6883_mod__mult2__eq_H,axiom,
% 5.24/5.55 ! [A: int,M: nat,N: nat] :
% 5.24/5.55 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mod_mult2_eq'
% 5.24/5.55 thf(fact_6884_mod__mult2__eq_H,axiom,
% 5.24/5.55 ! [A: nat,M: nat,N: nat] :
% 5.24/5.55 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mod_mult2_eq'
% 5.24/5.55 thf(fact_6885_of__int__neg__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_neg_numeral
% 5.24/5.55 thf(fact_6886_of__int__neg__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_neg_numeral
% 5.24/5.55 thf(fact_6887_of__int__neg__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.55 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_neg_numeral
% 5.24/5.55 thf(fact_6888_of__int__neg__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.55 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_neg_numeral
% 5.24/5.55 thf(fact_6889_of__int__neg__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.55 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_neg_numeral
% 5.24/5.55 thf(fact_6890_field__char__0__class_Oof__nat__div,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % field_char_0_class.of_nat_div
% 5.24/5.55 thf(fact_6891_field__char__0__class_Oof__nat__div,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.24/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % field_char_0_class.of_nat_div
% 5.24/5.55 thf(fact_6892_field__char__0__class_Oof__nat__div,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.24/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % field_char_0_class.of_nat_div
% 5.24/5.55 thf(fact_6893_int__le__real__less,axiom,
% 5.24/5.55 ( ord_less_eq_int
% 5.24/5.55 = ( ^ [N2: int,M2: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M2 ) @ one_one_real ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_le_real_less
% 5.24/5.55 thf(fact_6894_int__less__real__le,axiom,
% 5.24/5.55 ( ord_less_int
% 5.24/5.55 = ( ^ [N2: int,M2: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_less_real_le
% 5.24/5.55 thf(fact_6895_pos__int__cases,axiom,
% 5.24/5.55 ! [K: int] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ( ( K
% 5.24/5.55 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.24/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pos_int_cases
% 5.24/5.55 thf(fact_6896_zero__less__imp__eq__int,axiom,
% 5.24/5.55 ! [K: int] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.55 => ? [N3: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.24/5.55 & ( K
% 5.24/5.55 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % zero_less_imp_eq_int
% 5.24/5.55 thf(fact_6897_int__cases3,axiom,
% 5.24/5.55 ! [K: int] :
% 5.24/5.55 ( ( K != zero_zero_int )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( K
% 5.24/5.55 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.24/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ( ( K
% 5.24/5.55 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.24/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_cases3
% 5.24/5.55 thf(fact_6898_nat__less__real__le,axiom,
% 5.24/5.55 ( ord_less_nat
% 5.24/5.55 = ( ^ [N2: nat,M2: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_less_real_le
% 5.24/5.55 thf(fact_6899_nat__le__real__less,axiom,
% 5.24/5.55 ( ord_less_eq_nat
% 5.24/5.55 = ( ^ [N2: nat,M2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_le_real_less
% 5.24/5.55 thf(fact_6900_zmult__zless__mono2__lemma,axiom,
% 5.24/5.55 ! [I2: int,J: int,K: nat] :
% 5.24/5.55 ( ( ord_less_int @ I2 @ J )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.55 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % zmult_zless_mono2_lemma
% 5.24/5.55 thf(fact_6901_not__zle__0__negative,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % not_zle_0_negative
% 5.24/5.55 thf(fact_6902_negative__zless__0,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.24/5.55
% 5.24/5.55 % negative_zless_0
% 5.24/5.55 thf(fact_6903_negD,axiom,
% 5.24/5.55 ! [X: int] :
% 5.24/5.55 ( ( ord_less_int @ X @ zero_zero_int )
% 5.24/5.55 => ? [N3: nat] :
% 5.24/5.55 ( X
% 5.24/5.55 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % negD
% 5.24/5.55 thf(fact_6904_dbl__inc__def,axiom,
% 5.24/5.55 ( neg_nu8557863876264182079omplex
% 5.24/5.55 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % dbl_inc_def
% 5.24/5.55 thf(fact_6905_dbl__inc__def,axiom,
% 5.24/5.55 ( neg_nu8295874005876285629c_real
% 5.24/5.55 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % dbl_inc_def
% 5.24/5.55 thf(fact_6906_dbl__inc__def,axiom,
% 5.24/5.55 ( neg_nu5219082963157363817nc_rat
% 5.24/5.55 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % dbl_inc_def
% 5.24/5.55 thf(fact_6907_dbl__inc__def,axiom,
% 5.24/5.55 ( neg_nu5851722552734809277nc_int
% 5.24/5.55 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % dbl_inc_def
% 5.24/5.55 thf(fact_6908_int__ops_I6_J,axiom,
% 5.24/5.55 ! [A: nat,B: nat] :
% 5.24/5.55 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.24/5.55 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.24/5.55 = zero_zero_int ) )
% 5.24/5.55 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.24/5.55 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.24/5.55 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_ops(6)
% 5.24/5.55 thf(fact_6909_real__of__int__div__aux,axiom,
% 5.24/5.55 ! [X: int,D: int] :
% 5.24/5.55 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_int_div_aux
% 5.24/5.55 thf(fact_6910_real__of__nat__div__aux,axiom,
% 5.24/5.55 ! [X: nat,D: nat] :
% 5.24/5.55 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.24/5.55 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_nat_div_aux
% 5.24/5.55 thf(fact_6911_of__nat__less__two__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_less_two_power
% 5.24/5.55 thf(fact_6912_of__nat__less__two__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_less_two_power
% 5.24/5.55 thf(fact_6913_of__nat__less__two__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_less_two_power
% 5.24/5.55 thf(fact_6914_inverse__of__nat__le,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % inverse_of_nat_le
% 5.24/5.55 thf(fact_6915_inverse__of__nat__le,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % inverse_of_nat_le
% 5.24/5.55 thf(fact_6916_real__archimedian__rdiv__eq__0,axiom,
% 5.24/5.55 ! [X: real,C: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.24/5.55 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 5.24/5.55 => ( X = zero_zero_real ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_archimedian_rdiv_eq_0
% 5.24/5.55 thf(fact_6917_real__of__int__div3,axiom,
% 5.24/5.55 ! [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 ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_int_div3
% 5.24/5.55 thf(fact_6918_neg__int__cases,axiom,
% 5.24/5.55 ! [K: int] :
% 5.24/5.55 ( ( ord_less_int @ K @ zero_zero_int )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ( ( K
% 5.24/5.55 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.24/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % neg_int_cases
% 5.24/5.55 thf(fact_6919_zdiff__int__split,axiom,
% 5.24/5.55 ! [P: int > $o,X: nat,Y4: nat] :
% 5.24/5.55 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y4 ) ) )
% 5.24/5.55 = ( ( ( ord_less_eq_nat @ Y4 @ X )
% 5.24/5.55 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) )
% 5.24/5.55 & ( ( ord_less_nat @ X @ Y4 )
% 5.24/5.55 => ( P @ zero_zero_int ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % zdiff_int_split
% 5.24/5.55 thf(fact_6920_real__of__nat__div2,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_nat_div2
% 5.24/5.55 thf(fact_6921_real__of__nat__div3,axiom,
% 5.24/5.55 ! [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 ) ).
% 5.24/5.55
% 5.24/5.55 % real_of_nat_div3
% 5.24/5.55 thf(fact_6922_ln__realpow,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % ln_realpow
% 5.24/5.55 thf(fact_6923_even__of__int__iff,axiom,
% 5.24/5.55 ! [K: int] :
% 5.24/5.55 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.24/5.55 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % even_of_int_iff
% 5.24/5.55 thf(fact_6924_even__of__int__iff,axiom,
% 5.24/5.55 ! [K: int] :
% 5.24/5.55 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.24/5.55 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % even_of_int_iff
% 5.24/5.55 thf(fact_6925_Bernoulli__inequality,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.55 => ( 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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Bernoulli_inequality
% 5.24/5.55 thf(fact_6926_divmod__step__nat__def,axiom,
% 5.24/5.55 ( unique5026877609467782581ep_nat
% 5.24/5.55 = ( ^ [L: num] :
% 5.24/5.55 ( produc2626176000494625587at_nat
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_step_nat_def
% 5.24/5.55 thf(fact_6927_divmod__step__int__def,axiom,
% 5.24/5.55 ( unique5024387138958732305ep_int
% 5.24/5.55 = ( ^ [L: num] :
% 5.24/5.55 ( produc4245557441103728435nt_int
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_step_int_def
% 5.24/5.55 thf(fact_6928_Bernoulli__inequality__even,axiom,
% 5.24/5.55 ! [N: nat,X: real] :
% 5.24/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.55 => ( 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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Bernoulli_inequality_even
% 5.24/5.55 thf(fact_6929_double__gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum
% 5.24/5.55 thf(fact_6930_double__gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum
% 5.24/5.55 thf(fact_6931_double__gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum
% 5.24/5.55 thf(fact_6932_double__gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum
% 5.24/5.55 thf(fact_6933_double__gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum
% 5.24/5.55 thf(fact_6934_double__arith__series,axiom,
% 5.24/5.55 ! [A: complex,D: complex,N: nat] :
% 5.24/5.55 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.24/5.55 @ ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_arith_series
% 5.24/5.55 thf(fact_6935_double__arith__series,axiom,
% 5.24/5.55 ! [A: int,D: int,N: nat] :
% 5.24/5.55 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.24/5.55 @ ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_arith_series
% 5.24/5.55 thf(fact_6936_double__arith__series,axiom,
% 5.24/5.55 ! [A: rat,D: rat,N: nat] :
% 5.24/5.55 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.24/5.55 @ ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_arith_series
% 5.24/5.55 thf(fact_6937_double__arith__series,axiom,
% 5.24/5.55 ! [A: nat,D: nat,N: nat] :
% 5.24/5.55 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.24/5.55 @ ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_arith_series
% 5.24/5.55 thf(fact_6938_double__arith__series,axiom,
% 5.24/5.55 ! [A: real,D: real,N: nat] :
% 5.24/5.55 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_arith_series
% 5.24/5.55 thf(fact_6939_divmod__step__def,axiom,
% 5.24/5.55 ( unique5026877609467782581ep_nat
% 5.24/5.55 = ( ^ [L: num] :
% 5.24/5.55 ( produc2626176000494625587at_nat
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_step_def
% 5.24/5.55 thf(fact_6940_divmod__step__def,axiom,
% 5.24/5.55 ( unique5024387138958732305ep_int
% 5.24/5.55 = ( ^ [L: num] :
% 5.24/5.55 ( produc4245557441103728435nt_int
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_step_def
% 5.24/5.55 thf(fact_6941_divmod__step__def,axiom,
% 5.24/5.55 ( unique4921790084139445826nteger
% 5.24/5.55 = ( ^ [L: num] :
% 5.24/5.55 ( produc6916734918728496179nteger
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_step_def
% 5.24/5.55 thf(fact_6942_gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.55 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % gauss_sum
% 5.24/5.55 thf(fact_6943_gauss__sum,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.55 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % gauss_sum
% 5.24/5.55 thf(fact_6944_arith__series,axiom,
% 5.24/5.55 ! [A: int,D: int,N: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arith_series
% 5.24/5.55 thf(fact_6945_arith__series,axiom,
% 5.24/5.55 ! [A: nat,D: nat,N: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D ) )
% 5.24/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arith_series
% 5.24/5.55 thf(fact_6946_double__gauss__sum__from__Suc__0,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.24/5.55 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum_from_Suc_0
% 5.24/5.55 thf(fact_6947_double__gauss__sum__from__Suc__0,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.24/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum_from_Suc_0
% 5.24/5.55 thf(fact_6948_double__gauss__sum__from__Suc__0,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.24/5.55 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum_from_Suc_0
% 5.24/5.55 thf(fact_6949_double__gauss__sum__from__Suc__0,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.24/5.55 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum_from_Suc_0
% 5.24/5.55 thf(fact_6950_double__gauss__sum__from__Suc__0,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % double_gauss_sum_from_Suc_0
% 5.24/5.55 thf(fact_6951_sum__gp__offset,axiom,
% 5.24/5.55 ! [X: complex,M: nat,N: nat] :
% 5.24/5.55 ( ( ( X = one_one_complex )
% 5.24/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.55 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.24/5.55 & ( ( X != one_one_complex )
% 5.24/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_gp_offset
% 5.24/5.55 thf(fact_6952_sum__gp__offset,axiom,
% 5.24/5.55 ! [X: rat,M: nat,N: nat] :
% 5.24/5.55 ( ( ( X = one_one_rat )
% 5.24/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.55 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.24/5.55 & ( ( X != one_one_rat )
% 5.24/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_gp_offset
% 5.24/5.55 thf(fact_6953_sum__gp__offset,axiom,
% 5.24/5.55 ! [X: real,M: nat,N: nat] :
% 5.24/5.55 ( ( ( X = one_one_real )
% 5.24/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.55 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.24/5.55 & ( ( X != one_one_real )
% 5.24/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_gp_offset
% 5.24/5.55 thf(fact_6954_linear__plus__1__le__power,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( 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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % linear_plus_1_le_power
% 5.24/5.55 thf(fact_6955_nat__approx__posE,axiom,
% 5.24/5.55 ! [E: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ E )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_approx_posE
% 5.24/5.55 thf(fact_6956_nat__approx__posE,axiom,
% 5.24/5.55 ! [E: rat] :
% 5.24/5.55 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.24/5.55 => ~ ! [N3: nat] :
% 5.24/5.55 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_approx_posE
% 5.24/5.55 thf(fact_6957_floor__exists,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [Z: int] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 5.24/5.55 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z @ one_one_int ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % floor_exists
% 5.24/5.55 thf(fact_6958_floor__exists,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [Z: int] :
% 5.24/5.55 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 5.24/5.55 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z @ one_one_int ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % floor_exists
% 5.24/5.55 thf(fact_6959_floor__exists1,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [X3: int] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 5.24/5.55 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.24/5.55 & ! [Y5: int] :
% 5.24/5.55 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X )
% 5.24/5.55 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.24/5.55 => ( Y5 = X3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % floor_exists1
% 5.24/5.55 thf(fact_6960_floor__exists1,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [X3: int] :
% 5.24/5.55 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 5.24/5.55 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.24/5.55 & ! [Y5: int] :
% 5.24/5.55 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X )
% 5.24/5.55 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.24/5.55 => ( Y5 = X3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % floor_exists1
% 5.24/5.55 thf(fact_6961_monoseq__arctan__series,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.55 => ( topolo6980174941875973593q_real
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_arctan_series
% 5.24/5.55 thf(fact_6962_lemma__termdiff3,axiom,
% 5.24/5.55 ! [H2: real,Z2: real,K5: real,N: nat] :
% 5.24/5.55 ( ( H2 != zero_zero_real )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ K5 )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z2 @ H2 ) ) @ K5 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ N ) @ ( power_power_real @ Z2 @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z2 @ ( 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 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff3
% 5.24/5.55 thf(fact_6963_lemma__termdiff3,axiom,
% 5.24/5.55 ! [H2: complex,Z2: complex,K5: real,N: nat] :
% 5.24/5.55 ( ( H2 != zero_zero_complex )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ K5 )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z2 @ H2 ) ) @ K5 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ N ) @ ( power_power_complex @ Z2 @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z2 @ ( 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 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff3
% 5.24/5.55 thf(fact_6964_case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc8763457246119570046nteger,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 5.24/5.55 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.24/5.55 => ( C @ A3 @ B2 ) )
% 5.24/5.55 => ( produc127349428274296955eger_o @ C @ P6 ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI2
% 5.24/5.55 thf(fact_6965_case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 5.24/5.55 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 5.24/5.55 => ( C @ A3 @ B2 ) )
% 5.24/5.55 => ( produc6253627499356882019eger_o @ C @ P6 ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI2
% 5.24/5.55 thf(fact_6966_case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.24/5.55 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 5.24/5.55 => ( C @ A3 @ B2 ) )
% 5.24/5.55 => ( produc1573362020775583542_int_o @ C @ P6 ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI2
% 5.24/5.55 thf(fact_6967_case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.24/5.55 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.24/5.55 => ( C @ A3 @ B2 ) )
% 5.24/5.55 => ( produc2558449545302689196_int_o @ C @ P6 ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI2
% 5.24/5.55 thf(fact_6968_case__prodI2,axiom,
% 5.24/5.55 ! [P6: product_prod_int_int,C: int > int > $o] :
% 5.24/5.55 ( ! [A3: int,B2: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.55 => ( C @ A3 @ B2 ) )
% 5.24/5.55 => ( produc4947309494688390418_int_o @ C @ P6 ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI2
% 5.24/5.55 thf(fact_6969_case__prodI,axiom,
% 5.24/5.55 ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( F @ A @ B )
% 5.24/5.55 => ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI
% 5.24/5.55 thf(fact_6970_case__prodI,axiom,
% 5.24/5.55 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( F @ A @ B )
% 5.24/5.55 => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI
% 5.24/5.55 thf(fact_6971_case__prodI,axiom,
% 5.24/5.55 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.24/5.55 ( ( F @ A @ B )
% 5.24/5.55 => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI
% 5.24/5.55 thf(fact_6972_case__prodI,axiom,
% 5.24/5.55 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.24/5.55 ( ( F @ A @ B )
% 5.24/5.55 => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI
% 5.24/5.55 thf(fact_6973_case__prodI,axiom,
% 5.24/5.55 ! [F: int > int > $o,A: int,B: int] :
% 5.24/5.55 ( ( F @ A @ B )
% 5.24/5.55 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI
% 5.24/5.55 thf(fact_6974_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: product_prod_int_int,Z2: nat,C: int > int > set_nat] :
% 5.24/5.55 ( ! [A3: int,B2: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6975_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: product_prod_int_int,Z2: int,C: int > int > set_int] :
% 5.24/5.55 ( ! [A3: int,B2: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.55 => ( member_int @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6976_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: product_prod_int_int,Z2: real,C: int > int > set_real] :
% 5.24/5.55 ( ! [A3: int,B2: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.55 => ( member_real @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_real @ Z2 @ ( produc6452406959799940328t_real @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6977_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: product_prod_int_int,Z2: complex,C: int > int > set_complex] :
% 5.24/5.55 ( ! [A3: int,B2: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.55 => ( member_complex @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_complex @ Z2 @ ( produc8580519160106071146omplex @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6978_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: product_prod_int_int,Z2: product_prod_nat_nat,C: int > int > set_Pr1261947904930325089at_nat] :
% 5.24/5.55 ( ! [A3: int,B2: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.24/5.55 => ( member8440522571783428010at_nat @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member8440522571783428010at_nat @ Z2 @ ( produc1656060378719767003at_nat @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6979_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc8763457246119570046nteger,Z2: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 5.24/5.55 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( produc3558942015123893603et_nat @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6980_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc8763457246119570046nteger,Z2: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 5.24/5.55 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.24/5.55 => ( member_int @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_int @ Z2 @ ( produc8604463032469472703et_int @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6981_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc8763457246119570046nteger,Z2: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real] :
% 5.24/5.55 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.24/5.55 => ( member_real @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_real @ Z2 @ ( produc815715089573277247t_real @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6982_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc8763457246119570046nteger,Z2: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex] :
% 5.24/5.55 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.24/5.55 => ( member_complex @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_complex @ Z2 @ ( produc2592262431452330817omplex @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6983_mem__case__prodI2,axiom,
% 5.24/5.55 ! [P6: produc7773217078559923341nt_int,Z2: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 5.24/5.55 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( C @ A3 @ B2 ) ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( produc8289552606927098482et_nat @ C @ P6 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI2
% 5.24/5.55 thf(fact_6984_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: nat,C: int > int > set_nat,A: int,B: int] :
% 5.24/5.55 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6985_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: int,C: int > int > set_int,A: int,B: int] :
% 5.24/5.55 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6986_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: real,C: int > int > set_real,A: int,B: int] :
% 5.24/5.55 ( ( member_real @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_real @ Z2 @ ( produc6452406959799940328t_real @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6987_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: complex,C: int > int > set_complex,A: int,B: int] :
% 5.24/5.55 ( ( member_complex @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_complex @ Z2 @ ( produc8580519160106071146omplex @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6988_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: product_prod_nat_nat,C: int > int > set_Pr1261947904930325089at_nat,A: int,B: int] :
% 5.24/5.55 ( ( member8440522571783428010at_nat @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member8440522571783428010at_nat @ Z2 @ ( produc1656060378719767003at_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6989_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( produc3558942015123893603et_nat @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6990_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_int @ Z2 @ ( produc8604463032469472703et_int @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6991_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( member_real @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_real @ Z2 @ ( produc815715089573277247t_real @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6992_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( member_complex @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_complex @ Z2 @ ( produc2592262431452330817omplex @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6993_mem__case__prodI,axiom,
% 5.24/5.55 ! [Z2: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.24/5.55 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 5.24/5.55 => ( member_nat @ Z2 @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodI
% 5.24/5.55 thf(fact_6994_case__prodI2_H,axiom,
% 5.24/5.55 ! [P6: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.24/5.55 ( ! [A3: nat,B2: nat] :
% 5.24/5.55 ( ( ( product_Pair_nat_nat @ A3 @ B2 )
% 5.24/5.55 = P6 )
% 5.24/5.55 => ( C @ A3 @ B2 @ X ) )
% 5.24/5.55 => ( produc8739625826339149834_nat_o @ C @ P6 @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodI2'
% 5.24/5.55 thf(fact_6995_nat__int__comparison_I1_J,axiom,
% 5.24/5.55 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.24/5.55 = ( ^ [A4: nat,B3: nat] :
% 5.24/5.55 ( ( semiri1314217659103216013at_int @ A4 )
% 5.24/5.55 = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nat_int_comparison(1)
% 5.24/5.55 thf(fact_6996_int__if,axiom,
% 5.24/5.55 ! [P: $o,A: nat,B: nat] :
% 5.24/5.55 ( ( P
% 5.24/5.55 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.24/5.55 = ( semiri1314217659103216013at_int @ A ) ) )
% 5.24/5.55 & ( ~ P
% 5.24/5.55 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.24/5.55 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % int_if
% 5.24/5.55 thf(fact_6997_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: nat,C: int > int > set_nat,P6: product_prod_int_int] :
% 5.24/5.55 ( ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: int,Y3: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_nat @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_6998_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: int,C: int > int > set_int,P6: product_prod_int_int] :
% 5.24/5.55 ( ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: int,Y3: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_int @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_6999_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: real,C: int > int > set_real,P6: product_prod_int_int] :
% 5.24/5.55 ( ( member_real @ Z2 @ ( produc6452406959799940328t_real @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: int,Y3: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_real @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7000_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: complex,C: int > int > set_complex,P6: product_prod_int_int] :
% 5.24/5.55 ( ( member_complex @ Z2 @ ( produc8580519160106071146omplex @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: int,Y3: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_complex @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7001_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: product_prod_nat_nat,C: int > int > set_Pr1261947904930325089at_nat,P6: product_prod_int_int] :
% 5.24/5.55 ( ( member8440522571783428010at_nat @ Z2 @ ( produc1656060378719767003at_nat @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: int,Y3: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member8440522571783428010at_nat @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7002_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P6: produc8763457246119570046nteger] :
% 5.24/5.55 ( ( member_nat @ Z2 @ ( produc3558942015123893603et_nat @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_nat @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7003_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P6: produc8763457246119570046nteger] :
% 5.24/5.55 ( ( member_int @ Z2 @ ( produc8604463032469472703et_int @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_int @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7004_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,P6: produc8763457246119570046nteger] :
% 5.24/5.55 ( ( member_real @ Z2 @ ( produc815715089573277247t_real @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_real @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7005_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,P6: produc8763457246119570046nteger] :
% 5.24/5.55 ( ( member_complex @ Z2 @ ( produc2592262431452330817omplex @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_complex @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7006_mem__case__prodE,axiom,
% 5.24/5.55 ! [Z2: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P6: produc7773217078559923341nt_int] :
% 5.24/5.55 ( ( member_nat @ Z2 @ ( produc8289552606927098482et_nat @ C @ P6 ) )
% 5.24/5.55 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( member_nat @ Z2 @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mem_case_prodE
% 5.24/5.55 thf(fact_7007_case__prodE,axiom,
% 5.24/5.55 ! [C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P6: produc8763457246119570046nteger] :
% 5.24/5.55 ( ( produc127349428274296955eger_o @ C @ P6 )
% 5.24/5.55 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodE
% 5.24/5.55 thf(fact_7008_case__prodE,axiom,
% 5.24/5.55 ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P6: produc1908205239877642774nteger] :
% 5.24/5.55 ( ( produc6253627499356882019eger_o @ C @ P6 )
% 5.24/5.55 => ~ ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc8603105652947943368nteger @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodE
% 5.24/5.55 thf(fact_7009_case__prodE,axiom,
% 5.24/5.55 ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P6: produc2285326912895808259nt_int] :
% 5.24/5.55 ( ( produc1573362020775583542_int_o @ C @ P6 )
% 5.24/5.55 => ~ ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc5700946648718959541nt_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodE
% 5.24/5.55 thf(fact_7010_case__prodE,axiom,
% 5.24/5.55 ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P6: produc7773217078559923341nt_int] :
% 5.24/5.55 ( ( produc2558449545302689196_int_o @ C @ P6 )
% 5.24/5.55 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodE
% 5.24/5.55 thf(fact_7011_case__prodE,axiom,
% 5.24/5.55 ! [C: int > int > $o,P6: product_prod_int_int] :
% 5.24/5.55 ( ( produc4947309494688390418_int_o @ C @ P6 )
% 5.24/5.55 => ~ ! [X3: int,Y3: int] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodE
% 5.24/5.55 thf(fact_7012_case__prodD,axiom,
% 5.24/5.55 ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) )
% 5.24/5.55 => ( F @ A @ B ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodD
% 5.24/5.55 thf(fact_7013_case__prodD,axiom,
% 5.24/5.55 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.24/5.55 ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 5.24/5.55 => ( F @ A @ B ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodD
% 5.24/5.55 thf(fact_7014_case__prodD,axiom,
% 5.24/5.55 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.24/5.55 ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 5.24/5.55 => ( F @ A @ B ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodD
% 5.24/5.55 thf(fact_7015_case__prodD,axiom,
% 5.24/5.55 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.24/5.55 ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 5.24/5.55 => ( F @ A @ B ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodD
% 5.24/5.55 thf(fact_7016_case__prodD,axiom,
% 5.24/5.55 ! [F: int > int > $o,A: int,B: int] :
% 5.24/5.55 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.24/5.55 => ( F @ A @ B ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodD
% 5.24/5.55 thf(fact_7017_case__prodE_H,axiom,
% 5.24/5.55 ! [C: nat > nat > product_prod_nat_nat > $o,P6: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 5.24/5.55 ( ( produc8739625826339149834_nat_o @ C @ P6 @ Z2 )
% 5.24/5.55 => ~ ! [X3: nat,Y3: nat] :
% 5.24/5.55 ( ( P6
% 5.24/5.55 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.24/5.55 => ~ ( C @ X3 @ Y3 @ Z2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodE'
% 5.24/5.55 thf(fact_7018_case__prodD_H,axiom,
% 5.24/5.55 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.24/5.55 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.24/5.55 => ( R @ A @ B @ C ) ) ).
% 5.24/5.55
% 5.24/5.55 % case_prodD'
% 5.24/5.55 thf(fact_7019_complex__mod__triangle__ineq2,axiom,
% 5.24/5.55 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.24/5.55
% 5.24/5.55 % complex_mod_triangle_ineq2
% 5.24/5.55 thf(fact_7020_monoseq__realpow,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.55 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_realpow
% 5.24/5.55 thf(fact_7021_Divides_Oadjust__div__def,axiom,
% 5.24/5.55 ( adjust_div
% 5.24/5.55 = ( produc8211389475949308722nt_int
% 5.24/5.55 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Divides.adjust_div_def
% 5.24/5.55 thf(fact_7022_real__arch__simple,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_arch_simple
% 5.24/5.55 thf(fact_7023_real__arch__simple,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_arch_simple
% 5.24/5.55 thf(fact_7024_reals__Archimedean2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.24/5.55
% 5.24/5.55 % reals_Archimedean2
% 5.24/5.55 thf(fact_7025_reals__Archimedean2,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.24/5.55
% 5.24/5.55 % reals_Archimedean2
% 5.24/5.55 thf(fact_7026_exists__least__lemma,axiom,
% 5.24/5.55 ! [P: nat > $o] :
% 5.24/5.55 ( ~ ( P @ zero_zero_nat )
% 5.24/5.55 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.24/5.55 => ? [N3: nat] :
% 5.24/5.55 ( ~ ( P @ N3 )
% 5.24/5.55 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exists_least_lemma
% 5.24/5.55 thf(fact_7027_ex__le__of__int,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [Z: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ).
% 5.24/5.55
% 5.24/5.55 % ex_le_of_int
% 5.24/5.55 thf(fact_7028_ex__le__of__int,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [Z: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ).
% 5.24/5.55
% 5.24/5.55 % ex_le_of_int
% 5.24/5.55 thf(fact_7029_ex__less__of__int,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [Z: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ).
% 5.24/5.55
% 5.24/5.55 % ex_less_of_int
% 5.24/5.55 thf(fact_7030_ex__less__of__int,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [Z: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ).
% 5.24/5.55
% 5.24/5.55 % ex_less_of_int
% 5.24/5.55 thf(fact_7031_ex__of__int__less,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ? [Z: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ).
% 5.24/5.55
% 5.24/5.55 % ex_of_int_less
% 5.24/5.55 thf(fact_7032_ex__of__int__less,axiom,
% 5.24/5.55 ! [X: rat] :
% 5.24/5.55 ? [Z: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ).
% 5.24/5.55
% 5.24/5.55 % ex_of_int_less
% 5.24/5.55 thf(fact_7033_ex__less__of__nat__mult,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % ex_less_of_nat_mult
% 5.24/5.55 thf(fact_7034_ex__less__of__nat__mult,axiom,
% 5.24/5.55 ! [X: rat,Y4: rat] :
% 5.24/5.55 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.55 => ? [N3: nat] : ( ord_less_rat @ Y4 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % ex_less_of_nat_mult
% 5.24/5.55 thf(fact_7035_norm__divide__numeral,axiom,
% 5.24/5.55 ! [A: real,W2: num] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_divide_numeral
% 5.24/5.55 thf(fact_7036_norm__divide__numeral,axiom,
% 5.24/5.55 ! [A: complex,W2: num] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_divide_numeral
% 5.24/5.55 thf(fact_7037_norm__mult__numeral1,axiom,
% 5.24/5.55 ! [W2: num,A: real] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 5.24/5.55 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_numeral1
% 5.24/5.55 thf(fact_7038_norm__mult__numeral1,axiom,
% 5.24/5.55 ! [W2: num,A: complex] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 5.24/5.55 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_numeral1
% 5.24/5.55 thf(fact_7039_norm__mult__numeral2,axiom,
% 5.24/5.55 ! [A: real,W2: num] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.55 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_numeral2
% 5.24/5.55 thf(fact_7040_norm__mult__numeral2,axiom,
% 5.24/5.55 ! [A: complex,W2: num] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.55 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_numeral2
% 5.24/5.55 thf(fact_7041_norm__neg__numeral,axiom,
% 5.24/5.55 ! [W2: num] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.55 = ( numeral_numeral_real @ W2 ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_neg_numeral
% 5.24/5.55 thf(fact_7042_norm__neg__numeral,axiom,
% 5.24/5.55 ! [W2: num] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.55 = ( numeral_numeral_real @ W2 ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_neg_numeral
% 5.24/5.55 thf(fact_7043_norm__numeral,axiom,
% 5.24/5.55 ! [W2: num] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.55 = ( numeral_numeral_real @ W2 ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_numeral
% 5.24/5.55 thf(fact_7044_norm__numeral,axiom,
% 5.24/5.55 ! [W2: num] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.55 = ( numeral_numeral_real @ W2 ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_numeral
% 5.24/5.55 thf(fact_7045_norm__one,axiom,
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % norm_one
% 5.24/5.55 thf(fact_7046_norm__one,axiom,
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % norm_one
% 5.24/5.55 thf(fact_7047_norm__mult,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y4 ) )
% 5.24/5.55 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult
% 5.24/5.55 thf(fact_7048_norm__mult,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y4 ) )
% 5.24/5.55 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult
% 5.24/5.55 thf(fact_7049_norm__divide,axiom,
% 5.24/5.55 ! [A: real,B: real] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_divide
% 5.24/5.55 thf(fact_7050_norm__divide,axiom,
% 5.24/5.55 ! [A: complex,B: complex] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_divide
% 5.24/5.55 thf(fact_7051_norm__power,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 5.24/5.55 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_power
% 5.24/5.55 thf(fact_7052_norm__power,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 5.24/5.55 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_power
% 5.24/5.55 thf(fact_7053_norm__uminus__minus,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y4 ) )
% 5.24/5.55 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_uminus_minus
% 5.24/5.55 thf(fact_7054_norm__uminus__minus,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y4 ) )
% 5.24/5.55 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_uminus_minus
% 5.24/5.55 thf(fact_7055_nonzero__norm__divide,axiom,
% 5.24/5.55 ! [B: real,A: real] :
% 5.24/5.55 ( ( B != zero_zero_real )
% 5.24/5.55 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nonzero_norm_divide
% 5.24/5.55 thf(fact_7056_nonzero__norm__divide,axiom,
% 5.24/5.55 ! [B: complex,A: complex] :
% 5.24/5.55 ( ( B != zero_zero_complex )
% 5.24/5.55 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % nonzero_norm_divide
% 5.24/5.55 thf(fact_7057_power__eq__imp__eq__norm,axiom,
% 5.24/5.55 ! [W2: real,N: nat,Z2: real] :
% 5.24/5.55 ( ( ( power_power_real @ W2 @ N )
% 5.24/5.55 = ( power_power_real @ Z2 @ N ) )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( real_V7735802525324610683m_real @ W2 )
% 5.24/5.55 = ( real_V7735802525324610683m_real @ Z2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_eq_imp_eq_norm
% 5.24/5.55 thf(fact_7058_power__eq__imp__eq__norm,axiom,
% 5.24/5.55 ! [W2: complex,N: nat,Z2: complex] :
% 5.24/5.55 ( ( ( power_power_complex @ W2 @ N )
% 5.24/5.55 = ( power_power_complex @ Z2 @ N ) )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( real_V1022390504157884413omplex @ W2 )
% 5.24/5.55 = ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_eq_imp_eq_norm
% 5.24/5.55 thf(fact_7059_norm__mult__less,axiom,
% 5.24/5.55 ! [X: real,R2: real,Y4: real,S2: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y4 ) @ S2 )
% 5.24/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y4 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_less
% 5.24/5.55 thf(fact_7060_norm__mult__less,axiom,
% 5.24/5.55 ! [X: complex,R2: real,Y4: complex,S2: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y4 ) @ S2 )
% 5.24/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y4 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_less
% 5.24/5.55 thf(fact_7061_norm__mult__ineq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y4 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_ineq
% 5.24/5.55 thf(fact_7062_norm__mult__ineq,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y4 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_mult_ineq
% 5.24/5.55 thf(fact_7063_norm__triangle__lt,axiom,
% 5.24/5.55 ! [X: real,Y4: real,E: real] :
% 5.24/5.55 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E )
% 5.24/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_lt
% 5.24/5.55 thf(fact_7064_norm__triangle__lt,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex,E: real] :
% 5.24/5.55 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E )
% 5.24/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_lt
% 5.24/5.55 thf(fact_7065_norm__add__less,axiom,
% 5.24/5.55 ! [X: real,R2: real,Y4: real,S2: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y4 ) @ S2 )
% 5.24/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_add_less
% 5.24/5.55 thf(fact_7066_norm__add__less,axiom,
% 5.24/5.55 ! [X: complex,R2: real,Y4: complex,S2: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y4 ) @ S2 )
% 5.24/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_add_less
% 5.24/5.55 thf(fact_7067_norm__power__ineq,axiom,
% 5.24/5.55 ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_power_ineq
% 5.24/5.55 thf(fact_7068_norm__power__ineq,axiom,
% 5.24/5.55 ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_power_ineq
% 5.24/5.55 thf(fact_7069_norm__triangle__mono,axiom,
% 5.24/5.55 ! [A: real,R2: real,B: real,S2: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_mono
% 5.24/5.55 thf(fact_7070_norm__triangle__mono,axiom,
% 5.24/5.55 ! [A: complex,R2: real,B: complex,S2: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_mono
% 5.24/5.55 thf(fact_7071_norm__triangle__ineq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_ineq
% 5.24/5.55 thf(fact_7072_norm__triangle__ineq,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_ineq
% 5.24/5.55 thf(fact_7073_norm__triangle__le,axiom,
% 5.24/5.55 ! [X: real,Y4: real,E: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_le
% 5.24/5.55 thf(fact_7074_norm__triangle__le,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex,E: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_le
% 5.24/5.55 thf(fact_7075_norm__add__leD,axiom,
% 5.24/5.55 ! [A: real,B: real,C: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_add_leD
% 5.24/5.55 thf(fact_7076_norm__add__leD,axiom,
% 5.24/5.55 ! [A: complex,B: complex,C: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_add_leD
% 5.24/5.55 thf(fact_7077_norm__diff__triangle__less,axiom,
% 5.24/5.55 ! [X: real,Y4: real,E1: real,Z2: real,E22: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) @ E1 )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y4 @ Z2 ) ) @ E22 )
% 5.24/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_triangle_less
% 5.24/5.55 thf(fact_7078_norm__diff__triangle__less,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex,E1: real,Z2: complex,E22: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) @ E1 )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y4 @ Z2 ) ) @ E22 )
% 5.24/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_triangle_less
% 5.24/5.55 thf(fact_7079_norm__triangle__le__diff,axiom,
% 5.24/5.55 ! [X: real,Y4: real,E: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_le_diff
% 5.24/5.55 thf(fact_7080_norm__triangle__le__diff,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex,E: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) @ E ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_le_diff
% 5.24/5.55 thf(fact_7081_norm__diff__triangle__le,axiom,
% 5.24/5.55 ! [X: real,Y4: real,E1: real,Z2: real,E22: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) @ E1 )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y4 @ Z2 ) ) @ E22 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_triangle_le
% 5.24/5.55 thf(fact_7082_norm__diff__triangle__le,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex,E1: real,Z2: complex,E22: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) @ E1 )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y4 @ Z2 ) ) @ E22 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_triangle_le
% 5.24/5.55 thf(fact_7083_norm__triangle__ineq4,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_ineq4
% 5.24/5.55 thf(fact_7084_norm__triangle__ineq4,axiom,
% 5.24/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_ineq4
% 5.24/5.55 thf(fact_7085_norm__triangle__sub,axiom,
% 5.24/5.55 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y4 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_sub
% 5.24/5.55 thf(fact_7086_norm__triangle__sub,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y4 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_triangle_sub
% 5.24/5.55 thf(fact_7087_norm__diff__ineq,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_ineq
% 5.24/5.55 thf(fact_7088_norm__diff__ineq,axiom,
% 5.24/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_ineq
% 5.24/5.55 thf(fact_7089_power__eq__1__iff,axiom,
% 5.24/5.55 ! [W2: real,N: nat] :
% 5.24/5.55 ( ( ( power_power_real @ W2 @ N )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_eq_1_iff
% 5.24/5.55 thf(fact_7090_power__eq__1__iff,axiom,
% 5.24/5.55 ! [W2: complex,N: nat] :
% 5.24/5.55 ( ( ( power_power_complex @ W2 @ N )
% 5.24/5.55 = one_one_complex )
% 5.24/5.55 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 | ( N = zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_eq_1_iff
% 5.24/5.55 thf(fact_7091_norm__diff__triangle__ineq,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_triangle_ineq
% 5.24/5.55 thf(fact_7092_norm__diff__triangle__ineq,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_diff_triangle_ineq
% 5.24/5.55 thf(fact_7093_square__norm__one,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ( ( real_V7735802525324610683m_real @ X )
% 5.24/5.55 = one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % square_norm_one
% 5.24/5.55 thf(fact_7094_square__norm__one,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = one_one_complex )
% 5.24/5.55 => ( ( real_V1022390504157884413omplex @ X )
% 5.24/5.55 = one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % square_norm_one
% 5.24/5.55 thf(fact_7095_norm__power__diff,axiom,
% 5.24/5.55 ! [Z2: real,W2: real,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ one_one_real )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W2 ) @ one_one_real )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z2 @ M ) @ ( power_power_real @ W2 @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z2 @ W2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_power_diff
% 5.24/5.55 thf(fact_7096_norm__power__diff,axiom,
% 5.24/5.55 ! [Z2: complex,W2: complex,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ one_one_real )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W2 ) @ one_one_real )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z2 @ M ) @ ( power_power_complex @ W2 @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z2 @ W2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % norm_power_diff
% 5.24/5.55 thf(fact_7097_ln__series,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 => ( ( ln_ln_real @ X )
% 5.24/5.55 = ( suminf_real
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % ln_series
% 5.24/5.55 thf(fact_7098_of__nat__code__if,axiom,
% 5.24/5.55 ( semiri8010041392384452111omplex
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 5.24/5.55 @ ( produc1917071388513777916omplex
% 5.24/5.55 @ ^ [M2: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ one_one_complex ) )
% 5.24/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code_if
% 5.24/5.55 thf(fact_7099_of__nat__code__if,axiom,
% 5.24/5.55 ( semiri1314217659103216013at_int
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 5.24/5.55 @ ( produc6840382203811409530at_int
% 5.24/5.55 @ ^ [M2: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ one_one_int ) )
% 5.24/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code_if
% 5.24/5.55 thf(fact_7100_of__nat__code__if,axiom,
% 5.24/5.55 ( semiri5074537144036343181t_real
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.24/5.55 @ ( produc1703576794950452218t_real
% 5.24/5.55 @ ^ [M2: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ one_one_real ) )
% 5.24/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code_if
% 5.24/5.55 thf(fact_7101_of__nat__code__if,axiom,
% 5.24/5.55 ( semiri1316708129612266289at_nat
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.24/5.55 @ ( produc6842872674320459806at_nat
% 5.24/5.55 @ ^ [M2: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M2 ) ) @ one_one_nat ) )
% 5.24/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code_if
% 5.24/5.55 thf(fact_7102_of__nat__code__if,axiom,
% 5.24/5.55 ( semiri681578069525770553at_rat
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 5.24/5.55 @ ( produc6207742614233964070at_rat
% 5.24/5.55 @ ^ [M2: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) )
% 5.24/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code_if
% 5.24/5.55 thf(fact_7103_divmod__nat__if,axiom,
% 5.24/5.55 ( divmod_nat
% 5.24/5.55 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.55 ( if_Pro6206227464963214023at_nat
% 5.24/5.55 @ ( ( N2 = zero_zero_nat )
% 5.24/5.55 | ( ord_less_nat @ M2 @ N2 ) )
% 5.24/5.55 @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 5.24/5.55 @ ( produc2626176000494625587at_nat
% 5.24/5.55 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.24/5.55 @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_nat_if
% 5.24/5.55 thf(fact_7104_arctan__series,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.55 => ( ( arctan @ X )
% 5.24/5.55 = ( suminf_real
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_series
% 5.24/5.55 thf(fact_7105_round__unique,axiom,
% 5.24/5.55 ! [X: real,Y4: int] :
% 5.24/5.55 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y4 ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 => ( ( archim8280529875227126926d_real @ X )
% 5.24/5.55 = Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_unique
% 5.24/5.55 thf(fact_7106_round__unique,axiom,
% 5.24/5.55 ! [X: rat,Y4: int] :
% 5.24/5.55 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y4 ) )
% 5.24/5.55 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 => ( ( archim7778729529865785530nd_rat @ X )
% 5.24/5.55 = Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_unique
% 5.24/5.55 thf(fact_7107_lemma__termdiff2,axiom,
% 5.24/5.55 ! [H2: complex,Z2: complex,N: nat] :
% 5.24/5.55 ( ( H2 != zero_zero_complex )
% 5.24/5.55 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ N ) @ ( power_power_complex @ Z2 @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.24/5.55 = ( times_times_complex @ H2
% 5.24/5.55 @ ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [P4: nat] :
% 5.24/5.55 ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ Q4 ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff2
% 5.24/5.55 thf(fact_7108_lemma__termdiff2,axiom,
% 5.24/5.55 ! [H2: rat,Z2: rat,N: nat] :
% 5.24/5.55 ( ( H2 != zero_zero_rat )
% 5.24/5.55 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ N ) @ ( power_power_rat @ Z2 @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.24/5.55 = ( times_times_rat @ H2
% 5.24/5.55 @ ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [P4: nat] :
% 5.24/5.55 ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ Q4 ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff2
% 5.24/5.55 thf(fact_7109_lemma__termdiff2,axiom,
% 5.24/5.55 ! [H2: real,Z2: real,N: nat] :
% 5.24/5.55 ( ( H2 != zero_zero_real )
% 5.24/5.55 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ N ) @ ( power_power_real @ Z2 @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.24/5.55 = ( times_times_real @ H2
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [P4: nat] :
% 5.24/5.55 ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ Q4 ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff2
% 5.24/5.55 thf(fact_7110_lessThan__iff,axiom,
% 5.24/5.55 ! [I2: rat,K: rat] :
% 5.24/5.55 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 5.24/5.55 = ( ord_less_rat @ I2 @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_iff
% 5.24/5.55 thf(fact_7111_lessThan__iff,axiom,
% 5.24/5.55 ! [I2: num,K: num] :
% 5.24/5.55 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.24/5.55 = ( ord_less_num @ I2 @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_iff
% 5.24/5.55 thf(fact_7112_lessThan__iff,axiom,
% 5.24/5.55 ! [I2: int,K: int] :
% 5.24/5.55 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.24/5.55 = ( ord_less_int @ I2 @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_iff
% 5.24/5.55 thf(fact_7113_lessThan__iff,axiom,
% 5.24/5.55 ! [I2: nat,K: nat] :
% 5.24/5.55 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.24/5.55 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_iff
% 5.24/5.55 thf(fact_7114_lessThan__iff,axiom,
% 5.24/5.55 ! [I2: real,K: real] :
% 5.24/5.55 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 5.24/5.55 = ( ord_less_real @ I2 @ K ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_iff
% 5.24/5.55 thf(fact_7115_lessThan__subset__iff,axiom,
% 5.24/5.55 ! [X: rat,Y4: rat] :
% 5.24/5.55 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_subset_iff
% 5.24/5.55 thf(fact_7116_lessThan__subset__iff,axiom,
% 5.24/5.55 ! [X: num,Y4: num] :
% 5.24/5.55 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_num @ X @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_subset_iff
% 5.24/5.55 thf(fact_7117_lessThan__subset__iff,axiom,
% 5.24/5.55 ! [X: int,Y4: int] :
% 5.24/5.55 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_int @ X @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_subset_iff
% 5.24/5.55 thf(fact_7118_lessThan__subset__iff,axiom,
% 5.24/5.55 ! [X: nat,Y4: nat] :
% 5.24/5.55 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_nat @ X @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_subset_iff
% 5.24/5.55 thf(fact_7119_lessThan__subset__iff,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_subset_iff
% 5.24/5.55 thf(fact_7120_round__numeral,axiom,
% 5.24/5.55 ! [N: num] :
% 5.24/5.55 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.24/5.55 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_numeral
% 5.24/5.55 thf(fact_7121_round__numeral,axiom,
% 5.24/5.55 ! [N: num] :
% 5.24/5.55 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.24/5.55 = ( numeral_numeral_int @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_numeral
% 5.24/5.55 thf(fact_7122_lessThan__0,axiom,
% 5.24/5.55 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.24/5.55 = bot_bot_set_nat ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_0
% 5.24/5.55 thf(fact_7123_round__1,axiom,
% 5.24/5.55 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % round_1
% 5.24/5.55 thf(fact_7124_round__1,axiom,
% 5.24/5.55 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % round_1
% 5.24/5.55 thf(fact_7125_sum_OlessThan__Suc,axiom,
% 5.24/5.55 ! [G: nat > rat,N: nat] :
% 5.24/5.55 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc
% 5.24/5.55 thf(fact_7126_sum_OlessThan__Suc,axiom,
% 5.24/5.55 ! [G: nat > int,N: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc
% 5.24/5.55 thf(fact_7127_sum_OlessThan__Suc,axiom,
% 5.24/5.55 ! [G: nat > nat,N: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc
% 5.24/5.55 thf(fact_7128_sum_OlessThan__Suc,axiom,
% 5.24/5.55 ! [G: nat > real,N: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc
% 5.24/5.55 thf(fact_7129_round__neg__numeral,axiom,
% 5.24/5.55 ! [N: num] :
% 5.24/5.55 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_neg_numeral
% 5.24/5.55 thf(fact_7130_round__neg__numeral,axiom,
% 5.24/5.55 ! [N: num] :
% 5.24/5.55 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.24/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_neg_numeral
% 5.24/5.55 thf(fact_7131_powser__zero,axiom,
% 5.24/5.55 ! [F: nat > complex] :
% 5.24/5.55 ( ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.24/5.55 = ( F @ zero_zero_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_zero
% 5.24/5.55 thf(fact_7132_powser__zero,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.24/5.55 = ( F @ zero_zero_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_zero
% 5.24/5.55 thf(fact_7133_lessThan__non__empty,axiom,
% 5.24/5.55 ! [X: int] :
% 5.24/5.55 ( ( set_ord_lessThan_int @ X )
% 5.24/5.55 != bot_bot_set_int ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_non_empty
% 5.24/5.55 thf(fact_7134_lessThan__non__empty,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( set_or5984915006950818249n_real @ X )
% 5.24/5.55 != bot_bot_set_real ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_non_empty
% 5.24/5.55 thf(fact_7135_lessThan__def,axiom,
% 5.24/5.55 ( set_ord_lessThan_rat
% 5.24/5.55 = ( ^ [U3: rat] :
% 5.24/5.55 ( collect_rat
% 5.24/5.55 @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_def
% 5.24/5.55 thf(fact_7136_lessThan__def,axiom,
% 5.24/5.55 ( set_ord_lessThan_num
% 5.24/5.55 = ( ^ [U3: num] :
% 5.24/5.55 ( collect_num
% 5.24/5.55 @ ^ [X2: num] : ( ord_less_num @ X2 @ U3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_def
% 5.24/5.55 thf(fact_7137_lessThan__def,axiom,
% 5.24/5.55 ( set_ord_lessThan_int
% 5.24/5.55 = ( ^ [U3: int] :
% 5.24/5.55 ( collect_int
% 5.24/5.55 @ ^ [X2: int] : ( ord_less_int @ X2 @ U3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_def
% 5.24/5.55 thf(fact_7138_lessThan__def,axiom,
% 5.24/5.55 ( set_ord_lessThan_nat
% 5.24/5.55 = ( ^ [U3: nat] :
% 5.24/5.55 ( collect_nat
% 5.24/5.55 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_def
% 5.24/5.55 thf(fact_7139_lessThan__def,axiom,
% 5.24/5.55 ( set_or5984915006950818249n_real
% 5.24/5.55 = ( ^ [U3: real] :
% 5.24/5.55 ( collect_real
% 5.24/5.55 @ ^ [X2: real] : ( ord_less_real @ X2 @ U3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_def
% 5.24/5.55 thf(fact_7140_Iio__eq__empty__iff,axiom,
% 5.24/5.55 ! [N: extended_enat] :
% 5.24/5.55 ( ( ( set_or8419480210114673929d_enat @ N )
% 5.24/5.55 = bot_bo7653980558646680370d_enat )
% 5.24/5.55 = ( N = bot_bo4199563552545308370d_enat ) ) ).
% 5.24/5.55
% 5.24/5.55 % Iio_eq_empty_iff
% 5.24/5.55 thf(fact_7141_Iio__eq__empty__iff,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( set_ord_lessThan_nat @ N )
% 5.24/5.55 = bot_bot_set_nat )
% 5.24/5.55 = ( N = bot_bot_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % Iio_eq_empty_iff
% 5.24/5.55 thf(fact_7142_lessThan__strict__subset__iff,axiom,
% 5.24/5.55 ! [M: rat,N: rat] :
% 5.24/5.55 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.24/5.55 = ( ord_less_rat @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_strict_subset_iff
% 5.24/5.55 thf(fact_7143_lessThan__strict__subset__iff,axiom,
% 5.24/5.55 ! [M: num,N: num] :
% 5.24/5.55 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.24/5.55 = ( ord_less_num @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_strict_subset_iff
% 5.24/5.55 thf(fact_7144_lessThan__strict__subset__iff,axiom,
% 5.24/5.55 ! [M: int,N: int] :
% 5.24/5.55 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.24/5.55 = ( ord_less_int @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_strict_subset_iff
% 5.24/5.55 thf(fact_7145_lessThan__strict__subset__iff,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_strict_subset_iff
% 5.24/5.55 thf(fact_7146_lessThan__strict__subset__iff,axiom,
% 5.24/5.55 ! [M: real,N: real] :
% 5.24/5.55 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.24/5.55 = ( ord_less_real @ M @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_strict_subset_iff
% 5.24/5.55 thf(fact_7147_lessThan__empty__iff,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( set_ord_lessThan_nat @ N )
% 5.24/5.55 = bot_bot_set_nat )
% 5.24/5.55 = ( N = zero_zero_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % lessThan_empty_iff
% 5.24/5.55 thf(fact_7148_round__mono,axiom,
% 5.24/5.55 ! [X: rat,Y4: rat] :
% 5.24/5.55 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.24/5.55 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_mono
% 5.24/5.55 thf(fact_7149_sum_Onat__diff__reindex,axiom,
% 5.24/5.55 ! [G: nat > nat,N: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.nat_diff_reindex
% 5.24/5.55 thf(fact_7150_sum_Onat__diff__reindex,axiom,
% 5.24/5.55 ! [G: nat > real,N: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.nat_diff_reindex
% 5.24/5.55 thf(fact_7151_sum__diff__distrib,axiom,
% 5.24/5.55 ! [Q: real > nat,P: real > nat,N: real] :
% 5.24/5.55 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.24/5.55 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.24/5.55 = ( groups1935376822645274424al_nat
% 5.24/5.55 @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.24/5.55 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_diff_distrib
% 5.24/5.55 thf(fact_7152_sum__diff__distrib,axiom,
% 5.24/5.55 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.24/5.55 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.24/5.55 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.24/5.55 = ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_diff_distrib
% 5.24/5.55 thf(fact_7153_sum_OlessThan__Suc__shift,axiom,
% 5.24/5.55 ! [G: nat > rat,N: nat] :
% 5.24/5.55 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.24/5.55 @ ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc_shift
% 5.24/5.55 thf(fact_7154_sum_OlessThan__Suc__shift,axiom,
% 5.24/5.55 ! [G: nat > int,N: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.24/5.55 @ ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc_shift
% 5.24/5.55 thf(fact_7155_sum_OlessThan__Suc__shift,axiom,
% 5.24/5.55 ! [G: nat > nat,N: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.24/5.55 @ ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc_shift
% 5.24/5.55 thf(fact_7156_sum_OlessThan__Suc__shift,axiom,
% 5.24/5.55 ! [G: nat > real,N: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.lessThan_Suc_shift
% 5.24/5.55 thf(fact_7157_sumr__diff__mult__const2,axiom,
% 5.24/5.55 ! [F: nat > int,N: nat,R2: int] :
% 5.24/5.55 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 5.24/5.55 = ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R2 )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sumr_diff_mult_const2
% 5.24/5.55 thf(fact_7158_sumr__diff__mult__const2,axiom,
% 5.24/5.55 ! [F: nat > rat,N: nat,R2: rat] :
% 5.24/5.55 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 5.24/5.55 = ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R2 )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sumr_diff_mult_const2
% 5.24/5.55 thf(fact_7159_sumr__diff__mult__const2,axiom,
% 5.24/5.55 ! [F: nat > real,N: nat,R2: real] :
% 5.24/5.55 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 5.24/5.55 = ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R2 )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sumr_diff_mult_const2
% 5.24/5.55 thf(fact_7160_sum__lessThan__telescope_H,axiom,
% 5.24/5.55 ! [F: nat > rat,M: nat] :
% 5.24/5.55 ( ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_lessThan_telescope'
% 5.24/5.55 thf(fact_7161_sum__lessThan__telescope_H,axiom,
% 5.24/5.55 ! [F: nat > int,M: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_lessThan_telescope'
% 5.24/5.55 thf(fact_7162_sum__lessThan__telescope_H,axiom,
% 5.24/5.55 ! [F: nat > real,M: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_lessThan_telescope'
% 5.24/5.55 thf(fact_7163_sum__lessThan__telescope,axiom,
% 5.24/5.55 ! [F: nat > rat,M: nat] :
% 5.24/5.55 ( ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_lessThan_telescope
% 5.24/5.55 thf(fact_7164_sum__lessThan__telescope,axiom,
% 5.24/5.55 ! [F: nat > int,M: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_lessThan_telescope
% 5.24/5.55 thf(fact_7165_sum__lessThan__telescope,axiom,
% 5.24/5.55 ! [F: nat > real,M: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_lessThan_telescope
% 5.24/5.55 thf(fact_7166_sum_OatLeast1__atMost__eq,axiom,
% 5.24/5.55 ! [G: nat > nat,N: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.55 = ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.atLeast1_atMost_eq
% 5.24/5.55 thf(fact_7167_sum_OatLeast1__atMost__eq,axiom,
% 5.24/5.55 ! [G: nat > real,N: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.55 = ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum.atLeast1_atMost_eq
% 5.24/5.55 thf(fact_7168_one__diff__power__eq,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.24/5.55 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq
% 5.24/5.55 thf(fact_7169_one__diff__power__eq,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.24/5.55 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq
% 5.24/5.55 thf(fact_7170_one__diff__power__eq,axiom,
% 5.24/5.55 ! [X: int,N: nat] :
% 5.24/5.55 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.24/5.55 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq
% 5.24/5.55 thf(fact_7171_one__diff__power__eq,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.24/5.55 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq
% 5.24/5.55 thf(fact_7172_power__diff__1__eq,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 5.24/5.55 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_1_eq
% 5.24/5.55 thf(fact_7173_power__diff__1__eq,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 5.24/5.55 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_1_eq
% 5.24/5.55 thf(fact_7174_power__diff__1__eq,axiom,
% 5.24/5.55 ! [X: int,N: nat] :
% 5.24/5.55 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 5.24/5.55 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_1_eq
% 5.24/5.55 thf(fact_7175_power__diff__1__eq,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 5.24/5.55 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_1_eq
% 5.24/5.55 thf(fact_7176_geometric__sum,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( X != one_one_complex )
% 5.24/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_sum
% 5.24/5.55 thf(fact_7177_geometric__sum,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( X != one_one_rat )
% 5.24/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_sum
% 5.24/5.55 thf(fact_7178_geometric__sum,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( X != one_one_real )
% 5.24/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_sum
% 5.24/5.55 thf(fact_7179_round__diff__minimal,axiom,
% 5.24/5.55 ! [Z2: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z2 ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_diff_minimal
% 5.24/5.55 thf(fact_7180_round__diff__minimal,axiom,
% 5.24/5.55 ! [Z2: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z2 ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_diff_minimal
% 5.24/5.55 thf(fact_7181_sum__gp__strict,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( ( X = one_one_complex )
% 5.24/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.24/5.55 & ( ( X != one_one_complex )
% 5.24/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_gp_strict
% 5.24/5.55 thf(fact_7182_sum__gp__strict,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( ( X = one_one_rat )
% 5.24/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.24/5.55 & ( ( X != one_one_rat )
% 5.24/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_gp_strict
% 5.24/5.55 thf(fact_7183_sum__gp__strict,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ( X = one_one_real )
% 5.24/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.55 & ( ( X != one_one_real )
% 5.24/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_gp_strict
% 5.24/5.55 thf(fact_7184_lemma__termdiff1,axiom,
% 5.24/5.55 ! [Z2: complex,H2: complex,M: nat] :
% 5.24/5.55 ( ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [P4: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z2 @ P4 ) ) @ ( power_power_complex @ Z2 @ M ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ Z2 @ P4 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z2 @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff1
% 5.24/5.55 thf(fact_7185_lemma__termdiff1,axiom,
% 5.24/5.55 ! [Z2: rat,H2: rat,M: nat] :
% 5.24/5.55 ( ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [P4: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z2 @ P4 ) ) @ ( power_power_rat @ Z2 @ M ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ Z2 @ P4 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z2 @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff1
% 5.24/5.55 thf(fact_7186_lemma__termdiff1,axiom,
% 5.24/5.55 ! [Z2: int,H2: int,M: nat] :
% 5.24/5.55 ( ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [P4: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z2 @ P4 ) ) @ ( power_power_int @ Z2 @ M ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ Z2 @ P4 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z2 @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff1
% 5.24/5.55 thf(fact_7187_lemma__termdiff1,axiom,
% 5.24/5.55 ! [Z2: real,H2: real,M: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [P4: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z2 @ P4 ) ) @ ( power_power_real @ Z2 @ M ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.24/5.55 = ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ Z2 @ P4 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z2 @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_termdiff1
% 5.24/5.55 thf(fact_7188_diff__power__eq__sum,axiom,
% 5.24/5.55 ! [X: complex,N: nat,Y4: complex] :
% 5.24/5.55 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y4 @ ( suc @ N ) ) )
% 5.24/5.55 = ( times_times_complex @ ( minus_minus_complex @ X @ Y4 )
% 5.24/5.55 @ ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X @ P4 ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diff_power_eq_sum
% 5.24/5.55 thf(fact_7189_diff__power__eq__sum,axiom,
% 5.24/5.55 ! [X: rat,N: nat,Y4: rat] :
% 5.24/5.55 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y4 @ ( suc @ N ) ) )
% 5.24/5.55 = ( times_times_rat @ ( minus_minus_rat @ X @ Y4 )
% 5.24/5.55 @ ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ X @ P4 ) @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diff_power_eq_sum
% 5.24/5.55 thf(fact_7190_diff__power__eq__sum,axiom,
% 5.24/5.55 ! [X: int,N: nat,Y4: int] :
% 5.24/5.55 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y4 @ ( suc @ N ) ) )
% 5.24/5.55 = ( times_times_int @ ( minus_minus_int @ X @ Y4 )
% 5.24/5.55 @ ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X @ P4 ) @ ( power_power_int @ Y4 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diff_power_eq_sum
% 5.24/5.55 thf(fact_7191_diff__power__eq__sum,axiom,
% 5.24/5.55 ! [X: real,N: nat,Y4: real] :
% 5.24/5.55 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y4 @ ( suc @ N ) ) )
% 5.24/5.55 = ( times_times_real @ ( minus_minus_real @ X @ Y4 )
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X @ P4 ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diff_power_eq_sum
% 5.24/5.55 thf(fact_7192_power__diff__sumr2,axiom,
% 5.24/5.55 ! [X: complex,N: nat,Y4: complex] :
% 5.24/5.55 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ N ) )
% 5.24/5.55 = ( times_times_complex @ ( minus_minus_complex @ X @ Y4 )
% 5.24/5.55 @ ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_sumr2
% 5.24/5.55 thf(fact_7193_power__diff__sumr2,axiom,
% 5.24/5.55 ! [X: rat,N: nat,Y4: rat] :
% 5.24/5.55 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y4 @ N ) )
% 5.24/5.55 = ( times_times_rat @ ( minus_minus_rat @ X @ Y4 )
% 5.24/5.55 @ ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_sumr2
% 5.24/5.55 thf(fact_7194_power__diff__sumr2,axiom,
% 5.24/5.55 ! [X: int,N: nat,Y4: int] :
% 5.24/5.55 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ N ) )
% 5.24/5.55 = ( times_times_int @ ( minus_minus_int @ X @ Y4 )
% 5.24/5.55 @ ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_sumr2
% 5.24/5.55 thf(fact_7195_power__diff__sumr2,axiom,
% 5.24/5.55 ! [X: real,N: nat,Y4: real] :
% 5.24/5.55 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ N ) )
% 5.24/5.55 = ( times_times_real @ ( minus_minus_real @ X @ Y4 )
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % power_diff_sumr2
% 5.24/5.55 thf(fact_7196_real__sum__nat__ivl__bounded2,axiom,
% 5.24/5.55 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.24/5.55 ( ! [P7: nat] :
% 5.24/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.24/5.55 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.24/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.24/5.55 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sum_nat_ivl_bounded2
% 5.24/5.55 thf(fact_7197_real__sum__nat__ivl__bounded2,axiom,
% 5.24/5.55 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.24/5.55 ( ! [P7: nat] :
% 5.24/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.24/5.55 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.24/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.24/5.55 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sum_nat_ivl_bounded2
% 5.24/5.55 thf(fact_7198_real__sum__nat__ivl__bounded2,axiom,
% 5.24/5.55 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.24/5.55 ( ! [P7: nat] :
% 5.24/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.24/5.55 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.24/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.24/5.55 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sum_nat_ivl_bounded2
% 5.24/5.55 thf(fact_7199_real__sum__nat__ivl__bounded2,axiom,
% 5.24/5.55 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.24/5.55 ( ! [P7: nat] :
% 5.24/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.24/5.55 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.24/5.55 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sum_nat_ivl_bounded2
% 5.24/5.55 thf(fact_7200_divmod__nat__def,axiom,
% 5.24/5.55 ( divmod_nat
% 5.24/5.55 = ( ^ [M2: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M2 @ N2 ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % divmod_nat_def
% 5.24/5.55 thf(fact_7201_one__diff__power__eq_H,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.24/5.55 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.24/5.55 @ ( groups2073611262835488442omplex
% 5.24/5.55 @ ^ [I4: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq'
% 5.24/5.55 thf(fact_7202_one__diff__power__eq_H,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.24/5.55 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.24/5.55 @ ( groups2906978787729119204at_rat
% 5.24/5.55 @ ^ [I4: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq'
% 5.24/5.55 thf(fact_7203_one__diff__power__eq_H,axiom,
% 5.24/5.55 ! [X: int,N: nat] :
% 5.24/5.55 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.24/5.55 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.24/5.55 @ ( groups3539618377306564664at_int
% 5.24/5.55 @ ^ [I4: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq'
% 5.24/5.55 thf(fact_7204_one__diff__power__eq_H,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.24/5.55 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_diff_power_eq'
% 5.24/5.55 thf(fact_7205_sum__split__even__odd,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real,N: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_split_even_odd
% 5.24/5.55 thf(fact_7206_of__int__round__le,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_le
% 5.24/5.55 thf(fact_7207_of__int__round__le,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_le
% 5.24/5.55 thf(fact_7208_of__int__round__ge,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_ge
% 5.24/5.55 thf(fact_7209_of__int__round__ge,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_ge
% 5.24/5.55 thf(fact_7210_of__int__round__gt,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_gt
% 5.24/5.55 thf(fact_7211_of__int__round__gt,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_gt
% 5.24/5.55 thf(fact_7212_of__int__round__abs__le,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_abs_le
% 5.24/5.55 thf(fact_7213_of__int__round__abs__le,axiom,
% 5.24/5.55 ! [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_int_round_abs_le
% 5.24/5.55 thf(fact_7214_round__unique_H,axiom,
% 5.24/5.55 ! [X: real,N: int] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 => ( ( archim8280529875227126926d_real @ X )
% 5.24/5.55 = N ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_unique'
% 5.24/5.55 thf(fact_7215_round__unique_H,axiom,
% 5.24/5.55 ! [X: rat,N: int] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 => ( ( archim7778729529865785530nd_rat @ X )
% 5.24/5.55 = N ) ) ).
% 5.24/5.55
% 5.24/5.55 % round_unique'
% 5.24/5.55 thf(fact_7216_suminf__geometric,axiom,
% 5.24/5.55 ! [C: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.24/5.55 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.24/5.55 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_geometric
% 5.24/5.55 thf(fact_7217_suminf__geometric,axiom,
% 5.24/5.55 ! [C: complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.24/5.55 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_geometric
% 5.24/5.55 thf(fact_7218_sum__bounds__lt__plus1,axiom,
% 5.24/5.55 ! [F: nat > nat,Mm: nat] :
% 5.24/5.55 ( ( groups3542108847815614940at_nat
% 5.24/5.55 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.24/5.55 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_bounds_lt_plus1
% 5.24/5.55 thf(fact_7219_sum__bounds__lt__plus1,axiom,
% 5.24/5.55 ! [F: nat > real,Mm: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.24/5.55 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_bounds_lt_plus1
% 5.24/5.55 thf(fact_7220_pi__series,axiom,
% 5.24/5.55 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = ( suminf_real
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_series
% 5.24/5.55 thf(fact_7221_sumr__cos__zero__one,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ zero_zero_real @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sumr_cos_zero_one
% 5.24/5.55 thf(fact_7222_summable__arctan__series,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [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 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_arctan_series
% 5.24/5.55 thf(fact_7223_geometric__deriv__sums,axiom,
% 5.24/5.55 ! [Z2: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ one_one_real )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z2 @ N2 ) )
% 5.24/5.55 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_deriv_sums
% 5.24/5.55 thf(fact_7224_geometric__deriv__sums,axiom,
% 5.24/5.55 ! [Z2: complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ one_one_real )
% 5.24/5.55 => ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z2 @ N2 ) )
% 5.24/5.55 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_deriv_sums
% 5.24/5.55 thf(fact_7225_summable__iff__shift,axiom,
% 5.24/5.55 ! [F: nat > real,K: nat] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.24/5.55 = ( summable_real @ F ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_iff_shift
% 5.24/5.55 thf(fact_7226_cos__coeff__0,axiom,
% 5.24/5.55 ( ( cos_coeff @ zero_zero_nat )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_coeff_0
% 5.24/5.55 thf(fact_7227_summable__cmult__iff,axiom,
% 5.24/5.55 ! [C: complex,F: nat > complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.24/5.55 = ( ( C = zero_zero_complex )
% 5.24/5.55 | ( summable_complex @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_cmult_iff
% 5.24/5.55 thf(fact_7228_summable__cmult__iff,axiom,
% 5.24/5.55 ! [C: real,F: nat > real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.24/5.55 = ( ( C = zero_zero_real )
% 5.24/5.55 | ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_cmult_iff
% 5.24/5.55 thf(fact_7229_summable__divide__iff,axiom,
% 5.24/5.55 ! [F: nat > complex,C: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.24/5.55 = ( ( C = zero_zero_complex )
% 5.24/5.55 | ( summable_complex @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_divide_iff
% 5.24/5.55 thf(fact_7230_summable__divide__iff,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.24/5.55 = ( ( C = zero_zero_real )
% 5.24/5.55 | ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_divide_iff
% 5.24/5.55 thf(fact_7231_powser__sums__zero__iff,axiom,
% 5.24/5.55 ! [A: nat > complex,X: complex] :
% 5.24/5.55 ( ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.24/5.55 @ X )
% 5.24/5.55 = ( ( A @ zero_zero_nat )
% 5.24/5.55 = X ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_zero_iff
% 5.24/5.55 thf(fact_7232_powser__sums__zero__iff,axiom,
% 5.24/5.55 ! [A: nat > real,X: real] :
% 5.24/5.55 ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.24/5.55 @ X )
% 5.24/5.55 = ( ( A @ zero_zero_nat )
% 5.24/5.55 = X ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_zero_iff
% 5.24/5.55 thf(fact_7233_summable__geometric__iff,axiom,
% 5.24/5.55 ! [C: real] :
% 5.24/5.55 ( ( summable_real @ ( power_power_real @ C ) )
% 5.24/5.55 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_geometric_iff
% 5.24/5.55 thf(fact_7234_summable__geometric__iff,axiom,
% 5.24/5.55 ! [C: complex] :
% 5.24/5.55 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.24/5.55 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_geometric_iff
% 5.24/5.55 thf(fact_7235_summable__divide,axiom,
% 5.24/5.55 ! [F: nat > complex,C: complex] :
% 5.24/5.55 ( ( summable_complex @ F )
% 5.24/5.55 => ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_divide
% 5.24/5.55 thf(fact_7236_summable__divide,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_divide
% 5.24/5.55 thf(fact_7237_summable__Suc__iff,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.24/5.55 = ( summable_real @ F ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_Suc_iff
% 5.24/5.55 thf(fact_7238_sums__mult2,axiom,
% 5.24/5.55 ! [F: nat > real,A: real,C: real] :
% 5.24/5.55 ( ( sums_real @ F @ A )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.24/5.55 @ ( times_times_real @ A @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult2
% 5.24/5.55 thf(fact_7239_sums__mult,axiom,
% 5.24/5.55 ! [F: nat > real,A: real,C: real] :
% 5.24/5.55 ( ( sums_real @ F @ A )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.24/5.55 @ ( times_times_real @ C @ A ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult
% 5.24/5.55 thf(fact_7240_sums__divide,axiom,
% 5.24/5.55 ! [F: nat > complex,A: complex,C: complex] :
% 5.24/5.55 ( ( sums_complex @ F @ A )
% 5.24/5.55 => ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 5.24/5.55 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_divide
% 5.24/5.55 thf(fact_7241_sums__divide,axiom,
% 5.24/5.55 ! [F: nat > real,A: real,C: real] :
% 5.24/5.55 ( ( sums_real @ F @ A )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 5.24/5.55 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_divide
% 5.24/5.55 thf(fact_7242_sums__le,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real,S2: real,T: real] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.55 => ( ( sums_real @ F @ S2 )
% 5.24/5.55 => ( ( sums_real @ G @ T )
% 5.24/5.55 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_le
% 5.24/5.55 thf(fact_7243_sums__le,axiom,
% 5.24/5.55 ! [F: nat > nat,G: nat > nat,S2: nat,T: nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.55 => ( ( sums_nat @ F @ S2 )
% 5.24/5.55 => ( ( sums_nat @ G @ T )
% 5.24/5.55 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_le
% 5.24/5.55 thf(fact_7244_sums__le,axiom,
% 5.24/5.55 ! [F: nat > int,G: nat > int,S2: int,T: int] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.55 => ( ( sums_int @ F @ S2 )
% 5.24/5.55 => ( ( sums_int @ G @ T )
% 5.24/5.55 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_le
% 5.24/5.55 thf(fact_7245_summable__mult2,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_mult2
% 5.24/5.55 thf(fact_7246_summable__mult,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_mult
% 5.24/5.55 thf(fact_7247_summable__add,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_add
% 5.24/5.55 thf(fact_7248_summable__add,axiom,
% 5.24/5.55 ! [F: nat > nat,G: nat > nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ( summable_nat @ G )
% 5.24/5.55 => ( summable_nat
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_add
% 5.24/5.55 thf(fact_7249_summable__add,axiom,
% 5.24/5.55 ! [F: nat > int,G: nat > int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ( summable_int @ G )
% 5.24/5.55 => ( summable_int
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_add
% 5.24/5.55 thf(fact_7250_sums__add,axiom,
% 5.24/5.55 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.24/5.55 ( ( sums_real @ F @ A )
% 5.24/5.55 => ( ( sums_real @ G @ B )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.24/5.55 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_add
% 5.24/5.55 thf(fact_7251_sums__add,axiom,
% 5.24/5.55 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.24/5.55 ( ( sums_nat @ F @ A )
% 5.24/5.55 => ( ( sums_nat @ G @ B )
% 5.24/5.55 => ( sums_nat
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.24/5.55 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_add
% 5.24/5.55 thf(fact_7252_sums__add,axiom,
% 5.24/5.55 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.24/5.55 ( ( sums_int @ F @ A )
% 5.24/5.55 => ( ( sums_int @ G @ B )
% 5.24/5.55 => ( sums_int
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.24/5.55 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_add
% 5.24/5.55 thf(fact_7253_summable__ignore__initial__segment,axiom,
% 5.24/5.55 ! [F: nat > real,K: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_ignore_initial_segment
% 5.24/5.55 thf(fact_7254_summable__comparison__test_H,axiom,
% 5.24/5.55 ! [G: nat > real,N4: nat,F: nat > real] :
% 5.24/5.55 ( ( summable_real @ G )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.24/5.55 => ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_comparison_test'
% 5.24/5.55 thf(fact_7255_summable__comparison__test_H,axiom,
% 5.24/5.55 ! [G: nat > real,N4: nat,F: nat > complex] :
% 5.24/5.55 ( ( summable_real @ G )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.24/5.55 => ( summable_complex @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_comparison_test'
% 5.24/5.55 thf(fact_7256_summable__comparison__test,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real] :
% 5.24/5.55 ( ? [N7: nat] :
% 5.24/5.55 ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_comparison_test
% 5.24/5.55 thf(fact_7257_summable__comparison__test,axiom,
% 5.24/5.55 ! [F: nat > complex,G: nat > real] :
% 5.24/5.55 ( ? [N7: nat] :
% 5.24/5.55 ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( summable_complex @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_comparison_test
% 5.24/5.55 thf(fact_7258_suminf__le,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.55 => ( ( summable_real @ F )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_le
% 5.24/5.55 thf(fact_7259_suminf__le,axiom,
% 5.24/5.55 ! [F: nat > nat,G: nat > nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.55 => ( ( summable_nat @ F )
% 5.24/5.55 => ( ( summable_nat @ G )
% 5.24/5.55 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_le
% 5.24/5.55 thf(fact_7260_suminf__le,axiom,
% 5.24/5.55 ! [F: nat > int,G: nat > int] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.55 => ( ( summable_int @ F )
% 5.24/5.55 => ( ( summable_int @ G )
% 5.24/5.55 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_le
% 5.24/5.55 thf(fact_7261_sums__mult__iff,axiom,
% 5.24/5.55 ! [C: complex,F: nat > complex,D: complex] :
% 5.24/5.55 ( ( C != zero_zero_complex )
% 5.24/5.55 => ( ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.24/5.55 @ ( times_times_complex @ C @ D ) )
% 5.24/5.55 = ( sums_complex @ F @ D ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult_iff
% 5.24/5.55 thf(fact_7262_sums__mult__iff,axiom,
% 5.24/5.55 ! [C: real,F: nat > real,D: real] :
% 5.24/5.55 ( ( C != zero_zero_real )
% 5.24/5.55 => ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.24/5.55 @ ( times_times_real @ C @ D ) )
% 5.24/5.55 = ( sums_real @ F @ D ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult_iff
% 5.24/5.55 thf(fact_7263_sums__mult2__iff,axiom,
% 5.24/5.55 ! [C: complex,F: nat > complex,D: complex] :
% 5.24/5.55 ( ( C != zero_zero_complex )
% 5.24/5.55 => ( ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 5.24/5.55 @ ( times_times_complex @ D @ C ) )
% 5.24/5.55 = ( sums_complex @ F @ D ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult2_iff
% 5.24/5.55 thf(fact_7264_sums__mult2__iff,axiom,
% 5.24/5.55 ! [C: real,F: nat > real,D: real] :
% 5.24/5.55 ( ( C != zero_zero_real )
% 5.24/5.55 => ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.24/5.55 @ ( times_times_real @ D @ C ) )
% 5.24/5.55 = ( sums_real @ F @ D ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult2_iff
% 5.24/5.55 thf(fact_7265_summable__mult__D,axiom,
% 5.24/5.55 ! [C: complex,F: nat > complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.24/5.55 => ( ( C != zero_zero_complex )
% 5.24/5.55 => ( summable_complex @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_mult_D
% 5.24/5.55 thf(fact_7266_summable__mult__D,axiom,
% 5.24/5.55 ! [C: real,F: nat > real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.24/5.55 => ( ( C != zero_zero_real )
% 5.24/5.55 => ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_mult_D
% 5.24/5.55 thf(fact_7267_summable__zero__power,axiom,
% 5.24/5.55 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % summable_zero_power
% 5.24/5.55 thf(fact_7268_summable__zero__power,axiom,
% 5.24/5.55 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.24/5.55
% 5.24/5.55 % summable_zero_power
% 5.24/5.55 thf(fact_7269_summable__zero__power,axiom,
% 5.24/5.55 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.24/5.55
% 5.24/5.55 % summable_zero_power
% 5.24/5.55 thf(fact_7270_suminf__mult2,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.24/5.55 = ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_mult2
% 5.24/5.55 thf(fact_7271_suminf__mult,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.24/5.55 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_mult
% 5.24/5.55 thf(fact_7272_suminf__add,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.24/5.55 = ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_add
% 5.24/5.55 thf(fact_7273_suminf__add,axiom,
% 5.24/5.55 ! [F: nat > nat,G: nat > nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ( summable_nat @ G )
% 5.24/5.55 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.24/5.55 = ( suminf_nat
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_add
% 5.24/5.55 thf(fact_7274_suminf__add,axiom,
% 5.24/5.55 ! [F: nat > int,G: nat > int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ( summable_int @ G )
% 5.24/5.55 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.24/5.55 = ( suminf_int
% 5.24/5.55 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_add
% 5.24/5.55 thf(fact_7275_suminf__divide,axiom,
% 5.24/5.55 ! [F: nat > complex,C: complex] :
% 5.24/5.55 ( ( summable_complex @ F )
% 5.24/5.55 => ( ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_divide
% 5.24/5.55 thf(fact_7276_suminf__divide,axiom,
% 5.24/5.55 ! [F: nat > real,C: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.24/5.55 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_divide
% 5.24/5.55 thf(fact_7277_powser__insidea,axiom,
% 5.24/5.55 ! [F: nat > real,X: real,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_insidea
% 5.24/5.55 thf(fact_7278_powser__insidea,axiom,
% 5.24/5.55 ! [F: nat > complex,X: complex,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_insidea
% 5.24/5.55 thf(fact_7279_suminf__eq__zero__iff,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ( suminf_real @ F )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 = ( ! [N2: nat] :
% 5.24/5.55 ( ( F @ N2 )
% 5.24/5.55 = zero_zero_real ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_eq_zero_iff
% 5.24/5.55 thf(fact_7280_suminf__eq__zero__iff,axiom,
% 5.24/5.55 ! [F: nat > nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ( suminf_nat @ F )
% 5.24/5.55 = zero_zero_nat )
% 5.24/5.55 = ( ! [N2: nat] :
% 5.24/5.55 ( ( F @ N2 )
% 5.24/5.55 = zero_zero_nat ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_eq_zero_iff
% 5.24/5.55 thf(fact_7281_suminf__eq__zero__iff,axiom,
% 5.24/5.55 ! [F: nat > int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ( suminf_int @ F )
% 5.24/5.55 = zero_zero_int )
% 5.24/5.55 = ( ! [N2: nat] :
% 5.24/5.55 ( ( F @ N2 )
% 5.24/5.55 = zero_zero_int ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_eq_zero_iff
% 5.24/5.55 thf(fact_7282_suminf__nonneg,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_nonneg
% 5.24/5.55 thf(fact_7283_suminf__nonneg,axiom,
% 5.24/5.55 ! [F: nat > nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.24/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_nonneg
% 5.24/5.55 thf(fact_7284_suminf__nonneg,axiom,
% 5.24/5.55 ! [F: nat > int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.24/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_nonneg
% 5.24/5.55 thf(fact_7285_suminf__pos,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos
% 5.24/5.55 thf(fact_7286_suminf__pos,axiom,
% 5.24/5.55 ! [F: nat > nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.24/5.55 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos
% 5.24/5.55 thf(fact_7287_suminf__pos,axiom,
% 5.24/5.55 ! [F: nat > int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.24/5.55 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos
% 5.24/5.55 thf(fact_7288_sums__mult__D,axiom,
% 5.24/5.55 ! [C: complex,F: nat > complex,A: complex] :
% 5.24/5.55 ( ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.24/5.55 @ A )
% 5.24/5.55 => ( ( C != zero_zero_complex )
% 5.24/5.55 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult_D
% 5.24/5.55 thf(fact_7289_sums__mult__D,axiom,
% 5.24/5.55 ! [C: real,F: nat > real,A: real] :
% 5.24/5.55 ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.24/5.55 @ A )
% 5.24/5.55 => ( ( C != zero_zero_real )
% 5.24/5.55 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_mult_D
% 5.24/5.55 thf(fact_7290_sums__Suc__imp,axiom,
% 5.24/5.55 ! [F: nat > complex,S2: complex] :
% 5.24/5.55 ( ( ( F @ zero_zero_nat )
% 5.24/5.55 = zero_zero_complex )
% 5.24/5.55 => ( ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.24/5.55 @ S2 )
% 5.24/5.55 => ( sums_complex @ F @ S2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_Suc_imp
% 5.24/5.55 thf(fact_7291_sums__Suc__imp,axiom,
% 5.24/5.55 ! [F: nat > real,S2: real] :
% 5.24/5.55 ( ( ( F @ zero_zero_nat )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 => ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.24/5.55 @ S2 )
% 5.24/5.55 => ( sums_real @ F @ S2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_Suc_imp
% 5.24/5.55 thf(fact_7292_sums__Suc__iff,axiom,
% 5.24/5.55 ! [F: nat > real,S2: real] :
% 5.24/5.55 ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.24/5.55 @ S2 )
% 5.24/5.55 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_Suc_iff
% 5.24/5.55 thf(fact_7293_sums__Suc,axiom,
% 5.24/5.55 ! [F: nat > real,L2: real] :
% 5.24/5.55 ( ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.24/5.55 @ L2 )
% 5.24/5.55 => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_Suc
% 5.24/5.55 thf(fact_7294_sums__Suc,axiom,
% 5.24/5.55 ! [F: nat > nat,L2: nat] :
% 5.24/5.55 ( ( sums_nat
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.24/5.55 @ L2 )
% 5.24/5.55 => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_Suc
% 5.24/5.55 thf(fact_7295_sums__Suc,axiom,
% 5.24/5.55 ! [F: nat > int,L2: int] :
% 5.24/5.55 ( ( sums_int
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.24/5.55 @ L2 )
% 5.24/5.55 => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_Suc
% 5.24/5.55 thf(fact_7296_summable__0__powser,axiom,
% 5.24/5.55 ! [F: nat > complex] :
% 5.24/5.55 ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_0_powser
% 5.24/5.55 thf(fact_7297_summable__0__powser,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_0_powser
% 5.24/5.55 thf(fact_7298_summable__zero__power_H,axiom,
% 5.24/5.55 ! [F: nat > complex] :
% 5.24/5.55 ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_zero_power'
% 5.24/5.55 thf(fact_7299_summable__zero__power_H,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_zero_power'
% 5.24/5.55 thf(fact_7300_summable__zero__power_H,axiom,
% 5.24/5.55 ! [F: nat > int] :
% 5.24/5.55 ( summable_int
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_zero_power'
% 5.24/5.55 thf(fact_7301_sums__zero__iff__shift,axiom,
% 5.24/5.55 ! [N: nat,F: nat > complex,S2: complex] :
% 5.24/5.55 ( ! [I3: nat] :
% 5.24/5.55 ( ( ord_less_nat @ I3 @ N )
% 5.24/5.55 => ( ( F @ I3 )
% 5.24/5.55 = zero_zero_complex ) )
% 5.24/5.55 => ( ( sums_complex
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.24/5.55 @ S2 )
% 5.24/5.55 = ( sums_complex @ F @ S2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_zero_iff_shift
% 5.24/5.55 thf(fact_7302_sums__zero__iff__shift,axiom,
% 5.24/5.55 ! [N: nat,F: nat > real,S2: real] :
% 5.24/5.55 ( ! [I3: nat] :
% 5.24/5.55 ( ( ord_less_nat @ I3 @ N )
% 5.24/5.55 => ( ( F @ I3 )
% 5.24/5.55 = zero_zero_real ) )
% 5.24/5.55 => ( ( sums_real
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.24/5.55 @ S2 )
% 5.24/5.55 = ( sums_real @ F @ S2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_zero_iff_shift
% 5.24/5.55 thf(fact_7303_summable__powser__split__head,axiom,
% 5.24/5.55 ! [F: nat > complex,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 = ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_powser_split_head
% 5.24/5.55 thf(fact_7304_summable__powser__split__head,axiom,
% 5.24/5.55 ! [F: nat > real,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 = ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_powser_split_head
% 5.24/5.55 thf(fact_7305_powser__split__head_I3_J,axiom,
% 5.24/5.55 ! [F: nat > complex,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 => ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_split_head(3)
% 5.24/5.55 thf(fact_7306_powser__split__head_I3_J,axiom,
% 5.24/5.55 ! [F: nat > real,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_split_head(3)
% 5.24/5.55 thf(fact_7307_summable__powser__ignore__initial__segment,axiom,
% 5.24/5.55 ! [F: nat > complex,M: nat,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 = ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_powser_ignore_initial_segment
% 5.24/5.55 thf(fact_7308_summable__powser__ignore__initial__segment,axiom,
% 5.24/5.55 ! [F: nat > real,M: nat,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 = ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_powser_ignore_initial_segment
% 5.24/5.55 thf(fact_7309_summable__norm__comparison__test,axiom,
% 5.24/5.55 ! [F: nat > complex,G: nat > real] :
% 5.24/5.55 ( ? [N7: nat] :
% 5.24/5.55 ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_norm_comparison_test
% 5.24/5.55 thf(fact_7310_summable__rabs__comparison__test,axiom,
% 5.24/5.55 ! [F: nat > real,G: nat > real] :
% 5.24/5.55 ( ? [N7: nat] :
% 5.24/5.55 ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.24/5.55 => ( ( summable_real @ G )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_rabs_comparison_test
% 5.24/5.55 thf(fact_7311_suminf__pos2,axiom,
% 5.24/5.55 ! [F: nat > real,I2: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos2
% 5.24/5.55 thf(fact_7312_suminf__pos2,axiom,
% 5.24/5.55 ! [F: nat > nat,I2: nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.24/5.55 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos2
% 5.24/5.55 thf(fact_7313_suminf__pos2,axiom,
% 5.24/5.55 ! [F: nat > int,I2: nat] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.24/5.55 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos2
% 5.24/5.55 thf(fact_7314_suminf__pos__iff,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.24/5.55 = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos_iff
% 5.24/5.55 thf(fact_7315_suminf__pos__iff,axiom,
% 5.24/5.55 ! [F: nat > nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.24/5.55 = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos_iff
% 5.24/5.55 thf(fact_7316_suminf__pos__iff,axiom,
% 5.24/5.55 ! [F: nat > int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.24/5.55 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.24/5.55 = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_pos_iff
% 5.24/5.55 thf(fact_7317_suminf__le__const,axiom,
% 5.24/5.55 ! [F: nat > int,X: int] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.24/5.55 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_le_const
% 5.24/5.55 thf(fact_7318_suminf__le__const,axiom,
% 5.24/5.55 ! [F: nat > nat,X: nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.24/5.55 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_le_const
% 5.24/5.55 thf(fact_7319_suminf__le__const,axiom,
% 5.24/5.55 ! [F: nat > real,X: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.24/5.55 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_le_const
% 5.24/5.55 thf(fact_7320_powser__sums__if,axiom,
% 5.24/5.55 ! [M: nat,Z2: complex] :
% 5.24/5.55 ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z2 @ N2 ) )
% 5.24/5.55 @ ( power_power_complex @ Z2 @ M ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_if
% 5.24/5.55 thf(fact_7321_powser__sums__if,axiom,
% 5.24/5.55 ! [M: nat,Z2: real] :
% 5.24/5.55 ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z2 @ N2 ) )
% 5.24/5.55 @ ( power_power_real @ Z2 @ M ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_if
% 5.24/5.55 thf(fact_7322_powser__sums__if,axiom,
% 5.24/5.55 ! [M: nat,Z2: int] :
% 5.24/5.55 ( sums_int
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z2 @ N2 ) )
% 5.24/5.55 @ ( power_power_int @ Z2 @ M ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_if
% 5.24/5.55 thf(fact_7323_summableI__nonneg__bounded,axiom,
% 5.24/5.55 ! [F: nat > int,X: int] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.24/5.55 => ( summable_int @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summableI_nonneg_bounded
% 5.24/5.55 thf(fact_7324_summableI__nonneg__bounded,axiom,
% 5.24/5.55 ! [F: nat > nat,X: nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.24/5.55 => ( summable_nat @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summableI_nonneg_bounded
% 5.24/5.55 thf(fact_7325_summableI__nonneg__bounded,axiom,
% 5.24/5.55 ! [F: nat > real,X: real] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.24/5.55 => ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summableI_nonneg_bounded
% 5.24/5.55 thf(fact_7326_complete__algebra__summable__geometric,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 5.24/5.55 => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % complete_algebra_summable_geometric
% 5.24/5.55 thf(fact_7327_complete__algebra__summable__geometric,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 5.24/5.55 => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % complete_algebra_summable_geometric
% 5.24/5.55 thf(fact_7328_summable__geometric,axiom,
% 5.24/5.55 ! [C: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.24/5.55 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_geometric
% 5.24/5.55 thf(fact_7329_summable__geometric,axiom,
% 5.24/5.55 ! [C: complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.24/5.55 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_geometric
% 5.24/5.55 thf(fact_7330_sums__iff__shift,axiom,
% 5.24/5.55 ! [F: nat > real,N: nat,S2: real] :
% 5.24/5.55 ( ( sums_real
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.24/5.55 @ S2 )
% 5.24/5.55 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_iff_shift
% 5.24/5.55 thf(fact_7331_sums__split__initial__segment,axiom,
% 5.24/5.55 ! [F: nat > real,S2: real,N: nat] :
% 5.24/5.55 ( ( sums_real @ F @ S2 )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.24/5.55 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_split_initial_segment
% 5.24/5.55 thf(fact_7332_sums__iff__shift_H,axiom,
% 5.24/5.55 ! [F: nat > real,N: nat,S2: real] :
% 5.24/5.55 ( ( sums_real
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.24/5.55 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.24/5.55 = ( sums_real @ F @ S2 ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_iff_shift'
% 5.24/5.55 thf(fact_7333_suminf__split__head,axiom,
% 5.24/5.55 ! [F: nat > real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.24/5.55 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_split_head
% 5.24/5.55 thf(fact_7334_sums__If__finite__set_H,axiom,
% 5.24/5.55 ! [G: nat > real,S3: real,A2: set_nat,S4: real,F: nat > real] :
% 5.24/5.55 ( ( sums_real @ G @ S3 )
% 5.24/5.55 => ( ( finite_finite_nat @ A2 )
% 5.24/5.55 => ( ( S4
% 5.24/5.55 = ( plus_plus_real @ S3
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.24/5.55 @ A2 ) ) )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.24/5.55 @ S4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_If_finite_set'
% 5.24/5.55 thf(fact_7335_sum__le__suminf,axiom,
% 5.24/5.55 ! [F: nat > int,I5: set_nat] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ( finite_finite_nat @ I5 )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.24/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 5.24/5.55 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_le_suminf
% 5.24/5.55 thf(fact_7336_sum__le__suminf,axiom,
% 5.24/5.55 ! [F: nat > nat,I5: set_nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ( finite_finite_nat @ I5 )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.24/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 5.24/5.55 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_le_suminf
% 5.24/5.55 thf(fact_7337_sum__le__suminf,axiom,
% 5.24/5.55 ! [F: nat > real,I5: set_nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( finite_finite_nat @ I5 )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 5.24/5.55 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_le_suminf
% 5.24/5.55 thf(fact_7338_suminf__split__initial__segment,axiom,
% 5.24/5.55 ! [F: nat > real,K: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( suminf_real @ F )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.24/5.55 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_split_initial_segment
% 5.24/5.55 thf(fact_7339_suminf__minus__initial__segment,axiom,
% 5.24/5.55 ! [F: nat > real,K: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.24/5.55 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_minus_initial_segment
% 5.24/5.55 thf(fact_7340_powser__sums__zero,axiom,
% 5.24/5.55 ! [A: nat > complex] :
% 5.24/5.55 ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.24/5.55 @ ( A @ zero_zero_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_zero
% 5.24/5.55 thf(fact_7341_powser__sums__zero,axiom,
% 5.24/5.55 ! [A: nat > real] :
% 5.24/5.55 ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.24/5.55 @ ( A @ zero_zero_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_sums_zero
% 5.24/5.55 thf(fact_7342_powser__inside,axiom,
% 5.24/5.55 ! [F: nat > real,X: real,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_inside
% 5.24/5.55 thf(fact_7343_powser__inside,axiom,
% 5.24/5.55 ! [F: nat > complex,X: complex,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.24/5.55 => ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_inside
% 5.24/5.55 thf(fact_7344_sum__less__suminf,axiom,
% 5.24/5.55 ! [F: nat > int,N: nat] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M4 )
% 5.24/5.55 => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.24/5.55 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_less_suminf
% 5.24/5.55 thf(fact_7345_sum__less__suminf,axiom,
% 5.24/5.55 ! [F: nat > nat,N: nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M4 )
% 5.24/5.55 => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.24/5.55 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_less_suminf
% 5.24/5.55 thf(fact_7346_sum__less__suminf,axiom,
% 5.24/5.55 ! [F: nat > real,N: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M4 )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.24/5.55 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_less_suminf
% 5.24/5.55 thf(fact_7347_pi__less__4,axiom,
% 5.24/5.55 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_less_4
% 5.24/5.55 thf(fact_7348_pi__ge__two,axiom,
% 5.24/5.55 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.24/5.55
% 5.24/5.55 % pi_ge_two
% 5.24/5.55 thf(fact_7349_pi__half__neq__two,axiom,
% 5.24/5.55 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_half_neq_two
% 5.24/5.55 thf(fact_7350_powser__split__head_I1_J,axiom,
% 5.24/5.55 ! [F: nat > complex,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 => ( ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.24/5.55 @ ( times_times_complex
% 5.24/5.55 @ ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 @ Z2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_split_head(1)
% 5.24/5.55 thf(fact_7351_powser__split__head_I1_J,axiom,
% 5.24/5.55 ! [F: nat > real,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 => ( ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.24/5.55 @ ( times_times_real
% 5.24/5.55 @ ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 @ Z2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_split_head(1)
% 5.24/5.55 thf(fact_7352_powser__split__head_I2_J,axiom,
% 5.24/5.55 ! [F: nat > complex,Z2: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 => ( ( times_times_complex
% 5.24/5.55 @ ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 @ Z2 )
% 5.24/5.55 = ( minus_minus_complex
% 5.24/5.55 @ ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z2 @ N2 ) ) )
% 5.24/5.55 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_split_head(2)
% 5.24/5.55 thf(fact_7353_powser__split__head_I2_J,axiom,
% 5.24/5.55 ! [F: nat > real,Z2: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 => ( ( times_times_real
% 5.24/5.55 @ ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 @ Z2 )
% 5.24/5.55 = ( minus_minus_real
% 5.24/5.55 @ ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z2 @ N2 ) ) )
% 5.24/5.55 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % powser_split_head(2)
% 5.24/5.55 thf(fact_7354_summable__partial__sum__bound,axiom,
% 5.24/5.55 ! [F: nat > complex,E: real] :
% 5.24/5.55 ( ( summable_complex @ F )
% 5.24/5.55 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.24/5.55 => ~ ! [N8: nat] :
% 5.24/5.55 ~ ! [M3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N8 @ M3 )
% 5.24/5.55 => ! [N9: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M3 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_partial_sum_bound
% 5.24/5.55 thf(fact_7355_summable__partial__sum__bound,axiom,
% 5.24/5.55 ! [F: nat > real,E: real] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.24/5.55 => ~ ! [N8: nat] :
% 5.24/5.55 ~ ! [M3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N8 @ M3 )
% 5.24/5.55 => ! [N9: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M3 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_partial_sum_bound
% 5.24/5.55 thf(fact_7356_suminf__exist__split,axiom,
% 5.24/5.55 ! [R2: real,F: nat > real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.24/5.55 => ( ( summable_real @ F )
% 5.24/5.55 => ? [N8: nat] :
% 5.24/5.55 ! [N9: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.24/5.55 => ( ord_less_real
% 5.24/5.55 @ ( real_V7735802525324610683m_real
% 5.24/5.55 @ ( suminf_real
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N9 ) ) ) )
% 5.24/5.55 @ R2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_exist_split
% 5.24/5.55 thf(fact_7357_suminf__exist__split,axiom,
% 5.24/5.55 ! [R2: real,F: nat > complex] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.24/5.55 => ( ( summable_complex @ F )
% 5.24/5.55 => ? [N8: nat] :
% 5.24/5.55 ! [N9: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.24/5.55 => ( ord_less_real
% 5.24/5.55 @ ( real_V1022390504157884413omplex
% 5.24/5.55 @ ( suminf_complex
% 5.24/5.55 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N9 ) ) ) )
% 5.24/5.55 @ R2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % suminf_exist_split
% 5.24/5.55 thf(fact_7358_summable__power__series,axiom,
% 5.24/5.55 ! [F: nat > real,Z2: real] :
% 5.24/5.55 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.24/5.55 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Z2 )
% 5.24/5.55 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z2 @ I4 ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_power_series
% 5.24/5.55 thf(fact_7359_Abel__lemma,axiom,
% 5.24/5.55 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.24/5.55 => ( ( ord_less_real @ R2 @ R0 )
% 5.24/5.55 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R2 @ N2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Abel_lemma
% 5.24/5.55 thf(fact_7360_summable__ratio__test,axiom,
% 5.24/5.55 ! [C: real,N4: nat,F: nat > real] :
% 5.24/5.55 ( ( ord_less_real @ C @ one_one_real )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.24/5.55 => ( summable_real @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_ratio_test
% 5.24/5.55 thf(fact_7361_summable__ratio__test,axiom,
% 5.24/5.55 ! [C: real,N4: nat,F: nat > complex] :
% 5.24/5.55 ( ( ord_less_real @ C @ one_one_real )
% 5.24/5.55 => ( ! [N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.24/5.55 => ( summable_complex @ F ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % summable_ratio_test
% 5.24/5.55 thf(fact_7362_sum__less__suminf2,axiom,
% 5.24/5.55 ! [F: nat > int,N: nat,I2: nat] :
% 5.24/5.55 ( ( summable_int @ F )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M4 )
% 5.24/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.24/5.55 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.24/5.55 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_less_suminf2
% 5.24/5.55 thf(fact_7363_sum__less__suminf2,axiom,
% 5.24/5.55 ! [F: nat > nat,N: nat,I2: nat] :
% 5.24/5.55 ( ( summable_nat @ F )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M4 )
% 5.24/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.24/5.55 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_less_suminf2
% 5.24/5.55 thf(fact_7364_sum__less__suminf2,axiom,
% 5.24/5.55 ! [F: nat > real,N: nat,I2: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [M4: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M4 )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.24/5.55 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.24/5.55 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_less_suminf2
% 5.24/5.55 thf(fact_7365_geometric__sums,axiom,
% 5.24/5.55 ! [C: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.24/5.55 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_sums
% 5.24/5.55 thf(fact_7366_geometric__sums,axiom,
% 5.24/5.55 ! [C: complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.24/5.55 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % geometric_sums
% 5.24/5.55 thf(fact_7367_power__half__series,axiom,
% 5.24/5.55 ( sums_real
% 5.24/5.55 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.24/5.55 @ one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % power_half_series
% 5.24/5.55 thf(fact_7368_pi__half__neq__zero,axiom,
% 5.24/5.55 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 != zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % pi_half_neq_zero
% 5.24/5.55 thf(fact_7369_pi__half__less__two,axiom,
% 5.24/5.55 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_half_less_two
% 5.24/5.55 thf(fact_7370_pi__half__le__two,axiom,
% 5.24/5.55 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_half_le_two
% 5.24/5.55 thf(fact_7371_pi__half__gt__zero,axiom,
% 5.24/5.55 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_half_gt_zero
% 5.24/5.55 thf(fact_7372_pi__half__ge__zero,axiom,
% 5.24/5.55 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pi_half_ge_zero
% 5.24/5.55 thf(fact_7373_m2pi__less__pi,axiom,
% 5.24/5.55 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.24/5.55
% 5.24/5.55 % m2pi_less_pi
% 5.24/5.55 thf(fact_7374_arctan__ubound,axiom,
% 5.24/5.55 ! [Y4: real] : ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_ubound
% 5.24/5.55 thf(fact_7375_arctan__one,axiom,
% 5.24/5.55 ( ( arctan @ one_one_real )
% 5.24/5.55 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_one
% 5.24/5.55 thf(fact_7376_minus__pi__half__less__zero,axiom,
% 5.24/5.55 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.24/5.55
% 5.24/5.55 % minus_pi_half_less_zero
% 5.24/5.55 thf(fact_7377_arctan__lbound,axiom,
% 5.24/5.55 ! [Y4: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_lbound
% 5.24/5.55 thf(fact_7378_arctan__bounded,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) )
% 5.24/5.55 & ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_bounded
% 5.24/5.55 thf(fact_7379_sums__if_H,axiom,
% 5.24/5.55 ! [G: nat > real,X: real] :
% 5.24/5.55 ( ( sums_real @ G @ X )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [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 ) ) ) ) )
% 5.24/5.55 @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_if'
% 5.24/5.55 thf(fact_7380_sums__if,axiom,
% 5.24/5.55 ! [G: nat > real,X: real,F: nat > real,Y4: real] :
% 5.24/5.55 ( ( sums_real @ G @ X )
% 5.24/5.55 => ( ( sums_real @ F @ Y4 )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [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 ) ) ) ) )
% 5.24/5.55 @ ( plus_plus_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sums_if
% 5.24/5.55 thf(fact_7381_sum__pos__lt__pair,axiom,
% 5.24/5.55 ! [F: nat > real,K: nat] :
% 5.24/5.55 ( ( summable_real @ F )
% 5.24/5.55 => ( ! [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 ) ) ) ) )
% 5.24/5.55 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sum_pos_lt_pair
% 5.24/5.55 thf(fact_7382_machin__Euler,axiom,
% 5.24/5.55 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.24/5.55 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % machin_Euler
% 5.24/5.55 thf(fact_7383_machin,axiom,
% 5.24/5.55 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % machin
% 5.24/5.55 thf(fact_7384_sin__cos__npi,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_npi
% 5.24/5.55 thf(fact_7385_diffs__equiv,axiom,
% 5.24/5.55 ! [C: nat > complex,X: complex] :
% 5.24/5.55 ( ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.24/5.55 => ( sums_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.24/5.55 @ ( suminf_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diffs_equiv
% 5.24/5.55 thf(fact_7386_diffs__equiv,axiom,
% 5.24/5.55 ! [C: nat > real,X: real] :
% 5.24/5.55 ( ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 5.24/5.55 => ( sums_real
% 5.24/5.55 @ ^ [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 ) ) ) )
% 5.24/5.55 @ ( suminf_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diffs_equiv
% 5.24/5.55 thf(fact_7387_cos__pi__eq__zero,axiom,
% 5.24/5.55 ! [M: nat] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_pi_eq_zero
% 5.24/5.55 thf(fact_7388_monoI1,axiom,
% 5.24/5.55 ! [X7: nat > real] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.24/5.55 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI1
% 5.24/5.55 thf(fact_7389_monoI1,axiom,
% 5.24/5.55 ! [X7: nat > set_nat] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_set_nat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.24/5.55 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI1
% 5.24/5.55 thf(fact_7390_monoI1,axiom,
% 5.24/5.55 ! [X7: nat > rat] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_rat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.24/5.55 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI1
% 5.24/5.55 thf(fact_7391_monoI1,axiom,
% 5.24/5.55 ! [X7: nat > num] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_num @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.24/5.55 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI1
% 5.24/5.55 thf(fact_7392_monoI1,axiom,
% 5.24/5.55 ! [X7: nat > nat] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_nat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.24/5.55 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI1
% 5.24/5.55 thf(fact_7393_monoI1,axiom,
% 5.24/5.55 ! [X7: nat > int] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_int @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.24/5.55 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI1
% 5.24/5.55 thf(fact_7394_monoI2,axiom,
% 5.24/5.55 ! [X7: nat > real] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_real @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.24/5.55 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI2
% 5.24/5.55 thf(fact_7395_monoI2,axiom,
% 5.24/5.55 ! [X7: nat > set_nat] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_set_nat @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.24/5.55 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI2
% 5.24/5.55 thf(fact_7396_monoI2,axiom,
% 5.24/5.55 ! [X7: nat > rat] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_rat @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.24/5.55 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI2
% 5.24/5.55 thf(fact_7397_monoI2,axiom,
% 5.24/5.55 ! [X7: nat > num] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_num @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.24/5.55 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI2
% 5.24/5.55 thf(fact_7398_monoI2,axiom,
% 5.24/5.55 ! [X7: nat > nat] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_nat @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.24/5.55 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI2
% 5.24/5.55 thf(fact_7399_monoI2,axiom,
% 5.24/5.55 ! [X7: nat > int] :
% 5.24/5.55 ( ! [M4: nat,N3: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.24/5.55 => ( ord_less_eq_int @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.24/5.55 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoI2
% 5.24/5.55 thf(fact_7400_monoseq__def,axiom,
% 5.24/5.55 ( topolo6980174941875973593q_real
% 5.24/5.55 = ( ^ [X6: nat > real] :
% 5.24/5.55 ( ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_real @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) )
% 5.24/5.55 | ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_real @ ( X6 @ N2 ) @ ( X6 @ M2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_def
% 5.24/5.55 thf(fact_7401_monoseq__def,axiom,
% 5.24/5.55 ( topolo7278393974255667507et_nat
% 5.24/5.55 = ( ^ [X6: nat > set_nat] :
% 5.24/5.55 ( ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_set_nat @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) )
% 5.24/5.55 | ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_set_nat @ ( X6 @ N2 ) @ ( X6 @ M2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_def
% 5.24/5.55 thf(fact_7402_monoseq__def,axiom,
% 5.24/5.55 ( topolo4267028734544971653eq_rat
% 5.24/5.55 = ( ^ [X6: nat > rat] :
% 5.24/5.55 ( ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_rat @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) )
% 5.24/5.55 | ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_rat @ ( X6 @ N2 ) @ ( X6 @ M2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_def
% 5.24/5.55 thf(fact_7403_monoseq__def,axiom,
% 5.24/5.55 ( topolo1459490580787246023eq_num
% 5.24/5.55 = ( ^ [X6: nat > num] :
% 5.24/5.55 ( ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_num @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) )
% 5.24/5.55 | ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_num @ ( X6 @ N2 ) @ ( X6 @ M2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_def
% 5.24/5.55 thf(fact_7404_monoseq__def,axiom,
% 5.24/5.55 ( topolo4902158794631467389eq_nat
% 5.24/5.55 = ( ^ [X6: nat > nat] :
% 5.24/5.55 ( ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_nat @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) )
% 5.24/5.55 | ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_nat @ ( X6 @ N2 ) @ ( X6 @ M2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_def
% 5.24/5.55 thf(fact_7405_monoseq__def,axiom,
% 5.24/5.55 ( topolo4899668324122417113eq_int
% 5.24/5.55 = ( ^ [X6: nat > int] :
% 5.24/5.55 ( ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_int @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) )
% 5.24/5.55 | ! [M2: nat,N2: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.55 => ( ord_less_eq_int @ ( X6 @ N2 ) @ ( X6 @ M2 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_def
% 5.24/5.55 thf(fact_7406_cos__zero,axiom,
% 5.24/5.55 ( ( cos_complex @ zero_zero_complex )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % cos_zero
% 5.24/5.55 thf(fact_7407_cos__zero,axiom,
% 5.24/5.55 ( ( cos_real @ zero_zero_real )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_zero
% 5.24/5.55 thf(fact_7408_cos__pi,axiom,
% 5.24/5.55 ( ( cos_real @ pi )
% 5.24/5.55 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_pi
% 5.24/5.55 thf(fact_7409_cos__periodic__pi2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_periodic_pi2
% 5.24/5.55 thf(fact_7410_cos__periodic__pi,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_periodic_pi
% 5.24/5.55 thf(fact_7411_sin__periodic__pi2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_periodic_pi2
% 5.24/5.55 thf(fact_7412_sin__periodic__pi,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_periodic_pi
% 5.24/5.55 thf(fact_7413_sin__cos__squared__add3,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_squared_add3
% 5.24/5.55 thf(fact_7414_sin__cos__squared__add3,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_squared_add3
% 5.24/5.55 thf(fact_7415_sin__npi,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_npi
% 5.24/5.55 thf(fact_7416_sin__npi2,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_npi2
% 5.24/5.55 thf(fact_7417_sin__npi__int,axiom,
% 5.24/5.55 ! [N: int] :
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_npi_int
% 5.24/5.55 thf(fact_7418_cos__pi__half,axiom,
% 5.24/5.55 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_pi_half
% 5.24/5.55 thf(fact_7419_sin__two__pi,axiom,
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_two_pi
% 5.24/5.55 thf(fact_7420_sin__pi__half,axiom,
% 5.24/5.55 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_pi_half
% 5.24/5.55 thf(fact_7421_cos__two__pi,axiom,
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_two_pi
% 5.24/5.55 thf(fact_7422_cos__periodic,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.24/5.55 = ( cos_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_periodic
% 5.24/5.55 thf(fact_7423_sin__periodic,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.24/5.55 = ( sin_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_periodic
% 5.24/5.55 thf(fact_7424_cos__2pi__minus,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.24/5.55 = ( cos_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_2pi_minus
% 5.24/5.55 thf(fact_7425_cos__npi2,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.55 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_npi2
% 5.24/5.55 thf(fact_7426_cos__npi,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.24/5.55 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_npi
% 5.24/5.55 thf(fact_7427_sin__cos__squared__add2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_squared_add2
% 5.24/5.55 thf(fact_7428_sin__cos__squared__add2,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_squared_add2
% 5.24/5.55 thf(fact_7429_sin__cos__squared__add,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_squared_add
% 5.24/5.55 thf(fact_7430_sin__cos__squared__add,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( 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 ) ) ) )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_squared_add
% 5.24/5.55 thf(fact_7431_sin__2npi,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_2npi
% 5.24/5.55 thf(fact_7432_cos__2npi,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_2npi
% 5.24/5.55 thf(fact_7433_sin__2pi__minus,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_2pi_minus
% 5.24/5.55 thf(fact_7434_sin__int__2pin,axiom,
% 5.24/5.55 ! [N: int] :
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_int_2pin
% 5.24/5.55 thf(fact_7435_cos__int__2pin,axiom,
% 5.24/5.55 ! [N: int] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_int_2pin
% 5.24/5.55 thf(fact_7436_cos__3over2__pi,axiom,
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_3over2_pi
% 5.24/5.55 thf(fact_7437_sin__3over2__pi,axiom,
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.24/5.55 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_3over2_pi
% 5.24/5.55 thf(fact_7438_cos__npi__int,axiom,
% 5.24/5.55 ! [N: int] :
% 5.24/5.55 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.24/5.55 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.24/5.55 = one_one_real ) )
% 5.24/5.55 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.24/5.55 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.24/5.55 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_npi_int
% 5.24/5.55 thf(fact_7439_sin__add,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( sin_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.55 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_add
% 5.24/5.55 thf(fact_7440_sin__diff,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( sin_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.55 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_diff
% 5.24/5.55 thf(fact_7441_polar__Ex,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ? [R3: real,A3: real] :
% 5.24/5.55 ( ( X
% 5.24/5.55 = ( times_times_real @ R3 @ ( cos_real @ A3 ) ) )
% 5.24/5.55 & ( Y4
% 5.24/5.55 = ( times_times_real @ R3 @ ( sin_real @ A3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % polar_Ex
% 5.24/5.55 thf(fact_7442_cos__one__sin__zero,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( ( cos_complex @ X )
% 5.24/5.55 = one_one_complex )
% 5.24/5.55 => ( ( sin_complex @ X )
% 5.24/5.55 = zero_zero_complex ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_one_sin_zero
% 5.24/5.55 thf(fact_7443_cos__one__sin__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_one_sin_zero
% 5.24/5.55 thf(fact_7444_cos__add,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( cos_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.55 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_add
% 5.24/5.55 thf(fact_7445_cos__diff,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( cos_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.55 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_diff
% 5.24/5.55 thf(fact_7446_sin__zero__norm__cos__one,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 5.24/5.55 = one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_norm_cos_one
% 5.24/5.55 thf(fact_7447_sin__zero__norm__cos__one,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( ( sin_complex @ X )
% 5.24/5.55 = zero_zero_complex )
% 5.24/5.55 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 5.24/5.55 = one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_norm_cos_one
% 5.24/5.55 thf(fact_7448_sin__zero__abs__cos__one,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 5.24/5.55 = one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_abs_cos_one
% 5.24/5.55 thf(fact_7449_sin__double,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_double
% 5.24/5.55 thf(fact_7450_sin__double,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_double
% 5.24/5.55 thf(fact_7451_sin__le__one,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_le_one
% 5.24/5.55 thf(fact_7452_cos__le__one,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_le_one
% 5.24/5.55 thf(fact_7453_sin__cos__le1,axiom,
% 5.24/5.55 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) @ one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % sin_cos_le1
% 5.24/5.55 thf(fact_7454_sin__squared__eq,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_squared_eq
% 5.24/5.55 thf(fact_7455_sin__squared__eq,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_squared_eq
% 5.24/5.55 thf(fact_7456_cos__squared__eq,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_squared_eq
% 5.24/5.55 thf(fact_7457_cos__squared__eq,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_squared_eq
% 5.24/5.55 thf(fact_7458_sin__ge__minus__one,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_ge_minus_one
% 5.24/5.55 thf(fact_7459_cos__ge__minus__one,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_ge_minus_one
% 5.24/5.55 thf(fact_7460_abs__sin__le__one,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % abs_sin_le_one
% 5.24/5.55 thf(fact_7461_abs__cos__le__one,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % abs_cos_le_one
% 5.24/5.55 thf(fact_7462_sin__times__sin,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z2 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z2 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_times_sin
% 5.24/5.55 thf(fact_7463_sin__times__sin,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( times_times_real @ ( sin_real @ W2 ) @ ( sin_real @ Z2 ) )
% 5.24/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z2 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_times_sin
% 5.24/5.55 thf(fact_7464_sin__times__cos,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( cos_complex @ Z2 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z2 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_times_cos
% 5.24/5.55 thf(fact_7465_sin__times__cos,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( times_times_real @ ( sin_real @ W2 ) @ ( cos_real @ Z2 ) )
% 5.24/5.55 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z2 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_times_cos
% 5.24/5.55 thf(fact_7466_cos__times__sin,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( sin_complex @ Z2 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z2 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_times_sin
% 5.24/5.55 thf(fact_7467_cos__times__sin,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( times_times_real @ ( cos_real @ W2 ) @ ( sin_real @ Z2 ) )
% 5.24/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z2 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_times_sin
% 5.24/5.55 thf(fact_7468_sin__plus__sin,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( plus_plus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z2 ) )
% 5.24/5.55 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_plus_sin
% 5.24/5.55 thf(fact_7469_sin__plus__sin,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( plus_plus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z2 ) )
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_plus_sin
% 5.24/5.55 thf(fact_7470_sin__diff__sin,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( minus_minus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z2 ) )
% 5.24/5.55 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_diff_sin
% 5.24/5.55 thf(fact_7471_sin__diff__sin,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( minus_minus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z2 ) )
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_diff_sin
% 5.24/5.55 thf(fact_7472_cos__diff__cos,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( minus_minus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z2 ) )
% 5.24/5.55 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z2 @ W2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_diff_cos
% 5.24/5.55 thf(fact_7473_cos__diff__cos,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( minus_minus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z2 ) )
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z2 @ W2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_diff_cos
% 5.24/5.55 thf(fact_7474_cos__double,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double
% 5.24/5.55 thf(fact_7475_cos__double,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double
% 5.24/5.55 thf(fact_7476_cos__double__sin,axiom,
% 5.24/5.55 ! [W2: complex] :
% 5.24/5.55 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W2 ) )
% 5.24/5.55 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double_sin
% 5.24/5.55 thf(fact_7477_cos__double__sin,axiom,
% 5.24/5.55 ! [W2: real] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W2 ) )
% 5.24/5.55 = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double_sin
% 5.24/5.55 thf(fact_7478_cos__two__neq__zero,axiom,
% 5.24/5.55 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 != zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % cos_two_neq_zero
% 5.24/5.55 thf(fact_7479_sin__zero__iff__int2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 = ( ? [I4: int] :
% 5.24/5.55 ( X
% 5.24/5.55 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_iff_int2
% 5.24/5.55 thf(fact_7480_diffs__def,axiom,
% 5.24/5.55 ( diffs_int
% 5.24/5.55 = ( ^ [C2: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diffs_def
% 5.24/5.55 thf(fact_7481_diffs__def,axiom,
% 5.24/5.55 ( diffs_real
% 5.24/5.55 = ( ^ [C2: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diffs_def
% 5.24/5.55 thf(fact_7482_diffs__def,axiom,
% 5.24/5.55 ( diffs_rat
% 5.24/5.55 = ( ^ [C2: nat > rat,N2: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % diffs_def
% 5.24/5.55 thf(fact_7483_sincos__total__pi,axiom,
% 5.24/5.55 ! [Y4: real,X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.55 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.55 & ( ord_less_eq_real @ T3 @ pi )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( cos_real @ T3 ) )
% 5.24/5.55 & ( Y4
% 5.24/5.55 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sincos_total_pi
% 5.24/5.55 thf(fact_7484_sin__expansion__lemma,axiom,
% 5.24/5.55 ! [X: real,M: nat] :
% 5.24/5.55 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_expansion_lemma
% 5.24/5.55 thf(fact_7485_cos__expansion__lemma,axiom,
% 5.24/5.55 ! [X: real,M: nat] :
% 5.24/5.55 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_expansion_lemma
% 5.24/5.55 thf(fact_7486_termdiff__converges__all,axiom,
% 5.24/5.55 ! [C: nat > complex,X: complex] :
% 5.24/5.55 ( ! [X3: complex] :
% 5.24/5.55 ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 5.24/5.55 => ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % termdiff_converges_all
% 5.24/5.55 thf(fact_7487_termdiff__converges__all,axiom,
% 5.24/5.55 ! [C: nat > real,X: real] :
% 5.24/5.55 ( ! [X3: real] :
% 5.24/5.55 ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % termdiff_converges_all
% 5.24/5.55 thf(fact_7488_sin__gt__zero__02,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_gt_zero_02
% 5.24/5.55 thf(fact_7489_cos__two__less__zero,axiom,
% 5.24/5.55 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.24/5.55
% 5.24/5.55 % cos_two_less_zero
% 5.24/5.55 thf(fact_7490_cos__is__zero,axiom,
% 5.24/5.55 ? [X3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.24/5.55 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 & ( ( cos_real @ X3 )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 & ! [Y5: real] :
% 5.24/5.55 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.24/5.55 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 & ( ( cos_real @ Y5 )
% 5.24/5.55 = zero_zero_real ) )
% 5.24/5.55 => ( Y5 = X3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_is_zero
% 5.24/5.55 thf(fact_7491_cos__two__le__zero,axiom,
% 5.24/5.55 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.24/5.55
% 5.24/5.55 % cos_two_le_zero
% 5.24/5.55 thf(fact_7492_cos__total,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.55 => ? [X3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.24/5.55 & ( ord_less_eq_real @ X3 @ pi )
% 5.24/5.55 & ( ( cos_real @ X3 )
% 5.24/5.55 = Y4 )
% 5.24/5.55 & ! [Y5: real] :
% 5.24/5.55 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.24/5.55 & ( ord_less_eq_real @ Y5 @ pi )
% 5.24/5.55 & ( ( cos_real @ Y5 )
% 5.24/5.55 = Y4 ) )
% 5.24/5.55 => ( Y5 = X3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_total
% 5.24/5.55 thf(fact_7493_sincos__total__pi__half,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.55 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.55 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( cos_real @ T3 ) )
% 5.24/5.55 & ( Y4
% 5.24/5.55 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sincos_total_pi_half
% 5.24/5.55 thf(fact_7494_sincos__total__2pi__le,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.55 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( cos_real @ T3 ) )
% 5.24/5.55 & ( Y4
% 5.24/5.55 = ( sin_real @ T3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sincos_total_2pi_le
% 5.24/5.55 thf(fact_7495_sincos__total__2pi,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ~ ! [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.55 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 => ( ( X
% 5.24/5.55 = ( cos_real @ T3 ) )
% 5.24/5.55 => ( Y4
% 5.24/5.55 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sincos_total_2pi
% 5.24/5.55 thf(fact_7496_cos__times__cos,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z2 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z2 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_times_cos
% 5.24/5.55 thf(fact_7497_cos__times__cos,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( times_times_real @ ( cos_real @ W2 ) @ ( cos_real @ Z2 ) )
% 5.24/5.55 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z2 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_times_cos
% 5.24/5.55 thf(fact_7498_cos__plus__cos,axiom,
% 5.24/5.55 ! [W2: complex,Z2: complex] :
% 5.24/5.55 ( ( plus_plus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z2 ) )
% 5.24/5.55 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_plus_cos
% 5.24/5.55 thf(fact_7499_cos__plus__cos,axiom,
% 5.24/5.55 ! [W2: real,Z2: real] :
% 5.24/5.55 ( ( plus_plus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z2 ) )
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_plus_cos
% 5.24/5.55 thf(fact_7500_sin__gt__zero2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_gt_zero2
% 5.24/5.55 thf(fact_7501_sin__lt__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ pi @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_lt_zero
% 5.24/5.55 thf(fact_7502_cos__double__less__one,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.55 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double_less_one
% 5.24/5.55 thf(fact_7503_sin__30,axiom,
% 5.24/5.55 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.24/5.55 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_30
% 5.24/5.55 thf(fact_7504_cos__gt__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_gt_zero
% 5.24/5.55 thf(fact_7505_sin__monotone__2pi__le,axiom,
% 5.24/5.55 ! [Y4: real,X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_eq_real @ Y4 @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_eq_real @ ( sin_real @ Y4 ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_monotone_2pi_le
% 5.24/5.55 thf(fact_7506_sin__mono__le__eq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_mono_le_eq
% 5.24/5.55 thf(fact_7507_sin__inj__pi,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ( sin_real @ X )
% 5.24/5.55 = ( sin_real @ Y4 ) )
% 5.24/5.55 => ( X = Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_inj_pi
% 5.24/5.55 thf(fact_7508_cos__60,axiom,
% 5.24/5.55 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.24/5.55 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_60
% 5.24/5.55 thf(fact_7509_cos__one__2pi__int,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 = ( ? [X2: int] :
% 5.24/5.55 ( X
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_one_2pi_int
% 5.24/5.55 thf(fact_7510_cos__double__cos,axiom,
% 5.24/5.55 ! [W2: complex] :
% 5.24/5.55 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W2 ) )
% 5.24/5.55 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double_cos
% 5.24/5.55 thf(fact_7511_cos__double__cos,axiom,
% 5.24/5.55 ! [W2: real] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W2 ) )
% 5.24/5.55 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_double_cos
% 5.24/5.55 thf(fact_7512_cos__treble__cos,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_treble_cos
% 5.24/5.55 thf(fact_7513_cos__treble__cos,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_treble_cos
% 5.24/5.55 thf(fact_7514_termdiff__converges,axiom,
% 5.24/5.55 ! [X: real,K5: real,C: nat > real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 5.24/5.55 => ( ! [X3: real] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.24/5.55 => ( summable_real
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % termdiff_converges
% 5.24/5.55 thf(fact_7515_termdiff__converges,axiom,
% 5.24/5.55 ! [X: complex,K5: real,C: nat > complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 5.24/5.55 => ( ! [X3: complex] :
% 5.24/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 5.24/5.55 => ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) )
% 5.24/5.55 => ( summable_complex
% 5.24/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % termdiff_converges
% 5.24/5.55 thf(fact_7516_sin__le__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ pi @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_le_zero
% 5.24/5.55 thf(fact_7517_sin__less__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.55 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_less_zero
% 5.24/5.55 thf(fact_7518_sin__monotone__2pi,axiom,
% 5.24/5.55 ! [Y4: real,X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_real @ ( sin_real @ Y4 ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_monotone_2pi
% 5.24/5.55 thf(fact_7519_sin__mono__less__eq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) )
% 5.24/5.55 = ( ord_less_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_mono_less_eq
% 5.24/5.55 thf(fact_7520_sin__total,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.55 => ? [X3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.24/5.55 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( sin_real @ X3 )
% 5.24/5.55 = Y4 )
% 5.24/5.55 & ! [Y5: real] :
% 5.24/5.55 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.24/5.55 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( sin_real @ Y5 )
% 5.24/5.55 = Y4 ) )
% 5.24/5.55 => ( Y5 = X3 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_total
% 5.24/5.55 thf(fact_7521_cos__gt__zero__pi,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_gt_zero_pi
% 5.24/5.55 thf(fact_7522_cos__ge__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_ge_zero
% 5.24/5.55 thf(fact_7523_cos__one__2pi,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 = ( ? [X2: nat] :
% 5.24/5.55 ( X
% 5.24/5.55 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.24/5.55 | ? [X2: nat] :
% 5.24/5.55 ( X
% 5.24/5.55 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_one_2pi
% 5.24/5.55 thf(fact_7524_sin__pi__divide__n__gt__0,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_pi_divide_n_gt_0
% 5.24/5.55 thf(fact_7525_sin__zero__iff__int,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 = ( ? [I4: int] :
% 5.24/5.55 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_iff_int
% 5.24/5.55 thf(fact_7526_cos__zero__iff__int,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 = ( ? [I4: int] :
% 5.24/5.55 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_zero_iff_int
% 5.24/5.55 thf(fact_7527_sin__zero__lemma,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 => ? [N3: nat] :
% 5.24/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_lemma
% 5.24/5.55 thf(fact_7528_sin__zero__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( sin_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 = ( ? [N2: nat] :
% 5.24/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.55 | ? [N2: nat] :
% 5.24/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_zero_iff
% 5.24/5.55 thf(fact_7529_cos__zero__lemma,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ( cos_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 => ? [N3: nat] :
% 5.24/5.55 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_zero_lemma
% 5.24/5.55 thf(fact_7530_cos__zero__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 = ( ? [N2: nat] :
% 5.24/5.55 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.55 | ? [N2: nat] :
% 5.24/5.55 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.24/5.55 & ( X
% 5.24/5.55 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_zero_iff
% 5.24/5.55 thf(fact_7531_mono__SucI1,axiom,
% 5.24/5.55 ! [X7: nat > real] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_real @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.24/5.55 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI1
% 5.24/5.55 thf(fact_7532_mono__SucI1,axiom,
% 5.24/5.55 ! [X7: nat > set_nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.24/5.55 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI1
% 5.24/5.55 thf(fact_7533_mono__SucI1,axiom,
% 5.24/5.55 ! [X7: nat > rat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.24/5.55 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI1
% 5.24/5.55 thf(fact_7534_mono__SucI1,axiom,
% 5.24/5.55 ! [X7: nat > num] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_num @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.24/5.55 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI1
% 5.24/5.55 thf(fact_7535_mono__SucI1,axiom,
% 5.24/5.55 ! [X7: nat > nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.24/5.55 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI1
% 5.24/5.55 thf(fact_7536_mono__SucI1,axiom,
% 5.24/5.55 ! [X7: nat > int] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_int @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.24/5.55 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI1
% 5.24/5.55 thf(fact_7537_mono__SucI2,axiom,
% 5.24/5.55 ! [X7: nat > real] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_real @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.24/5.55 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI2
% 5.24/5.55 thf(fact_7538_mono__SucI2,axiom,
% 5.24/5.55 ! [X7: nat > set_nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.24/5.55 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI2
% 5.24/5.55 thf(fact_7539_mono__SucI2,axiom,
% 5.24/5.55 ! [X7: nat > rat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.24/5.55 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI2
% 5.24/5.55 thf(fact_7540_mono__SucI2,axiom,
% 5.24/5.55 ! [X7: nat > num] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_num @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.24/5.55 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI2
% 5.24/5.55 thf(fact_7541_mono__SucI2,axiom,
% 5.24/5.55 ! [X7: nat > nat] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.24/5.55 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI2
% 5.24/5.55 thf(fact_7542_mono__SucI2,axiom,
% 5.24/5.55 ! [X7: nat > int] :
% 5.24/5.55 ( ! [N3: nat] : ( ord_less_eq_int @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.24/5.55 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.24/5.55
% 5.24/5.55 % mono_SucI2
% 5.24/5.55 thf(fact_7543_monoseq__Suc,axiom,
% 5.24/5.55 ( topolo6980174941875973593q_real
% 5.24/5.55 = ( ^ [X6: nat > real] :
% 5.24/5.55 ( ! [N2: nat] : ( ord_less_eq_real @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.24/5.55 | ! [N2: nat] : ( ord_less_eq_real @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_Suc
% 5.24/5.55 thf(fact_7544_monoseq__Suc,axiom,
% 5.24/5.55 ( topolo7278393974255667507et_nat
% 5.24/5.55 = ( ^ [X6: nat > set_nat] :
% 5.24/5.55 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.24/5.55 | ! [N2: nat] : ( ord_less_eq_set_nat @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_Suc
% 5.24/5.55 thf(fact_7545_monoseq__Suc,axiom,
% 5.24/5.55 ( topolo4267028734544971653eq_rat
% 5.24/5.55 = ( ^ [X6: nat > rat] :
% 5.24/5.55 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.24/5.55 | ! [N2: nat] : ( ord_less_eq_rat @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_Suc
% 5.24/5.55 thf(fact_7546_monoseq__Suc,axiom,
% 5.24/5.55 ( topolo1459490580787246023eq_num
% 5.24/5.55 = ( ^ [X6: nat > num] :
% 5.24/5.55 ( ! [N2: nat] : ( ord_less_eq_num @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.24/5.55 | ! [N2: nat] : ( ord_less_eq_num @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_Suc
% 5.24/5.55 thf(fact_7547_monoseq__Suc,axiom,
% 5.24/5.55 ( topolo4902158794631467389eq_nat
% 5.24/5.55 = ( ^ [X6: nat > nat] :
% 5.24/5.55 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.24/5.55 | ! [N2: nat] : ( ord_less_eq_nat @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_Suc
% 5.24/5.55 thf(fact_7548_monoseq__Suc,axiom,
% 5.24/5.55 ( topolo4899668324122417113eq_int
% 5.24/5.55 = ( ^ [X6: nat > int] :
% 5.24/5.55 ( ! [N2: nat] : ( ord_less_eq_int @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.24/5.55 | ! [N2: nat] : ( ord_less_eq_int @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % monoseq_Suc
% 5.24/5.55 thf(fact_7549_Maclaurin__cos__expansion2,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.24/5.55 & ( ord_less_real @ T3 @ X )
% 5.24/5.55 & ( ( cos_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_cos_expansion2
% 5.24/5.55 thf(fact_7550_Maclaurin__minus__cos__expansion,axiom,
% 5.24/5.55 ! [N: nat,X: real] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_real @ X @ T3 )
% 5.24/5.55 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.24/5.55 & ( ( cos_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_minus_cos_expansion
% 5.24/5.55 thf(fact_7551_Maclaurin__cos__expansion,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ? [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.55 & ( ( cos_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_cos_expansion
% 5.24/5.55 thf(fact_7552_sin__paired,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( sums_real
% 5.24/5.55 @ ^ [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 ) ) )
% 5.24/5.55 @ ( sin_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_paired
% 5.24/5.55 thf(fact_7553_tan__double,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( ( cos_complex @ X )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_double
% 5.24/5.55 thf(fact_7554_tan__double,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.55 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_double
% 5.24/5.55 thf(fact_7555_complex__unimodular__polar,axiom,
% 5.24/5.55 ! [Z2: complex] :
% 5.24/5.55 ( ( ( real_V1022390504157884413omplex @ Z2 )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 => ~ ! [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.55 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.55 => ( Z2
% 5.24/5.55 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % complex_unimodular_polar
% 5.24/5.55 thf(fact_7556_tan__periodic__pi,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.24/5.55 = ( tan_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_periodic_pi
% 5.24/5.55 thf(fact_7557_fact__0,axiom,
% 5.24/5.55 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % fact_0
% 5.24/5.55 thf(fact_7558_fact__0,axiom,
% 5.24/5.55 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.24/5.55 = one_one_rat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_0
% 5.24/5.55 thf(fact_7559_fact__0,axiom,
% 5.24/5.55 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % fact_0
% 5.24/5.55 thf(fact_7560_fact__0,axiom,
% 5.24/5.55 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % fact_0
% 5.24/5.55 thf(fact_7561_fact__0,axiom,
% 5.24/5.55 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.24/5.55 = one_one_nat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_0
% 5.24/5.55 thf(fact_7562_fact__1,axiom,
% 5.24/5.55 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % fact_1
% 5.24/5.55 thf(fact_7563_fact__1,axiom,
% 5.24/5.55 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.24/5.55 = one_one_rat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_1
% 5.24/5.55 thf(fact_7564_fact__1,axiom,
% 5.24/5.55 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % fact_1
% 5.24/5.55 thf(fact_7565_fact__1,axiom,
% 5.24/5.55 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % fact_1
% 5.24/5.55 thf(fact_7566_fact__1,axiom,
% 5.24/5.55 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.24/5.55 = one_one_nat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_1
% 5.24/5.55 thf(fact_7567_fact__Suc__0,axiom,
% 5.24/5.55 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc_0
% 5.24/5.55 thf(fact_7568_fact__Suc__0,axiom,
% 5.24/5.55 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.24/5.55 = one_one_rat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc_0
% 5.24/5.55 thf(fact_7569_fact__Suc__0,axiom,
% 5.24/5.55 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc_0
% 5.24/5.55 thf(fact_7570_fact__Suc__0,axiom,
% 5.24/5.55 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc_0
% 5.24/5.55 thf(fact_7571_fact__Suc__0,axiom,
% 5.24/5.55 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.24/5.55 = one_one_nat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc_0
% 5.24/5.55 thf(fact_7572_fact__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.24/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc
% 5.24/5.55 thf(fact_7573_fact__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.24/5.55 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc
% 5.24/5.55 thf(fact_7574_fact__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc
% 5.24/5.55 thf(fact_7575_fact__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.24/5.55 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_Suc
% 5.24/5.55 thf(fact_7576_tan__npi,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.24/5.55 = zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % tan_npi
% 5.24/5.55 thf(fact_7577_tan__periodic__n,axiom,
% 5.24/5.55 ! [X: real,N: num] :
% 5.24/5.55 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.24/5.55 = ( tan_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_periodic_n
% 5.24/5.55 thf(fact_7578_tan__periodic__nat,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.24/5.55 = ( tan_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_periodic_nat
% 5.24/5.55 thf(fact_7579_tan__periodic__int,axiom,
% 5.24/5.55 ! [X: real,I2: int] :
% 5.24/5.55 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 5.24/5.55 = ( tan_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_periodic_int
% 5.24/5.55 thf(fact_7580_fact__2,axiom,
% 5.24/5.55 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_2
% 5.24/5.55 thf(fact_7581_fact__2,axiom,
% 5.24/5.55 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_2
% 5.24/5.55 thf(fact_7582_fact__2,axiom,
% 5.24/5.55 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_2
% 5.24/5.55 thf(fact_7583_fact__2,axiom,
% 5.24/5.55 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_2
% 5.24/5.55 thf(fact_7584_fact__2,axiom,
% 5.24/5.55 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_2
% 5.24/5.55 thf(fact_7585_norm__cos__sin,axiom,
% 5.24/5.55 ! [T: real] :
% 5.24/5.55 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % norm_cos_sin
% 5.24/5.55 thf(fact_7586_tan__periodic,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.24/5.55 = ( tan_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_periodic
% 5.24/5.55 thf(fact_7587_fact__ge__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_zero
% 5.24/5.55 thf(fact_7588_fact__ge__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_zero
% 5.24/5.55 thf(fact_7589_fact__ge__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_zero
% 5.24/5.55 thf(fact_7590_fact__ge__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_zero
% 5.24/5.55 thf(fact_7591_fact__gt__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_gt_zero
% 5.24/5.55 thf(fact_7592_fact__gt__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_gt_zero
% 5.24/5.55 thf(fact_7593_fact__gt__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_gt_zero
% 5.24/5.55 thf(fact_7594_fact__gt__zero,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_gt_zero
% 5.24/5.55 thf(fact_7595_fact__not__neg,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_not_neg
% 5.24/5.55 thf(fact_7596_fact__not__neg,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.24/5.55
% 5.24/5.55 % fact_not_neg
% 5.24/5.55 thf(fact_7597_fact__not__neg,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.24/5.55
% 5.24/5.55 % fact_not_neg
% 5.24/5.55 thf(fact_7598_fact__not__neg,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.24/5.55
% 5.24/5.55 % fact_not_neg
% 5.24/5.55 thf(fact_7599_fact__ge__1,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_1
% 5.24/5.55 thf(fact_7600_fact__ge__1,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_1
% 5.24/5.55 thf(fact_7601_fact__ge__1,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_1
% 5.24/5.55 thf(fact_7602_fact__ge__1,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_1
% 5.24/5.55 thf(fact_7603_fact__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mono
% 5.24/5.55 thf(fact_7604_fact__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mono
% 5.24/5.55 thf(fact_7605_fact__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mono
% 5.24/5.55 thf(fact_7606_fact__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mono
% 5.24/5.55 thf(fact_7607_fact__dvd,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_dvd
% 5.24/5.55 thf(fact_7608_fact__dvd,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_dvd
% 5.24/5.55 thf(fact_7609_fact__dvd,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_dvd
% 5.24/5.55 thf(fact_7610_fact__dvd,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_dvd
% 5.24/5.55 thf(fact_7611_complex__add,axiom,
% 5.24/5.55 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.55 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.24/5.55 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % complex_add
% 5.24/5.55 thf(fact_7612_fact__less__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.55 => ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_less_mono
% 5.24/5.55 thf(fact_7613_fact__less__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.55 => ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_less_mono
% 5.24/5.55 thf(fact_7614_fact__less__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.55 => ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_less_mono
% 5.24/5.55 thf(fact_7615_fact__less__mono,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.55 => ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_less_mono
% 5.24/5.55 thf(fact_7616_fact__mod,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.24/5.55 = zero_zero_int ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mod
% 5.24/5.55 thf(fact_7617_fact__mod,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.24/5.55 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mod
% 5.24/5.55 thf(fact_7618_fact__mod,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.24/5.55 = zero_zero_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mod
% 5.24/5.55 thf(fact_7619_fact__fact__dvd__fact,axiom,
% 5.24/5.55 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_fact_dvd_fact
% 5.24/5.55 thf(fact_7620_fact__fact__dvd__fact,axiom,
% 5.24/5.55 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_fact_dvd_fact
% 5.24/5.55 thf(fact_7621_fact__fact__dvd__fact,axiom,
% 5.24/5.55 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_fact_dvd_fact
% 5.24/5.55 thf(fact_7622_fact__fact__dvd__fact,axiom,
% 5.24/5.55 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_fact_dvd_fact
% 5.24/5.55 thf(fact_7623_fact__fact__dvd__fact,axiom,
% 5.24/5.55 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_fact_dvd_fact
% 5.24/5.55 thf(fact_7624_fact__le__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_le_power
% 5.24/5.55 thf(fact_7625_fact__le__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_le_power
% 5.24/5.55 thf(fact_7626_fact__le__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_le_power
% 5.24/5.55 thf(fact_7627_fact__le__power,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_le_power
% 5.24/5.55 thf(fact_7628_complex__mult,axiom,
% 5.24/5.55 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.55 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.24/5.55 = ( 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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % complex_mult
% 5.24/5.55 thf(fact_7629_one__complex_Ocode,axiom,
% 5.24/5.55 ( one_one_complex
% 5.24/5.55 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_complex.code
% 5.24/5.55 thf(fact_7630_Complex__eq__1,axiom,
% 5.24/5.55 ! [A: real,B: real] :
% 5.24/5.55 ( ( ( complex2 @ A @ B )
% 5.24/5.55 = one_one_complex )
% 5.24/5.55 = ( ( A = one_one_real )
% 5.24/5.55 & ( B = zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Complex_eq_1
% 5.24/5.55 thf(fact_7631_tan__def,axiom,
% 5.24/5.55 ( tan_complex
% 5.24/5.55 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_def
% 5.24/5.55 thf(fact_7632_tan__def,axiom,
% 5.24/5.55 ( tan_real
% 5.24/5.55 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_def
% 5.24/5.55 thf(fact_7633_choose__dvd,axiom,
% 5.24/5.55 ! [K: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.55 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % choose_dvd
% 5.24/5.55 thf(fact_7634_choose__dvd,axiom,
% 5.24/5.55 ! [K: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.55 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % choose_dvd
% 5.24/5.55 thf(fact_7635_choose__dvd,axiom,
% 5.24/5.55 ! [K: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.55 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % choose_dvd
% 5.24/5.55 thf(fact_7636_choose__dvd,axiom,
% 5.24/5.55 ! [K: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.55 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % choose_dvd
% 5.24/5.55 thf(fact_7637_choose__dvd,axiom,
% 5.24/5.55 ! [K: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.55 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % choose_dvd
% 5.24/5.55 thf(fact_7638_fact__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.24/5.55 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_numeral
% 5.24/5.55 thf(fact_7639_fact__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.24/5.55 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_numeral
% 5.24/5.55 thf(fact_7640_fact__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.24/5.55 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_numeral
% 5.24/5.55 thf(fact_7641_fact__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.24/5.55 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_numeral
% 5.24/5.55 thf(fact_7642_fact__numeral,axiom,
% 5.24/5.55 ! [K: num] :
% 5.24/5.55 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.24/5.55 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_numeral
% 5.24/5.55 thf(fact_7643_Complex__eq__neg__1,axiom,
% 5.24/5.55 ! [A: real,B: real] :
% 5.24/5.55 ( ( ( complex2 @ A @ B )
% 5.24/5.55 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.24/5.55 = ( ( A
% 5.24/5.55 = ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.55 & ( B = zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Complex_eq_neg_1
% 5.24/5.55 thf(fact_7644_square__fact__le__2__fact,axiom,
% 5.24/5.55 ! [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % square_fact_le_2_fact
% 5.24/5.55 thf(fact_7645_tan__45,axiom,
% 5.24/5.55 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % tan_45
% 5.24/5.55 thf(fact_7646_fact__num__eq__if,axiom,
% 5.24/5.55 ( semiri5044797733671781792omplex
% 5.24/5.55 = ( ^ [M2: nat] : ( if_complex @ ( M2 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_num_eq_if
% 5.24/5.55 thf(fact_7647_fact__num__eq__if,axiom,
% 5.24/5.55 ( semiri1406184849735516958ct_int
% 5.24/5.55 = ( ^ [M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_num_eq_if
% 5.24/5.55 thf(fact_7648_fact__num__eq__if,axiom,
% 5.24/5.55 ( semiri773545260158071498ct_rat
% 5.24/5.55 = ( ^ [M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_num_eq_if
% 5.24/5.55 thf(fact_7649_fact__num__eq__if,axiom,
% 5.24/5.55 ( semiri2265585572941072030t_real
% 5.24/5.55 = ( ^ [M2: nat] : ( if_real @ ( M2 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_num_eq_if
% 5.24/5.55 thf(fact_7650_fact__num__eq__if,axiom,
% 5.24/5.55 ( semiri1408675320244567234ct_nat
% 5.24/5.55 = ( ^ [M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_num_eq_if
% 5.24/5.55 thf(fact_7651_fact__reduce,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( semiri1406184849735516958ct_int @ N )
% 5.24/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_reduce
% 5.24/5.55 thf(fact_7652_fact__reduce,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( semiri773545260158071498ct_rat @ N )
% 5.24/5.55 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_reduce
% 5.24/5.55 thf(fact_7653_fact__reduce,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( semiri2265585572941072030t_real @ N )
% 5.24/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_reduce
% 5.24/5.55 thf(fact_7654_fact__reduce,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.24/5.55 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_reduce
% 5.24/5.55 thf(fact_7655_tan__gt__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_gt_zero
% 5.24/5.55 thf(fact_7656_lemma__tan__total,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.55 => ? [X3: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.24/5.55 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ord_less_real @ Y4 @ ( tan_real @ X3 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_tan_total
% 5.24/5.55 thf(fact_7657_tan__total,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ? [X3: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.24/5.55 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( tan_real @ X3 )
% 5.24/5.55 = Y4 )
% 5.24/5.55 & ! [Y5: real] :
% 5.24/5.55 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.24/5.55 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( tan_real @ Y5 )
% 5.24/5.55 = Y4 ) )
% 5.24/5.55 => ( Y5 = X3 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_total
% 5.24/5.55 thf(fact_7658_tan__monotone,axiom,
% 5.24/5.55 ! [Y4: real,X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_real @ ( tan_real @ Y4 ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_monotone
% 5.24/5.55 thf(fact_7659_tan__monotone_H,axiom,
% 5.24/5.55 ! [Y4: real,X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ X )
% 5.24/5.55 = ( ord_less_real @ ( tan_real @ Y4 ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_monotone'
% 5.24/5.55 thf(fact_7660_tan__mono__lt__eq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) )
% 5.24/5.55 = ( ord_less_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_mono_lt_eq
% 5.24/5.55 thf(fact_7661_lemma__tan__total1,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ? [X3: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.24/5.55 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( tan_real @ X3 )
% 5.24/5.55 = Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_tan_total1
% 5.24/5.55 thf(fact_7662_tan__minus__45,axiom,
% 5.24/5.55 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.55 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_minus_45
% 5.24/5.55 thf(fact_7663_tan__inverse,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y4 ) )
% 5.24/5.55 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_inverse
% 5.24/5.55 thf(fact_7664_add__tan__eq,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( ( cos_complex @ X )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ Y4 )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % add_tan_eq
% 5.24/5.55 thf(fact_7665_add__tan__eq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ Y4 )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) )
% 5.24/5.55 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % add_tan_eq
% 5.24/5.55 thf(fact_7666_tan__total__pos,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.55 => ? [X3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.24/5.55 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( tan_real @ X3 )
% 5.24/5.55 = Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_total_pos
% 5.24/5.55 thf(fact_7667_tan__pos__pi2__le,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_pos_pi2_le
% 5.24/5.55 thf(fact_7668_tan__less__zero,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.55 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_less_zero
% 5.24/5.55 thf(fact_7669_tan__mono__le,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_mono_le
% 5.24/5.55 thf(fact_7670_tan__mono__le__eq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.24/5.55 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_mono_le_eq
% 5.24/5.55 thf(fact_7671_tan__bound__pi2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_bound_pi2
% 5.24/5.55 thf(fact_7672_arctan__unique,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( ( tan_real @ X )
% 5.24/5.55 = Y4 )
% 5.24/5.55 => ( ( arctan @ Y4 )
% 5.24/5.55 = X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_unique
% 5.24/5.55 thf(fact_7673_arctan__tan,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.55 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( arctan @ ( tan_real @ X ) )
% 5.24/5.55 = X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan_tan
% 5.24/5.55 thf(fact_7674_arctan,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) )
% 5.24/5.55 & ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 & ( ( tan_real @ ( arctan @ Y4 ) )
% 5.24/5.55 = Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % arctan
% 5.24/5.55 thf(fact_7675_Maclaurin__zero,axiom,
% 5.24/5.55 ! [X: real,N: nat,Diff: nat > complex > real] :
% 5.24/5.55 ( ( X = zero_zero_real )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_zero
% 5.24/5.55 thf(fact_7676_Maclaurin__zero,axiom,
% 5.24/5.55 ! [X: real,N: nat,Diff: nat > real > real] :
% 5.24/5.55 ( ( X = zero_zero_real )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_zero
% 5.24/5.55 thf(fact_7677_Maclaurin__zero,axiom,
% 5.24/5.55 ! [X: real,N: nat,Diff: nat > rat > real] :
% 5.24/5.55 ( ( X = zero_zero_real )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_zero
% 5.24/5.55 thf(fact_7678_Maclaurin__zero,axiom,
% 5.24/5.55 ! [X: real,N: nat,Diff: nat > nat > real] :
% 5.24/5.55 ( ( X = zero_zero_real )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_zero
% 5.24/5.55 thf(fact_7679_Maclaurin__zero,axiom,
% 5.24/5.55 ! [X: real,N: nat,Diff: nat > int > real] :
% 5.24/5.55 ( ( X = zero_zero_real )
% 5.24/5.55 => ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_zero
% 5.24/5.55 thf(fact_7680_Maclaurin__lemma,axiom,
% 5.24/5.55 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.24/5.55 => ? [B7: real] :
% 5.24/5.55 ( ( F @ H2 )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ B7 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_lemma
% 5.24/5.55 thf(fact_7681_lemma__tan__add1,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( ( cos_complex @ X )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ Y4 )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_tan_add1
% 5.24/5.55 thf(fact_7682_lemma__tan__add1,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ Y4 )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) )
% 5.24/5.55 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_tan_add1
% 5.24/5.55 thf(fact_7683_tan__diff,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( ( cos_complex @ X )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ Y4 )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y4 ) )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y4 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_diff
% 5.24/5.55 thf(fact_7684_tan__diff,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ Y4 )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( tan_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_diff
% 5.24/5.55 thf(fact_7685_tan__add,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( ( cos_complex @ X )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ Y4 )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_add
% 5.24/5.55 thf(fact_7686_tan__add,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( cos_real @ X )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ Y4 )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( tan_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.55 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_add
% 5.24/5.55 thf(fact_7687_tan__total__pi4,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.55 => ? [Z: real] :
% 5.24/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z )
% 5.24/5.55 & ( ord_less_real @ Z @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.24/5.55 & ( ( tan_real @ Z )
% 5.24/5.55 = X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_total_pi4
% 5.24/5.55 thf(fact_7688_tan__half,axiom,
% 5.24/5.55 ( tan_complex
% 5.24/5.55 = ( ^ [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_half
% 5.24/5.55 thf(fact_7689_tan__half,axiom,
% 5.24/5.55 ( tan_real
% 5.24/5.55 = ( ^ [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 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % tan_half
% 5.24/5.55 thf(fact_7690_cos__coeff__def,axiom,
% 5.24/5.55 ( cos_coeff
% 5.24/5.55 = ( ^ [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 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_coeff_def
% 5.24/5.55 thf(fact_7691_cos__paired,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( sums_real
% 5.24/5.55 @ ^ [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 ) ) )
% 5.24/5.55 @ ( cos_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_paired
% 5.24/5.55 thf(fact_7692_Maclaurin__sin__expansion3,axiom,
% 5.24/5.55 ! [N: nat,X: real] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.24/5.55 & ( ord_less_real @ T3 @ X )
% 5.24/5.55 & ( ( sin_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_sin_expansion3
% 5.24/5.55 thf(fact_7693_Maclaurin__sin__expansion4,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.24/5.55 & ( ord_less_eq_real @ T3 @ X )
% 5.24/5.55 & ( ( sin_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_sin_expansion4
% 5.24/5.55 thf(fact_7694_Maclaurin__sin__expansion2,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ? [T3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.55 & ( ( sin_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_sin_expansion2
% 5.24/5.55 thf(fact_7695_Maclaurin__sin__expansion,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ? [T3: real] :
% 5.24/5.55 ( ( sin_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_sin_expansion
% 5.24/5.55 thf(fact_7696_sin__coeff__def,axiom,
% 5.24/5.55 ( sin_coeff
% 5.24/5.55 = ( ^ [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 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_coeff_def
% 5.24/5.55 thf(fact_7697_fact__ge__self,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_self
% 5.24/5.55 thf(fact_7698_fact__mono__nat,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_mono_nat
% 5.24/5.55 thf(fact_7699_fact__less__mono__nat,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.55 => ( ( ord_less_nat @ M @ N )
% 5.24/5.55 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_less_mono_nat
% 5.24/5.55 thf(fact_7700_fact__ge__Suc__0__nat,axiom,
% 5.24/5.55 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_ge_Suc_0_nat
% 5.24/5.55 thf(fact_7701_dvd__fact,axiom,
% 5.24/5.55 ! [M: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.24/5.55 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.55 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % dvd_fact
% 5.24/5.55 thf(fact_7702_fact__diff__Suc,axiom,
% 5.24/5.55 ! [N: nat,M: nat] :
% 5.24/5.55 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.24/5.55 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.24/5.55 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_diff_Suc
% 5.24/5.55 thf(fact_7703_fact__div__fact__le__pow,axiom,
% 5.24/5.55 ! [R2: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_eq_nat @ R2 @ N )
% 5.24/5.55 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % fact_div_fact_le_pow
% 5.24/5.55 thf(fact_7704_sin__coeff__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( sin_coeff @ ( suc @ N ) )
% 5.24/5.55 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_coeff_Suc
% 5.24/5.55 thf(fact_7705_cos__coeff__Suc,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( cos_coeff @ ( suc @ N ) )
% 5.24/5.55 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_coeff_Suc
% 5.24/5.55 thf(fact_7706_sin__tan,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( sin_real @ X )
% 5.24/5.55 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sin_tan
% 5.24/5.55 thf(fact_7707_cos__tan,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.55 => ( ( cos_real @ X )
% 5.24/5.55 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % cos_tan
% 5.24/5.55 thf(fact_7708_Maclaurin__exp__lt,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( X != zero_zero_real )
% 5.24/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.55 => ? [T3: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.24/5.55 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.55 & ( ( exp_real @ X )
% 5.24/5.55 = ( plus_plus_real
% 5.24/5.55 @ ( groups6591440286371151544t_real
% 5.24/5.55 @ ^ [M2: nat] : ( divide_divide_real @ ( power_power_real @ X @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) )
% 5.24/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.55 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % Maclaurin_exp_lt
% 5.24/5.55 thf(fact_7709_pochhammer__double,axiom,
% 5.24/5.55 ! [Z2: complex,N: nat] :
% 5.24/5.55 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.55 = ( 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 @ Z2 @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_double
% 5.24/5.55 thf(fact_7710_pochhammer__double,axiom,
% 5.24/5.55 ! [Z2: real,N: nat] :
% 5.24/5.55 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.55 = ( 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 @ Z2 @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_double
% 5.24/5.55 thf(fact_7711_pochhammer__double,axiom,
% 5.24/5.55 ! [Z2: rat,N: nat] :
% 5.24/5.55 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.55 = ( 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 @ Z2 @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_double
% 5.24/5.55 thf(fact_7712_of__nat__code,axiom,
% 5.24/5.55 ( semiri8010041392384452111omplex
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( semiri2816024913162550771omplex
% 5.24/5.55 @ ^ [I4: complex] : ( plus_plus_complex @ I4 @ one_one_complex )
% 5.24/5.55 @ N2
% 5.24/5.55 @ zero_zero_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code
% 5.24/5.55 thf(fact_7713_of__nat__code,axiom,
% 5.24/5.55 ( semiri1314217659103216013at_int
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( semiri8420488043553186161ux_int
% 5.24/5.55 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.24/5.55 @ N2
% 5.24/5.55 @ zero_zero_int ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code
% 5.24/5.55 thf(fact_7714_of__nat__code,axiom,
% 5.24/5.55 ( semiri5074537144036343181t_real
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( semiri7260567687927622513x_real
% 5.24/5.55 @ ^ [I4: real] : ( plus_plus_real @ I4 @ one_one_real )
% 5.24/5.55 @ N2
% 5.24/5.55 @ zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code
% 5.24/5.55 thf(fact_7715_of__nat__code,axiom,
% 5.24/5.55 ( semiri1316708129612266289at_nat
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( semiri8422978514062236437ux_nat
% 5.24/5.55 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.24/5.55 @ N2
% 5.24/5.55 @ zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code
% 5.24/5.55 thf(fact_7716_of__nat__code,axiom,
% 5.24/5.55 ( semiri681578069525770553at_rat
% 5.24/5.55 = ( ^ [N2: nat] :
% 5.24/5.55 ( semiri7787848453975740701ux_rat
% 5.24/5.55 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.24/5.55 @ N2
% 5.24/5.55 @ zero_zero_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % of_nat_code
% 5.24/5.55 thf(fact_7717_real__sqrt__eq__1__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( sqrt @ X )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 = ( X = one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_eq_1_iff
% 5.24/5.55 thf(fact_7718_real__sqrt__one,axiom,
% 5.24/5.55 ( ( sqrt @ one_one_real )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_one
% 5.24/5.55 thf(fact_7719_exp__zero,axiom,
% 5.24/5.55 ( ( exp_complex @ zero_zero_complex )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % exp_zero
% 5.24/5.55 thf(fact_7720_exp__zero,axiom,
% 5.24/5.55 ( ( exp_real @ zero_zero_real )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % exp_zero
% 5.24/5.55 thf(fact_7721_real__sqrt__gt__1__iff,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y4 ) )
% 5.24/5.55 = ( ord_less_real @ one_one_real @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_gt_1_iff
% 5.24/5.55 thf(fact_7722_real__sqrt__lt__1__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.24/5.55 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_lt_1_iff
% 5.24/5.55 thf(fact_7723_real__sqrt__le__1__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.24/5.55 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_le_1_iff
% 5.24/5.55 thf(fact_7724_real__sqrt__ge__1__iff,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y4 ) )
% 5.24/5.55 = ( ord_less_eq_real @ one_one_real @ Y4 ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_ge_1_iff
% 5.24/5.55 thf(fact_7725_pochhammer__0,axiom,
% 5.24/5.55 ! [A: complex] :
% 5.24/5.55 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0
% 5.24/5.55 thf(fact_7726_pochhammer__0,axiom,
% 5.24/5.55 ! [A: real] :
% 5.24/5.55 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0
% 5.24/5.55 thf(fact_7727_pochhammer__0,axiom,
% 5.24/5.55 ! [A: rat] :
% 5.24/5.55 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.24/5.55 = one_one_rat ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0
% 5.24/5.55 thf(fact_7728_pochhammer__0,axiom,
% 5.24/5.55 ! [A: nat] :
% 5.24/5.55 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.24/5.55 = one_one_nat ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0
% 5.24/5.55 thf(fact_7729_pochhammer__0,axiom,
% 5.24/5.55 ! [A: int] :
% 5.24/5.55 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.24/5.55 = one_one_int ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0
% 5.24/5.55 thf(fact_7730_exp__eq__one__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( exp_real @ X )
% 5.24/5.55 = one_one_real )
% 5.24/5.55 = ( X = zero_zero_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_eq_one_iff
% 5.24/5.55 thf(fact_7731_real__sqrt__mult__self,axiom,
% 5.24/5.55 ! [A: real] :
% 5.24/5.55 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.24/5.55 = ( abs_abs_real @ A ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_mult_self
% 5.24/5.55 thf(fact_7732_real__sqrt__abs2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.24/5.55 = ( abs_abs_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_abs2
% 5.24/5.55 thf(fact_7733_real__sqrt__four,axiom,
% 5.24/5.55 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_four
% 5.24/5.55 thf(fact_7734_one__less__exp__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 5.24/5.55 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_less_exp_iff
% 5.24/5.55 thf(fact_7735_exp__less__one__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 5.24/5.55 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_less_one_iff
% 5.24/5.55 thf(fact_7736_one__le__exp__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.24/5.55 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % one_le_exp_iff
% 5.24/5.55 thf(fact_7737_exp__le__one__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.24/5.55 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_le_one_iff
% 5.24/5.55 thf(fact_7738_real__sqrt__abs,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.55 = ( abs_abs_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_abs
% 5.24/5.55 thf(fact_7739_real__sqrt__pow2,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = X ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_pow2
% 5.24/5.55 thf(fact_7740_real__sqrt__pow2__iff,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = X )
% 5.24/5.55 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_pow2_iff
% 5.24/5.55 thf(fact_7741_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.24/5.55 ! [X: real,Y4: real,Xa2: real,Ya: real] :
% 5.24/5.55 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.55 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_sum_squares_mult_squared_eq
% 5.24/5.55 thf(fact_7742_real__sqrt__mult,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( sqrt @ ( times_times_real @ X @ Y4 ) )
% 5.24/5.55 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_mult
% 5.24/5.55 thf(fact_7743_exp__times__arg__commute,axiom,
% 5.24/5.55 ! [A2: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.24/5.55 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_times_arg_commute
% 5.24/5.55 thf(fact_7744_exp__times__arg__commute,axiom,
% 5.24/5.55 ! [A2: real] :
% 5.24/5.55 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.24/5.55 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_times_arg_commute
% 5.24/5.55 thf(fact_7745_real__sqrt__ge__one,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.55 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % real_sqrt_ge_one
% 5.24/5.55 thf(fact_7746_mult__exp__exp,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y4 ) )
% 5.24/5.55 = ( exp_complex @ ( plus_plus_complex @ X @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mult_exp_exp
% 5.24/5.55 thf(fact_7747_mult__exp__exp,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) )
% 5.24/5.55 = ( exp_real @ ( plus_plus_real @ X @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % mult_exp_exp
% 5.24/5.55 thf(fact_7748_exp__add__commuting,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( ( times_times_complex @ X @ Y4 )
% 5.24/5.55 = ( times_times_complex @ Y4 @ X ) )
% 5.24/5.55 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.55 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_add_commuting
% 5.24/5.55 thf(fact_7749_exp__add__commuting,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ( times_times_real @ X @ Y4 )
% 5.24/5.55 = ( times_times_real @ Y4 @ X ) )
% 5.24/5.55 => ( ( exp_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.55 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_add_commuting
% 5.24/5.55 thf(fact_7750_exp__diff,axiom,
% 5.24/5.55 ! [X: complex,Y4: complex] :
% 5.24/5.55 ( ( exp_complex @ ( minus_minus_complex @ X @ Y4 ) )
% 5.24/5.55 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_diff
% 5.24/5.55 thf(fact_7751_exp__diff,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( exp_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.55 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_diff
% 5.24/5.55 thf(fact_7752_pochhammer__pos,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_pos
% 5.24/5.55 thf(fact_7753_pochhammer__pos,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.55 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_pos
% 5.24/5.55 thf(fact_7754_pochhammer__pos,axiom,
% 5.24/5.55 ! [X: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.24/5.55 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_pos
% 5.24/5.55 thf(fact_7755_pochhammer__pos,axiom,
% 5.24/5.55 ! [X: int,N: nat] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ X )
% 5.24/5.55 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_pos
% 5.24/5.55 thf(fact_7756_pochhammer__eq__0__mono,axiom,
% 5.24/5.55 ! [A: complex,N: nat,M: nat] :
% 5.24/5.55 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.24/5.55 = zero_zero_complex )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.24/5.55 = zero_zero_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_eq_0_mono
% 5.24/5.55 thf(fact_7757_pochhammer__eq__0__mono,axiom,
% 5.24/5.55 ! [A: real,N: nat,M: nat] :
% 5.24/5.55 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.24/5.55 = zero_zero_real )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.24/5.55 = zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_eq_0_mono
% 5.24/5.55 thf(fact_7758_pochhammer__eq__0__mono,axiom,
% 5.24/5.55 ! [A: rat,N: nat,M: nat] :
% 5.24/5.55 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.24/5.55 = zero_zero_rat )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.24/5.55 = zero_zero_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_eq_0_mono
% 5.24/5.55 thf(fact_7759_pochhammer__neq__0__mono,axiom,
% 5.24/5.55 ! [A: complex,M: nat,N: nat] :
% 5.24/5.55 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.24/5.55 != zero_zero_complex )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.24/5.55 != zero_zero_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_neq_0_mono
% 5.24/5.55 thf(fact_7760_pochhammer__neq__0__mono,axiom,
% 5.24/5.55 ! [A: real,M: nat,N: nat] :
% 5.24/5.55 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.24/5.55 != zero_zero_real )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.24/5.55 != zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_neq_0_mono
% 5.24/5.55 thf(fact_7761_pochhammer__neq__0__mono,axiom,
% 5.24/5.55 ! [A: rat,M: nat,N: nat] :
% 5.24/5.55 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.24/5.55 != zero_zero_rat )
% 5.24/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.55 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.24/5.55 != zero_zero_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_neq_0_mono
% 5.24/5.55 thf(fact_7762_pochhammer__fact,axiom,
% 5.24/5.55 ( semiri5044797733671781792omplex
% 5.24/5.55 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_fact
% 5.24/5.55 thf(fact_7763_pochhammer__fact,axiom,
% 5.24/5.55 ( semiri773545260158071498ct_rat
% 5.24/5.55 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_fact
% 5.24/5.55 thf(fact_7764_pochhammer__fact,axiom,
% 5.24/5.55 ( semiri1406184849735516958ct_int
% 5.24/5.55 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_fact
% 5.24/5.55 thf(fact_7765_pochhammer__fact,axiom,
% 5.24/5.55 ( semiri2265585572941072030t_real
% 5.24/5.55 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_fact
% 5.24/5.55 thf(fact_7766_pochhammer__fact,axiom,
% 5.24/5.55 ( semiri1408675320244567234ct_nat
% 5.24/5.55 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_fact
% 5.24/5.55 thf(fact_7767_exp__gt__one,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_gt_one
% 5.24/5.55 thf(fact_7768_sqrt__add__le__add__sqrt,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.55 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y4 ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % sqrt_add_le_add_sqrt
% 5.24/5.55 thf(fact_7769_exp__ge__add__one__self,axiom,
% 5.24/5.55 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_ge_add_one_self
% 5.24/5.55 thf(fact_7770_le__real__sqrt__sumsq,axiom,
% 5.24/5.55 ! [X: real,Y4: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % le_real_sqrt_sumsq
% 5.24/5.55 thf(fact_7771_exp__minus__inverse,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.24/5.55 = one_one_real ) ).
% 5.24/5.55
% 5.24/5.55 % exp_minus_inverse
% 5.24/5.55 thf(fact_7772_exp__minus__inverse,axiom,
% 5.24/5.55 ! [X: complex] :
% 5.24/5.55 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.24/5.55 = one_one_complex ) ).
% 5.24/5.55
% 5.24/5.55 % exp_minus_inverse
% 5.24/5.55 thf(fact_7773_exp__of__nat__mult,axiom,
% 5.24/5.55 ! [N: nat,X: complex] :
% 5.24/5.55 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 5.24/5.55 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_of_nat_mult
% 5.24/5.55 thf(fact_7774_exp__of__nat__mult,axiom,
% 5.24/5.55 ! [N: nat,X: real] :
% 5.24/5.55 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 5.24/5.55 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_of_nat_mult
% 5.24/5.55 thf(fact_7775_exp__of__nat2__mult,axiom,
% 5.24/5.55 ! [X: complex,N: nat] :
% 5.24/5.55 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.24/5.55 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_of_nat2_mult
% 5.24/5.55 thf(fact_7776_exp__of__nat2__mult,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.55 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_of_nat2_mult
% 5.24/5.55 thf(fact_7777_pochhammer__nonneg,axiom,
% 5.24/5.55 ! [X: real,N: nat] :
% 5.24/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_nonneg
% 5.24/5.55 thf(fact_7778_pochhammer__nonneg,axiom,
% 5.24/5.55 ! [X: rat,N: nat] :
% 5.24/5.55 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.55 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_nonneg
% 5.24/5.55 thf(fact_7779_pochhammer__nonneg,axiom,
% 5.24/5.55 ! [X: nat,N: nat] :
% 5.24/5.55 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.24/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_nonneg
% 5.24/5.55 thf(fact_7780_pochhammer__nonneg,axiom,
% 5.24/5.55 ! [X: int,N: nat] :
% 5.24/5.55 ( ( ord_less_int @ zero_zero_int @ X )
% 5.24/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_nonneg
% 5.24/5.55 thf(fact_7781_pochhammer__0__left,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( N = zero_zero_nat )
% 5.24/5.55 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.24/5.55 = one_one_complex ) )
% 5.24/5.55 & ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.24/5.55 = zero_zero_complex ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0_left
% 5.24/5.55 thf(fact_7782_pochhammer__0__left,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( N = zero_zero_nat )
% 5.24/5.55 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.24/5.55 = one_one_real ) )
% 5.24/5.55 & ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.24/5.55 = zero_zero_real ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0_left
% 5.24/5.55 thf(fact_7783_pochhammer__0__left,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( N = zero_zero_nat )
% 5.24/5.55 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.24/5.55 = one_one_rat ) )
% 5.24/5.55 & ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.24/5.55 = zero_zero_rat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0_left
% 5.24/5.55 thf(fact_7784_pochhammer__0__left,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( N = zero_zero_nat )
% 5.24/5.55 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.24/5.55 = one_one_nat ) )
% 5.24/5.55 & ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.24/5.55 = zero_zero_nat ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0_left
% 5.24/5.55 thf(fact_7785_pochhammer__0__left,axiom,
% 5.24/5.55 ! [N: nat] :
% 5.24/5.55 ( ( ( N = zero_zero_nat )
% 5.24/5.55 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.24/5.55 = one_one_int ) )
% 5.24/5.55 & ( ( N != zero_zero_nat )
% 5.24/5.55 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.24/5.55 = zero_zero_int ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_0_left
% 5.24/5.55 thf(fact_7786_sqrt2__less__2,axiom,
% 5.24/5.55 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.24/5.55
% 5.24/5.55 % sqrt2_less_2
% 5.24/5.55 thf(fact_7787_exp__ge__add__one__self__aux,axiom,
% 5.24/5.55 ! [X: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.55 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % exp_ge_add_one_self_aux
% 5.24/5.55 thf(fact_7788_lemma__exp__total,axiom,
% 5.24/5.55 ! [Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ one_one_real @ Y4 )
% 5.24/5.55 => ? [X3: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.24/5.55 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y4 @ one_one_real ) )
% 5.24/5.55 & ( ( exp_real @ X3 )
% 5.24/5.55 = Y4 ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % lemma_exp_total
% 5.24/5.55 thf(fact_7789_ln__x__over__x__mono,axiom,
% 5.24/5.55 ! [X: real,Y4: real] :
% 5.24/5.55 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.24/5.55 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.55 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y4 ) @ Y4 ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % ln_x_over_x_mono
% 5.24/5.55 thf(fact_7790_pochhammer__rec,axiom,
% 5.24/5.55 ! [A: complex,N: nat] :
% 5.24/5.55 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.24/5.55 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_rec
% 5.24/5.55 thf(fact_7791_pochhammer__rec,axiom,
% 5.24/5.55 ! [A: real,N: nat] :
% 5.24/5.55 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.24/5.55 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.24/5.55
% 5.24/5.55 % pochhammer_rec
% 5.24/5.55 thf(fact_7792_pochhammer__rec,axiom,
% 5.24/5.56 ! [A: rat,N: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec
% 5.24/5.56 thf(fact_7793_pochhammer__rec,axiom,
% 5.24/5.56 ! [A: nat,N: nat] :
% 5.24/5.56 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec
% 5.24/5.56 thf(fact_7794_pochhammer__rec,axiom,
% 5.24/5.56 ! [A: int,N: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec
% 5.24/5.56 thf(fact_7795_pochhammer__Suc,axiom,
% 5.24/5.56 ! [A: int,N: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc
% 5.24/5.56 thf(fact_7796_pochhammer__Suc,axiom,
% 5.24/5.56 ! [A: real,N: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc
% 5.24/5.56 thf(fact_7797_pochhammer__Suc,axiom,
% 5.24/5.56 ! [A: nat,N: nat] :
% 5.24/5.56 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc
% 5.24/5.56 thf(fact_7798_pochhammer__Suc,axiom,
% 5.24/5.56 ! [A: rat,N: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc
% 5.24/5.56 thf(fact_7799_pochhammer__rec_H,axiom,
% 5.24/5.56 ! [Z2: int,N: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ Z2 @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z2 @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec'
% 5.24/5.56 thf(fact_7800_pochhammer__rec_H,axiom,
% 5.24/5.56 ! [Z2: real,N: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z2 @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec'
% 5.24/5.56 thf(fact_7801_pochhammer__rec_H,axiom,
% 5.24/5.56 ! [Z2: nat,N: nat] :
% 5.24/5.56 ( ( comm_s4663373288045622133er_nat @ Z2 @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec'
% 5.24/5.56 thf(fact_7802_pochhammer__rec_H,axiom,
% 5.24/5.56 ! [Z2: rat,N: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N ) )
% 5.24/5.56 = ( times_times_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_rec'
% 5.24/5.56 thf(fact_7803_pochhammer__eq__0__iff,axiom,
% 5.24/5.56 ! [A: complex,N: nat] :
% 5.24/5.56 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.24/5.56 = zero_zero_complex )
% 5.24/5.56 = ( ? [K3: nat] :
% 5.24/5.56 ( ( ord_less_nat @ K3 @ N )
% 5.24/5.56 & ( A
% 5.24/5.56 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_eq_0_iff
% 5.24/5.56 thf(fact_7804_pochhammer__eq__0__iff,axiom,
% 5.24/5.56 ! [A: real,N: nat] :
% 5.24/5.56 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.24/5.56 = zero_zero_real )
% 5.24/5.56 = ( ? [K3: nat] :
% 5.24/5.56 ( ( ord_less_nat @ K3 @ N )
% 5.24/5.56 & ( A
% 5.24/5.56 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_eq_0_iff
% 5.24/5.56 thf(fact_7805_pochhammer__eq__0__iff,axiom,
% 5.24/5.56 ! [A: rat,N: nat] :
% 5.24/5.56 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.24/5.56 = zero_zero_rat )
% 5.24/5.56 = ( ? [K3: nat] :
% 5.24/5.56 ( ( ord_less_nat @ K3 @ N )
% 5.24/5.56 & ( A
% 5.24/5.56 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_eq_0_iff
% 5.24/5.56 thf(fact_7806_pochhammer__of__nat__eq__0__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.24/5.56 = zero_zero_complex )
% 5.24/5.56 = ( ord_less_nat @ N @ K ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_iff
% 5.24/5.56 thf(fact_7807_pochhammer__of__nat__eq__0__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.24/5.56 = zero_z3403309356797280102nteger )
% 5.24/5.56 = ( ord_less_nat @ N @ K ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_iff
% 5.24/5.56 thf(fact_7808_pochhammer__of__nat__eq__0__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.24/5.56 = zero_zero_int )
% 5.24/5.56 = ( ord_less_nat @ N @ K ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_iff
% 5.24/5.56 thf(fact_7809_pochhammer__of__nat__eq__0__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.24/5.56 = zero_zero_real )
% 5.24/5.56 = ( ord_less_nat @ N @ K ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_iff
% 5.24/5.56 thf(fact_7810_pochhammer__of__nat__eq__0__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.24/5.56 = zero_zero_rat )
% 5.24/5.56 = ( ord_less_nat @ N @ K ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_iff
% 5.24/5.56 thf(fact_7811_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ N @ K )
% 5.24/5.56 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.24/5.56 = zero_zero_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.24/5.56 thf(fact_7812_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ N @ K )
% 5.24/5.56 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.24/5.56 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.24/5.56 thf(fact_7813_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ N @ K )
% 5.24/5.56 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.24/5.56 = zero_zero_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.24/5.56 thf(fact_7814_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ N @ K )
% 5.24/5.56 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.24/5.56 = zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.24/5.56 thf(fact_7815_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ N @ K )
% 5.24/5.56 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.24/5.56 = zero_zero_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.24/5.56 thf(fact_7816_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.24/5.56 != zero_zero_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.24/5.56 thf(fact_7817_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.24/5.56 != zero_z3403309356797280102nteger ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.24/5.56 thf(fact_7818_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.24/5.56 != zero_zero_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.24/5.56 thf(fact_7819_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.24/5.56 != zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.24/5.56 thf(fact_7820_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.24/5.56 != zero_zero_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.24/5.56 thf(fact_7821_pochhammer__product_H,axiom,
% 5.24/5.56 ! [Z2: int,N: nat,M: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product'
% 5.24/5.56 thf(fact_7822_pochhammer__product_H,axiom,
% 5.24/5.56 ! [Z2: real,N: nat,M: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product'
% 5.24/5.56 thf(fact_7823_pochhammer__product_H,axiom,
% 5.24/5.56 ! [Z2: nat,N: nat,M: nat] :
% 5.24/5.56 ( ( comm_s4663373288045622133er_nat @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product'
% 5.24/5.56 thf(fact_7824_pochhammer__product_H,axiom,
% 5.24/5.56 ! [Z2: rat,N: nat,M: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product'
% 5.24/5.56 thf(fact_7825_real__less__rsqrt,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 )
% 5.24/5.56 => ( ord_less_real @ X @ ( sqrt @ Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_less_rsqrt
% 5.24/5.56 thf(fact_7826_sqrt__le__D,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y4 )
% 5.24/5.56 => ( ord_less_eq_real @ X @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sqrt_le_D
% 5.24/5.56 thf(fact_7827_real__le__rsqrt,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 )
% 5.24/5.56 => ( ord_less_eq_real @ X @ ( sqrt @ Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_le_rsqrt
% 5.24/5.56 thf(fact_7828_exp__le,axiom,
% 5.24/5.56 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_le
% 5.24/5.56 thf(fact_7829_exp__divide__power__eq,axiom,
% 5.24/5.56 ! [N: nat,X: complex] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.56 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.24/5.56 = ( exp_complex @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_divide_power_eq
% 5.24/5.56 thf(fact_7830_exp__divide__power__eq,axiom,
% 5.24/5.56 ! [N: nat,X: real] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.56 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.24/5.56 = ( exp_real @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_divide_power_eq
% 5.24/5.56 thf(fact_7831_tanh__altdef,axiom,
% 5.24/5.56 ( tanh_real
% 5.24/5.56 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % tanh_altdef
% 5.24/5.56 thf(fact_7832_tanh__altdef,axiom,
% 5.24/5.56 ( tanh_complex
% 5.24/5.56 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % tanh_altdef
% 5.24/5.56 thf(fact_7833_pochhammer__product,axiom,
% 5.24/5.56 ! [M: nat,N: nat,Z2: int] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( comm_s4660882817536571857er_int @ Z2 @ N )
% 5.24/5.56 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product
% 5.24/5.56 thf(fact_7834_pochhammer__product,axiom,
% 5.24/5.56 ! [M: nat,N: nat,Z2: real] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( comm_s7457072308508201937r_real @ Z2 @ N )
% 5.24/5.56 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product
% 5.24/5.56 thf(fact_7835_pochhammer__product,axiom,
% 5.24/5.56 ! [M: nat,N: nat,Z2: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( comm_s4663373288045622133er_nat @ Z2 @ N )
% 5.24/5.56 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product
% 5.24/5.56 thf(fact_7836_pochhammer__product,axiom,
% 5.24/5.56 ! [M: nat,N: nat,Z2: rat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( comm_s4028243227959126397er_rat @ Z2 @ N )
% 5.24/5.56 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_product
% 5.24/5.56 thf(fact_7837_real__le__lsqrt,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_le_lsqrt
% 5.24/5.56 thf(fact_7838_real__sqrt__unique,axiom,
% 5.24/5.56 ! [Y4: real,X: real] :
% 5.24/5.56 ( ( ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.56 = X )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ( sqrt @ X )
% 5.24/5.56 = Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_unique
% 5.24/5.56 thf(fact_7839_lemma__real__divide__sqrt__less,axiom,
% 5.24/5.56 ! [U2: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ U2 )
% 5.24/5.56 => ( ord_less_real @ ( divide_divide_real @ U2 @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % lemma_real_divide_sqrt_less
% 5.24/5.56 thf(fact_7840_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.56 = X )
% 5.24/5.56 => ( Y4 = zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_eq_cancel
% 5.24/5.56 thf(fact_7841_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.56 = Y4 )
% 5.24/5.56 => ( X = zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_eq_cancel2
% 5.24/5.56 thf(fact_7842_real__sqrt__sum__squares__ge1,axiom,
% 5.24/5.56 ! [X: real,Y4: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_ge1
% 5.24/5.56 thf(fact_7843_real__sqrt__sum__squares__ge2,axiom,
% 5.24/5.56 ! [Y4: real,X: real] : ( ord_less_eq_real @ Y4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_ge2
% 5.24/5.56 thf(fact_7844_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.24/5.56 ! [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 ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_triangle_ineq
% 5.24/5.56 thf(fact_7845_exp__half__le2,axiom,
% 5.24/5.56 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_half_le2
% 5.24/5.56 thf(fact_7846_sqrt__ge__absD,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y4 ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 ) ) ).
% 5.24/5.56
% 5.24/5.56 % sqrt_ge_absD
% 5.24/5.56 thf(fact_7847_cos__45,axiom,
% 5.24/5.56 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.24/5.56 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_45
% 5.24/5.56 thf(fact_7848_sin__45,axiom,
% 5.24/5.56 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.24/5.56 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_45
% 5.24/5.56 thf(fact_7849_tan__60,axiom,
% 5.24/5.56 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.24/5.56 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % tan_60
% 5.24/5.56 thf(fact_7850_exp__double,axiom,
% 5.24/5.56 ! [Z2: complex] :
% 5.24/5.56 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 ) )
% 5.24/5.56 = ( power_power_complex @ ( exp_complex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_double
% 5.24/5.56 thf(fact_7851_exp__double,axiom,
% 5.24/5.56 ! [Z2: real] :
% 5.24/5.56 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 ) )
% 5.24/5.56 = ( power_power_real @ ( exp_real @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_double
% 5.24/5.56 thf(fact_7852_pochhammer__absorb__comp,axiom,
% 5.24/5.56 ! [R2: complex,K: nat] :
% 5.24/5.56 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.24/5.56 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_absorb_comp
% 5.24/5.56 thf(fact_7853_pochhammer__absorb__comp,axiom,
% 5.24/5.56 ! [R2: code_integer,K: nat] :
% 5.24/5.56 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.24/5.56 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_absorb_comp
% 5.24/5.56 thf(fact_7854_pochhammer__absorb__comp,axiom,
% 5.24/5.56 ! [R2: int,K: nat] :
% 5.24/5.56 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.24/5.56 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_absorb_comp
% 5.24/5.56 thf(fact_7855_pochhammer__absorb__comp,axiom,
% 5.24/5.56 ! [R2: real,K: nat] :
% 5.24/5.56 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.24/5.56 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_absorb_comp
% 5.24/5.56 thf(fact_7856_pochhammer__absorb__comp,axiom,
% 5.24/5.56 ! [R2: rat,K: nat] :
% 5.24/5.56 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.24/5.56 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_absorb_comp
% 5.24/5.56 thf(fact_7857_pochhammer__same,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.24/5.56 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_same
% 5.24/5.56 thf(fact_7858_pochhammer__same,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.24/5.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_same
% 5.24/5.56 thf(fact_7859_pochhammer__same,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.24/5.56 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_same
% 5.24/5.56 thf(fact_7860_pochhammer__same,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.24/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_same
% 5.24/5.56 thf(fact_7861_pochhammer__same,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.24/5.56 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_same
% 5.24/5.56 thf(fact_7862_real__less__lsqrt,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ( ord_less_real @ X @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_real @ ( sqrt @ X ) @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_less_lsqrt
% 5.24/5.56 thf(fact_7863_sqrt__sum__squares__le__sum,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sqrt_sum_squares_le_sum
% 5.24/5.56 thf(fact_7864_sqrt__even__pow2,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.56 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.56 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sqrt_even_pow2
% 5.24/5.56 thf(fact_7865_sqrt__sum__squares__le__sum__abs,axiom,
% 5.24/5.56 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sqrt_sum_squares_le_sum_abs
% 5.24/5.56 thf(fact_7866_real__sqrt__ge__abs2,axiom,
% 5.24/5.56 ! [Y4: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_ge_abs2
% 5.24/5.56 thf(fact_7867_real__sqrt__ge__abs1,axiom,
% 5.24/5.56 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_ge_abs1
% 5.24/5.56 thf(fact_7868_ln__sqrt,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.24/5.56 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % ln_sqrt
% 5.24/5.56 thf(fact_7869_cos__30,axiom,
% 5.24/5.56 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.24/5.56 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_30
% 5.24/5.56 thf(fact_7870_sin__60,axiom,
% 5.24/5.56 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.24/5.56 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_60
% 5.24/5.56 thf(fact_7871_complex__norm,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y4 ) )
% 5.24/5.56 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % complex_norm
% 5.24/5.56 thf(fact_7872_exp__bound__half,axiom,
% 5.24/5.56 ! [Z2: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_bound_half
% 5.24/5.56 thf(fact_7873_exp__bound__half,axiom,
% 5.24/5.56 ! [Z2: complex] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_bound_half
% 5.24/5.56 thf(fact_7874_pochhammer__minus_H,axiom,
% 5.24/5.56 ! [B: complex,K: nat] :
% 5.24/5.56 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.24/5.56 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus'
% 5.24/5.56 thf(fact_7875_pochhammer__minus_H,axiom,
% 5.24/5.56 ! [B: code_integer,K: nat] :
% 5.24/5.56 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.24/5.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus'
% 5.24/5.56 thf(fact_7876_pochhammer__minus_H,axiom,
% 5.24/5.56 ! [B: int,K: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.24/5.56 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus'
% 5.24/5.56 thf(fact_7877_pochhammer__minus_H,axiom,
% 5.24/5.56 ! [B: real,K: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.24/5.56 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus'
% 5.24/5.56 thf(fact_7878_pochhammer__minus_H,axiom,
% 5.24/5.56 ! [B: rat,K: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.24/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus'
% 5.24/5.56 thf(fact_7879_pochhammer__minus,axiom,
% 5.24/5.56 ! [B: complex,K: nat] :
% 5.24/5.56 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus
% 5.24/5.56 thf(fact_7880_pochhammer__minus,axiom,
% 5.24/5.56 ! [B: code_integer,K: nat] :
% 5.24/5.56 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.24/5.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus
% 5.24/5.56 thf(fact_7881_pochhammer__minus,axiom,
% 5.24/5.56 ! [B: int,K: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus
% 5.24/5.56 thf(fact_7882_pochhammer__minus,axiom,
% 5.24/5.56 ! [B: real,K: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus
% 5.24/5.56 thf(fact_7883_pochhammer__minus,axiom,
% 5.24/5.56 ! [B: rat,K: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_minus
% 5.24/5.56 thf(fact_7884_arsinh__real__aux,axiom,
% 5.24/5.56 ! [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 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arsinh_real_aux
% 5.24/5.56 thf(fact_7885_exp__bound,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_bound
% 5.24/5.56 thf(fact_7886_real__sqrt__power__even,axiom,
% 5.24/5.56 ! [N: nat,X: real] :
% 5.24/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 5.24/5.56 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_power_even
% 5.24/5.56 thf(fact_7887_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.24/5.56 ! [X: real,Y4: 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 @ Y4 @ ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_mult_ge_zero
% 5.24/5.56 thf(fact_7888_arith__geo__mean__sqrt,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y4 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arith_geo_mean_sqrt
% 5.24/5.56 thf(fact_7889_tan__30,axiom,
% 5.24/5.56 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.24/5.56 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % tan_30
% 5.24/5.56 thf(fact_7890_real__exp__bound__lemma,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_exp_bound_lemma
% 5.24/5.56 thf(fact_7891_cos__x__y__le__one,axiom,
% 5.24/5.56 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.24/5.56
% 5.24/5.56 % cos_x_y_le_one
% 5.24/5.56 thf(fact_7892_real__sqrt__sum__squares__less,axiom,
% 5.24/5.56 ! [X: real,U2: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U2 @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.56 => ( ( ord_less_real @ ( abs_abs_real @ Y4 ) @ ( divide_divide_real @ U2 @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.56 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % real_sqrt_sum_squares_less
% 5.24/5.56 thf(fact_7893_arcosh__real__def,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.56 => ( ( arcosh_real @ X )
% 5.24/5.56 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcosh_real_def
% 5.24/5.56 thf(fact_7894_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.24/5.56 ! [N: nat,X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 5.24/5.56 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.56 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_ge_one_plus_x_over_n_power_n
% 5.24/5.56 thf(fact_7895_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.24/5.56 ! [X: real,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.24/5.56 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.56 => ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_ge_one_minus_x_over_n_power_n
% 5.24/5.56 thf(fact_7896_cos__arctan,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( cos_real @ ( arctan @ X ) )
% 5.24/5.56 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_arctan
% 5.24/5.56 thf(fact_7897_sin__arctan,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( sin_real @ ( arctan @ X ) )
% 5.24/5.56 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_arctan
% 5.24/5.56 thf(fact_7898_exp__bound__lemma,axiom,
% 5.24/5.56 ! [Z2: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_bound_lemma
% 5.24/5.56 thf(fact_7899_exp__bound__lemma,axiom,
% 5.24/5.56 ! [Z2: complex] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_bound_lemma
% 5.24/5.56 thf(fact_7900_Maclaurin__exp__le,axiom,
% 5.24/5.56 ! [X: real,N: nat] :
% 5.24/5.56 ? [T3: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.56 & ( ( exp_real @ X )
% 5.24/5.56 = ( plus_plus_real
% 5.24/5.56 @ ( groups6591440286371151544t_real
% 5.24/5.56 @ ^ [M2: nat] : ( divide_divide_real @ ( power_power_real @ X @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.56 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Maclaurin_exp_le
% 5.24/5.56 thf(fact_7901_sqrt__sum__squares__half__less,axiom,
% 5.24/5.56 ! [X: real,U2: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_real @ X @ ( divide_divide_real @ U2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ U2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sqrt_sum_squares_half_less
% 5.24/5.56 thf(fact_7902_exp__lower__Taylor__quadratic,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.56 => ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % exp_lower_Taylor_quadratic
% 5.24/5.56 thf(fact_7903_sin__cos__sqrt,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.24/5.56 => ( ( sin_real @ X )
% 5.24/5.56 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_cos_sqrt
% 5.24/5.56 thf(fact_7904_arctan__half,axiom,
% 5.24/5.56 ( arctan
% 5.24/5.56 = ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arctan_half
% 5.24/5.56 thf(fact_7905_tanh__real__altdef,axiom,
% 5.24/5.56 ( tanh_real
% 5.24/5.56 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % tanh_real_altdef
% 5.24/5.56 thf(fact_7906_fact__double,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_double
% 5.24/5.56 thf(fact_7907_fact__double,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_double
% 5.24/5.56 thf(fact_7908_fact__double,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.56 = ( 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 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_double
% 5.24/5.56 thf(fact_7909_pochhammer__times__pochhammer__half,axiom,
% 5.24/5.56 ! [Z2: complex,N: nat] :
% 5.24/5.56 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z2 @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.24/5.56 = ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [K3: nat] : ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_times_pochhammer_half
% 5.24/5.56 thf(fact_7910_pochhammer__times__pochhammer__half,axiom,
% 5.24/5.56 ! [Z2: real,N: nat] :
% 5.24/5.56 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.24/5.56 = ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [K3: nat] : ( plus_plus_real @ Z2 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_times_pochhammer_half
% 5.24/5.56 thf(fact_7911_pochhammer__times__pochhammer__half,axiom,
% 5.24/5.56 ! [Z2: rat,N: nat] :
% 5.24/5.56 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.24/5.56 = ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [K3: nat] : ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_times_pochhammer_half
% 5.24/5.56 thf(fact_7912_pochhammer__code,axiom,
% 5.24/5.56 ( comm_s2602460028002588243omplex
% 5.24/5.56 = ( ^ [A4: complex,N2: nat] :
% 5.24/5.56 ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 5.24/5.56 @ ( set_fo1517530859248394432omplex
% 5.24/5.56 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.24/5.56 @ zero_zero_nat
% 5.24/5.56 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.24/5.56 @ one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_code
% 5.24/5.56 thf(fact_7913_pochhammer__code,axiom,
% 5.24/5.56 ( comm_s4660882817536571857er_int
% 5.24/5.56 = ( ^ [A4: int,N2: nat] :
% 5.24/5.56 ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 5.24/5.56 @ ( set_fo2581907887559384638at_int
% 5.24/5.56 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.24/5.56 @ zero_zero_nat
% 5.24/5.56 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.24/5.56 @ one_one_int ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_code
% 5.24/5.56 thf(fact_7914_pochhammer__code,axiom,
% 5.24/5.56 ( comm_s7457072308508201937r_real
% 5.24/5.56 = ( ^ [A4: real,N2: nat] :
% 5.24/5.56 ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 5.24/5.56 @ ( set_fo3111899725591712190t_real
% 5.24/5.56 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.24/5.56 @ zero_zero_nat
% 5.24/5.56 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.24/5.56 @ one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_code
% 5.24/5.56 thf(fact_7915_pochhammer__code,axiom,
% 5.24/5.56 ( comm_s4028243227959126397er_rat
% 5.24/5.56 = ( ^ [A4: rat,N2: nat] :
% 5.24/5.56 ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 5.24/5.56 @ ( set_fo1949268297981939178at_rat
% 5.24/5.56 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.24/5.56 @ zero_zero_nat
% 5.24/5.56 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.24/5.56 @ one_one_rat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_code
% 5.24/5.56 thf(fact_7916_pochhammer__code,axiom,
% 5.24/5.56 ( comm_s4663373288045622133er_nat
% 5.24/5.56 = ( ^ [A4: nat,N2: nat] :
% 5.24/5.56 ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 5.24/5.56 @ ( set_fo2584398358068434914at_nat
% 5.24/5.56 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.24/5.56 @ zero_zero_nat
% 5.24/5.56 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.24/5.56 @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_code
% 5.24/5.56 thf(fact_7917_arsinh__real__def,axiom,
% 5.24/5.56 ( arsinh_real
% 5.24/5.56 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arsinh_real_def
% 5.24/5.56 thf(fact_7918_cos__arcsin,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( ( cos_real @ ( arcsin @ X ) )
% 5.24/5.56 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_arcsin
% 5.24/5.56 thf(fact_7919_sin__arccos__abs,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( sin_real @ ( arccos @ Y4 ) )
% 5.24/5.56 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_arccos_abs
% 5.24/5.56 thf(fact_7920_prod_Oneutral__const,axiom,
% 5.24/5.56 ! [A2: set_nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [Uu2: nat] : one_one_nat
% 5.24/5.56 @ A2 )
% 5.24/5.56 = one_one_nat ) ).
% 5.24/5.56
% 5.24/5.56 % prod.neutral_const
% 5.24/5.56 thf(fact_7921_prod_Oneutral__const,axiom,
% 5.24/5.56 ! [A2: set_nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [Uu2: nat] : one_one_int
% 5.24/5.56 @ A2 )
% 5.24/5.56 = one_one_int ) ).
% 5.24/5.56
% 5.24/5.56 % prod.neutral_const
% 5.24/5.56 thf(fact_7922_prod_Oneutral__const,axiom,
% 5.24/5.56 ! [A2: set_int] :
% 5.24/5.56 ( ( groups1705073143266064639nt_int
% 5.24/5.56 @ ^ [Uu2: int] : one_one_int
% 5.24/5.56 @ A2 )
% 5.24/5.56 = one_one_int ) ).
% 5.24/5.56
% 5.24/5.56 % prod.neutral_const
% 5.24/5.56 thf(fact_7923_prod_Oempty,axiom,
% 5.24/5.56 ! [G: nat > complex] :
% 5.24/5.56 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.24/5.56 = one_one_complex ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7924_prod_Oempty,axiom,
% 5.24/5.56 ! [G: nat > real] :
% 5.24/5.56 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.24/5.56 = one_one_real ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7925_prod_Oempty,axiom,
% 5.24/5.56 ! [G: nat > rat] :
% 5.24/5.56 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.24/5.56 = one_one_rat ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7926_prod_Oempty,axiom,
% 5.24/5.56 ! [G: int > complex] :
% 5.24/5.56 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.24/5.56 = one_one_complex ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7927_prod_Oempty,axiom,
% 5.24/5.56 ! [G: int > real] :
% 5.24/5.56 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.24/5.56 = one_one_real ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7928_prod_Oempty,axiom,
% 5.24/5.56 ! [G: int > rat] :
% 5.24/5.56 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.24/5.56 = one_one_rat ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7929_prod_Oempty,axiom,
% 5.24/5.56 ! [G: int > nat] :
% 5.24/5.56 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.24/5.56 = one_one_nat ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7930_prod_Oempty,axiom,
% 5.24/5.56 ! [G: real > complex] :
% 5.24/5.56 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.24/5.56 = one_one_complex ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7931_prod_Oempty,axiom,
% 5.24/5.56 ! [G: real > real] :
% 5.24/5.56 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.24/5.56 = one_one_real ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7932_prod_Oempty,axiom,
% 5.24/5.56 ! [G: real > rat] :
% 5.24/5.56 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.24/5.56 = one_one_rat ) ).
% 5.24/5.56
% 5.24/5.56 % prod.empty
% 5.24/5.56 thf(fact_7933_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > complex] :
% 5.24/5.56 ( ~ ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.24/5.56 = one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7934_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > complex] :
% 5.24/5.56 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.24/5.56 = one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7935_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > real] :
% 5.24/5.56 ( ~ ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.24/5.56 = one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7936_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > real] :
% 5.24/5.56 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.24/5.56 = one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7937_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > rat] :
% 5.24/5.56 ( ~ ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.24/5.56 = one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7938_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > rat] :
% 5.24/5.56 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.24/5.56 = one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7939_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > nat] :
% 5.24/5.56 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.24/5.56 = one_one_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7940_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > int] :
% 5.24/5.56 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.24/5.56 = one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7941_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > nat] :
% 5.24/5.56 ( ~ ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.24/5.56 = one_one_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7942_prod_Oinfinite,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > int] :
% 5.24/5.56 ( ~ ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.24/5.56 = one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.infinite
% 5.24/5.56 thf(fact_7943_arccos__1,axiom,
% 5.24/5.56 ( ( arccos @ one_one_real )
% 5.24/5.56 = zero_zero_real ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_1
% 5.24/5.56 thf(fact_7944_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_int,A: int,B: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ S3 )
% 5.24/5.56 => ( ( ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups7440179247065528705omplex
% 5.24/5.56 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups7440179247065528705omplex
% 5.24/5.56 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7945_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_real,A: real,B: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ S3 )
% 5.24/5.56 => ( ( ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups713298508707869441omplex
% 5.24/5.56 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups713298508707869441omplex
% 5.24/5.56 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7946_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.24/5.56 ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ( ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7947_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ( ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex
% 5.24/5.56 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex
% 5.24/5.56 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7948_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_int,A: int,B: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ S3 )
% 5.24/5.56 => ( ( ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups2316167850115554303t_real
% 5.24/5.56 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups2316167850115554303t_real
% 5.24/5.56 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7949_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_real,A: real,B: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ S3 )
% 5.24/5.56 => ( ( ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups1681761925125756287l_real
% 5.24/5.56 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups1681761925125756287l_real
% 5.24/5.56 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7950_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ( ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7951_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ( ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups766887009212190081x_real
% 5.24/5.56 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups766887009212190081x_real
% 5.24/5.56 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7952_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_int,A: int,B: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ S3 )
% 5.24/5.56 => ( ( ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat
% 5.24/5.56 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat
% 5.24/5.56 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_rat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7953_prod_Odelta_H,axiom,
% 5.24/5.56 ! [S3: set_real,A: real,B: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ S3 )
% 5.24/5.56 => ( ( ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat
% 5.24/5.56 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat
% 5.24/5.56 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_rat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta'
% 5.24/5.56 thf(fact_7954_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_int,A: int,B: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ S3 )
% 5.24/5.56 => ( ( ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups7440179247065528705omplex
% 5.24/5.56 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups7440179247065528705omplex
% 5.24/5.56 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7955_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_real,A: real,B: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ S3 )
% 5.24/5.56 => ( ( ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups713298508707869441omplex
% 5.24/5.56 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups713298508707869441omplex
% 5.24/5.56 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7956_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.24/5.56 ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ( ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7957_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ( ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex
% 5.24/5.56 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex
% 5.24/5.56 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_complex ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7958_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_int,A: int,B: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ S3 )
% 5.24/5.56 => ( ( ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups2316167850115554303t_real
% 5.24/5.56 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups2316167850115554303t_real
% 5.24/5.56 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7959_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_real,A: real,B: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ S3 )
% 5.24/5.56 => ( ( ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups1681761925125756287l_real
% 5.24/5.56 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups1681761925125756287l_real
% 5.24/5.56 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7960_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ( ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_nat @ A @ S3 )
% 5.24/5.56 => ( ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7961_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ( ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups766887009212190081x_real
% 5.24/5.56 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_complex @ A @ S3 )
% 5.24/5.56 => ( ( groups766887009212190081x_real
% 5.24/5.56 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_real ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7962_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_int,A: int,B: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ S3 )
% 5.24/5.56 => ( ( ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat
% 5.24/5.56 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_int @ A @ S3 )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat
% 5.24/5.56 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_rat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7963_prod_Odelta,axiom,
% 5.24/5.56 ! [S3: set_real,A: real,B: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ S3 )
% 5.24/5.56 => ( ( ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat
% 5.24/5.56 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = ( B @ A ) ) )
% 5.24/5.56 & ( ~ ( member_real @ A @ S3 )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat
% 5.24/5.56 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.24/5.56 @ S3 )
% 5.24/5.56 = one_one_rat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.delta
% 5.24/5.56 thf(fact_7964_prod_OlessThan__Suc,axiom,
% 5.24/5.56 ! [G: nat > real,N: nat] :
% 5.24/5.56 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc
% 5.24/5.56 thf(fact_7965_prod_OlessThan__Suc,axiom,
% 5.24/5.56 ! [G: nat > rat,N: nat] :
% 5.24/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc
% 5.24/5.56 thf(fact_7966_prod_OlessThan__Suc,axiom,
% 5.24/5.56 ! [G: nat > nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc
% 5.24/5.56 thf(fact_7967_prod_OlessThan__Suc,axiom,
% 5.24/5.56 ! [G: nat > int,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc
% 5.24/5.56 thf(fact_7968_arccos__minus__1,axiom,
% 5.24/5.56 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.56 = pi ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_minus_1
% 5.24/5.56 thf(fact_7969_cos__arccos,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( cos_real @ ( arccos @ Y4 ) )
% 5.24/5.56 = Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_arccos
% 5.24/5.56 thf(fact_7970_sin__arcsin,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.24/5.56 = Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_arcsin
% 5.24/5.56 thf(fact_7971_prod_Ocl__ivl__Suc,axiom,
% 5.24/5.56 ! [N: nat,M: nat,G: nat > complex] :
% 5.24/5.56 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.cl_ivl_Suc
% 5.24/5.56 thf(fact_7972_prod_Ocl__ivl__Suc,axiom,
% 5.24/5.56 ! [N: nat,M: nat,G: nat > real] :
% 5.24/5.56 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.cl_ivl_Suc
% 5.24/5.56 thf(fact_7973_prod_Ocl__ivl__Suc,axiom,
% 5.24/5.56 ! [N: nat,M: nat,G: nat > rat] :
% 5.24/5.56 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.cl_ivl_Suc
% 5.24/5.56 thf(fact_7974_prod_Ocl__ivl__Suc,axiom,
% 5.24/5.56 ! [N: nat,M: nat,G: nat > nat] :
% 5.24/5.56 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.cl_ivl_Suc
% 5.24/5.56 thf(fact_7975_prod_Ocl__ivl__Suc,axiom,
% 5.24/5.56 ! [N: nat,M: nat,G: nat > int] :
% 5.24/5.56 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.cl_ivl_Suc
% 5.24/5.56 thf(fact_7976_arccos__0,axiom,
% 5.24/5.56 ( ( arccos @ zero_zero_real )
% 5.24/5.56 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_0
% 5.24/5.56 thf(fact_7977_arcsin__1,axiom,
% 5.24/5.56 ( ( arcsin @ one_one_real )
% 5.24/5.56 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_1
% 5.24/5.56 thf(fact_7978_arcsin__minus__1,axiom,
% 5.24/5.56 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.56 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_minus_1
% 5.24/5.56 thf(fact_7979_prod_Oneutral,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > nat] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.24/5.56 = one_one_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.neutral
% 5.24/5.56 thf(fact_7980_prod_Oneutral,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > int] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.24/5.56 = one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.neutral
% 5.24/5.56 thf(fact_7981_prod_Oneutral,axiom,
% 5.24/5.56 ! [A2: set_int,G: int > int] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.24/5.56 = one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.neutral
% 5.24/5.56 thf(fact_7982_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: nat > complex,A2: set_nat] :
% 5.24/5.56 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.24/5.56 != one_one_complex )
% 5.24/5.56 => ~ ! [A3: nat] :
% 5.24/5.56 ( ( member_nat @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7983_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: int > complex,A2: set_int] :
% 5.24/5.56 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.24/5.56 != one_one_complex )
% 5.24/5.56 => ~ ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7984_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: real > complex,A2: set_real] :
% 5.24/5.56 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.24/5.56 != one_one_complex )
% 5.24/5.56 => ~ ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7985_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: complex > complex,A2: set_complex] :
% 5.24/5.56 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.24/5.56 != one_one_complex )
% 5.24/5.56 => ~ ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7986_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: nat > real,A2: set_nat] :
% 5.24/5.56 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.24/5.56 != one_one_real )
% 5.24/5.56 => ~ ! [A3: nat] :
% 5.24/5.56 ( ( member_nat @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7987_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: int > real,A2: set_int] :
% 5.24/5.56 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.24/5.56 != one_one_real )
% 5.24/5.56 => ~ ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7988_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: real > real,A2: set_real] :
% 5.24/5.56 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.24/5.56 != one_one_real )
% 5.24/5.56 => ~ ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7989_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: complex > real,A2: set_complex] :
% 5.24/5.56 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.24/5.56 != one_one_real )
% 5.24/5.56 => ~ ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7990_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: nat > rat,A2: set_nat] :
% 5.24/5.56 ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.24/5.56 != one_one_rat )
% 5.24/5.56 => ~ ! [A3: nat] :
% 5.24/5.56 ( ( member_nat @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7991_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.24/5.56 ! [G: int > rat,A2: set_int] :
% 5.24/5.56 ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.24/5.56 != one_one_rat )
% 5.24/5.56 => ~ ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ A2 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.not_neutral_contains_not_neutral
% 5.24/5.56 thf(fact_7992_prod_Odistrib,axiom,
% 5.24/5.56 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.56 @ A2 )
% 5.24/5.56 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.distrib
% 5.24/5.56 thf(fact_7993_prod_Odistrib,axiom,
% 5.24/5.56 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.56 @ A2 )
% 5.24/5.56 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.distrib
% 5.24/5.56 thf(fact_7994_prod_Odistrib,axiom,
% 5.24/5.56 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.24/5.56 ( ( groups1705073143266064639nt_int
% 5.24/5.56 @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.24/5.56 @ A2 )
% 5.24/5.56 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.distrib
% 5.24/5.56 thf(fact_7995_prod__power__distrib,axiom,
% 5.24/5.56 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.24/5.56 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_power_distrib
% 5.24/5.56 thf(fact_7996_prod__power__distrib,axiom,
% 5.24/5.56 ! [F: nat > int,A2: set_nat,N: nat] :
% 5.24/5.56 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_power_distrib
% 5.24/5.56 thf(fact_7997_prod__power__distrib,axiom,
% 5.24/5.56 ! [F: int > int,A2: set_int,N: nat] :
% 5.24/5.56 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 5.24/5.56 = ( groups1705073143266064639nt_int
% 5.24/5.56 @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_power_distrib
% 5.24/5.56 thf(fact_7998_mod__prod__eq,axiom,
% 5.24/5.56 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.24/5.56 ( ( modulo_modulo_nat
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.24/5.56 @ A2 )
% 5.24/5.56 @ A )
% 5.24/5.56 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % mod_prod_eq
% 5.24/5.56 thf(fact_7999_mod__prod__eq,axiom,
% 5.24/5.56 ! [F: nat > int,A: int,A2: set_nat] :
% 5.24/5.56 ( ( modulo_modulo_int
% 5.24/5.56 @ ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.24/5.56 @ A2 )
% 5.24/5.56 @ A )
% 5.24/5.56 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % mod_prod_eq
% 5.24/5.56 thf(fact_8000_mod__prod__eq,axiom,
% 5.24/5.56 ! [F: int > int,A: int,A2: set_int] :
% 5.24/5.56 ( ( modulo_modulo_int
% 5.24/5.56 @ ( groups1705073143266064639nt_int
% 5.24/5.56 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.24/5.56 @ A2 )
% 5.24/5.56 @ A )
% 5.24/5.56 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % mod_prod_eq
% 5.24/5.56 thf(fact_8001_prod__nonneg,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_nonneg
% 5.24/5.56 thf(fact_8002_prod__nonneg,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > int] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_nonneg
% 5.24/5.56 thf(fact_8003_prod__nonneg,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > int] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_nonneg
% 5.24/5.56 thf(fact_8004_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.24/5.56 ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8005_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > real,G: int > real] :
% 5.24/5.56 ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8006_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > real,G: real > real] :
% 5.24/5.56 ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8007_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.24/5.56 ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8008_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.24/5.56 ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8009_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.24/5.56 ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8010_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.24/5.56 ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8011_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.24/5.56 ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8012_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.24/5.56 ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8013_prod__mono,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.24/5.56 ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono
% 5.24/5.56 thf(fact_8014_prod__pos,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_pos
% 5.24/5.56 thf(fact_8015_prod__pos,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > int] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_pos
% 5.24/5.56 thf(fact_8016_prod__pos,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > int] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_pos
% 5.24/5.56 thf(fact_8017_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > real] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8018_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > real] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8019_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > real] :
% 5.24/5.56 ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8020_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > real] :
% 5.24/5.56 ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8021_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > rat] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8022_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > rat] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8023_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > rat] :
% 5.24/5.56 ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8024_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > rat] :
% 5.24/5.56 ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8025_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > nat] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8026_prod__ge__1,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > nat] :
% 5.24/5.56 ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_ge_1
% 5.24/5.56 thf(fact_8027_prod__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > complex,A: nat,B: nat] :
% 5.24/5.56 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo1517530859248394432omplex
% 5.24/5.56 @ ^ [A4: nat] : ( times_times_complex @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_atLeastAtMost_code
% 5.24/5.56 thf(fact_8028_prod__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > real,A: nat,B: nat] :
% 5.24/5.56 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo3111899725591712190t_real
% 5.24/5.56 @ ^ [A4: nat] : ( times_times_real @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_atLeastAtMost_code
% 5.24/5.56 thf(fact_8029_prod__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > rat,A: nat,B: nat] :
% 5.24/5.56 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo1949268297981939178at_rat
% 5.24/5.56 @ ^ [A4: nat] : ( times_times_rat @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_atLeastAtMost_code
% 5.24/5.56 thf(fact_8030_prod__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > nat,A: nat,B: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo2584398358068434914at_nat
% 5.24/5.56 @ ^ [A4: nat] : ( times_times_nat @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ one_one_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_atLeastAtMost_code
% 5.24/5.56 thf(fact_8031_prod__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > int,A: nat,B: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo2581907887559384638at_int
% 5.24/5.56 @ ^ [A4: nat] : ( times_times_int @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_atLeastAtMost_code
% 5.24/5.56 thf(fact_8032_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G
% 5.24/5.56 @ ( collect_int
% 5.24/5.56 @ ^ [X2: int] :
% 5.24/5.56 ( ( member_int @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups7440179247065528705omplex
% 5.24/5.56 @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8033_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( member_real @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups713298508707869441omplex
% 5.24/5.56 @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8034_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups6464643781859351333omplex @ G
% 5.24/5.56 @ ( collect_nat
% 5.24/5.56 @ ^ [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8035_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups3708469109370488835omplex
% 5.24/5.56 @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8036_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ( groups2316167850115554303t_real @ G
% 5.24/5.56 @ ( collect_int
% 5.24/5.56 @ ^ [X2: int] :
% 5.24/5.56 ( ( member_int @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups2316167850115554303t_real
% 5.24/5.56 @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8037_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups1681761925125756287l_real @ G
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( member_real @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups1681761925125756287l_real
% 5.24/5.56 @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8038_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G
% 5.24/5.56 @ ( collect_nat
% 5.24/5.56 @ ^ [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8039_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups766887009212190081x_real
% 5.24/5.56 @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8040_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_int,G: int > rat,P: int > $o] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat @ G
% 5.24/5.56 @ ( collect_int
% 5.24/5.56 @ ^ [X2: int] :
% 5.24/5.56 ( ( member_int @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups1072433553688619179nt_rat
% 5.24/5.56 @ ^ [X2: int] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8041_prod_Ointer__filter,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > rat,P: real > $o] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat @ G
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( member_real @ X2 @ A2 )
% 5.24/5.56 & ( P @ X2 ) ) ) )
% 5.24/5.56 = ( groups4061424788464935467al_rat
% 5.24/5.56 @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 5.24/5.56 @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.inter_filter
% 5.24/5.56 thf(fact_8042_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.24/5.56 ! [G: nat > nat,M: nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.shift_bounds_cl_Suc_ivl
% 5.24/5.56 thf(fact_8043_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.24/5.56 ! [G: nat > int,M: nat,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.shift_bounds_cl_Suc_ivl
% 5.24/5.56 thf(fact_8044_power__sum,axiom,
% 5.24/5.56 ! [C: real,F: nat > nat,A2: set_nat] :
% 5.24/5.56 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.24/5.56 = ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [A4: nat] : ( power_power_real @ C @ ( F @ A4 ) )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_sum
% 5.24/5.56 thf(fact_8045_power__sum,axiom,
% 5.24/5.56 ! [C: complex,F: nat > nat,A2: set_nat] :
% 5.24/5.56 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.24/5.56 = ( groups6464643781859351333omplex
% 5.24/5.56 @ ^ [A4: nat] : ( power_power_complex @ C @ ( F @ A4 ) )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_sum
% 5.24/5.56 thf(fact_8046_power__sum,axiom,
% 5.24/5.56 ! [C: nat,F: nat > nat,A2: set_nat] :
% 5.24/5.56 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [A4: nat] : ( power_power_nat @ C @ ( F @ A4 ) )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_sum
% 5.24/5.56 thf(fact_8047_power__sum,axiom,
% 5.24/5.56 ! [C: int,F: nat > nat,A2: set_nat] :
% 5.24/5.56 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [A4: nat] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_sum
% 5.24/5.56 thf(fact_8048_power__sum,axiom,
% 5.24/5.56 ! [C: int,F: int > nat,A2: set_int] :
% 5.24/5.56 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.24/5.56 = ( groups1705073143266064639nt_int
% 5.24/5.56 @ ^ [A4: int] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.24/5.56 @ A2 ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_sum
% 5.24/5.56 thf(fact_8049_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.24/5.56 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.shift_bounds_cl_nat_ivl
% 5.24/5.56 thf(fact_8050_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.24/5.56 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.shift_bounds_cl_nat_ivl
% 5.24/5.56 thf(fact_8051_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > real] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8052_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > real] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8053_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > real] :
% 5.24/5.56 ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8054_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > real] :
% 5.24/5.56 ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8055_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > rat] :
% 5.24/5.56 ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8056_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > rat] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8057_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > rat] :
% 5.24/5.56 ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8058_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > rat] :
% 5.24/5.56 ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8059_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > nat] :
% 5.24/5.56 ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8060_prod__le__1,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > nat] :
% 5.24/5.56 ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.24/5.56 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.24/5.56 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_le_1
% 5.24/5.56 thf(fact_8061_prod_Orelated,axiom,
% 5.24/5.56 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.24/5.56 ( ( R @ one_one_complex @ one_one_complex )
% 5.24/5.56 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups6464643781859351333omplex @ H2 @ S3 ) @ ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8062_prod_Orelated,axiom,
% 5.24/5.56 ! [R: complex > complex > $o,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.24/5.56 ( ( R @ one_one_complex @ one_one_complex )
% 5.24/5.56 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups3708469109370488835omplex @ H2 @ S3 ) @ ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8063_prod_Orelated,axiom,
% 5.24/5.56 ! [R: real > real > $o,S3: set_nat,H2: nat > real,G: nat > real] :
% 5.24/5.56 ( ( R @ one_one_real @ one_one_real )
% 5.24/5.56 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups129246275422532515t_real @ H2 @ S3 ) @ ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8064_prod_Orelated,axiom,
% 5.24/5.56 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.24/5.56 ( ( R @ one_one_real @ one_one_real )
% 5.24/5.56 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups766887009212190081x_real @ H2 @ S3 ) @ ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8065_prod_Orelated,axiom,
% 5.24/5.56 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.24/5.56 ( ( R @ one_one_rat @ one_one_rat )
% 5.24/5.56 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups73079841787564623at_rat @ H2 @ S3 ) @ ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8066_prod_Orelated,axiom,
% 5.24/5.56 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.24/5.56 ( ( R @ one_one_rat @ one_one_rat )
% 5.24/5.56 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups225925009352817453ex_rat @ H2 @ S3 ) @ ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8067_prod_Orelated,axiom,
% 5.24/5.56 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.24/5.56 ( ( R @ one_one_nat @ one_one_nat )
% 5.24/5.56 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups861055069439313189ex_nat @ H2 @ S3 ) @ ( groups861055069439313189ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8068_prod_Orelated,axiom,
% 5.24/5.56 ! [R: int > int > $o,S3: set_complex,H2: complex > int,G: complex > int] :
% 5.24/5.56 ( ( R @ one_one_int @ one_one_int )
% 5.24/5.56 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ S3 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups858564598930262913ex_int @ H2 @ S3 ) @ ( groups858564598930262913ex_int @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8069_prod_Orelated,axiom,
% 5.24/5.56 ! [R: nat > nat > $o,S3: set_nat,H2: nat > nat,G: nat > nat] :
% 5.24/5.56 ( ( R @ one_one_nat @ one_one_nat )
% 5.24/5.56 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups708209901874060359at_nat @ H2 @ S3 ) @ ( groups708209901874060359at_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8070_prod_Orelated,axiom,
% 5.24/5.56 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.24/5.56 ( ( R @ one_one_int @ one_one_int )
% 5.24/5.56 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.24/5.56 ( ( ( R @ X15 @ X23 )
% 5.24/5.56 & ( R @ Y15 @ Y23 ) )
% 5.24/5.56 => ( R @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.24/5.56 => ( ( finite_finite_nat @ S3 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ S3 )
% 5.24/5.56 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.24/5.56 => ( R @ ( groups705719431365010083at_int @ H2 @ S3 ) @ ( groups705719431365010083at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.related
% 5.24/5.56 thf(fact_8071_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_int,T4: set_int,S3: set_int,I2: int > int,J: int > int,T5: set_int,G: int > complex,H2: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ S4 )
% 5.24/5.56 => ( ( finite_finite_int @ T4 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8072_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_int,T4: set_real,S3: set_int,I2: real > int,J: int > real,T5: set_real,G: int > complex,H2: real > complex] :
% 5.24/5.56 ( ( finite_finite_int @ S4 )
% 5.24/5.56 => ( ( finite_finite_real @ T4 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.24/5.56 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8073_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_real,T4: set_int,S3: set_real,I2: int > real,J: real > int,T5: set_int,G: real > complex,H2: int > complex] :
% 5.24/5.56 ( ( finite_finite_real @ S4 )
% 5.24/5.56 => ( ( finite_finite_int @ T4 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.24/5.56 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8074_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_real,T4: set_real,S3: set_real,I2: real > real,J: real > real,T5: set_real,G: real > complex,H2: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ S4 )
% 5.24/5.56 => ( ( finite_finite_real @ T4 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.24/5.56 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.24/5.56 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8075_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_int,T4: set_complex,S3: set_int,I2: complex > int,J: int > complex,T5: set_complex,G: int > complex,H2: complex > complex] :
% 5.24/5.56 ( ( finite_finite_int @ S4 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ T4 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.24/5.56 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8076_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_real,T4: set_complex,S3: set_real,I2: complex > real,J: real > complex,T5: set_complex,G: real > complex,H2: complex > complex] :
% 5.24/5.56 ( ( finite_finite_real @ S4 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ T4 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.24/5.56 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.24/5.56 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8077_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_complex,T4: set_int,S3: set_complex,I2: int > complex,J: complex > int,T5: set_int,G: complex > complex,H2: int > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S4 )
% 5.24/5.56 => ( ( finite_finite_int @ T4 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S4 ) )
% 5.24/5.56 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( member_complex @ ( I2 @ B2 ) @ ( minus_811609699411566653omplex @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8078_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_complex,T4: set_real,S3: set_complex,I2: real > complex,J: complex > real,T5: set_real,G: complex > complex,H2: real > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S4 )
% 5.24/5.56 => ( ( finite_finite_real @ T4 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S4 ) )
% 5.24/5.56 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.24/5.56 => ( member_complex @ ( I2 @ B2 ) @ ( minus_811609699411566653omplex @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8079_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_complex,T4: set_complex,S3: set_complex,I2: complex > complex,J: complex > complex,T5: set_complex,G: complex > complex,H2: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ S4 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ T4 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S4 ) )
% 5.24/5.56 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.24/5.56 => ( member_complex @ ( I2 @ B2 ) @ ( minus_811609699411566653omplex @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8080_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.24/5.56 ! [S4: set_int,T4: set_int,S3: set_int,I2: int > int,J: int > int,T5: set_int,G: int > real,H2: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ S4 )
% 5.24/5.56 => ( ( finite_finite_int @ T4 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( ( I2 @ ( J @ A3 ) )
% 5.24/5.56 = A3 ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.24/5.56 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( ( J @ ( I2 @ B2 ) )
% 5.24/5.56 = B2 ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.24/5.56 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S4 )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ T4 )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ S3 )
% 5.24/5.56 => ( ( H2 @ ( J @ A3 ) )
% 5.24/5.56 = ( G @ A3 ) ) )
% 5.24/5.56 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.reindex_bij_witness_not_neutral
% 5.24/5.56 thf(fact_8081_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G
% 5.24/5.56 @ ( minus_minus_set_real @ A2
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_complex ) ) ) )
% 5.24/5.56 = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8082_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G
% 5.24/5.56 @ ( minus_811609699411566653omplex @ A2
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_complex ) ) ) )
% 5.24/5.56 = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8083_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups1681761925125756287l_real @ G
% 5.24/5.56 @ ( minus_minus_set_real @ A2
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_real ) ) ) )
% 5.24/5.56 = ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8084_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G
% 5.24/5.56 @ ( minus_811609699411566653omplex @ A2
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_real ) ) ) )
% 5.24/5.56 = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8085_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat @ G
% 5.24/5.56 @ ( minus_minus_set_real @ A2
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_rat ) ) ) )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8086_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G
% 5.24/5.56 @ ( minus_811609699411566653omplex @ A2
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_rat ) ) ) )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8087_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > nat] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups4696554848551431203al_nat @ G
% 5.24/5.56 @ ( minus_minus_set_real @ A2
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_nat ) ) ) )
% 5.24/5.56 = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8088_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups861055069439313189ex_nat @ G
% 5.24/5.56 @ ( minus_811609699411566653omplex @ A2
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_nat ) ) ) )
% 5.24/5.56 = ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8089_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_real,G: real > int] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ( groups4694064378042380927al_int @ G
% 5.24/5.56 @ ( minus_minus_set_real @ A2
% 5.24/5.56 @ ( collect_real
% 5.24/5.56 @ ^ [X2: real] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_int ) ) ) )
% 5.24/5.56 = ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8090_prod_Osetdiff__irrelevant,axiom,
% 5.24/5.56 ! [A2: set_complex,G: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups858564598930262913ex_int @ G
% 5.24/5.56 @ ( minus_811609699411566653omplex @ A2
% 5.24/5.56 @ ( collect_complex
% 5.24/5.56 @ ^ [X2: complex] :
% 5.24/5.56 ( ( G @ X2 )
% 5.24/5.56 = one_one_int ) ) ) )
% 5.24/5.56 = ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.setdiff_irrelevant
% 5.24/5.56 thf(fact_8091_prod_Onat__diff__reindex,axiom,
% 5.24/5.56 ! [G: nat > nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.56 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.nat_diff_reindex
% 5.24/5.56 thf(fact_8092_prod_Onat__diff__reindex,axiom,
% 5.24/5.56 ! [G: nat > int,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.56 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.nat_diff_reindex
% 5.24/5.56 thf(fact_8093_prod_OatLeastAtMost__rev,axiom,
% 5.24/5.56 ! [G: nat > nat,N: nat,M: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeastAtMost_rev
% 5.24/5.56 thf(fact_8094_prod_OatLeastAtMost__rev,axiom,
% 5.24/5.56 ! [G: nat > int,N: nat,M: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeastAtMost_rev
% 5.24/5.56 thf(fact_8095_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_int,I2: int,F: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ I5 )
% 5.24/5.56 => ( ( member_int @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8096_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_real,I2: real,F: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ I5 )
% 5.24/5.56 => ( ( member_real @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8097_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_nat,I2: nat,F: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ I5 )
% 5.24/5.56 => ( ( member_nat @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8098_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_complex,I2: complex,F: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.56 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8099_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_int,I2: int,F: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ I5 )
% 5.24/5.56 => ( ( member_int @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8100_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_real,I2: real,F: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ I5 )
% 5.24/5.56 => ( ( member_real @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8101_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 5.24/5.56 ( ( finite_finite_nat @ I5 )
% 5.24/5.56 => ( ( member_nat @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8102_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_complex,I2: complex,F: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.56 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8103_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_real,I2: real,F: real > int] :
% 5.24/5.56 ( ( finite_finite_real @ I5 )
% 5.24/5.56 => ( ( member_real @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8104_less__1__prod2,axiom,
% 5.24/5.56 ! [I5: set_complex,I2: complex,F: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.56 => ( ( member_complex @ I2 @ I5 )
% 5.24/5.56 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod2
% 5.24/5.56 thf(fact_8105_arccos__le__arccos,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ ( arccos @ X ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_le_arccos
% 5.24/5.56 thf(fact_8106_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_complex,F: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_complex )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8107_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_nat,F: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_nat )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8108_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_int,F: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_int )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8109_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_real,F: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_real )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8110_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_complex,F: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_complex )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8111_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_nat,F: nat > rat] :
% 5.24/5.56 ( ( finite_finite_nat @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_nat )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8112_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_int,F: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_int )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8113_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_real,F: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_real )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8114_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_complex,F: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_complex )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8115_less__1__prod,axiom,
% 5.24/5.56 ! [I5: set_real,F: real > int] :
% 5.24/5.56 ( ( finite_finite_real @ I5 )
% 5.24/5.56 => ( ( I5 != bot_bot_set_real )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 5.24/5.56 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_1_prod
% 5.24/5.56 thf(fact_8116_arccos__eq__iff,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 & ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real ) )
% 5.24/5.56 => ( ( ( arccos @ X )
% 5.24/5.56 = ( arccos @ Y4 ) )
% 5.24/5.56 = ( X = Y4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_eq_iff
% 5.24/5.56 thf(fact_8117_arccos__le__mono,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y4 ) )
% 5.24/5.56 = ( ord_less_eq_real @ Y4 @ X ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_le_mono
% 5.24/5.56 thf(fact_8118_arcsin__minus,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.24/5.56 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_minus
% 5.24/5.56 thf(fact_8119_arcsin__le__arcsin,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_le_arcsin
% 5.24/5.56 thf(fact_8120_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,G: complex > real] :
% 5.24/5.56 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.24/5.56 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups766887009212190081x_real @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8121_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,G: complex > rat] :
% 5.24/5.56 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.24/5.56 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8122_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,G: complex > nat] :
% 5.24/5.56 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.24/5.56 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8123_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,G: complex > int] :
% 5.24/5.56 ( ( ord_le211207098394363844omplex @ B5 @ A2 )
% 5.24/5.56 => ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.24/5.56 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) @ ( groups858564598930262913ex_int @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8124_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_nat,A2: set_nat,G: nat > real] :
% 5.24/5.56 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.56 => ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.24/5.56 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups129246275422532515t_real @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8125_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_nat,A2: set_nat,G: nat > rat] :
% 5.24/5.56 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.56 => ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.24/5.56 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups73079841787564623at_rat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8126_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_nat,A2: set_nat,G: nat > nat] :
% 5.24/5.56 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.56 => ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.24/5.56 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups708209901874060359at_nat @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8127_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_nat,A2: set_nat,G: nat > int] :
% 5.24/5.56 ( ( ord_less_eq_set_nat @ B5 @ A2 )
% 5.24/5.56 => ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.24/5.56 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ A2 @ B5 ) ) @ ( groups705719431365010083at_int @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8128_prod_Osubset__diff,axiom,
% 5.24/5.56 ! [B5: set_int,A2: set_int,G: int > int] :
% 5.24/5.56 ( ( ord_less_eq_set_int @ B5 @ A2 )
% 5.24/5.56 => ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.24/5.56 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ ( minus_minus_set_int @ A2 @ B5 ) ) @ ( groups1705073143266064639nt_int @ G @ B5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.subset_diff
% 5.24/5.56 thf(fact_8129_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > complex,H2: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups7440179247065528705omplex @ G @ C5 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8130_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_real,A2: set_real,B5: set_real,G: real > complex,H2: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups713298508707869441omplex @ G @ C5 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8131_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_complex,A2: set_complex,B5: set_complex,G: complex > complex,H2: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups3708469109370488835omplex @ G @ C5 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8132_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > real,H2: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups2316167850115554303t_real @ G @ C5 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8133_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_real,A2: set_real,B5: set_real,G: real > real,H2: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.24/5.56 = ( groups1681761925125756287l_real @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups1681761925125756287l_real @ G @ C5 )
% 5.24/5.56 = ( groups1681761925125756287l_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8134_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_complex,A2: set_complex,B5: set_complex,G: complex > real,H2: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.24/5.56 = ( groups766887009212190081x_real @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups766887009212190081x_real @ G @ C5 )
% 5.24/5.56 = ( groups766887009212190081x_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8135_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > rat,H2: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.24/5.56 = ( groups1072433553688619179nt_rat @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups1072433553688619179nt_rat @ G @ C5 )
% 5.24/5.56 = ( groups1072433553688619179nt_rat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8136_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_real,A2: set_real,B5: set_real,G: real > rat,H2: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups4061424788464935467al_rat @ G @ C5 )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8137_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_complex,A2: set_complex,B5: set_complex,G: complex > rat,H2: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups225925009352817453ex_rat @ G @ C5 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8138_prod_Osame__carrier,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > nat,H2: int > nat] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.24/5.56 = ( groups1707563613775114915nt_nat @ H2 @ B5 ) )
% 5.24/5.56 = ( ( groups1707563613775114915nt_nat @ G @ C5 )
% 5.24/5.56 = ( groups1707563613775114915nt_nat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrier
% 5.24/5.56 thf(fact_8139_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > complex,H2: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( ( groups7440179247065528705omplex @ G @ C5 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8140_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_real,A2: set_real,B5: set_real,G: real > complex,H2: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( ( groups713298508707869441omplex @ G @ C5 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G @ A2 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8141_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_complex,A2: set_complex,B5: set_complex,G: complex > complex,H2: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( ( groups3708469109370488835omplex @ G @ C5 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8142_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > real,H2: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( ( groups2316167850115554303t_real @ G @ C5 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8143_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_real,A2: set_real,B5: set_real,G: real > real,H2: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( ( groups1681761925125756287l_real @ G @ C5 )
% 5.24/5.56 = ( groups1681761925125756287l_real @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.24/5.56 = ( groups1681761925125756287l_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8144_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_complex,A2: set_complex,B5: set_complex,G: complex > real,H2: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( ( groups766887009212190081x_real @ G @ C5 )
% 5.24/5.56 = ( groups766887009212190081x_real @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.24/5.56 = ( groups766887009212190081x_real @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8145_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > rat,H2: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( ( groups1072433553688619179nt_rat @ G @ C5 )
% 5.24/5.56 = ( groups1072433553688619179nt_rat @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.24/5.56 = ( groups1072433553688619179nt_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8146_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_real,A2: set_real,B5: set_real,G: real > rat,H2: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( ( groups4061424788464935467al_rat @ G @ C5 )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8147_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_complex,A2: set_complex,B5: set_complex,G: complex > rat,H2: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( ( groups225925009352817453ex_rat @ G @ C5 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8148_prod_Osame__carrierI,axiom,
% 5.24/5.56 ! [C5: set_int,A2: set_int,B5: set_int,G: int > nat,H2: int > nat] :
% 5.24/5.56 ( ( finite_finite_int @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ B5 @ C5 )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.24/5.56 => ( ( G @ A3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B5 ) )
% 5.24/5.56 => ( ( H2 @ B2 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( ( groups1707563613775114915nt_nat @ G @ C5 )
% 5.24/5.56 = ( groups1707563613775114915nt_nat @ H2 @ C5 ) )
% 5.24/5.56 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.24/5.56 = ( groups1707563613775114915nt_nat @ H2 @ B5 ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.same_carrierI
% 5.24/5.56 thf(fact_8149_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8150_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.24/5.56 = ( groups766887009212190081x_real @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8151_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8152_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( groups861055069439313189ex_nat @ G @ S3 )
% 5.24/5.56 = ( groups861055069439313189ex_nat @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8153_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 => ( ( groups858564598930262913ex_int @ G @ S3 )
% 5.24/5.56 = ( groups858564598930262913ex_int @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8154_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > complex] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.24/5.56 = ( groups6464643781859351333omplex @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8155_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ S3 )
% 5.24/5.56 = ( groups129246275422532515t_real @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8156_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > rat] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ S3 )
% 5.24/5.56 = ( groups73079841787564623at_rat @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8157_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > nat] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ S3 )
% 5.24/5.56 = ( groups708209901874060359at_nat @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8158_prod_Omono__neutral__left,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > int] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ S3 )
% 5.24/5.56 = ( groups705719431365010083at_int @ G @ T5 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_left
% 5.24/5.56 thf(fact_8159_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ T5 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8160_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ T5 )
% 5.24/5.56 = ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8161_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ T5 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8162_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( groups861055069439313189ex_nat @ G @ T5 )
% 5.24/5.56 = ( groups861055069439313189ex_nat @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8163_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 => ( ( groups858564598930262913ex_int @ G @ T5 )
% 5.24/5.56 = ( groups858564598930262913ex_int @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8164_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > complex] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ( groups6464643781859351333omplex @ G @ T5 )
% 5.24/5.56 = ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8165_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ T5 )
% 5.24/5.56 = ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8166_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > rat] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ T5 )
% 5.24/5.56 = ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8167_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > nat] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ T5 )
% 5.24/5.56 = ( groups708209901874060359at_nat @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8168_prod_Omono__neutral__right,axiom,
% 5.24/5.56 ! [T5: set_nat,S3: set_nat,G: nat > int] :
% 5.24/5.56 ( ( finite_finite_nat @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: nat] :
% 5.24/5.56 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_int ) )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ T5 )
% 5.24/5.56 = ( groups705719431365010083at_int @ G @ S3 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_right
% 5.24/5.56 thf(fact_8169_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,H2: int > complex,G: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8170_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_real,S3: set_real,H2: real > complex,G: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8171_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8172_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,H2: int > real,G: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8173_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_real,S3: set_real,H2: real > real,G: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups1681761925125756287l_real @ G @ S3 )
% 5.24/5.56 = ( groups1681761925125756287l_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8174_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.24/5.56 = ( groups766887009212190081x_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8175_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,H2: int > rat,G: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat @ G @ S3 )
% 5.24/5.56 = ( groups1072433553688619179nt_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8176_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat @ G @ S3 )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8177_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8178_prod_Omono__neutral__cong__left,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,H2: int > nat,G: int > nat] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( H2 @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups1707563613775114915nt_nat @ G @ S3 )
% 5.24/5.56 = ( groups1707563613775114915nt_nat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_left
% 5.24/5.56 thf(fact_8179_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,G: int > complex,H2: int > complex] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups7440179247065528705omplex @ G @ T5 )
% 5.24/5.56 = ( groups7440179247065528705omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8180_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_real,S3: set_real,G: real > complex,H2: real > complex] :
% 5.24/5.56 ( ( finite_finite_real @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups713298508707869441omplex @ G @ T5 )
% 5.24/5.56 = ( groups713298508707869441omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8181_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > complex,H2: complex > complex] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_complex ) )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups3708469109370488835omplex @ G @ T5 )
% 5.24/5.56 = ( groups3708469109370488835omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8182_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,G: int > real,H2: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups2316167850115554303t_real @ G @ T5 )
% 5.24/5.56 = ( groups2316167850115554303t_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8183_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_real,S3: set_real,G: real > real,H2: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups1681761925125756287l_real @ G @ T5 )
% 5.24/5.56 = ( groups1681761925125756287l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8184_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_real ) )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups766887009212190081x_real @ G @ T5 )
% 5.24/5.56 = ( groups766887009212190081x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8185_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,G: int > rat,H2: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups1072433553688619179nt_rat @ G @ T5 )
% 5.24/5.56 = ( groups1072433553688619179nt_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8186_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [X3: real] :
% 5.24/5.56 ( ( member_real @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups4061424788464935467al_rat @ G @ T5 )
% 5.24/5.56 = ( groups4061424788464935467al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8187_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_complex,S3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ T5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_rat ) )
% 5.24/5.56 => ( ! [X3: complex] :
% 5.24/5.56 ( ( member_complex @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups225925009352817453ex_rat @ G @ T5 )
% 5.24/5.56 = ( groups225925009352817453ex_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8188_prod_Omono__neutral__cong__right,axiom,
% 5.24/5.56 ! [T5: set_int,S3: set_int,G: int > nat,H2: int > nat] :
% 5.24/5.56 ( ( finite_finite_int @ T5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = one_one_nat ) )
% 5.24/5.56 => ( ! [X3: int] :
% 5.24/5.56 ( ( member_int @ X3 @ S3 )
% 5.24/5.56 => ( ( G @ X3 )
% 5.24/5.56 = ( H2 @ X3 ) ) )
% 5.24/5.56 => ( ( groups1707563613775114915nt_nat @ G @ T5 )
% 5.24/5.56 = ( groups1707563613775114915nt_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.mono_neutral_cong_right
% 5.24/5.56 thf(fact_8189_arcsin__eq__iff,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( ( arcsin @ X )
% 5.24/5.56 = ( arcsin @ Y4 ) )
% 5.24/5.56 = ( X = Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_eq_iff
% 5.24/5.56 thf(fact_8190_arcsin__le__mono,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) )
% 5.24/5.56 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_le_mono
% 5.24/5.56 thf(fact_8191_prod_OatLeast0__atMost__Suc,axiom,
% 5.24/5.56 ! [G: nat > real,N: nat] :
% 5.24/5.56 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast0_atMost_Suc
% 5.24/5.56 thf(fact_8192_prod_OatLeast0__atMost__Suc,axiom,
% 5.24/5.56 ! [G: nat > rat,N: nat] :
% 5.24/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast0_atMost_Suc
% 5.24/5.56 thf(fact_8193_prod_OatLeast0__atMost__Suc,axiom,
% 5.24/5.56 ! [G: nat > nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast0_atMost_Suc
% 5.24/5.56 thf(fact_8194_prod_OatLeast0__atMost__Suc,axiom,
% 5.24/5.56 ! [G: nat > int,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast0_atMost_Suc
% 5.24/5.56 thf(fact_8195_prod_OatLeast__Suc__atMost,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > real] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.56 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast_Suc_atMost
% 5.24/5.56 thf(fact_8196_prod_OatLeast__Suc__atMost,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > rat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.56 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast_Suc_atMost
% 5.24/5.56 thf(fact_8197_prod_OatLeast__Suc__atMost,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.56 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast_Suc_atMost
% 5.24/5.56 thf(fact_8198_prod_OatLeast__Suc__atMost,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > int] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.56 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast_Suc_atMost
% 5.24/5.56 thf(fact_8199_prod_Onat__ivl__Suc_H,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > real] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.nat_ivl_Suc'
% 5.24/5.56 thf(fact_8200_prod_Onat__ivl__Suc_H,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > rat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.nat_ivl_Suc'
% 5.24/5.56 thf(fact_8201_prod_Onat__ivl__Suc_H,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.nat_ivl_Suc'
% 5.24/5.56 thf(fact_8202_prod_Onat__ivl__Suc_H,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > int] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.nat_ivl_Suc'
% 5.24/5.56 thf(fact_8203_prod_OlessThan__Suc__shift,axiom,
% 5.24/5.56 ! [G: nat > real,N: nat] :
% 5.24/5.56 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.24/5.56 @ ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc_shift
% 5.24/5.56 thf(fact_8204_prod_OlessThan__Suc__shift,axiom,
% 5.24/5.56 ! [G: nat > rat,N: nat] :
% 5.24/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.24/5.56 @ ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc_shift
% 5.24/5.56 thf(fact_8205_prod_OlessThan__Suc__shift,axiom,
% 5.24/5.56 ! [G: nat > nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc_shift
% 5.24/5.56 thf(fact_8206_prod_OlessThan__Suc__shift,axiom,
% 5.24/5.56 ! [G: nat > int,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.24/5.56 @ ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.lessThan_Suc_shift
% 5.24/5.56 thf(fact_8207_prod_OSuc__reindex__ivl,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > real] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_real @ ( G @ M )
% 5.24/5.56 @ ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.Suc_reindex_ivl
% 5.24/5.56 thf(fact_8208_prod_OSuc__reindex__ivl,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > rat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_rat @ ( G @ M )
% 5.24/5.56 @ ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.Suc_reindex_ivl
% 5.24/5.56 thf(fact_8209_prod_OSuc__reindex__ivl,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_nat @ ( G @ M )
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.Suc_reindex_ivl
% 5.24/5.56 thf(fact_8210_prod_OSuc__reindex__ivl,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > int] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.24/5.56 = ( times_times_int @ ( G @ M )
% 5.24/5.56 @ ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.Suc_reindex_ivl
% 5.24/5.56 thf(fact_8211_prod_OatLeast1__atMost__eq,axiom,
% 5.24/5.56 ! [G: nat > nat,N: nat] :
% 5.24/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast1_atMost_eq
% 5.24/5.56 thf(fact_8212_prod_OatLeast1__atMost__eq,axiom,
% 5.24/5.56 ! [G: nat > int,N: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.atLeast1_atMost_eq
% 5.24/5.56 thf(fact_8213_fact__prod,axiom,
% 5.24/5.56 ( semiri1406184849735516958ct_int
% 5.24/5.56 = ( ^ [N2: nat] :
% 5.24/5.56 ( semiri1314217659103216013at_int
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : X2
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_prod
% 5.24/5.56 thf(fact_8214_fact__prod,axiom,
% 5.24/5.56 ( semiri773545260158071498ct_rat
% 5.24/5.56 = ( ^ [N2: nat] :
% 5.24/5.56 ( semiri681578069525770553at_rat
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : X2
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_prod
% 5.24/5.56 thf(fact_8215_fact__prod,axiom,
% 5.24/5.56 ( semiri2265585572941072030t_real
% 5.24/5.56 = ( ^ [N2: nat] :
% 5.24/5.56 ( semiri5074537144036343181t_real
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : X2
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_prod
% 5.24/5.56 thf(fact_8216_fact__prod,axiom,
% 5.24/5.56 ( semiri1408675320244567234ct_nat
% 5.24/5.56 = ( ^ [N2: nat] :
% 5.24/5.56 ( semiri1316708129612266289at_nat
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : X2
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_prod
% 5.24/5.56 thf(fact_8217_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_complex )
% 5.24/5.56 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8218_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_nat )
% 5.24/5.56 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8219_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > real,G: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_int )
% 5.24/5.56 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8220_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > real,G: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_real )
% 5.24/5.56 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8221_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_complex )
% 5.24/5.56 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8222_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_nat )
% 5.24/5.56 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8223_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_int )
% 5.24/5.56 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8224_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ A2 )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_real )
% 5.24/5.56 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8225_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_complex )
% 5.24/5.56 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8226_prod__mono__strict,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ A2 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.24/5.56 & ( ord_less_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.24/5.56 => ( ( A2 != bot_bot_set_int )
% 5.24/5.56 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono_strict
% 5.24/5.56 thf(fact_8227_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > code_integer] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8228_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > code_integer] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8229_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8230_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8231_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8232_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > int] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8233_even__prod__iff,axiom,
% 5.24/5.56 ! [A2: set_int,F: int > int] :
% 5.24/5.56 ( ( finite_finite_int @ A2 )
% 5.24/5.56 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.24/5.56 = ( ? [X2: int] :
% 5.24/5.56 ( ( member_int @ X2 @ A2 )
% 5.24/5.56 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % even_prod_iff
% 5.24/5.56 thf(fact_8234_arccos__lbound,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_lbound
% 5.24/5.56 thf(fact_8235_arccos__less__arccos,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_real @ X @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_real @ ( arccos @ Y4 ) @ ( arccos @ X ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_less_arccos
% 5.24/5.56 thf(fact_8236_arccos__less__mono,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y4 ) )
% 5.24/5.56 = ( ord_less_real @ Y4 @ X ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_less_mono
% 5.24/5.56 thf(fact_8237_arccos__ubound,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ pi ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_ubound
% 5.24/5.56 thf(fact_8238_prod_Oub__add__nat,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.56 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.56 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.ub_add_nat
% 5.24/5.56 thf(fact_8239_prod_Oub__add__nat,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.56 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.56 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.ub_add_nat
% 5.24/5.56 thf(fact_8240_prod_Oub__add__nat,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.56 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.56 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.ub_add_nat
% 5.24/5.56 thf(fact_8241_prod_Oub__add__nat,axiom,
% 5.24/5.56 ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.24/5.56 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.24/5.56 = ( 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 @ P6 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.ub_add_nat
% 5.24/5.56 thf(fact_8242_arcsin__less__arcsin,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_real @ X @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_less_arcsin
% 5.24/5.56 thf(fact_8243_arcsin__less__mono,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) )
% 5.24/5.56 = ( ord_less_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_less_mono
% 5.24/5.56 thf(fact_8244_cos__arccos__abs,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.24/5.56 => ( ( cos_real @ ( arccos @ Y4 ) )
% 5.24/5.56 = Y4 ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_arccos_abs
% 5.24/5.56 thf(fact_8245_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.24/5.56 ( set_fo2584398358068434914at_nat
% 5.24/5.56 = ( ^ [F3: nat > nat > nat,A4: nat,B3: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F3 @ A4 @ Acc ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fold_atLeastAtMost_nat.simps
% 5.24/5.56 thf(fact_8246_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.24/5.56 ! [X: nat > nat > nat,Xa2: nat,Xb2: nat,Xc: nat,Y4: nat] :
% 5.24/5.56 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb2 @ Xc )
% 5.24/5.56 = Y4 )
% 5.24/5.56 => ( ( ( ord_less_nat @ Xb2 @ Xa2 )
% 5.24/5.56 => ( Y4 = Xc ) )
% 5.24/5.56 & ( ~ ( ord_less_nat @ Xb2 @ Xa2 )
% 5.24/5.56 => ( Y4
% 5.24/5.56 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb2 @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fold_atLeastAtMost_nat.elims
% 5.24/5.56 thf(fact_8247_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_int,Z2: int > real,W2: int > real] :
% 5.24/5.56 ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z2 @ I5 ) @ ( groups2316167850115554303t_real @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups8778361861064173332t_real
% 5.24/5.56 @ ^ [I4: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8248_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_real,Z2: real > real,W2: real > real] :
% 5.24/5.56 ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z2 @ I5 ) @ ( groups1681761925125756287l_real @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups8097168146408367636l_real
% 5.24/5.56 @ ^ [I4: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8249_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_complex,Z2: complex > real,W2: complex > real] :
% 5.24/5.56 ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups766887009212190081x_real @ Z2 @ I5 ) @ ( groups766887009212190081x_real @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups5808333547571424918x_real
% 5.24/5.56 @ ^ [I4: complex] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8250_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_Pr1261947904930325089at_nat,Z2: product_prod_nat_nat > real,W2: product_prod_nat_nat > real] :
% 5.24/5.56 ( ! [I3: product_prod_nat_nat] :
% 5.24/5.56 ( ( member8440522571783428010at_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: product_prod_nat_nat] :
% 5.24/5.56 ( ( member8440522571783428010at_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups6036352826371341000t_real @ Z2 @ I5 ) @ ( groups6036352826371341000t_real @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups4567486121110086003t_real
% 5.24/5.56 @ ^ [I4: product_prod_nat_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8251_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_int,Z2: int > complex,W2: int > complex] :
% 5.24/5.56 ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: int] :
% 5.24/5.56 ( ( member_int @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z2 @ I5 ) @ ( groups7440179247065528705omplex @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups8778361861064173332t_real
% 5.24/5.56 @ ^ [I4: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8252_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_real,Z2: real > complex,W2: real > complex] :
% 5.24/5.56 ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: real] :
% 5.24/5.56 ( ( member_real @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z2 @ I5 ) @ ( groups713298508707869441omplex @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups8097168146408367636l_real
% 5.24/5.56 @ ^ [I4: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8253_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_complex,Z2: complex > complex,W2: complex > complex] :
% 5.24/5.56 ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: complex] :
% 5.24/5.56 ( ( member_complex @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z2 @ I5 ) @ ( groups3708469109370488835omplex @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups5808333547571424918x_real
% 5.24/5.56 @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8254_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_Pr1261947904930325089at_nat,Z2: product_prod_nat_nat > complex,W2: product_prod_nat_nat > complex] :
% 5.24/5.56 ( ! [I3: product_prod_nat_nat] :
% 5.24/5.56 ( ( member8440522571783428010at_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: product_prod_nat_nat] :
% 5.24/5.56 ( ( member8440522571783428010at_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups8110221916422527690omplex @ Z2 @ I5 ) @ ( groups8110221916422527690omplex @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups4567486121110086003t_real
% 5.24/5.56 @ ^ [I4: product_prod_nat_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8255_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_nat,Z2: nat > real,W2: nat > real] :
% 5.24/5.56 ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z2 @ I5 ) @ ( groups129246275422532515t_real @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups6591440286371151544t_real
% 5.24/5.56 @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8256_norm__prod__diff,axiom,
% 5.24/5.56 ! [I5: set_nat,Z2: nat > complex,W2: nat > complex] :
% 5.24/5.56 ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ! [I3: nat] :
% 5.24/5.56 ( ( member_nat @ I3 @ I5 )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W2 @ I3 ) ) @ one_one_real ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z2 @ I5 ) @ ( groups6464643781859351333omplex @ W2 @ I5 ) ) )
% 5.24/5.56 @ ( groups6591440286371151544t_real
% 5.24/5.56 @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z2 @ I4 ) @ ( W2 @ I4 ) ) )
% 5.24/5.56 @ I5 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % norm_prod_diff
% 5.24/5.56 thf(fact_8257_fact__eq__fact__times,axiom,
% 5.24/5.56 ! [N: nat,M: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.56 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.24/5.56 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.24/5.56 @ ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : X2
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_eq_fact_times
% 5.24/5.56 thf(fact_8258_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_int,A2: set_int,F: int > real] :
% 5.24/5.56 ( ( finite_finite_int @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8259_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_real,A2: set_real,F: real > real] :
% 5.24/5.56 ( ( finite_finite_real @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8260_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,F: complex > real] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8261_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_int,A2: set_int,F: int > rat] :
% 5.24/5.56 ( ( finite_finite_int @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_int @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: int] :
% 5.24/5.56 ( ( member_int @ B2 @ ( minus_minus_set_int @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: int] :
% 5.24/5.56 ( ( member_int @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8262_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_real,A2: set_real,F: real > rat] :
% 5.24/5.56 ( ( finite_finite_real @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8263_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,F: complex > rat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8264_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_real,A2: set_real,F: real > int] :
% 5.24/5.56 ( ( finite_finite_real @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_real @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: real] :
% 5.24/5.56 ( ( member_real @ B2 @ ( minus_minus_set_real @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: real] :
% 5.24/5.56 ( ( member_real @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8265_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_complex,A2: set_complex,F: complex > int] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ B5 )
% 5.24/5.56 => ( ( ord_le211207098394363844omplex @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: complex] :
% 5.24/5.56 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: complex] :
% 5.24/5.56 ( ( member_complex @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8266_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_nat,A2: set_nat,F: nat > real] :
% 5.24/5.56 ( ( finite_finite_nat @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: nat] :
% 5.24/5.56 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: nat] :
% 5.24/5.56 ( ( member_nat @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8267_prod__mono2,axiom,
% 5.24/5.56 ! [B5: set_nat,A2: set_nat,F: nat > rat] :
% 5.24/5.56 ( ( finite_finite_nat @ B5 )
% 5.24/5.56 => ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 5.24/5.56 => ( ! [B2: nat] :
% 5.24/5.56 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B5 @ A2 ) )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.24/5.56 => ( ! [A3: nat] :
% 5.24/5.56 ( ( member_nat @ A3 @ A2 )
% 5.24/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.24/5.56 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B5 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_mono2
% 5.24/5.56 thf(fact_8268_arccos__lt__bounded,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.24/5.56 & ( ord_less_real @ ( arccos @ Y4 ) @ pi ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_lt_bounded
% 5.24/5.56 thf(fact_8269_arccos__bounded,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( arccos @ Y4 ) @ pi ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_bounded
% 5.24/5.56 thf(fact_8270_sin__arccos__nonzero,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.56 => ( ( sin_real @ ( arccos @ X ) )
% 5.24/5.56 != zero_zero_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_arccos_nonzero
% 5.24/5.56 thf(fact_8271_arccos__minus,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.24/5.56 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_minus
% 5.24/5.56 thf(fact_8272_cos__arcsin__nonzero,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.56 => ( ( cos_real @ ( arcsin @ X ) )
% 5.24/5.56 != zero_zero_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cos_arcsin_nonzero
% 5.24/5.56 thf(fact_8273_pochhammer__Suc__prod,axiom,
% 5.24/5.56 ! [A: real,N: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod
% 5.24/5.56 thf(fact_8274_pochhammer__Suc__prod,axiom,
% 5.24/5.56 ! [A: rat,N: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod
% 5.24/5.56 thf(fact_8275_pochhammer__Suc__prod,axiom,
% 5.24/5.56 ! [A: nat,N: nat] :
% 5.24/5.56 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod
% 5.24/5.56 thf(fact_8276_pochhammer__Suc__prod,axiom,
% 5.24/5.56 ! [A: int,N: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod
% 5.24/5.56 thf(fact_8277_pochhammer__prod__rev,axiom,
% 5.24/5.56 ( comm_s7457072308508201937r_real
% 5.24/5.56 = ( ^ [A4: real,N2: nat] :
% 5.24/5.56 ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_prod_rev
% 5.24/5.56 thf(fact_8278_pochhammer__prod__rev,axiom,
% 5.24/5.56 ( comm_s4028243227959126397er_rat
% 5.24/5.56 = ( ^ [A4: rat,N2: nat] :
% 5.24/5.56 ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_prod_rev
% 5.24/5.56 thf(fact_8279_pochhammer__prod__rev,axiom,
% 5.24/5.56 ( comm_s4663373288045622133er_nat
% 5.24/5.56 = ( ^ [A4: nat,N2: nat] :
% 5.24/5.56 ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_prod_rev
% 5.24/5.56 thf(fact_8280_pochhammer__prod__rev,axiom,
% 5.24/5.56 ( comm_s4660882817536571857er_int
% 5.24/5.56 = ( ^ [A4: int,N2: nat] :
% 5.24/5.56 ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_prod_rev
% 5.24/5.56 thf(fact_8281_fact__div__fact,axiom,
% 5.24/5.56 ! [N: nat,M: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.56 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [X2: nat] : X2
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_div_fact
% 5.24/5.56 thf(fact_8282_prod_Oin__pairs,axiom,
% 5.24/5.56 ! [G: nat > real,M: nat,N: nat] :
% 5.24/5.56 ( ( 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 ) ) ) )
% 5.24/5.56 = ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.in_pairs
% 5.24/5.56 thf(fact_8283_prod_Oin__pairs,axiom,
% 5.24/5.56 ! [G: nat > rat,M: nat,N: nat] :
% 5.24/5.56 ( ( 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 ) ) ) )
% 5.24/5.56 = ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.in_pairs
% 5.24/5.56 thf(fact_8284_prod_Oin__pairs,axiom,
% 5.24/5.56 ! [G: nat > nat,M: nat,N: nat] :
% 5.24/5.56 ( ( 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 ) ) ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.in_pairs
% 5.24/5.56 thf(fact_8285_prod_Oin__pairs,axiom,
% 5.24/5.56 ! [G: nat > int,M: nat,N: nat] :
% 5.24/5.56 ( ( 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 ) ) ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod.in_pairs
% 5.24/5.56 thf(fact_8286_sum__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > complex,A: nat,B: nat] :
% 5.24/5.56 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo1517530859248394432omplex
% 5.24/5.56 @ ^ [A4: nat] : ( plus_plus_complex @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ zero_zero_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % sum_atLeastAtMost_code
% 5.24/5.56 thf(fact_8287_sum__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > rat,A: nat,B: nat] :
% 5.24/5.56 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo1949268297981939178at_rat
% 5.24/5.56 @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ zero_zero_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % sum_atLeastAtMost_code
% 5.24/5.56 thf(fact_8288_sum__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > int,A: nat,B: nat] :
% 5.24/5.56 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo2581907887559384638at_int
% 5.24/5.56 @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ zero_zero_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % sum_atLeastAtMost_code
% 5.24/5.56 thf(fact_8289_sum__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > nat,A: nat,B: nat] :
% 5.24/5.56 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo2584398358068434914at_nat
% 5.24/5.56 @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ zero_zero_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % sum_atLeastAtMost_code
% 5.24/5.56 thf(fact_8290_sum__atLeastAtMost__code,axiom,
% 5.24/5.56 ! [F: nat > real,A: nat,B: nat] :
% 5.24/5.56 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.24/5.56 = ( set_fo3111899725591712190t_real
% 5.24/5.56 @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 5.24/5.56 @ A
% 5.24/5.56 @ B
% 5.24/5.56 @ zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % sum_atLeastAtMost_code
% 5.24/5.56 thf(fact_8291_pochhammer__Suc__prod__rev,axiom,
% 5.24/5.56 ! [A: real,N: nat] :
% 5.24/5.56 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups129246275422532515t_real
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod_rev
% 5.24/5.56 thf(fact_8292_pochhammer__Suc__prod__rev,axiom,
% 5.24/5.56 ! [A: rat,N: nat] :
% 5.24/5.56 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups73079841787564623at_rat
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod_rev
% 5.24/5.56 thf(fact_8293_pochhammer__Suc__prod__rev,axiom,
% 5.24/5.56 ! [A: nat,N: nat] :
% 5.24/5.56 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups708209901874060359at_nat
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod_rev
% 5.24/5.56 thf(fact_8294_pochhammer__Suc__prod__rev,axiom,
% 5.24/5.56 ! [A: int,N: nat] :
% 5.24/5.56 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.24/5.56 = ( groups705719431365010083at_int
% 5.24/5.56 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pochhammer_Suc_prod_rev
% 5.24/5.56 thf(fact_8295_arccos,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( arccos @ Y4 ) @ pi )
% 5.24/5.56 & ( ( cos_real @ ( arccos @ Y4 ) )
% 5.24/5.56 = Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos
% 5.24/5.56 thf(fact_8296_arccos__minus__abs,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.56 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.24/5.56 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_minus_abs
% 5.24/5.56 thf(fact_8297_arccos__le__pi2,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_le_pi2
% 5.24/5.56 thf(fact_8298_arcsin__lt__bounded,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.24/5.56 & ( ord_less_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_lt_bounded
% 5.24/5.56 thf(fact_8299_arcsin__lbound,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_lbound
% 5.24/5.56 thf(fact_8300_arcsin__ubound,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_ubound
% 5.24/5.56 thf(fact_8301_arcsin__bounded,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_bounded
% 5.24/5.56 thf(fact_8302_arcsin__sin,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ( arcsin @ ( sin_real @ X ) )
% 5.24/5.56 = X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_sin
% 5.24/5.56 thf(fact_8303_fact__code,axiom,
% 5.24/5.56 ( semiri1406184849735516958ct_int
% 5.24/5.56 = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_code
% 5.24/5.56 thf(fact_8304_fact__code,axiom,
% 5.24/5.56 ( semiri773545260158071498ct_rat
% 5.24/5.56 = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_code
% 5.24/5.56 thf(fact_8305_fact__code,axiom,
% 5.24/5.56 ( semiri2265585572941072030t_real
% 5.24/5.56 = ( ^ [N2: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_code
% 5.24/5.56 thf(fact_8306_fact__code,axiom,
% 5.24/5.56 ( semiri1408675320244567234ct_nat
% 5.24/5.56 = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % fact_code
% 5.24/5.56 thf(fact_8307_arcsin,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 & ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.24/5.56 = Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin
% 5.24/5.56 thf(fact_8308_arcsin__pi,axiom,
% 5.24/5.56 ! [Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.24/5.56 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ pi )
% 5.24/5.56 & ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.24/5.56 = Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_pi
% 5.24/5.56 thf(fact_8309_arcsin__le__iff,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y4 )
% 5.24/5.56 = ( ord_less_eq_real @ X @ ( sin_real @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arcsin_le_iff
% 5.24/5.56 thf(fact_8310_le__arcsin__iff,axiom,
% 5.24/5.56 ! [X: real,Y4: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ( ord_less_eq_real @ Y4 @ ( arcsin @ X ) )
% 5.24/5.56 = ( ord_less_eq_real @ ( sin_real @ Y4 ) @ X ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % le_arcsin_iff
% 5.24/5.56 thf(fact_8311_arccos__cos__eq__abs__2pi,axiom,
% 5.24/5.56 ! [Theta: real] :
% 5.24/5.56 ~ ! [K2: int] :
% 5.24/5.56 ( ( arccos @ ( cos_real @ Theta ) )
% 5.24/5.56 != ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % arccos_cos_eq_abs_2pi
% 5.24/5.56 thf(fact_8312_sin__arccos,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.56 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.56 => ( ( sin_real @ ( arccos @ X ) )
% 5.24/5.56 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % sin_arccos
% 5.24/5.56 thf(fact_8313_gchoose__row__sum__weighted,axiom,
% 5.24/5.56 ! [R2: complex,M: nat] :
% 5.24/5.56 ( ( groups2073611262835488442omplex
% 5.24/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.24/5.56 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gchoose_row_sum_weighted
% 5.24/5.56 thf(fact_8314_gchoose__row__sum__weighted,axiom,
% 5.24/5.56 ! [R2: rat,M: nat] :
% 5.24/5.56 ( ( groups2906978787729119204at_rat
% 5.24/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.24/5.56 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gchoose_row_sum_weighted
% 5.24/5.56 thf(fact_8315_gchoose__row__sum__weighted,axiom,
% 5.24/5.56 ! [R2: real,M: nat] :
% 5.24/5.56 ( ( groups6591440286371151544t_real
% 5.24/5.56 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.24/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.24/5.56 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gchoose_row_sum_weighted
% 5.24/5.56 thf(fact_8316_central__binomial__lower__bound,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.56 => ( 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 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % central_binomial_lower_bound
% 5.24/5.56 thf(fact_8317_Maclaurin__sin__bound,axiom,
% 5.24/5.56 ! [X: real,N: nat] :
% 5.24/5.56 ( ord_less_eq_real
% 5.24/5.56 @ ( abs_abs_real
% 5.24/5.56 @ ( minus_minus_real @ ( sin_real @ X )
% 5.24/5.56 @ ( groups6591440286371151544t_real
% 5.24/5.56 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.24/5.56 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Maclaurin_sin_bound
% 5.24/5.56 thf(fact_8318_divmod__BitM__2__eq,axiom,
% 5.24/5.56 ! [M: num] :
% 5.24/5.56 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.24/5.56 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % divmod_BitM_2_eq
% 5.24/5.56 thf(fact_8319_cot__less__zero,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.24/5.56 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cot_less_zero
% 5.24/5.56 thf(fact_8320_inverse__mult__distrib,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.24/5.56 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_mult_distrib
% 5.24/5.56 thf(fact_8321_inverse__mult__distrib,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.24/5.56 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_mult_distrib
% 5.24/5.56 thf(fact_8322_inverse__mult__distrib,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.24/5.56 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_mult_distrib
% 5.24/5.56 thf(fact_8323_inverse__1,axiom,
% 5.24/5.56 ( ( inverse_inverse_real @ one_one_real )
% 5.24/5.56 = one_one_real ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_1
% 5.24/5.56 thf(fact_8324_inverse__1,axiom,
% 5.24/5.56 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.24/5.56 = one_one_complex ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_1
% 5.24/5.56 thf(fact_8325_inverse__1,axiom,
% 5.24/5.56 ( ( inverse_inverse_rat @ one_one_rat )
% 5.24/5.56 = one_one_rat ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_1
% 5.24/5.56 thf(fact_8326_inverse__eq__1__iff,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ( inverse_inverse_real @ X )
% 5.24/5.56 = one_one_real )
% 5.24/5.56 = ( X = one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_1_iff
% 5.24/5.56 thf(fact_8327_inverse__eq__1__iff,axiom,
% 5.24/5.56 ! [X: complex] :
% 5.24/5.56 ( ( ( invers8013647133539491842omplex @ X )
% 5.24/5.56 = one_one_complex )
% 5.24/5.56 = ( X = one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_1_iff
% 5.24/5.56 thf(fact_8328_inverse__eq__1__iff,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ( inverse_inverse_rat @ X )
% 5.24/5.56 = one_one_rat )
% 5.24/5.56 = ( X = one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_1_iff
% 5.24/5.56 thf(fact_8329_inverse__divide,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.24/5.56 = ( divide_divide_real @ B @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_divide
% 5.24/5.56 thf(fact_8330_inverse__divide,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.56 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_divide
% 5.24/5.56 thf(fact_8331_inverse__divide,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.24/5.56 = ( divide_divide_rat @ B @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_divide
% 5.24/5.56 thf(fact_8332_binomial__Suc__n,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( binomial @ ( suc @ N ) @ N )
% 5.24/5.56 = ( suc @ N ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_Suc_n
% 5.24/5.56 thf(fact_8333_binomial__n__n,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( binomial @ N @ N )
% 5.24/5.56 = one_one_nat ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_n_n
% 5.24/5.56 thf(fact_8334_inverse__nonnegative__iff__nonnegative,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.24/5.56 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_nonnegative_iff_nonnegative
% 5.24/5.56 thf(fact_8335_inverse__nonnegative__iff__nonnegative,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.24/5.56 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_nonnegative_iff_nonnegative
% 5.24/5.56 thf(fact_8336_inverse__nonpositive__iff__nonpositive,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.24/5.56 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_nonpositive_iff_nonpositive
% 5.24/5.56 thf(fact_8337_inverse__nonpositive__iff__nonpositive,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.24/5.56 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_nonpositive_iff_nonpositive
% 5.24/5.56 thf(fact_8338_inverse__less__iff__less,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.56 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_iff_less
% 5.24/5.56 thf(fact_8339_inverse__less__iff__less,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.24/5.56 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_iff_less
% 5.24/5.56 thf(fact_8340_inverse__less__iff__less__neg,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.24/5.56 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.24/5.56 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_iff_less_neg
% 5.24/5.56 thf(fact_8341_inverse__less__iff__less__neg,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.24/5.56 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.24/5.56 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_iff_less_neg
% 5.24/5.56 thf(fact_8342_inverse__negative__iff__negative,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.24/5.56 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_negative_iff_negative
% 5.24/5.56 thf(fact_8343_inverse__negative__iff__negative,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.24/5.56 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_negative_iff_negative
% 5.24/5.56 thf(fact_8344_inverse__positive__iff__positive,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.24/5.56 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_positive_iff_positive
% 5.24/5.56 thf(fact_8345_inverse__positive__iff__positive,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.24/5.56 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_positive_iff_positive
% 5.24/5.56 thf(fact_8346_gbinomial__0_I2_J,axiom,
% 5.24/5.56 ! [K: nat] :
% 5.24/5.56 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.24/5.56 = zero_zero_complex ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(2)
% 5.24/5.56 thf(fact_8347_gbinomial__0_I2_J,axiom,
% 5.24/5.56 ! [K: nat] :
% 5.24/5.56 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.24/5.56 = zero_zero_real ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(2)
% 5.24/5.56 thf(fact_8348_gbinomial__0_I2_J,axiom,
% 5.24/5.56 ! [K: nat] :
% 5.24/5.56 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.24/5.56 = zero_zero_rat ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(2)
% 5.24/5.56 thf(fact_8349_gbinomial__0_I2_J,axiom,
% 5.24/5.56 ! [K: nat] :
% 5.24/5.56 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.24/5.56 = zero_zero_nat ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(2)
% 5.24/5.56 thf(fact_8350_gbinomial__0_I2_J,axiom,
% 5.24/5.56 ! [K: nat] :
% 5.24/5.56 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.24/5.56 = zero_zero_int ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(2)
% 5.24/5.56 thf(fact_8351_binomial__1,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.56 = N ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_1
% 5.24/5.56 thf(fact_8352_binomial__0__Suc,axiom,
% 5.24/5.56 ! [K: nat] :
% 5.24/5.56 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.24/5.56 = zero_zero_nat ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_0_Suc
% 5.24/5.56 thf(fact_8353_binomial__eq__0__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ( binomial @ N @ K )
% 5.24/5.56 = zero_zero_nat )
% 5.24/5.56 = ( ord_less_nat @ N @ K ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_eq_0_iff
% 5.24/5.56 thf(fact_8354_gbinomial__0_I1_J,axiom,
% 5.24/5.56 ! [A: complex] :
% 5.24/5.56 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.24/5.56 = one_one_complex ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(1)
% 5.24/5.56 thf(fact_8355_gbinomial__0_I1_J,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.24/5.56 = one_one_real ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(1)
% 5.24/5.56 thf(fact_8356_gbinomial__0_I1_J,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.24/5.56 = one_one_rat ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(1)
% 5.24/5.56 thf(fact_8357_gbinomial__0_I1_J,axiom,
% 5.24/5.56 ! [A: nat] :
% 5.24/5.56 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.24/5.56 = one_one_nat ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(1)
% 5.24/5.56 thf(fact_8358_gbinomial__0_I1_J,axiom,
% 5.24/5.56 ! [A: int] :
% 5.24/5.56 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.24/5.56 = one_one_int ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_0(1)
% 5.24/5.56 thf(fact_8359_binomial__Suc__Suc,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_Suc_Suc
% 5.24/5.56 thf(fact_8360_binomial__n__0,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( binomial @ N @ zero_zero_nat )
% 5.24/5.56 = one_one_nat ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_n_0
% 5.24/5.56 thf(fact_8361_prod__eq__1__iff,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 5.24/5.56 = one_one_nat )
% 5.24/5.56 = ( ! [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 => ( ( F @ X2 )
% 5.24/5.56 = one_one_nat ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_eq_1_iff
% 5.24/5.56 thf(fact_8362_prod__eq__1__iff,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 5.24/5.56 = one_one_nat )
% 5.24/5.56 = ( ! [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 => ( ( F @ X2 )
% 5.24/5.56 = one_one_nat ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_eq_1_iff
% 5.24/5.56 thf(fact_8363_dbl__dec__simps_I5_J,axiom,
% 5.24/5.56 ! [K: num] :
% 5.24/5.56 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.24/5.56 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % dbl_dec_simps(5)
% 5.24/5.56 thf(fact_8364_dbl__dec__simps_I5_J,axiom,
% 5.24/5.56 ! [K: num] :
% 5.24/5.56 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.24/5.56 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % dbl_dec_simps(5)
% 5.24/5.56 thf(fact_8365_dbl__dec__simps_I5_J,axiom,
% 5.24/5.56 ! [K: num] :
% 5.24/5.56 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.24/5.56 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % dbl_dec_simps(5)
% 5.24/5.56 thf(fact_8366_dbl__dec__simps_I5_J,axiom,
% 5.24/5.56 ! [K: num] :
% 5.24/5.56 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.24/5.56 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % dbl_dec_simps(5)
% 5.24/5.56 thf(fact_8367_inverse__le__iff__le__neg,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.24/5.56 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_iff_le_neg
% 5.24/5.56 thf(fact_8368_inverse__le__iff__le__neg,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.24/5.56 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.24/5.56 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_iff_le_neg
% 5.24/5.56 thf(fact_8369_inverse__le__iff__le,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.56 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_iff_le
% 5.24/5.56 thf(fact_8370_inverse__le__iff__le,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.24/5.56 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_iff_le
% 5.24/5.56 thf(fact_8371_right__inverse,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.24/5.56 = one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % right_inverse
% 5.24/5.56 thf(fact_8372_right__inverse,axiom,
% 5.24/5.56 ! [A: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.24/5.56 = one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % right_inverse
% 5.24/5.56 thf(fact_8373_right__inverse,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.24/5.56 = one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % right_inverse
% 5.24/5.56 thf(fact_8374_left__inverse,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.24/5.56 = one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % left_inverse
% 5.24/5.56 thf(fact_8375_left__inverse,axiom,
% 5.24/5.56 ! [A: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.24/5.56 = one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % left_inverse
% 5.24/5.56 thf(fact_8376_left__inverse,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.24/5.56 = one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % left_inverse
% 5.24/5.56 thf(fact_8377_inverse__eq__divide__numeral,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W2 ) )
% 5.24/5.56 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide_numeral
% 5.24/5.56 thf(fact_8378_inverse__eq__divide__numeral,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.24/5.56 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide_numeral
% 5.24/5.56 thf(fact_8379_inverse__eq__divide__numeral,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.24/5.56 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide_numeral
% 5.24/5.56 thf(fact_8380_zero__less__binomial__iff,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.24/5.56 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.24/5.56
% 5.24/5.56 % zero_less_binomial_iff
% 5.24/5.56 thf(fact_8381_prod__pos__nat__iff,axiom,
% 5.24/5.56 ! [A2: set_complex,F: complex > nat] :
% 5.24/5.56 ( ( finite3207457112153483333omplex @ A2 )
% 5.24/5.56 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.24/5.56 = ( ! [X2: complex] :
% 5.24/5.56 ( ( member_complex @ X2 @ A2 )
% 5.24/5.56 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_pos_nat_iff
% 5.24/5.56 thf(fact_8382_prod__pos__nat__iff,axiom,
% 5.24/5.56 ! [A2: set_nat,F: nat > nat] :
% 5.24/5.56 ( ( finite_finite_nat @ A2 )
% 5.24/5.56 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.24/5.56 = ( ! [X2: nat] :
% 5.24/5.56 ( ( member_nat @ X2 @ A2 )
% 5.24/5.56 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_pos_nat_iff
% 5.24/5.56 thf(fact_8383_pred__numeral__simps_I2_J,axiom,
% 5.24/5.56 ! [K: num] :
% 5.24/5.56 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.24/5.56 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % pred_numeral_simps(2)
% 5.24/5.56 thf(fact_8384_inverse__eq__divide__neg__numeral,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.24/5.56 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide_neg_numeral
% 5.24/5.56 thf(fact_8385_inverse__eq__divide__neg__numeral,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.24/5.56 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide_neg_numeral
% 5.24/5.56 thf(fact_8386_inverse__eq__divide__neg__numeral,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.24/5.56 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide_neg_numeral
% 5.24/5.56 thf(fact_8387_cot__npi,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.24/5.56 = zero_zero_real ) ).
% 5.24/5.56
% 5.24/5.56 % cot_npi
% 5.24/5.56 thf(fact_8388_cot__periodic,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.24/5.56 = ( cot_real @ X ) ) ).
% 5.24/5.56
% 5.24/5.56 % cot_periodic
% 5.24/5.56 thf(fact_8389_mult__commute__imp__mult__inverse__commute,axiom,
% 5.24/5.56 ! [Y4: real,X: real] :
% 5.24/5.56 ( ( ( times_times_real @ Y4 @ X )
% 5.24/5.56 = ( times_times_real @ X @ Y4 ) )
% 5.24/5.56 => ( ( times_times_real @ ( inverse_inverse_real @ Y4 ) @ X )
% 5.24/5.56 = ( times_times_real @ X @ ( inverse_inverse_real @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_commute_imp_mult_inverse_commute
% 5.24/5.56 thf(fact_8390_mult__commute__imp__mult__inverse__commute,axiom,
% 5.24/5.56 ! [Y4: complex,X: complex] :
% 5.24/5.56 ( ( ( times_times_complex @ Y4 @ X )
% 5.24/5.56 = ( times_times_complex @ X @ Y4 ) )
% 5.24/5.56 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y4 ) @ X )
% 5.24/5.56 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_commute_imp_mult_inverse_commute
% 5.24/5.56 thf(fact_8391_mult__commute__imp__mult__inverse__commute,axiom,
% 5.24/5.56 ! [Y4: rat,X: rat] :
% 5.24/5.56 ( ( ( times_times_rat @ Y4 @ X )
% 5.24/5.56 = ( times_times_rat @ X @ Y4 ) )
% 5.24/5.56 => ( ( times_times_rat @ ( inverse_inverse_rat @ Y4 ) @ X )
% 5.24/5.56 = ( times_times_rat @ X @ ( inverse_inverse_rat @ Y4 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_commute_imp_mult_inverse_commute
% 5.24/5.56 thf(fact_8392_choose__one,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ( binomial @ N @ one_one_nat )
% 5.24/5.56 = N ) ).
% 5.24/5.56
% 5.24/5.56 % choose_one
% 5.24/5.56 thf(fact_8393_power__inverse,axiom,
% 5.24/5.56 ! [A: real,N: nat] :
% 5.24/5.56 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 5.24/5.56 = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_inverse
% 5.24/5.56 thf(fact_8394_power__inverse,axiom,
% 5.24/5.56 ! [A: complex,N: nat] :
% 5.24/5.56 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N )
% 5.24/5.56 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_inverse
% 5.24/5.56 thf(fact_8395_power__inverse,axiom,
% 5.24/5.56 ! [A: rat,N: nat] :
% 5.24/5.56 ( ( power_power_rat @ ( inverse_inverse_rat @ A ) @ N )
% 5.24/5.56 = ( inverse_inverse_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_inverse
% 5.24/5.56 thf(fact_8396_semiring__norm_I26_J,axiom,
% 5.24/5.56 ( ( bitM @ one )
% 5.24/5.56 = one ) ).
% 5.24/5.56
% 5.24/5.56 % semiring_norm(26)
% 5.24/5.56 thf(fact_8397_binomial__eq__0,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ N @ K )
% 5.24/5.56 => ( ( binomial @ N @ K )
% 5.24/5.56 = zero_zero_nat ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_eq_0
% 5.24/5.56 thf(fact_8398_inverse__less__imp__less,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ord_less_real @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_imp_less
% 5.24/5.56 thf(fact_8399_inverse__less__imp__less,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_imp_less
% 5.24/5.56 thf(fact_8400_less__imp__inverse__less,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ A @ B )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_imp_inverse_less
% 5.24/5.56 thf(fact_8401_less__imp__inverse__less,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ A @ B )
% 5.24/5.56 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_imp_inverse_less
% 5.24/5.56 thf(fact_8402_inverse__less__imp__less__neg,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_imp_less_neg
% 5.24/5.56 thf(fact_8403_inverse__less__imp__less__neg,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_imp_less_neg
% 5.24/5.56 thf(fact_8404_less__imp__inverse__less__neg,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ A @ B )
% 5.24/5.56 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_imp_inverse_less_neg
% 5.24/5.56 thf(fact_8405_less__imp__inverse__less__neg,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ A @ B )
% 5.24/5.56 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % less_imp_inverse_less_neg
% 5.24/5.56 thf(fact_8406_inverse__negative__imp__negative,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.24/5.56 => ( ( A != zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_negative_imp_negative
% 5.24/5.56 thf(fact_8407_inverse__negative__imp__negative,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.24/5.56 => ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_negative_imp_negative
% 5.24/5.56 thf(fact_8408_inverse__positive__imp__positive,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.24/5.56 => ( ( A != zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_positive_imp_positive
% 5.24/5.56 thf(fact_8409_inverse__positive__imp__positive,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.24/5.56 => ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_positive_imp_positive
% 5.24/5.56 thf(fact_8410_negative__imp__inverse__negative,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % negative_imp_inverse_negative
% 5.24/5.56 thf(fact_8411_negative__imp__inverse__negative,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % negative_imp_inverse_negative
% 5.24/5.56 thf(fact_8412_positive__imp__inverse__positive,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % positive_imp_inverse_positive
% 5.24/5.56 thf(fact_8413_positive__imp__inverse__positive,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % positive_imp_inverse_positive
% 5.24/5.56 thf(fact_8414_nonzero__inverse__mult__distrib,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( B != zero_zero_real )
% 5.24/5.56 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.24/5.56 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % nonzero_inverse_mult_distrib
% 5.24/5.56 thf(fact_8415_nonzero__inverse__mult__distrib,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( B != zero_zero_complex )
% 5.24/5.56 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.24/5.56 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % nonzero_inverse_mult_distrib
% 5.24/5.56 thf(fact_8416_nonzero__inverse__mult__distrib,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( B != zero_zero_rat )
% 5.24/5.56 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.24/5.56 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % nonzero_inverse_mult_distrib
% 5.24/5.56 thf(fact_8417_Suc__times__binomial,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Suc_times_binomial
% 5.24/5.56 thf(fact_8418_Suc__times__binomial__eq,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.24/5.56 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Suc_times_binomial_eq
% 5.24/5.56 thf(fact_8419_inverse__numeral__1,axiom,
% 5.24/5.56 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.24/5.56 = ( numeral_numeral_real @ one ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_numeral_1
% 5.24/5.56 thf(fact_8420_inverse__numeral__1,axiom,
% 5.24/5.56 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.24/5.56 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_numeral_1
% 5.24/5.56 thf(fact_8421_inverse__numeral__1,axiom,
% 5.24/5.56 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.24/5.56 = ( numeral_numeral_rat @ one ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_numeral_1
% 5.24/5.56 thf(fact_8422_inverse__unique,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ( times_times_real @ A @ B )
% 5.24/5.56 = one_one_real )
% 5.24/5.56 => ( ( inverse_inverse_real @ A )
% 5.24/5.56 = B ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_unique
% 5.24/5.56 thf(fact_8423_inverse__unique,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( ( times_times_complex @ A @ B )
% 5.24/5.56 = one_one_complex )
% 5.24/5.56 => ( ( invers8013647133539491842omplex @ A )
% 5.24/5.56 = B ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_unique
% 5.24/5.56 thf(fact_8424_inverse__unique,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ( times_times_rat @ A @ B )
% 5.24/5.56 = one_one_rat )
% 5.24/5.56 => ( ( inverse_inverse_rat @ A )
% 5.24/5.56 = B ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_unique
% 5.24/5.56 thf(fact_8425_field__class_Ofield__divide__inverse,axiom,
% 5.24/5.56 ( divide_divide_real
% 5.24/5.56 = ( ^ [A4: real,B3: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B3 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % field_class.field_divide_inverse
% 5.24/5.56 thf(fact_8426_field__class_Ofield__divide__inverse,axiom,
% 5.24/5.56 ( divide1717551699836669952omplex
% 5.24/5.56 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B3 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % field_class.field_divide_inverse
% 5.24/5.56 thf(fact_8427_field__class_Ofield__divide__inverse,axiom,
% 5.24/5.56 ( divide_divide_rat
% 5.24/5.56 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ A4 @ ( inverse_inverse_rat @ B3 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % field_class.field_divide_inverse
% 5.24/5.56 thf(fact_8428_divide__inverse,axiom,
% 5.24/5.56 ( divide_divide_real
% 5.24/5.56 = ( ^ [A4: real,B3: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B3 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_inverse
% 5.24/5.56 thf(fact_8429_divide__inverse,axiom,
% 5.24/5.56 ( divide1717551699836669952omplex
% 5.24/5.56 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B3 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_inverse
% 5.24/5.56 thf(fact_8430_divide__inverse,axiom,
% 5.24/5.56 ( divide_divide_rat
% 5.24/5.56 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ A4 @ ( inverse_inverse_rat @ B3 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_inverse
% 5.24/5.56 thf(fact_8431_divide__inverse__commute,axiom,
% 5.24/5.56 ( divide_divide_real
% 5.24/5.56 = ( ^ [A4: real,B3: real] : ( times_times_real @ ( inverse_inverse_real @ B3 ) @ A4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_inverse_commute
% 5.24/5.56 thf(fact_8432_divide__inverse__commute,axiom,
% 5.24/5.56 ( divide1717551699836669952omplex
% 5.24/5.56 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B3 ) @ A4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_inverse_commute
% 5.24/5.56 thf(fact_8433_divide__inverse__commute,axiom,
% 5.24/5.56 ( divide_divide_rat
% 5.24/5.56 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B3 ) @ A4 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_inverse_commute
% 5.24/5.56 thf(fact_8434_inverse__eq__divide,axiom,
% 5.24/5.56 ( inverse_inverse_real
% 5.24/5.56 = ( divide_divide_real @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide
% 5.24/5.56 thf(fact_8435_inverse__eq__divide,axiom,
% 5.24/5.56 ( invers8013647133539491842omplex
% 5.24/5.56 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide
% 5.24/5.56 thf(fact_8436_inverse__eq__divide,axiom,
% 5.24/5.56 ( inverse_inverse_rat
% 5.24/5.56 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_eq_divide
% 5.24/5.56 thf(fact_8437_binomial__symmetric,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( binomial @ N @ K )
% 5.24/5.56 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_symmetric
% 5.24/5.56 thf(fact_8438_power__mult__power__inverse__commute,axiom,
% 5.24/5.56 ! [X: real,M: nat,N: nat] :
% 5.24/5.56 ( ( times_times_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N ) )
% 5.24/5.56 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N ) @ ( power_power_real @ X @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_mult_power_inverse_commute
% 5.24/5.56 thf(fact_8439_power__mult__power__inverse__commute,axiom,
% 5.24/5.56 ! [X: complex,M: nat,N: nat] :
% 5.24/5.56 ( ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N ) )
% 5.24/5.56 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N ) @ ( power_power_complex @ X @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_mult_power_inverse_commute
% 5.24/5.56 thf(fact_8440_power__mult__power__inverse__commute,axiom,
% 5.24/5.56 ! [X: rat,M: nat,N: nat] :
% 5.24/5.56 ( ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ N ) )
% 5.24/5.56 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ N ) @ ( power_power_rat @ X @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_mult_power_inverse_commute
% 5.24/5.56 thf(fact_8441_power__mult__inverse__distrib,axiom,
% 5.24/5.56 ! [X: real,M: nat] :
% 5.24/5.56 ( ( times_times_real @ ( power_power_real @ X @ M ) @ ( inverse_inverse_real @ X ) )
% 5.24/5.56 = ( times_times_real @ ( inverse_inverse_real @ X ) @ ( power_power_real @ X @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_mult_inverse_distrib
% 5.24/5.56 thf(fact_8442_power__mult__inverse__distrib,axiom,
% 5.24/5.56 ! [X: complex,M: nat] :
% 5.24/5.56 ( ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( invers8013647133539491842omplex @ X ) )
% 5.24/5.56 = ( times_times_complex @ ( invers8013647133539491842omplex @ X ) @ ( power_power_complex @ X @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_mult_inverse_distrib
% 5.24/5.56 thf(fact_8443_power__mult__inverse__distrib,axiom,
% 5.24/5.56 ! [X: rat,M: nat] :
% 5.24/5.56 ( ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( inverse_inverse_rat @ X ) )
% 5.24/5.56 = ( times_times_rat @ ( inverse_inverse_rat @ X ) @ ( power_power_rat @ X @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_mult_inverse_distrib
% 5.24/5.56 thf(fact_8444_choose__mult__lemma,axiom,
% 5.24/5.56 ! [M: nat,R2: nat,K: nat] :
% 5.24/5.56 ( ( 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 ) )
% 5.24/5.56 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % choose_mult_lemma
% 5.24/5.56 thf(fact_8445_mult__inverse__of__nat__commute,axiom,
% 5.24/5.56 ! [Xa2: nat,X: real] :
% 5.24/5.56 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) @ X )
% 5.24/5.56 = ( times_times_real @ X @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_inverse_of_nat_commute
% 5.24/5.56 thf(fact_8446_mult__inverse__of__nat__commute,axiom,
% 5.24/5.56 ! [Xa2: nat,X: complex] :
% 5.24/5.56 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) @ X )
% 5.24/5.56 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_inverse_of_nat_commute
% 5.24/5.56 thf(fact_8447_mult__inverse__of__nat__commute,axiom,
% 5.24/5.56 ! [Xa2: nat,X: rat] :
% 5.24/5.56 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa2 ) ) @ X )
% 5.24/5.56 = ( times_times_rat @ X @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_inverse_of_nat_commute
% 5.24/5.56 thf(fact_8448_binomial__le__pow,axiom,
% 5.24/5.56 ! [R2: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ R2 @ N )
% 5.24/5.56 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_le_pow
% 5.24/5.56 thf(fact_8449_mult__inverse__of__int__commute,axiom,
% 5.24/5.56 ! [Xa2: int,X: real] :
% 5.24/5.56 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) @ X )
% 5.24/5.56 = ( times_times_real @ X @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_inverse_of_int_commute
% 5.24/5.56 thf(fact_8450_mult__inverse__of__int__commute,axiom,
% 5.24/5.56 ! [Xa2: int,X: complex] :
% 5.24/5.56 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) @ X )
% 5.24/5.56 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_inverse_of_int_commute
% 5.24/5.56 thf(fact_8451_mult__inverse__of__int__commute,axiom,
% 5.24/5.56 ! [Xa2: int,X: rat] :
% 5.24/5.56 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa2 ) ) @ X )
% 5.24/5.56 = ( times_times_rat @ X @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % mult_inverse_of_int_commute
% 5.24/5.56 thf(fact_8452_divide__real__def,axiom,
% 5.24/5.56 ( divide_divide_real
% 5.24/5.56 = ( ^ [X2: real,Y: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % divide_real_def
% 5.24/5.56 thf(fact_8453_semiring__norm_I28_J,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( bitM @ ( bit1 @ N ) )
% 5.24/5.56 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % semiring_norm(28)
% 5.24/5.56 thf(fact_8454_semiring__norm_I27_J,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( bitM @ ( bit0 @ N ) )
% 5.24/5.56 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % semiring_norm(27)
% 5.24/5.56 thf(fact_8455_le__imp__inverse__le__neg,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.56 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.24/5.56 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % le_imp_inverse_le_neg
% 5.24/5.56 thf(fact_8456_le__imp__inverse__le__neg,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.56 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % le_imp_inverse_le_neg
% 5.24/5.56 thf(fact_8457_inverse__le__imp__le__neg,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.24/5.56 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_imp_le_neg
% 5.24/5.56 thf(fact_8458_inverse__le__imp__le__neg,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_imp_le_neg
% 5.24/5.56 thf(fact_8459_le__imp__inverse__le,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % le_imp_inverse_le
% 5.24/5.56 thf(fact_8460_le__imp__inverse__le,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.24/5.56 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % le_imp_inverse_le
% 5.24/5.56 thf(fact_8461_inverse__le__imp__le,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_imp_le
% 5.24/5.56 thf(fact_8462_inverse__le__imp__le,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_imp_le
% 5.24/5.56 thf(fact_8463_inverse__le__1__iff,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.24/5.56 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.24/5.56 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_1_iff
% 5.24/5.56 thf(fact_8464_inverse__le__1__iff,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 5.24/5.56 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.24/5.56 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_1_iff
% 5.24/5.56 thf(fact_8465_zero__less__binomial,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % zero_less_binomial
% 5.24/5.56 thf(fact_8466_one__less__inverse,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ( ord_less_real @ A @ one_one_real )
% 5.24/5.56 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_less_inverse
% 5.24/5.56 thf(fact_8467_one__less__inverse,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.24/5.56 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_less_inverse
% 5.24/5.56 thf(fact_8468_one__less__inverse__iff,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.24/5.56 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.56 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_less_inverse_iff
% 5.24/5.56 thf(fact_8469_one__less__inverse__iff,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 5.24/5.56 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.56 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_less_inverse_iff
% 5.24/5.56 thf(fact_8470_field__class_Ofield__inverse,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.24/5.56 = one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % field_class.field_inverse
% 5.24/5.56 thf(fact_8471_field__class_Ofield__inverse,axiom,
% 5.24/5.56 ! [A: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.24/5.56 = one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % field_class.field_inverse
% 5.24/5.56 thf(fact_8472_field__class_Ofield__inverse,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.24/5.56 = one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % field_class.field_inverse
% 5.24/5.56 thf(fact_8473_inverse__add,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( B != zero_zero_real )
% 5.24/5.56 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_add
% 5.24/5.56 thf(fact_8474_inverse__add,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( B != zero_zero_complex )
% 5.24/5.56 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.24/5.56 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_add
% 5.24/5.56 thf(fact_8475_inverse__add,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( B != zero_zero_rat )
% 5.24/5.56 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_add
% 5.24/5.56 thf(fact_8476_division__ring__inverse__add,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( B != zero_zero_real )
% 5.24/5.56 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % division_ring_inverse_add
% 5.24/5.56 thf(fact_8477_division__ring__inverse__add,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( B != zero_zero_complex )
% 5.24/5.56 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.24/5.56 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % division_ring_inverse_add
% 5.24/5.56 thf(fact_8478_division__ring__inverse__add,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( B != zero_zero_rat )
% 5.24/5.56 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % division_ring_inverse_add
% 5.24/5.56 thf(fact_8479_division__ring__inverse__diff,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( B != zero_zero_real )
% 5.24/5.56 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % division_ring_inverse_diff
% 5.24/5.56 thf(fact_8480_division__ring__inverse__diff,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( B != zero_zero_complex )
% 5.24/5.56 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.24/5.56 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % division_ring_inverse_diff
% 5.24/5.56 thf(fact_8481_division__ring__inverse__diff,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( B != zero_zero_rat )
% 5.24/5.56 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % division_ring_inverse_diff
% 5.24/5.56 thf(fact_8482_nonzero__inverse__eq__divide,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( inverse_inverse_real @ A )
% 5.24/5.56 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % nonzero_inverse_eq_divide
% 5.24/5.56 thf(fact_8483_nonzero__inverse__eq__divide,axiom,
% 5.24/5.56 ! [A: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( invers8013647133539491842omplex @ A )
% 5.24/5.56 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % nonzero_inverse_eq_divide
% 5.24/5.56 thf(fact_8484_nonzero__inverse__eq__divide,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( inverse_inverse_rat @ A )
% 5.24/5.56 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % nonzero_inverse_eq_divide
% 5.24/5.56 thf(fact_8485_Suc__times__binomial__add,axiom,
% 5.24/5.56 ! [A: nat,B: nat] :
% 5.24/5.56 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.24/5.56 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Suc_times_binomial_add
% 5.24/5.56 thf(fact_8486_binomial__Suc__Suc__eq__times,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.24/5.56 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_Suc_Suc_eq_times
% 5.24/5.56 thf(fact_8487_choose__mult,axiom,
% 5.24/5.56 ! [K: nat,M: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ M )
% 5.24/5.56 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.24/5.56 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % choose_mult
% 5.24/5.56 thf(fact_8488_binomial__absorb__comp,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.24/5.56 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_absorb_comp
% 5.24/5.56 thf(fact_8489_gbinomial__Suc__Suc,axiom,
% 5.24/5.56 ! [A: complex,K: nat] :
% 5.24/5.56 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_Suc_Suc
% 5.24/5.56 thf(fact_8490_gbinomial__Suc__Suc,axiom,
% 5.24/5.56 ! [A: real,K: nat] :
% 5.24/5.56 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_Suc_Suc
% 5.24/5.56 thf(fact_8491_gbinomial__Suc__Suc,axiom,
% 5.24/5.56 ! [A: rat,K: nat] :
% 5.24/5.56 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_Suc_Suc
% 5.24/5.56 thf(fact_8492_gbinomial__of__nat__symmetric,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.24/5.56 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_of_nat_symmetric
% 5.24/5.56 thf(fact_8493_gbinomial__of__nat__symmetric,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.24/5.56 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_of_nat_symmetric
% 5.24/5.56 thf(fact_8494_eval__nat__numeral_I2_J,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.24/5.56 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % eval_nat_numeral(2)
% 5.24/5.56 thf(fact_8495_inverse__less__iff,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.24/5.56 => ( ord_less_real @ B @ A ) )
% 5.24/5.56 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.24/5.56 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_iff
% 5.24/5.56 thf(fact_8496_inverse__less__iff,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.24/5.56 => ( ord_less_rat @ B @ A ) )
% 5.24/5.56 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_iff
% 5.24/5.56 thf(fact_8497_inverse__le__iff,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.24/5.56 => ( ord_less_eq_real @ B @ A ) )
% 5.24/5.56 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.24/5.56 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_iff
% 5.24/5.56 thf(fact_8498_inverse__le__iff,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.24/5.56 => ( ord_less_eq_rat @ B @ A ) )
% 5.24/5.56 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.24/5.56 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_le_iff
% 5.24/5.56 thf(fact_8499_one__le__inverse__iff,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.24/5.56 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.56 & ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_le_inverse_iff
% 5.24/5.56 thf(fact_8500_one__le__inverse__iff,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 5.24/5.56 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.56 & ( ord_less_eq_rat @ X @ one_one_rat ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_le_inverse_iff
% 5.24/5.56 thf(fact_8501_inverse__less__1__iff,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.24/5.56 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.24/5.56 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_1_iff
% 5.24/5.56 thf(fact_8502_inverse__less__1__iff,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ord_less_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 5.24/5.56 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.24/5.56 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_less_1_iff
% 5.24/5.56 thf(fact_8503_one__le__inverse,axiom,
% 5.24/5.56 ! [A: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.56 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.24/5.56 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_le_inverse
% 5.24/5.56 thf(fact_8504_one__le__inverse,axiom,
% 5.24/5.56 ! [A: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.24/5.56 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.24/5.56 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_le_inverse
% 5.24/5.56 thf(fact_8505_BitM__plus__one,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.24/5.56 = ( bit0 @ N ) ) ).
% 5.24/5.56
% 5.24/5.56 % BitM_plus_one
% 5.24/5.56 thf(fact_8506_one__plus__BitM,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.24/5.56 = ( bit0 @ N ) ) ).
% 5.24/5.56
% 5.24/5.56 % one_plus_BitM
% 5.24/5.56 thf(fact_8507_inverse__diff__inverse,axiom,
% 5.24/5.56 ! [A: real,B: real] :
% 5.24/5.56 ( ( A != zero_zero_real )
% 5.24/5.56 => ( ( B != zero_zero_real )
% 5.24/5.56 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.24/5.56 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_diff_inverse
% 5.24/5.56 thf(fact_8508_inverse__diff__inverse,axiom,
% 5.24/5.56 ! [A: complex,B: complex] :
% 5.24/5.56 ( ( A != zero_zero_complex )
% 5.24/5.56 => ( ( B != zero_zero_complex )
% 5.24/5.56 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.24/5.56 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_diff_inverse
% 5.24/5.56 thf(fact_8509_inverse__diff__inverse,axiom,
% 5.24/5.56 ! [A: rat,B: rat] :
% 5.24/5.56 ( ( A != zero_zero_rat )
% 5.24/5.56 => ( ( B != zero_zero_rat )
% 5.24/5.56 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.24/5.56 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % inverse_diff_inverse
% 5.24/5.56 thf(fact_8510_reals__Archimedean,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.56 => ? [N3: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ X ) ) ).
% 5.24/5.56
% 5.24/5.56 % reals_Archimedean
% 5.24/5.56 thf(fact_8511_reals__Archimedean,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.56 => ? [N3: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ X ) ) ).
% 5.24/5.56
% 5.24/5.56 % reals_Archimedean
% 5.24/5.56 thf(fact_8512_binomial__absorption,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_absorption
% 5.24/5.56 thf(fact_8513_gbinomial__addition__formula,axiom,
% 5.24/5.56 ! [A: complex,K: nat] :
% 5.24/5.56 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_addition_formula
% 5.24/5.56 thf(fact_8514_gbinomial__addition__formula,axiom,
% 5.24/5.56 ! [A: real,K: nat] :
% 5.24/5.56 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_addition_formula
% 5.24/5.56 thf(fact_8515_gbinomial__addition__formula,axiom,
% 5.24/5.56 ! [A: rat,K: nat] :
% 5.24/5.56 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.24/5.56 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_addition_formula
% 5.24/5.56 thf(fact_8516_gbinomial__absorb__comp,axiom,
% 5.24/5.56 ! [A: complex,K: nat] :
% 5.24/5.56 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.24/5.56 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_absorb_comp
% 5.24/5.56 thf(fact_8517_gbinomial__absorb__comp,axiom,
% 5.24/5.56 ! [A: real,K: nat] :
% 5.24/5.56 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.24/5.56 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_absorb_comp
% 5.24/5.56 thf(fact_8518_gbinomial__absorb__comp,axiom,
% 5.24/5.56 ! [A: rat,K: nat] :
% 5.24/5.56 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.24/5.56 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_absorb_comp
% 5.24/5.56 thf(fact_8519_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.24/5.56 ! [K: nat,A: real] :
% 5.24/5.56 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.24/5.56 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_ge_n_over_k_pow_k
% 5.24/5.56 thf(fact_8520_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.24/5.56 ! [K: nat,A: rat] :
% 5.24/5.56 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.24/5.56 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_ge_n_over_k_pow_k
% 5.24/5.56 thf(fact_8521_gbinomial__mult__1,axiom,
% 5.24/5.56 ! [A: real,K: nat] :
% 5.24/5.56 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.24/5.56 = ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_mult_1
% 5.24/5.56 thf(fact_8522_gbinomial__mult__1,axiom,
% 5.24/5.56 ! [A: rat,K: nat] :
% 5.24/5.56 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.24/5.56 = ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_mult_1
% 5.24/5.56 thf(fact_8523_gbinomial__mult__1_H,axiom,
% 5.24/5.56 ! [A: real,K: nat] :
% 5.24/5.56 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.24/5.56 = ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_mult_1'
% 5.24/5.56 thf(fact_8524_gbinomial__mult__1_H,axiom,
% 5.24/5.56 ! [A: rat,K: nat] :
% 5.24/5.56 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.24/5.56 = ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_mult_1'
% 5.24/5.56 thf(fact_8525_forall__pos__mono__1,axiom,
% 5.24/5.56 ! [P: real > $o,E: real] :
% 5.24/5.56 ( ! [D3: real,E2: real] :
% 5.24/5.56 ( ( ord_less_real @ D3 @ E2 )
% 5.24/5.56 => ( ( P @ D3 )
% 5.24/5.56 => ( P @ E2 ) ) )
% 5.24/5.56 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.24/5.56 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.24/5.56 => ( P @ E ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % forall_pos_mono_1
% 5.24/5.56 thf(fact_8526_binomial__fact__lemma,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.24/5.56 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_fact_lemma
% 5.24/5.56 thf(fact_8527_prod__int__plus__eq,axiom,
% 5.24/5.56 ! [I2: nat,J: nat] :
% 5.24/5.56 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 5.24/5.56 = ( groups1705073143266064639nt_int
% 5.24/5.56 @ ^ [X2: int] : X2
% 5.24/5.56 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % prod_int_plus_eq
% 5.24/5.56 thf(fact_8528_summable__exp,axiom,
% 5.24/5.56 ! [X: complex] :
% 5.24/5.56 ( summable_complex
% 5.24/5.56 @ ^ [N2: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N2 ) ) @ ( power_power_complex @ X @ N2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % summable_exp
% 5.24/5.56 thf(fact_8529_summable__exp,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( summable_real
% 5.24/5.56 @ ^ [N2: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % summable_exp
% 5.24/5.56 thf(fact_8530_binomial__ge__n__over__k__pow__k,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_ge_n_over_k_pow_k
% 5.24/5.56 thf(fact_8531_binomial__ge__n__over__k__pow__k,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_ge_n_over_k_pow_k
% 5.24/5.56 thf(fact_8532_binomial__mono,axiom,
% 5.24/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ K6 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.24/5.56 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_mono
% 5.24/5.56 thf(fact_8533_binomial__maximum_H,axiom,
% 5.24/5.56 ! [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 ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_maximum'
% 5.24/5.56 thf(fact_8534_binomial__maximum,axiom,
% 5.24/5.56 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_maximum
% 5.24/5.56 thf(fact_8535_binomial__antimono,axiom,
% 5.24/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ K6 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.24/5.56 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.24/5.56 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_antimono
% 5.24/5.56 thf(fact_8536_binomial__le__pow2,axiom,
% 5.24/5.56 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_le_pow2
% 5.24/5.56 thf(fact_8537_numeral__BitM,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.24/5.56 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.24/5.56
% 5.24/5.56 % numeral_BitM
% 5.24/5.56 thf(fact_8538_numeral__BitM,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.24/5.56 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.24/5.56
% 5.24/5.56 % numeral_BitM
% 5.24/5.56 thf(fact_8539_numeral__BitM,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.24/5.56 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.24/5.56
% 5.24/5.56 % numeral_BitM
% 5.24/5.56 thf(fact_8540_numeral__BitM,axiom,
% 5.24/5.56 ! [N: num] :
% 5.24/5.56 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.24/5.56 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.24/5.56
% 5.24/5.56 % numeral_BitM
% 5.24/5.56 thf(fact_8541_odd__numeral__BitM,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % odd_numeral_BitM
% 5.24/5.56 thf(fact_8542_odd__numeral__BitM,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % odd_numeral_BitM
% 5.24/5.56 thf(fact_8543_odd__numeral__BitM,axiom,
% 5.24/5.56 ! [W2: num] :
% 5.24/5.56 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W2 ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % odd_numeral_BitM
% 5.24/5.56 thf(fact_8544_choose__reduce__nat,axiom,
% 5.24/5.56 ! [N: nat,K: nat] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.56 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.56 => ( ( binomial @ N @ K )
% 5.24/5.56 = ( 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 ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % choose_reduce_nat
% 5.24/5.56 thf(fact_8545_ex__inverse__of__nat__less,axiom,
% 5.24/5.56 ! [X: real] :
% 5.24/5.56 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.56 => ? [N3: nat] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.24/5.56 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % ex_inverse_of_nat_less
% 5.24/5.56 thf(fact_8546_ex__inverse__of__nat__less,axiom,
% 5.24/5.56 ! [X: rat] :
% 5.24/5.56 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.24/5.56 => ? [N3: nat] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.24/5.56 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N3 ) ) @ X ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % ex_inverse_of_nat_less
% 5.24/5.56 thf(fact_8547_times__binomial__minus1__eq,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.56 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.24/5.56 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % times_binomial_minus1_eq
% 5.24/5.56 thf(fact_8548_power__diff__conv__inverse,axiom,
% 5.24/5.56 ! [X: real,M: nat,N: nat] :
% 5.24/5.56 ( ( X != zero_zero_real )
% 5.24/5.56 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( power_power_real @ X @ ( minus_minus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_diff_conv_inverse
% 5.24/5.56 thf(fact_8549_power__diff__conv__inverse,axiom,
% 5.24/5.56 ! [X: complex,M: nat,N: nat] :
% 5.24/5.56 ( ( X != zero_zero_complex )
% 5.24/5.56 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( power_power_complex @ X @ ( minus_minus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_diff_conv_inverse
% 5.24/5.56 thf(fact_8550_power__diff__conv__inverse,axiom,
% 5.24/5.56 ! [X: rat,M: nat,N: nat] :
% 5.24/5.56 ( ( X != zero_zero_rat )
% 5.24/5.56 => ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.56 => ( ( power_power_rat @ X @ ( minus_minus_nat @ N @ M ) )
% 5.24/5.56 = ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ M ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % power_diff_conv_inverse
% 5.24/5.56 thf(fact_8551_cot__def,axiom,
% 5.24/5.56 ( cot_complex
% 5.24/5.56 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X2 ) @ ( sin_complex @ X2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cot_def
% 5.24/5.56 thf(fact_8552_cot__def,axiom,
% 5.24/5.56 ( cot_real
% 5.24/5.56 = ( ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % cot_def
% 5.24/5.56 thf(fact_8553_Suc__times__gbinomial,axiom,
% 5.24/5.56 ! [K: nat,A: complex] :
% 5.24/5.56 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Suc_times_gbinomial
% 5.24/5.56 thf(fact_8554_Suc__times__gbinomial,axiom,
% 5.24/5.56 ! [K: nat,A: real] :
% 5.24/5.56 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Suc_times_gbinomial
% 5.24/5.56 thf(fact_8555_Suc__times__gbinomial,axiom,
% 5.24/5.56 ! [K: nat,A: rat] :
% 5.24/5.56 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % Suc_times_gbinomial
% 5.24/5.56 thf(fact_8556_gbinomial__absorption,axiom,
% 5.24/5.56 ! [K: nat,A: complex] :
% 5.24/5.56 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_absorption
% 5.24/5.56 thf(fact_8557_gbinomial__absorption,axiom,
% 5.24/5.56 ! [K: nat,A: real] :
% 5.24/5.56 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_absorption
% 5.24/5.56 thf(fact_8558_gbinomial__absorption,axiom,
% 5.24/5.56 ! [K: nat,A: rat] :
% 5.24/5.56 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.24/5.56 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_absorption
% 5.24/5.56 thf(fact_8559_binomial__altdef__nat,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.56 => ( ( binomial @ N @ K )
% 5.24/5.56 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_altdef_nat
% 5.24/5.56 thf(fact_8560_gbinomial__trinomial__revision,axiom,
% 5.24/5.56 ! [K: nat,M: nat,A: real] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ M )
% 5.24/5.56 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.24/5.56 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_trinomial_revision
% 5.24/5.56 thf(fact_8561_gbinomial__trinomial__revision,axiom,
% 5.24/5.56 ! [K: nat,M: nat,A: rat] :
% 5.24/5.56 ( ( ord_less_eq_nat @ K @ M )
% 5.24/5.56 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.24/5.56 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % gbinomial_trinomial_revision
% 5.24/5.56 thf(fact_8562_binomial__less__binomial__Suc,axiom,
% 5.24/5.56 ! [K: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.56 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_less_binomial_Suc
% 5.24/5.56 thf(fact_8563_binomial__strict__mono,axiom,
% 5.24/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_nat @ K @ K6 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.24/5.56 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_strict_mono
% 5.24/5.56 thf(fact_8564_binomial__strict__antimono,axiom,
% 5.24/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.24/5.56 ( ( ord_less_nat @ K @ K6 )
% 5.24/5.56 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.24/5.56 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.24/5.56 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.24/5.56
% 5.24/5.56 % binomial_strict_antimono
% 5.24/5.56 thf(fact_8565_central__binomial__odd,axiom,
% 5.24/5.56 ! [N: nat] :
% 5.24/5.56 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.57 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.57 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % central_binomial_odd
% 5.24/5.57 thf(fact_8566_binomial__addition__formula,axiom,
% 5.24/5.57 ! [N: nat,K: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( binomial @ N @ ( suc @ K ) )
% 5.24/5.57 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_addition_formula
% 5.24/5.57 thf(fact_8567_fact__binomial,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.24/5.57 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % fact_binomial
% 5.24/5.57 thf(fact_8568_fact__binomial,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.24/5.57 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % fact_binomial
% 5.24/5.57 thf(fact_8569_fact__binomial,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.24/5.57 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % fact_binomial
% 5.24/5.57 thf(fact_8570_binomial__fact,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.24/5.57 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_fact
% 5.24/5.57 thf(fact_8571_binomial__fact,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.24/5.57 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_fact
% 5.24/5.57 thf(fact_8572_binomial__fact,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.24/5.57 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_fact
% 5.24/5.57 thf(fact_8573_gbinomial__rec,axiom,
% 5.24/5.57 ! [A: complex,K: nat] :
% 5.24/5.57 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.24/5.57 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_rec
% 5.24/5.57 thf(fact_8574_gbinomial__rec,axiom,
% 5.24/5.57 ! [A: real,K: nat] :
% 5.24/5.57 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.24/5.57 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_rec
% 5.24/5.57 thf(fact_8575_gbinomial__rec,axiom,
% 5.24/5.57 ! [A: rat,K: nat] :
% 5.24/5.57 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.24/5.57 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_rec
% 5.24/5.57 thf(fact_8576_gbinomial__factors,axiom,
% 5.24/5.57 ! [A: complex,K: nat] :
% 5.24/5.57 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.24/5.57 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_factors
% 5.24/5.57 thf(fact_8577_gbinomial__factors,axiom,
% 5.24/5.57 ! [A: real,K: nat] :
% 5.24/5.57 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.24/5.57 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_factors
% 5.24/5.57 thf(fact_8578_gbinomial__factors,axiom,
% 5.24/5.57 ! [A: rat,K: nat] :
% 5.24/5.57 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.24/5.57 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_factors
% 5.24/5.57 thf(fact_8579_gbinomial__negated__upper,axiom,
% 5.24/5.57 ( gbinomial_complex
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_negated_upper
% 5.24/5.57 thf(fact_8580_gbinomial__negated__upper,axiom,
% 5.24/5.57 ( gbinomial_real
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_negated_upper
% 5.24/5.57 thf(fact_8581_gbinomial__negated__upper,axiom,
% 5.24/5.57 ( gbinomial_rat
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_negated_upper
% 5.24/5.57 thf(fact_8582_gbinomial__index__swap,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.24/5.57 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_index_swap
% 5.24/5.57 thf(fact_8583_gbinomial__index__swap,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( 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 ) )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_index_swap
% 5.24/5.57 thf(fact_8584_gbinomial__index__swap,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( 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 ) )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_index_swap
% 5.24/5.57 thf(fact_8585_exp__plus__inverse__exp,axiom,
% 5.24/5.57 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_plus_inverse_exp
% 5.24/5.57 thf(fact_8586_choose__two,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_two
% 5.24/5.57 thf(fact_8587_gbinomial__minus,axiom,
% 5.24/5.57 ! [A: complex,K: nat] :
% 5.24/5.57 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_minus
% 5.24/5.57 thf(fact_8588_gbinomial__minus,axiom,
% 5.24/5.57 ! [A: real,K: nat] :
% 5.24/5.57 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_minus
% 5.24/5.57 thf(fact_8589_gbinomial__minus,axiom,
% 5.24/5.57 ! [A: rat,K: nat] :
% 5.24/5.57 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_minus
% 5.24/5.57 thf(fact_8590_plus__inverse__ge__2,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % plus_inverse_ge_2
% 5.24/5.57 thf(fact_8591_real__inv__sqrt__pow2,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( inverse_inverse_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_inv_sqrt_pow2
% 5.24/5.57 thf(fact_8592_gbinomial__reduce__nat,axiom,
% 5.24/5.57 ! [K: nat,A: complex] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( gbinomial_complex @ A @ K )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_reduce_nat
% 5.24/5.57 thf(fact_8593_gbinomial__reduce__nat,axiom,
% 5.24/5.57 ! [K: nat,A: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( gbinomial_real @ A @ K )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_reduce_nat
% 5.24/5.57 thf(fact_8594_gbinomial__reduce__nat,axiom,
% 5.24/5.57 ! [K: nat,A: rat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( gbinomial_rat @ A @ K )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_reduce_nat
% 5.24/5.57 thf(fact_8595_gbinomial__pochhammer,axiom,
% 5.24/5.57 ( gbinomial_complex
% 5.24/5.57 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_pochhammer
% 5.24/5.57 thf(fact_8596_gbinomial__pochhammer,axiom,
% 5.24/5.57 ( gbinomial_rat
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_pochhammer
% 5.24/5.57 thf(fact_8597_gbinomial__pochhammer,axiom,
% 5.24/5.57 ( gbinomial_real
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_pochhammer
% 5.24/5.57 thf(fact_8598_gbinomial__pochhammer_H,axiom,
% 5.24/5.57 ( gbinomial_complex
% 5.24/5.57 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_pochhammer'
% 5.24/5.57 thf(fact_8599_gbinomial__pochhammer_H,axiom,
% 5.24/5.57 ( gbinomial_rat
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_pochhammer'
% 5.24/5.57 thf(fact_8600_gbinomial__pochhammer_H,axiom,
% 5.24/5.57 ( gbinomial_real
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_pochhammer'
% 5.24/5.57 thf(fact_8601_tan__cot,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.24/5.57 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tan_cot
% 5.24/5.57 thf(fact_8602_real__le__x__sinh,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( 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 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_le_x_sinh
% 5.24/5.57 thf(fact_8603_real__le__abs__sinh,axiom,
% 5.24/5.57 ! [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 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_le_abs_sinh
% 5.24/5.57 thf(fact_8604_gbinomial__sum__up__index,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.57 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_up_index
% 5.24/5.57 thf(fact_8605_gbinomial__sum__up__index,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.57 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_up_index
% 5.24/5.57 thf(fact_8606_gbinomial__sum__up__index,axiom,
% 5.24/5.57 ! [K: nat,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.24/5.57 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_up_index
% 5.24/5.57 thf(fact_8607_gbinomial__Suc,axiom,
% 5.24/5.57 ! [A: complex,K: nat] :
% 5.24/5.57 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.24/5.57 = ( divide1717551699836669952omplex
% 5.24/5.57 @ ( groups6464643781859351333omplex
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I4 ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.24/5.57 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_Suc
% 5.24/5.57 thf(fact_8608_gbinomial__Suc,axiom,
% 5.24/5.57 ! [A: rat,K: nat] :
% 5.24/5.57 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.24/5.57 = ( divide_divide_rat
% 5.24/5.57 @ ( groups73079841787564623at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.24/5.57 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_Suc
% 5.24/5.57 thf(fact_8609_gbinomial__Suc,axiom,
% 5.24/5.57 ! [A: real,K: nat] :
% 5.24/5.57 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.24/5.57 = ( divide_divide_real
% 5.24/5.57 @ ( groups129246275422532515t_real
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.24/5.57 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_Suc
% 5.24/5.57 thf(fact_8610_gbinomial__Suc,axiom,
% 5.24/5.57 ! [A: nat,K: nat] :
% 5.24/5.57 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.24/5.57 = ( divide_divide_nat
% 5.24/5.57 @ ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.24/5.57 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_Suc
% 5.24/5.57 thf(fact_8611_gbinomial__Suc,axiom,
% 5.24/5.57 ! [A: int,K: nat] :
% 5.24/5.57 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.24/5.57 = ( divide_divide_int
% 5.24/5.57 @ ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.24/5.57 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_Suc
% 5.24/5.57 thf(fact_8612_tan__sec,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ( cos_real @ X )
% 5.24/5.57 != zero_zero_real )
% 5.24/5.57 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tan_sec
% 5.24/5.57 thf(fact_8613_tan__sec,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( ( cos_complex @ X )
% 5.24/5.57 != zero_zero_complex )
% 5.24/5.57 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tan_sec
% 5.24/5.57 thf(fact_8614_gbinomial__absorption_H,axiom,
% 5.24/5.57 ! [K: nat,A: complex] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( gbinomial_complex @ A @ K )
% 5.24/5.57 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_absorption'
% 5.24/5.57 thf(fact_8615_gbinomial__absorption_H,axiom,
% 5.24/5.57 ! [K: nat,A: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( gbinomial_real @ A @ K )
% 5.24/5.57 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_absorption'
% 5.24/5.57 thf(fact_8616_gbinomial__absorption_H,axiom,
% 5.24/5.57 ! [K: nat,A: rat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( gbinomial_rat @ A @ K )
% 5.24/5.57 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_absorption'
% 5.24/5.57 thf(fact_8617_cot__gt__zero,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.57 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cot_gt_zero
% 5.24/5.57 thf(fact_8618_tan__cot_H,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.24/5.57 = ( cot_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % tan_cot'
% 5.24/5.57 thf(fact_8619_binomial__code,axiom,
% 5.24/5.57 ( binomial
% 5.24/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_code
% 5.24/5.57 thf(fact_8620_gbinomial__code,axiom,
% 5.24/5.57 ( gbinomial_complex
% 5.24/5.57 = ( ^ [A4: complex,K3: nat] :
% 5.24/5.57 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.24/5.57 @ ( divide1717551699836669952omplex
% 5.24/5.57 @ ( set_fo1517530859248394432omplex
% 5.24/5.57 @ ^ [L: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L ) ) )
% 5.24/5.57 @ zero_zero_nat
% 5.24/5.57 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.24/5.57 @ one_one_complex )
% 5.24/5.57 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_code
% 5.24/5.57 thf(fact_8621_gbinomial__code,axiom,
% 5.24/5.57 ( gbinomial_rat
% 5.24/5.57 = ( ^ [A4: rat,K3: nat] :
% 5.24/5.57 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.24/5.57 @ ( divide_divide_rat
% 5.24/5.57 @ ( set_fo1949268297981939178at_rat
% 5.24/5.57 @ ^ [L: nat] : ( times_times_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ L ) ) )
% 5.24/5.57 @ zero_zero_nat
% 5.24/5.57 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.24/5.57 @ one_one_rat )
% 5.24/5.57 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_code
% 5.24/5.57 thf(fact_8622_gbinomial__code,axiom,
% 5.24/5.57 ( gbinomial_real
% 5.24/5.57 = ( ^ [A4: real,K3: nat] :
% 5.24/5.57 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.24/5.57 @ ( divide_divide_real
% 5.24/5.57 @ ( set_fo3111899725591712190t_real
% 5.24/5.57 @ ^ [L: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L ) ) )
% 5.24/5.57 @ zero_zero_nat
% 5.24/5.57 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.24/5.57 @ one_one_real )
% 5.24/5.57 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_code
% 5.24/5.57 thf(fact_8623_gbinomial__partial__row__sum,axiom,
% 5.24/5.57 ! [A: complex,M: nat] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_row_sum
% 5.24/5.57 thf(fact_8624_gbinomial__partial__row__sum,axiom,
% 5.24/5.57 ! [A: rat,M: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_row_sum
% 5.24/5.57 thf(fact_8625_gbinomial__partial__row__sum,axiom,
% 5.24/5.57 ! [A: real,M: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_row_sum
% 5.24/5.57 thf(fact_8626_choose__even__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) @ zero_zero_complex )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_even_sum
% 5.24/5.57 thf(fact_8627_choose__even__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) @ zero_zero_int )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_even_sum
% 5.24/5.57 thf(fact_8628_choose__even__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) @ zero_zero_rat )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_even_sum
% 5.24/5.57 thf(fact_8629_choose__even__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) @ zero_zero_real )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_even_sum
% 5.24/5.57 thf(fact_8630_choose__odd__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] :
% 5.24/5.57 ( if_complex
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.24/5.57 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) )
% 5.24/5.57 @ zero_zero_complex )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_odd_sum
% 5.24/5.57 thf(fact_8631_choose__odd__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] :
% 5.24/5.57 ( if_int
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.24/5.57 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) )
% 5.24/5.57 @ zero_zero_int )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_odd_sum
% 5.24/5.57 thf(fact_8632_choose__odd__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] :
% 5.24/5.57 ( if_rat
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.24/5.57 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) )
% 5.24/5.57 @ zero_zero_rat )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_odd_sum
% 5.24/5.57 thf(fact_8633_choose__odd__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] :
% 5.24/5.57 ( if_real
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.24/5.57 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) )
% 5.24/5.57 @ zero_zero_real )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_odd_sum
% 5.24/5.57 thf(fact_8634_gbinomial__r__part__sum,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_r_part_sum
% 5.24/5.57 thf(fact_8635_gbinomial__r__part__sum,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_r_part_sum
% 5.24/5.57 thf(fact_8636_gbinomial__r__part__sum,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_r_part_sum
% 5.24/5.57 thf(fact_8637_exp__first__two__terms,axiom,
% 5.24/5.57 ( exp_real
% 5.24/5.57 = ( ^ [X2: real] :
% 5.24/5.57 ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 )
% 5.24/5.57 @ ( suminf_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_first_two_terms
% 5.24/5.57 thf(fact_8638_exp__first__two__terms,axiom,
% 5.24/5.57 ( exp_complex
% 5.24/5.57 = ( ^ [X2: complex] :
% 5.24/5.57 ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ X2 )
% 5.24/5.57 @ ( suminf_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_complex @ X2 @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_first_two_terms
% 5.24/5.57 thf(fact_8639_mult__scaleR__right,axiom,
% 5.24/5.57 ! [X: real,A: real,Y4: real] :
% 5.24/5.57 ( ( times_times_real @ X @ ( real_V1485227260804924795R_real @ A @ Y4 ) )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mult_scaleR_right
% 5.24/5.57 thf(fact_8640_mult__scaleR__right,axiom,
% 5.24/5.57 ! [X: complex,A: real,Y4: complex] :
% 5.24/5.57 ( ( times_times_complex @ X @ ( real_V2046097035970521341omplex @ A @ Y4 ) )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mult_scaleR_right
% 5.24/5.57 thf(fact_8641_mult__scaleR__left,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( times_times_real @ ( real_V1485227260804924795R_real @ A @ X ) @ Y4 )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mult_scaleR_left
% 5.24/5.57 thf(fact_8642_mult__scaleR__left,axiom,
% 5.24/5.57 ! [A: real,X: complex,Y4: complex] :
% 5.24/5.57 ( ( times_times_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ Y4 )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mult_scaleR_left
% 5.24/5.57 thf(fact_8643_atMost__iff,axiom,
% 5.24/5.57 ! [I2: real,K: real] :
% 5.24/5.57 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 5.24/5.57 = ( ord_less_eq_real @ I2 @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_iff
% 5.24/5.57 thf(fact_8644_atMost__iff,axiom,
% 5.24/5.57 ! [I2: set_nat,K: set_nat] :
% 5.24/5.57 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K ) )
% 5.24/5.57 = ( ord_less_eq_set_nat @ I2 @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_iff
% 5.24/5.57 thf(fact_8645_atMost__iff,axiom,
% 5.24/5.57 ! [I2: rat,K: rat] :
% 5.24/5.57 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 5.24/5.57 = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_iff
% 5.24/5.57 thf(fact_8646_atMost__iff,axiom,
% 5.24/5.57 ! [I2: num,K: num] :
% 5.24/5.57 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.24/5.57 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_iff
% 5.24/5.57 thf(fact_8647_atMost__iff,axiom,
% 5.24/5.57 ! [I2: int,K: int] :
% 5.24/5.57 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.24/5.57 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_iff
% 5.24/5.57 thf(fact_8648_atMost__iff,axiom,
% 5.24/5.57 ! [I2: nat,K: nat] :
% 5.24/5.57 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.24/5.57 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_iff
% 5.24/5.57 thf(fact_8649_scaleR__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ one_one_real @ X )
% 5.24/5.57 = X ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_one
% 5.24/5.57 thf(fact_8650_scaleR__one,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ one_one_real @ X )
% 5.24/5.57 = X ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_one
% 5.24/5.57 thf(fact_8651_scaleR__scaleR,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ A @ ( real_V1485227260804924795R_real @ B @ X ) )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_scaleR
% 5.24/5.57 thf(fact_8652_scaleR__scaleR,axiom,
% 5.24/5.57 ! [A: real,B: real,X: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ A @ ( real_V2046097035970521341omplex @ B @ X ) )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_scaleR
% 5.24/5.57 thf(fact_8653_atMost__subset__iff,axiom,
% 5.24/5.57 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.57 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_set_nat @ X @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_subset_iff
% 5.24/5.57 thf(fact_8654_atMost__subset__iff,axiom,
% 5.24/5.57 ! [X: rat,Y4: rat] :
% 5.24/5.57 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_subset_iff
% 5.24/5.57 thf(fact_8655_atMost__subset__iff,axiom,
% 5.24/5.57 ! [X: num,Y4: num] :
% 5.24/5.57 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_num @ X @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_subset_iff
% 5.24/5.57 thf(fact_8656_atMost__subset__iff,axiom,
% 5.24/5.57 ! [X: int,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_int @ X @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_subset_iff
% 5.24/5.57 thf(fact_8657_atMost__subset__iff,axiom,
% 5.24/5.57 ! [X: nat,Y4: nat] :
% 5.24/5.57 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_nat @ X @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_subset_iff
% 5.24/5.57 thf(fact_8658_scaleR__eq__iff,axiom,
% 5.24/5.57 ! [B: real,U2: real,A: real] :
% 5.24/5.57 ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U2 @ A ) )
% 5.24/5.57 = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U2 @ B ) ) )
% 5.24/5.57 = ( ( A = B )
% 5.24/5.57 | ( U2 = one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_eq_iff
% 5.24/5.57 thf(fact_8659_scaleR__eq__iff,axiom,
% 5.24/5.57 ! [B: complex,U2: real,A: complex] :
% 5.24/5.57 ( ( ( plus_plus_complex @ B @ ( real_V2046097035970521341omplex @ U2 @ A ) )
% 5.24/5.57 = ( plus_plus_complex @ A @ ( real_V2046097035970521341omplex @ U2 @ B ) ) )
% 5.24/5.57 = ( ( A = B )
% 5.24/5.57 | ( U2 = one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_eq_iff
% 5.24/5.57 thf(fact_8660_scaleR__power,axiom,
% 5.24/5.57 ! [X: real,Y4: real,N: nat] :
% 5.24/5.57 ( ( power_power_real @ ( real_V1485227260804924795R_real @ X @ Y4 ) @ N )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_power
% 5.24/5.57 thf(fact_8661_scaleR__power,axiom,
% 5.24/5.57 ! [X: real,Y4: complex,N: nat] :
% 5.24/5.57 ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X @ Y4 ) @ N )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ ( power_power_real @ X @ N ) @ ( power_power_complex @ Y4 @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_power
% 5.24/5.57 thf(fact_8662_Icc__subset__Iic__iff,axiom,
% 5.24/5.57 ! [L2: set_nat,H2: set_nat,H3: set_nat] :
% 5.24/5.57 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L2 @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.24/5.57 = ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.24/5.57 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_subset_Iic_iff
% 5.24/5.57 thf(fact_8663_Icc__subset__Iic__iff,axiom,
% 5.24/5.57 ! [L2: rat,H2: rat,H3: rat] :
% 5.24/5.57 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L2 @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.24/5.57 = ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.24/5.57 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_subset_Iic_iff
% 5.24/5.57 thf(fact_8664_Icc__subset__Iic__iff,axiom,
% 5.24/5.57 ! [L2: num,H2: num,H3: num] :
% 5.24/5.57 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L2 @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.24/5.57 = ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.24/5.57 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_subset_Iic_iff
% 5.24/5.57 thf(fact_8665_Icc__subset__Iic__iff,axiom,
% 5.24/5.57 ! [L2: nat,H2: nat,H3: nat] :
% 5.24/5.57 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L2 @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.24/5.57 = ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.24/5.57 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_subset_Iic_iff
% 5.24/5.57 thf(fact_8666_Icc__subset__Iic__iff,axiom,
% 5.24/5.57 ! [L2: int,H2: int,H3: int] :
% 5.24/5.57 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L2 @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.24/5.57 = ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.24/5.57 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_subset_Iic_iff
% 5.24/5.57 thf(fact_8667_Icc__subset__Iic__iff,axiom,
% 5.24/5.57 ! [L2: real,H2: real,H3: real] :
% 5.24/5.57 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L2 @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.24/5.57 = ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.24/5.57 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_subset_Iic_iff
% 5.24/5.57 thf(fact_8668_sum_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc
% 5.24/5.57 thf(fact_8669_sum_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc
% 5.24/5.57 thf(fact_8670_sum_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc
% 5.24/5.57 thf(fact_8671_sum_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc
% 5.24/5.57 thf(fact_8672_scaleR__minus1__left,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.57 = ( uminus_uminus_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_minus1_left
% 5.24/5.57 thf(fact_8673_scaleR__minus1__left,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_minus1_left
% 5.24/5.57 thf(fact_8674_scaleR__collapse,axiom,
% 5.24/5.57 ! [U2: real,A: real] :
% 5.24/5.57 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U2 ) @ A ) @ ( real_V1485227260804924795R_real @ U2 @ A ) )
% 5.24/5.57 = A ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_collapse
% 5.24/5.57 thf(fact_8675_scaleR__collapse,axiom,
% 5.24/5.57 ! [U2: real,A: complex] :
% 5.24/5.57 ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ ( minus_minus_real @ one_one_real @ U2 ) @ A ) @ ( real_V2046097035970521341omplex @ U2 @ A ) )
% 5.24/5.57 = A ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_collapse
% 5.24/5.57 thf(fact_8676_prod_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc
% 5.24/5.57 thf(fact_8677_prod_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc
% 5.24/5.57 thf(fact_8678_prod_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc
% 5.24/5.57 thf(fact_8679_prod_OatMost__Suc,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc
% 5.24/5.57 thf(fact_8680_norm__scaleR,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ A @ X ) )
% 5.24/5.57 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % norm_scaleR
% 5.24/5.57 thf(fact_8681_norm__scaleR,axiom,
% 5.24/5.57 ! [A: real,X: complex] :
% 5.24/5.57 ( ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ A @ X ) )
% 5.24/5.57 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % norm_scaleR
% 5.24/5.57 thf(fact_8682_scaleR__times,axiom,
% 5.24/5.57 ! [U2: num,W2: num,A: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U2 ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ W2 ) ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_times
% 5.24/5.57 thf(fact_8683_scaleR__times,axiom,
% 5.24/5.57 ! [U2: num,W2: num,A: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ W2 ) ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_times
% 5.24/5.57 thf(fact_8684_inverse__scaleR__times,axiom,
% 5.24/5.57 ! [V: num,W2: num,A: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W2 ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % inverse_scaleR_times
% 5.24/5.57 thf(fact_8685_inverse__scaleR__times,axiom,
% 5.24/5.57 ! [V: num,W2: num,A: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W2 ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % inverse_scaleR_times
% 5.24/5.57 thf(fact_8686_fraction__scaleR__times,axiom,
% 5.24/5.57 ! [U2: num,V: num,W2: num,A: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 5.24/5.57 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ W2 ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % fraction_scaleR_times
% 5.24/5.57 thf(fact_8687_fraction__scaleR__times,axiom,
% 5.24/5.57 ! [U2: num,V: num,W2: num,A: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 5.24/5.57 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U2 ) @ ( numeral_numeral_real @ W2 ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % fraction_scaleR_times
% 5.24/5.57 thf(fact_8688_scaleR__half__double,axiom,
% 5.24/5.57 ! [A: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 5.24/5.57 = A ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_half_double
% 5.24/5.57 thf(fact_8689_scaleR__half__double,axiom,
% 5.24/5.57 ! [A: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ A @ A ) )
% 5.24/5.57 = A ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_half_double
% 5.24/5.57 thf(fact_8690_scaleR__right__distrib,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_right_distrib
% 5.24/5.57 thf(fact_8691_scaleR__right__distrib,axiom,
% 5.24/5.57 ! [A: real,X: complex,Y4: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ A @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ A @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_right_distrib
% 5.24/5.57 thf(fact_8692_real__scaleR__def,axiom,
% 5.24/5.57 real_V1485227260804924795R_real = times_times_real ).
% 5.24/5.57
% 5.24/5.57 % real_scaleR_def
% 5.24/5.57 thf(fact_8693_divide__complex__def,axiom,
% 5.24/5.57 ( divide1717551699836669952omplex
% 5.24/5.57 = ( ^ [X2: complex,Y: complex] : ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % divide_complex_def
% 5.24/5.57 thf(fact_8694_not__empty__eq__Iic__eq__empty,axiom,
% 5.24/5.57 ! [H2: int] :
% 5.24/5.57 ( bot_bot_set_int
% 5.24/5.57 != ( set_ord_atMost_int @ H2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % not_empty_eq_Iic_eq_empty
% 5.24/5.57 thf(fact_8695_not__empty__eq__Iic__eq__empty,axiom,
% 5.24/5.57 ! [H2: real] :
% 5.24/5.57 ( bot_bot_set_real
% 5.24/5.57 != ( set_ord_atMost_real @ H2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % not_empty_eq_Iic_eq_empty
% 5.24/5.57 thf(fact_8696_not__empty__eq__Iic__eq__empty,axiom,
% 5.24/5.57 ! [H2: nat] :
% 5.24/5.57 ( bot_bot_set_nat
% 5.24/5.57 != ( set_ord_atMost_nat @ H2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % not_empty_eq_Iic_eq_empty
% 5.24/5.57 thf(fact_8697_atMost__def,axiom,
% 5.24/5.57 ( set_ord_atMost_real
% 5.24/5.57 = ( ^ [U3: real] :
% 5.24/5.57 ( collect_real
% 5.24/5.57 @ ^ [X2: real] : ( ord_less_eq_real @ X2 @ U3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_def
% 5.24/5.57 thf(fact_8698_atMost__def,axiom,
% 5.24/5.57 ( set_or4236626031148496127et_nat
% 5.24/5.57 = ( ^ [U3: set_nat] :
% 5.24/5.57 ( collect_set_nat
% 5.24/5.57 @ ^ [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ U3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_def
% 5.24/5.57 thf(fact_8699_atMost__def,axiom,
% 5.24/5.57 ( set_ord_atMost_rat
% 5.24/5.57 = ( ^ [U3: rat] :
% 5.24/5.57 ( collect_rat
% 5.24/5.57 @ ^ [X2: rat] : ( ord_less_eq_rat @ X2 @ U3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_def
% 5.24/5.57 thf(fact_8700_atMost__def,axiom,
% 5.24/5.57 ( set_ord_atMost_num
% 5.24/5.57 = ( ^ [U3: num] :
% 5.24/5.57 ( collect_num
% 5.24/5.57 @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_def
% 5.24/5.57 thf(fact_8701_atMost__def,axiom,
% 5.24/5.57 ( set_ord_atMost_int
% 5.24/5.57 = ( ^ [U3: int] :
% 5.24/5.57 ( collect_int
% 5.24/5.57 @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_def
% 5.24/5.57 thf(fact_8702_atMost__def,axiom,
% 5.24/5.57 ( set_ord_atMost_nat
% 5.24/5.57 = ( ^ [U3: nat] :
% 5.24/5.57 ( collect_nat
% 5.24/5.57 @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_def
% 5.24/5.57 thf(fact_8703_lessThan__Suc__atMost,axiom,
% 5.24/5.57 ! [K: nat] :
% 5.24/5.57 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.24/5.57 = ( set_ord_atMost_nat @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % lessThan_Suc_atMost
% 5.24/5.57 thf(fact_8704_scaleR__left_Oadd,axiom,
% 5.24/5.57 ! [X: real,Y4: real,Xa2: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X @ Y4 ) @ Xa2 )
% 5.24/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X @ Xa2 ) @ ( real_V1485227260804924795R_real @ Y4 @ Xa2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left.add
% 5.24/5.57 thf(fact_8705_scaleR__left_Oadd,axiom,
% 5.24/5.57 ! [X: real,Y4: real,Xa2: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ X @ Y4 ) @ Xa2 )
% 5.24/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ X @ Xa2 ) @ ( real_V2046097035970521341omplex @ Y4 @ Xa2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left.add
% 5.24/5.57 thf(fact_8706_scaleR__left__distrib,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X )
% 5.24/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left_distrib
% 5.24/5.57 thf(fact_8707_scaleR__left__distrib,axiom,
% 5.24/5.57 ! [A: real,B: real,X: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ A @ B ) @ X )
% 5.24/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ B @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left_distrib
% 5.24/5.57 thf(fact_8708_complex__scaleR,axiom,
% 5.24/5.57 ! [R2: real,A: real,B: real] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.24/5.57 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_scaleR
% 5.24/5.57 thf(fact_8709_scaleR__right__mono,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_right_mono
% 5.24/5.57 thf(fact_8710_scaleR__right__mono__neg,axiom,
% 5.24/5.57 ! [B: real,A: real,C: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ B @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_right_mono_neg
% 5.24/5.57 thf(fact_8711_scaleR__le__cancel__left,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.24/5.57 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ord_less_eq_real @ A @ B ) )
% 5.24/5.57 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_le_cancel_left
% 5.24/5.57 thf(fact_8712_scaleR__le__cancel__left__neg,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.24/5.57 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_le_cancel_left_neg
% 5.24/5.57 thf(fact_8713_scaleR__le__cancel__left__pos,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.24/5.57 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_le_cancel_left_pos
% 5.24/5.57 thf(fact_8714_scaleR__left__mono,axiom,
% 5.24/5.57 ! [X: real,Y4: real,A: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left_mono
% 5.24/5.57 thf(fact_8715_scaleR__left__mono__neg,axiom,
% 5.24/5.57 ! [B: real,A: real,C: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ B @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left_mono_neg
% 5.24/5.57 thf(fact_8716_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 5.24/5.57 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.24/5.57 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.24/5.57
% 5.24/5.57 % Real_Vector_Spaces.le_add_iff1
% 5.24/5.57 thf(fact_8717_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 5.24/5.57 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.24/5.57 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Real_Vector_Spaces.le_add_iff2
% 5.24/5.57 thf(fact_8718_Iic__subset__Iio__iff,axiom,
% 5.24/5.57 ! [A: rat,B: rat] :
% 5.24/5.57 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.24/5.57 = ( ord_less_rat @ A @ B ) ) ).
% 5.24/5.57
% 5.24/5.57 % Iic_subset_Iio_iff
% 5.24/5.57 thf(fact_8719_Iic__subset__Iio__iff,axiom,
% 5.24/5.57 ! [A: num,B: num] :
% 5.24/5.57 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.24/5.57 = ( ord_less_num @ A @ B ) ) ).
% 5.24/5.57
% 5.24/5.57 % Iic_subset_Iio_iff
% 5.24/5.57 thf(fact_8720_Iic__subset__Iio__iff,axiom,
% 5.24/5.57 ! [A: int,B: int] :
% 5.24/5.57 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.24/5.57 = ( ord_less_int @ A @ B ) ) ).
% 5.24/5.57
% 5.24/5.57 % Iic_subset_Iio_iff
% 5.24/5.57 thf(fact_8721_Iic__subset__Iio__iff,axiom,
% 5.24/5.57 ! [A: nat,B: nat] :
% 5.24/5.57 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.24/5.57 = ( ord_less_nat @ A @ B ) ) ).
% 5.24/5.57
% 5.24/5.57 % Iic_subset_Iio_iff
% 5.24/5.57 thf(fact_8722_Iic__subset__Iio__iff,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.24/5.57 = ( ord_less_real @ A @ B ) ) ).
% 5.24/5.57
% 5.24/5.57 % Iic_subset_Iio_iff
% 5.24/5.57 thf(fact_8723_exp__series__add__commuting,axiom,
% 5.24/5.57 ! [X: real,Y4: real,N: nat] :
% 5.24/5.57 ( ( ( times_times_real @ X @ Y4 )
% 5.24/5.57 = ( times_times_real @ Y4 @ X ) )
% 5.24/5.57 => ( ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y4 ) @ N ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I4 ) ) @ ( power_power_real @ X @ I4 ) ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ I4 ) ) ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ N @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_series_add_commuting
% 5.24/5.57 thf(fact_8724_exp__series__add__commuting,axiom,
% 5.24/5.57 ! [X: complex,Y4: complex,N: nat] :
% 5.24/5.57 ( ( ( times_times_complex @ X @ Y4 )
% 5.24/5.57 = ( times_times_complex @ Y4 @ X ) )
% 5.24/5.57 => ( ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y4 ) @ N ) )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I4 ) ) @ ( power_power_complex @ X @ I4 ) ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ I4 ) ) ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ N @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_series_add_commuting
% 5.24/5.57 thf(fact_8725_sum__choose__upper,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_choose_upper
% 5.24/5.57 thf(fact_8726_scaleR__le__0__iff,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 5.24/5.57 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.24/5.57 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.24/5.57 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.24/5.57 | ( A = zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_le_0_iff
% 5.24/5.57 thf(fact_8727_zero__le__scaleR__iff,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 5.24/5.57 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.24/5.57 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.24/5.57 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.24/5.57 | ( A = zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_le_scaleR_iff
% 5.24/5.57 thf(fact_8728_scaleR__nonpos__nonpos,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.24/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_nonpos_nonpos
% 5.24/5.57 thf(fact_8729_scaleR__nonpos__nonneg,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_nonpos_nonneg
% 5.24/5.57 thf(fact_8730_scaleR__nonneg__nonpos,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_nonneg_nonpos
% 5.24/5.57 thf(fact_8731_scaleR__nonneg__nonneg,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_nonneg_nonneg
% 5.24/5.57 thf(fact_8732_split__scaleR__pos__le,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.24/5.57 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.24/5.57 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.24/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % split_scaleR_pos_le
% 5.24/5.57 thf(fact_8733_split__scaleR__neg__le,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 & ( ord_less_eq_real @ X @ zero_zero_real ) )
% 5.24/5.57 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.24/5.57 & ( ord_less_eq_real @ zero_zero_real @ X ) ) )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % split_scaleR_neg_le
% 5.24/5.57 thf(fact_8734_scaleR__mono_H,axiom,
% 5.24/5.57 ! [A: real,B: real,C: real,D: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.57 => ( ( ord_less_eq_real @ C @ D )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_mono'
% 5.24/5.57 thf(fact_8735_scaleR__mono,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ Y4 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_mono
% 5.24/5.57 thf(fact_8736_scaleR__left__le__one__le,axiom,
% 5.24/5.57 ! [X: real,A: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.24/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_left_le_one_le
% 5.24/5.57 thf(fact_8737_scaleR__2,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.24/5.57 = ( plus_plus_real @ X @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_2
% 5.24/5.57 thf(fact_8738_scaleR__2,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.24/5.57 = ( plus_plus_complex @ X @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % scaleR_2
% 5.24/5.57 thf(fact_8739_real__vector__affinity__eq,axiom,
% 5.24/5.57 ! [M: real,X: real,C: real,Y4: real] :
% 5.24/5.57 ( ( M != zero_zero_real )
% 5.24/5.57 => ( ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X ) @ C )
% 5.24/5.57 = Y4 )
% 5.24/5.57 = ( X
% 5.24/5.57 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_vector_affinity_eq
% 5.24/5.57 thf(fact_8740_real__vector__affinity__eq,axiom,
% 5.24/5.57 ! [M: real,X: complex,C: complex,Y4: complex] :
% 5.24/5.57 ( ( M != zero_zero_real )
% 5.24/5.57 => ( ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ M @ X ) @ C )
% 5.24/5.57 = Y4 )
% 5.24/5.57 = ( X
% 5.24/5.57 = ( minus_minus_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_vector_affinity_eq
% 5.24/5.57 thf(fact_8741_real__vector__eq__affinity,axiom,
% 5.24/5.57 ! [M: real,Y4: real,X: real,C: real] :
% 5.24/5.57 ( ( M != zero_zero_real )
% 5.24/5.57 => ( ( Y4
% 5.24/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X ) @ C ) )
% 5.24/5.57 = ( ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) )
% 5.24/5.57 = X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_vector_eq_affinity
% 5.24/5.57 thf(fact_8742_real__vector__eq__affinity,axiom,
% 5.24/5.57 ! [M: real,Y4: complex,X: complex,C: complex] :
% 5.24/5.57 ( ( M != zero_zero_real )
% 5.24/5.57 => ( ( Y4
% 5.24/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ M @ X ) @ C ) )
% 5.24/5.57 = ( ( minus_minus_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ C ) )
% 5.24/5.57 = X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_vector_eq_affinity
% 5.24/5.57 thf(fact_8743_pos__divideR__le__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.24/5.57 = ( ord_less_eq_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_divideR_le_eq
% 5.24/5.57 thf(fact_8744_pos__le__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_eq_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.24/5.57 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_le_divideR_eq
% 5.24/5.57 thf(fact_8745_neg__divideR__le__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.24/5.57 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_divideR_le_eq
% 5.24/5.57 thf(fact_8746_neg__le__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.24/5.57 = ( ord_less_eq_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_le_divideR_eq
% 5.24/5.57 thf(fact_8747_neg__less__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.24/5.57 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_less_divideR_eq
% 5.24/5.57 thf(fact_8748_neg__divideR__less__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.24/5.57 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_divideR_less_eq
% 5.24/5.57 thf(fact_8749_pos__less__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.24/5.57 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_less_divideR_eq
% 5.24/5.57 thf(fact_8750_pos__divideR__less__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.24/5.57 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_divideR_less_eq
% 5.24/5.57 thf(fact_8751_sum_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc_shift
% 5.24/5.57 thf(fact_8752_sum_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc_shift
% 5.24/5.57 thf(fact_8753_sum_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc_shift
% 5.24/5.57 thf(fact_8754_sum_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_Suc_shift
% 5.24/5.57 thf(fact_8755_sum__telescope,axiom,
% 5.24/5.57 ! [F: nat > rat,I2: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ I2 ) )
% 5.24/5.57 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_telescope
% 5.24/5.57 thf(fact_8756_sum__telescope,axiom,
% 5.24/5.57 ! [F: nat > int,I2: nat] :
% 5.24/5.57 ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ I2 ) )
% 5.24/5.57 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_telescope
% 5.24/5.57 thf(fact_8757_sum__telescope,axiom,
% 5.24/5.57 ! [F: nat > real,I2: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ I2 ) )
% 5.24/5.57 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_telescope
% 5.24/5.57 thf(fact_8758_polyfun__eq__coeffs,axiom,
% 5.24/5.57 ! [C: nat > complex,N: nat,D: nat > complex] :
% 5.24/5.57 ( ( ! [X2: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( D @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.24/5.57 = ( ! [I4: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.24/5.57 => ( ( C @ I4 )
% 5.24/5.57 = ( D @ I4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_eq_coeffs
% 5.24/5.57 thf(fact_8759_polyfun__eq__coeffs,axiom,
% 5.24/5.57 ! [C: nat > real,N: nat,D: nat > real] :
% 5.24/5.57 ( ( ! [X2: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( D @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.24/5.57 = ( ! [I4: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.24/5.57 => ( ( C @ I4 )
% 5.24/5.57 = ( D @ I4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_eq_coeffs
% 5.24/5.57 thf(fact_8760_bounded__imp__summable,axiom,
% 5.24/5.57 ! [A: nat > int,B5: int] :
% 5.24/5.57 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 5.24/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B5 )
% 5.24/5.57 => ( summable_int @ A ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bounded_imp_summable
% 5.24/5.57 thf(fact_8761_bounded__imp__summable,axiom,
% 5.24/5.57 ! [A: nat > nat,B5: nat] :
% 5.24/5.57 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 5.24/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B5 )
% 5.24/5.57 => ( summable_nat @ A ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bounded_imp_summable
% 5.24/5.57 thf(fact_8762_bounded__imp__summable,axiom,
% 5.24/5.57 ! [A: nat > real,B5: real] :
% 5.24/5.57 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B5 )
% 5.24/5.57 => ( summable_real @ A ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bounded_imp_summable
% 5.24/5.57 thf(fact_8763_prod_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups129246275422532515t_real
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc_shift
% 5.24/5.57 thf(fact_8764_prod_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups73079841787564623at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc_shift
% 5.24/5.57 thf(fact_8765_prod_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc_shift
% 5.24/5.57 thf(fact_8766_prod_OatMost__Suc__shift,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_Suc_shift
% 5.24/5.57 thf(fact_8767_sum_Onested__swap_H,axiom,
% 5.24/5.57 ! [A: nat > nat > nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.nested_swap'
% 5.24/5.57 thf(fact_8768_sum_Onested__swap_H,axiom,
% 5.24/5.57 ! [A: nat > nat > real,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.nested_swap'
% 5.24/5.57 thf(fact_8769_prod_Onested__swap_H,axiom,
% 5.24/5.57 ! [A: nat > nat > nat,N: nat] :
% 5.24/5.57 ( ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.nested_swap'
% 5.24/5.57 thf(fact_8770_prod_Onested__swap_H,axiom,
% 5.24/5.57 ! [A: nat > nat > int,N: nat] :
% 5.24/5.57 ( ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.nested_swap'
% 5.24/5.57 thf(fact_8771_sum__choose__lower,axiom,
% 5.24/5.57 ! [R2: nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_choose_lower
% 5.24/5.57 thf(fact_8772_choose__rising__sum_I1_J,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_rising_sum(1)
% 5.24/5.57 thf(fact_8773_choose__rising__sum_I2_J,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_rising_sum(2)
% 5.24/5.57 thf(fact_8774_summable__exp__generic,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_exp_generic
% 5.24/5.57 thf(fact_8775_summable__exp__generic,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( summable_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X @ N2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_exp_generic
% 5.24/5.57 thf(fact_8776_sin__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) )
% 5.24/5.57 @ ( sin_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_converges
% 5.24/5.57 thf(fact_8777_sin__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) )
% 5.24/5.57 @ ( sin_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_converges
% 5.24/5.57 thf(fact_8778_sin__def,axiom,
% 5.24/5.57 ( sin_real
% 5.24/5.57 = ( ^ [X2: real] :
% 5.24/5.57 ( suminf_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_def
% 5.24/5.57 thf(fact_8779_sin__def,axiom,
% 5.24/5.57 ( sin_complex
% 5.24/5.57 = ( ^ [X2: complex] :
% 5.24/5.57 ( suminf_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_def
% 5.24/5.57 thf(fact_8780_cos__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) )
% 5.24/5.57 @ ( cos_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_converges
% 5.24/5.57 thf(fact_8781_cos__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) )
% 5.24/5.57 @ ( cos_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_converges
% 5.24/5.57 thf(fact_8782_cos__def,axiom,
% 5.24/5.57 ( cos_real
% 5.24/5.57 = ( ^ [X2: real] :
% 5.24/5.57 ( suminf_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_def
% 5.24/5.57 thf(fact_8783_cos__def,axiom,
% 5.24/5.57 ( cos_complex
% 5.24/5.57 = ( ^ [X2: complex] :
% 5.24/5.57 ( suminf_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_def
% 5.24/5.57 thf(fact_8784_summable__norm__sin,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_norm_sin
% 5.24/5.57 thf(fact_8785_summable__norm__sin,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_norm_sin
% 5.24/5.57 thf(fact_8786_summable__norm__cos,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_norm_cos
% 5.24/5.57 thf(fact_8787_summable__norm__cos,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_norm_cos
% 5.24/5.57 thf(fact_8788_neg__minus__divideR__le__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.24/5.57 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_minus_divideR_le_eq
% 5.24/5.57 thf(fact_8789_neg__le__minus__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.24/5.57 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_le_minus_divideR_eq
% 5.24/5.57 thf(fact_8790_pos__minus__divideR__le__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.24/5.57 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_minus_divideR_le_eq
% 5.24/5.57 thf(fact_8791_pos__le__minus__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.24/5.57 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_le_minus_divideR_eq
% 5.24/5.57 thf(fact_8792_pos__less__minus__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.24/5.57 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_less_minus_divideR_eq
% 5.24/5.57 thf(fact_8793_pos__minus__divideR__less__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.57 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.24/5.57 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pos_minus_divideR_less_eq
% 5.24/5.57 thf(fact_8794_neg__less__minus__divideR__eq,axiom,
% 5.24/5.57 ! [C: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.24/5.57 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_less_minus_divideR_eq
% 5.24/5.57 thf(fact_8795_neg__minus__divideR__less__eq,axiom,
% 5.24/5.57 ! [C: real,B: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.24/5.57 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.24/5.57 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_minus_divideR_less_eq
% 5.24/5.57 thf(fact_8796_polyfun__eq__0,axiom,
% 5.24/5.57 ! [C: nat > complex,N: nat] :
% 5.24/5.57 ( ( ! [X2: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex ) )
% 5.24/5.57 = ( ! [I4: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.24/5.57 => ( ( C @ I4 )
% 5.24/5.57 = zero_zero_complex ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_eq_0
% 5.24/5.57 thf(fact_8797_polyfun__eq__0,axiom,
% 5.24/5.57 ! [C: nat > real,N: nat] :
% 5.24/5.57 ( ( ! [X2: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real ) )
% 5.24/5.57 = ( ! [I4: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.24/5.57 => ( ( C @ I4 )
% 5.24/5.57 = zero_zero_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_eq_0
% 5.24/5.57 thf(fact_8798_zero__polynom__imp__zero__coeffs,axiom,
% 5.24/5.57 ! [C: nat > complex,N: nat,K: nat] :
% 5.24/5.57 ( ! [W: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ W @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( C @ K )
% 5.24/5.57 = zero_zero_complex ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_polynom_imp_zero_coeffs
% 5.24/5.57 thf(fact_8799_zero__polynom__imp__zero__coeffs,axiom,
% 5.24/5.57 ! [C: nat > real,N: nat,K: nat] :
% 5.24/5.57 ( ! [W: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ W @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( ( C @ K )
% 5.24/5.57 = zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_polynom_imp_zero_coeffs
% 5.24/5.57 thf(fact_8800_sum_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_shift
% 5.24/5.57 thf(fact_8801_sum_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_shift
% 5.24/5.57 thf(fact_8802_sum_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_shift
% 5.24/5.57 thf(fact_8803_sum_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.atMost_shift
% 5.24/5.57 thf(fact_8804_sum__up__index__split,axiom,
% 5.24/5.57 ! [F: nat > rat,M: nat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.57 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_up_index_split
% 5.24/5.57 thf(fact_8805_sum__up__index__split,axiom,
% 5.24/5.57 ! [F: nat > int,M: nat,N: nat] :
% 5.24/5.57 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_up_index_split
% 5.24/5.57 thf(fact_8806_sum__up__index__split,axiom,
% 5.24/5.57 ! [F: nat > nat,M: nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.57 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_up_index_split
% 5.24/5.57 thf(fact_8807_sum__up__index__split,axiom,
% 5.24/5.57 ! [F: nat > real,M: nat,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.24/5.57 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_up_index_split
% 5.24/5.57 thf(fact_8808_prod_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups129246275422532515t_real
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_shift
% 5.24/5.57 thf(fact_8809_prod_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups73079841787564623at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_shift
% 5.24/5.57 thf(fact_8810_prod_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_shift
% 5.24/5.57 thf(fact_8811_prod_OatMost__shift,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.24/5.57 @ ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.atMost_shift
% 5.24/5.57 thf(fact_8812_gbinomial__parallel__sum,axiom,
% 5.24/5.57 ! [A: complex,N: nat] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_parallel_sum
% 5.24/5.57 thf(fact_8813_gbinomial__parallel__sum,axiom,
% 5.24/5.57 ! [A: rat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_parallel_sum
% 5.24/5.57 thf(fact_8814_gbinomial__parallel__sum,axiom,
% 5.24/5.57 ! [A: real,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_parallel_sum
% 5.24/5.57 thf(fact_8815_sum_Otriangle__reindex__eq,axiom,
% 5.24/5.57 ! [G: nat > nat > nat,N: nat] :
% 5.24/5.57 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.triangle_reindex_eq
% 5.24/5.57 thf(fact_8816_sum_Otriangle__reindex__eq,axiom,
% 5.24/5.57 ! [G: nat > nat > real,N: nat] :
% 5.24/5.57 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.triangle_reindex_eq
% 5.24/5.57 thf(fact_8817_prod_Otriangle__reindex__eq,axiom,
% 5.24/5.57 ! [G: nat > nat > nat,N: nat] :
% 5.24/5.57 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.triangle_reindex_eq
% 5.24/5.57 thf(fact_8818_prod_Otriangle__reindex__eq,axiom,
% 5.24/5.57 ! [G: nat > nat > int,N: nat] :
% 5.24/5.57 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.triangle_reindex_eq
% 5.24/5.57 thf(fact_8819_sum__choose__diagonal,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_choose_diagonal
% 5.24/5.57 thf(fact_8820_vandermonde,axiom,
% 5.24/5.57 ! [M: nat,N: nat,R2: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ R2 ) )
% 5.24/5.57 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % vandermonde
% 5.24/5.57 thf(fact_8821_exp__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) )
% 5.24/5.57 @ ( exp_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_converges
% 5.24/5.57 thf(fact_8822_exp__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X @ N2 ) )
% 5.24/5.57 @ ( exp_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_converges
% 5.24/5.57 thf(fact_8823_exp__def,axiom,
% 5.24/5.57 ( exp_real
% 5.24/5.57 = ( ^ [X2: real] :
% 5.24/5.57 ( suminf_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_def
% 5.24/5.57 thf(fact_8824_exp__def,axiom,
% 5.24/5.57 ( exp_complex
% 5.24/5.57 = ( ^ [X2: complex] :
% 5.24/5.57 ( suminf_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_def
% 5.24/5.57 thf(fact_8825_summable__norm__exp,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_norm_exp
% 5.24/5.57 thf(fact_8826_summable__norm__exp,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( summable_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_norm_exp
% 5.24/5.57 thf(fact_8827_sin__minus__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ N2 ) ) )
% 5.24/5.57 @ ( sin_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_minus_converges
% 5.24/5.57 thf(fact_8828_sin__minus__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ N2 ) ) )
% 5.24/5.57 @ ( sin_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_minus_converges
% 5.24/5.57 thf(fact_8829_cos__minus__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ N2 ) )
% 5.24/5.57 @ ( cos_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_minus_converges
% 5.24/5.57 thf(fact_8830_cos__minus__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ N2 ) )
% 5.24/5.57 @ ( cos_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_minus_converges
% 5.24/5.57 thf(fact_8831_sum__gp__basic,axiom,
% 5.24/5.57 ! [X: complex,N: nat] :
% 5.24/5.57 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp_basic
% 5.24/5.57 thf(fact_8832_sum__gp__basic,axiom,
% 5.24/5.57 ! [X: rat,N: nat] :
% 5.24/5.57 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp_basic
% 5.24/5.57 thf(fact_8833_sum__gp__basic,axiom,
% 5.24/5.57 ! [X: int,N: nat] :
% 5.24/5.57 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp_basic
% 5.24/5.57 thf(fact_8834_sum__gp__basic,axiom,
% 5.24/5.57 ! [X: real,N: nat] :
% 5.24/5.57 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp_basic
% 5.24/5.57 thf(fact_8835_polyfun__finite__roots,axiom,
% 5.24/5.57 ! [C: nat > complex,N: nat] :
% 5.24/5.57 ( ( finite3207457112153483333omplex
% 5.24/5.57 @ ( collect_complex
% 5.24/5.57 @ ^ [X2: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex ) ) )
% 5.24/5.57 = ( ? [I4: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.24/5.57 & ( ( C @ I4 )
% 5.24/5.57 != zero_zero_complex ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_finite_roots
% 5.24/5.57 thf(fact_8836_polyfun__finite__roots,axiom,
% 5.24/5.57 ! [C: nat > real,N: nat] :
% 5.24/5.57 ( ( finite_finite_real
% 5.24/5.57 @ ( collect_real
% 5.24/5.57 @ ^ [X2: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real ) ) )
% 5.24/5.57 = ( ? [I4: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.24/5.57 & ( ( C @ I4 )
% 5.24/5.57 != zero_zero_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_finite_roots
% 5.24/5.57 thf(fact_8837_polyfun__roots__finite,axiom,
% 5.24/5.57 ! [C: nat > complex,K: nat,N: nat] :
% 5.24/5.57 ( ( ( C @ K )
% 5.24/5.57 != zero_zero_complex )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( finite3207457112153483333omplex
% 5.24/5.57 @ ( collect_complex
% 5.24/5.57 @ ^ [Z4: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_roots_finite
% 5.24/5.57 thf(fact_8838_polyfun__roots__finite,axiom,
% 5.24/5.57 ! [C: nat > real,K: nat,N: nat] :
% 5.24/5.57 ( ( ( C @ K )
% 5.24/5.57 != zero_zero_real )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ N )
% 5.24/5.57 => ( finite_finite_real
% 5.24/5.57 @ ( collect_real
% 5.24/5.57 @ ^ [Z4: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_roots_finite
% 5.24/5.57 thf(fact_8839_polyfun__linear__factor__root,axiom,
% 5.24/5.57 ! [C: nat > complex,A: complex,N: nat] :
% 5.24/5.57 ( ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex )
% 5.24/5.57 => ~ ! [B2: nat > complex] :
% 5.24/5.57 ~ ! [Z5: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( B2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor_root
% 5.24/5.57 thf(fact_8840_polyfun__linear__factor__root,axiom,
% 5.24/5.57 ! [C: nat > rat,A: rat,N: nat] :
% 5.24/5.57 ( ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_rat )
% 5.24/5.57 => ~ ! [B2: nat > rat] :
% 5.24/5.57 ~ ! [Z5: rat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( B2 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor_root
% 5.24/5.57 thf(fact_8841_polyfun__linear__factor__root,axiom,
% 5.24/5.57 ! [C: nat > int,A: int,N: nat] :
% 5.24/5.57 ( ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 => ~ ! [B2: nat > int] :
% 5.24/5.57 ~ ! [Z5: int] :
% 5.24/5.57 ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( B2 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor_root
% 5.24/5.57 thf(fact_8842_polyfun__linear__factor__root,axiom,
% 5.24/5.57 ! [C: nat > real,A: real,N: nat] :
% 5.24/5.57 ( ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real )
% 5.24/5.57 => ~ ! [B2: nat > real] :
% 5.24/5.57 ~ ! [Z5: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( B2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor_root
% 5.24/5.57 thf(fact_8843_polyfun__linear__factor,axiom,
% 5.24/5.57 ! [C: nat > complex,N: nat,A: complex] :
% 5.24/5.57 ? [B2: nat > complex] :
% 5.24/5.57 ! [Z5: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_complex
% 5.24/5.57 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( B2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor
% 5.24/5.57 thf(fact_8844_polyfun__linear__factor,axiom,
% 5.24/5.57 ! [C: nat > rat,N: nat,A: rat] :
% 5.24/5.57 ? [B2: nat > rat] :
% 5.24/5.57 ! [Z5: rat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_rat
% 5.24/5.57 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( B2 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor
% 5.24/5.57 thf(fact_8845_polyfun__linear__factor,axiom,
% 5.24/5.57 ! [C: nat > int,N: nat,A: int] :
% 5.24/5.57 ? [B2: nat > int] :
% 5.24/5.57 ! [Z5: int] :
% 5.24/5.57 ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_int
% 5.24/5.57 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( B2 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( C @ I4 ) @ ( power_power_int @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor
% 5.24/5.57 thf(fact_8846_polyfun__linear__factor,axiom,
% 5.24/5.57 ! [C: nat > real,N: nat,A: real] :
% 5.24/5.57 ? [B2: nat > real] :
% 5.24/5.57 ! [Z5: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( plus_plus_real
% 5.24/5.57 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( B2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ A @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_linear_factor
% 5.24/5.57 thf(fact_8847_sum__power__shift,axiom,
% 5.24/5.57 ! [M: nat,N: nat,X: complex] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.57 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_power_shift
% 5.24/5.57 thf(fact_8848_sum__power__shift,axiom,
% 5.24/5.57 ! [M: nat,N: nat,X: rat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.57 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_power_shift
% 5.24/5.57 thf(fact_8849_sum__power__shift,axiom,
% 5.24/5.57 ! [M: nat,N: nat,X: int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.57 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_power_shift
% 5.24/5.57 thf(fact_8850_sum__power__shift,axiom,
% 5.24/5.57 ! [M: nat,N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.24/5.57 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_power_shift
% 5.24/5.57 thf(fact_8851_sum_Otriangle__reindex,axiom,
% 5.24/5.57 ! [G: nat > nat > nat,N: nat] :
% 5.24/5.57 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.triangle_reindex
% 5.24/5.57 thf(fact_8852_sum_Otriangle__reindex,axiom,
% 5.24/5.57 ! [G: nat > nat > real,N: nat] :
% 5.24/5.57 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.triangle_reindex
% 5.24/5.57 thf(fact_8853_prod_Otriangle__reindex,axiom,
% 5.24/5.57 ! [G: nat > nat > nat,N: nat] :
% 5.24/5.57 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.triangle_reindex
% 5.24/5.57 thf(fact_8854_prod_Otriangle__reindex,axiom,
% 5.24/5.57 ! [G: nat > nat > int,N: nat] :
% 5.24/5.57 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.24/5.57 @ ( collec3392354462482085612at_nat
% 5.24/5.57 @ ( produc6081775807080527818_nat_o
% 5.24/5.57 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N ) ) ) )
% 5.24/5.57 = ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.triangle_reindex
% 5.24/5.57 thf(fact_8855_summable__Cauchy__product,axiom,
% 5.24/5.57 ! [A: nat > complex,B: nat > complex] :
% 5.24/5.57 ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.24/5.57 => ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.24/5.57 => ( summable_complex
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_Cauchy_product
% 5.24/5.57 thf(fact_8856_summable__Cauchy__product,axiom,
% 5.24/5.57 ! [A: nat > real,B: nat > real] :
% 5.24/5.57 ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.24/5.57 => ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.24/5.57 => ( summable_real
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % summable_Cauchy_product
% 5.24/5.57 thf(fact_8857_choose__row__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_row_sum
% 5.24/5.57 thf(fact_8858_Cauchy__product,axiom,
% 5.24/5.57 ! [A: nat > complex,B: nat > complex] :
% 5.24/5.57 ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.24/5.57 => ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.24/5.57 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.24/5.57 = ( suminf_complex
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Cauchy_product
% 5.24/5.57 thf(fact_8859_Cauchy__product,axiom,
% 5.24/5.57 ! [A: nat > real,B: nat > real] :
% 5.24/5.57 ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.24/5.57 => ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.24/5.57 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.24/5.57 = ( suminf_real
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Cauchy_product
% 5.24/5.57 thf(fact_8860_binomial,axiom,
% 5.24/5.57 ! [A: nat,B: nat,N: nat] :
% 5.24/5.57 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial
% 5.24/5.57 thf(fact_8861_sum_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.in_pairs_0
% 5.24/5.57 thf(fact_8862_sum_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.in_pairs_0
% 5.24/5.57 thf(fact_8863_sum_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.in_pairs_0
% 5.24/5.57 thf(fact_8864_sum_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.in_pairs_0
% 5.24/5.57 thf(fact_8865_polynomial__product,axiom,
% 5.24/5.57 ! [M: nat,A: nat > complex,N: nat,B: nat > complex,X: complex] :
% 5.24/5.57 ( ! [I3: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ I3 )
% 5.24/5.57 => ( ( A @ I3 )
% 5.24/5.57 = zero_zero_complex ) )
% 5.24/5.57 => ( ! [J2: nat] :
% 5.24/5.57 ( ( ord_less_nat @ N @ J2 )
% 5.24/5.57 => ( ( B @ J2 )
% 5.24/5.57 = zero_zero_complex ) )
% 5.24/5.57 => ( ( times_times_complex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [R5: nat] :
% 5.24/5.57 ( times_times_complex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ R5 ) )
% 5.24/5.57 @ ( power_power_complex @ X @ R5 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polynomial_product
% 5.24/5.57 thf(fact_8866_polynomial__product,axiom,
% 5.24/5.57 ! [M: nat,A: nat > rat,N: nat,B: nat > rat,X: rat] :
% 5.24/5.57 ( ! [I3: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ I3 )
% 5.24/5.57 => ( ( A @ I3 )
% 5.24/5.57 = zero_zero_rat ) )
% 5.24/5.57 => ( ! [J2: nat] :
% 5.24/5.57 ( ( ord_less_nat @ N @ J2 )
% 5.24/5.57 => ( ( B @ J2 )
% 5.24/5.57 = zero_zero_rat ) )
% 5.24/5.57 => ( ( times_times_rat
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [R5: nat] :
% 5.24/5.57 ( times_times_rat
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ R5 ) )
% 5.24/5.57 @ ( power_power_rat @ X @ R5 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polynomial_product
% 5.24/5.57 thf(fact_8867_polynomial__product,axiom,
% 5.24/5.57 ! [M: nat,A: nat > int,N: nat,B: nat > int,X: int] :
% 5.24/5.57 ( ! [I3: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ I3 )
% 5.24/5.57 => ( ( A @ I3 )
% 5.24/5.57 = zero_zero_int ) )
% 5.24/5.57 => ( ! [J2: nat] :
% 5.24/5.57 ( ( ord_less_nat @ N @ J2 )
% 5.24/5.57 => ( ( B @ J2 )
% 5.24/5.57 = zero_zero_int ) )
% 5.24/5.57 => ( ( times_times_int
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [R5: nat] :
% 5.24/5.57 ( times_times_int
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ R5 ) )
% 5.24/5.57 @ ( power_power_int @ X @ R5 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polynomial_product
% 5.24/5.57 thf(fact_8868_polynomial__product,axiom,
% 5.24/5.57 ! [M: nat,A: nat > real,N: nat,B: nat > real,X: real] :
% 5.24/5.57 ( ! [I3: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ I3 )
% 5.24/5.57 => ( ( A @ I3 )
% 5.24/5.57 = zero_zero_real ) )
% 5.24/5.57 => ( ! [J2: nat] :
% 5.24/5.57 ( ( ord_less_nat @ N @ J2 )
% 5.24/5.57 => ( ( B @ J2 )
% 5.24/5.57 = zero_zero_real ) )
% 5.24/5.57 => ( ( times_times_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [R5: nat] :
% 5.24/5.57 ( times_times_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ R5 ) )
% 5.24/5.57 @ ( power_power_real @ X @ R5 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polynomial_product
% 5.24/5.57 thf(fact_8869_prod_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > real,N: nat] :
% 5.24/5.57 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups129246275422532515t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.in_pairs_0
% 5.24/5.57 thf(fact_8870_prod_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > rat,N: nat] :
% 5.24/5.57 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups73079841787564623at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.in_pairs_0
% 5.24/5.57 thf(fact_8871_prod_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > nat,N: nat] :
% 5.24/5.57 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.in_pairs_0
% 5.24/5.57 thf(fact_8872_prod_Oin__pairs__0,axiom,
% 5.24/5.57 ! [G: nat > int,N: nat] :
% 5.24/5.57 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.24/5.57 = ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.in_pairs_0
% 5.24/5.57 thf(fact_8873_polyfun__eq__const,axiom,
% 5.24/5.57 ! [C: nat > complex,N: nat,K: complex] :
% 5.24/5.57 ( ( ! [X2: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = K ) )
% 5.24/5.57 = ( ( ( C @ zero_zero_nat )
% 5.24/5.57 = K )
% 5.24/5.57 & ! [X2: nat] :
% 5.24/5.57 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.24/5.57 => ( ( C @ X2 )
% 5.24/5.57 = zero_zero_complex ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_eq_const
% 5.24/5.57 thf(fact_8874_polyfun__eq__const,axiom,
% 5.24/5.57 ! [C: nat > real,N: nat,K: real] :
% 5.24/5.57 ( ( ! [X2: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = K ) )
% 5.24/5.57 = ( ( ( C @ zero_zero_nat )
% 5.24/5.57 = K )
% 5.24/5.57 & ! [X2: nat] :
% 5.24/5.57 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.24/5.57 => ( ( C @ X2 )
% 5.24/5.57 = zero_zero_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_eq_const
% 5.24/5.57 thf(fact_8875_gbinomial__sum__lower__neg,axiom,
% 5.24/5.57 ! [A: complex,M: nat] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_lower_neg
% 5.24/5.57 thf(fact_8876_gbinomial__sum__lower__neg,axiom,
% 5.24/5.57 ! [A: rat,M: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_lower_neg
% 5.24/5.57 thf(fact_8877_gbinomial__sum__lower__neg,axiom,
% 5.24/5.57 ! [A: real,M: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_lower_neg
% 5.24/5.57 thf(fact_8878_binomial__ring,axiom,
% 5.24/5.57 ! [A: complex,B: complex,N: nat] :
% 5.24/5.57 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_ring
% 5.24/5.57 thf(fact_8879_binomial__ring,axiom,
% 5.24/5.57 ! [A: int,B: int,N: nat] :
% 5.24/5.57 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.24/5.57 = ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_ring
% 5.24/5.57 thf(fact_8880_binomial__ring,axiom,
% 5.24/5.57 ! [A: rat,B: rat,N: nat] :
% 5.24/5.57 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_ring
% 5.24/5.57 thf(fact_8881_binomial__ring,axiom,
% 5.24/5.57 ! [A: nat,B: nat,N: nat] :
% 5.24/5.57 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_ring
% 5.24/5.57 thf(fact_8882_binomial__ring,axiom,
% 5.24/5.57 ! [A: real,B: real,N: nat] :
% 5.24/5.57 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_ring
% 5.24/5.57 thf(fact_8883_pochhammer__binomial__sum,axiom,
% 5.24/5.57 ! [A: int,B: int,N: nat] :
% 5.24/5.57 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.24/5.57 = ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pochhammer_binomial_sum
% 5.24/5.57 thf(fact_8884_pochhammer__binomial__sum,axiom,
% 5.24/5.57 ! [A: rat,B: rat,N: nat] :
% 5.24/5.57 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pochhammer_binomial_sum
% 5.24/5.57 thf(fact_8885_pochhammer__binomial__sum,axiom,
% 5.24/5.57 ! [A: real,B: real,N: nat] :
% 5.24/5.57 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [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 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pochhammer_binomial_sum
% 5.24/5.57 thf(fact_8886_polynomial__product__nat,axiom,
% 5.24/5.57 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 5.24/5.57 ( ! [I3: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ I3 )
% 5.24/5.57 => ( ( A @ I3 )
% 5.24/5.57 = zero_zero_nat ) )
% 5.24/5.57 => ( ! [J2: nat] :
% 5.24/5.57 ( ( ord_less_nat @ N @ J2 )
% 5.24/5.57 => ( ( B @ J2 )
% 5.24/5.57 = zero_zero_nat ) )
% 5.24/5.57 => ( ( times_times_nat
% 5.24/5.57 @ ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 @ ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [R5: nat] :
% 5.24/5.57 ( times_times_nat
% 5.24/5.57 @ ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ R5 ) )
% 5.24/5.57 @ ( power_power_nat @ X @ R5 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polynomial_product_nat
% 5.24/5.57 thf(fact_8887_choose__square__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_square_sum
% 5.24/5.57 thf(fact_8888_Cauchy__product__sums,axiom,
% 5.24/5.57 ! [A: nat > complex,B: nat > complex] :
% 5.24/5.57 ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.24/5.57 => ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.24/5.57 => ( sums_complex
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Cauchy_product_sums
% 5.24/5.57 thf(fact_8889_Cauchy__product__sums,axiom,
% 5.24/5.57 ! [A: nat > real,B: nat > real] :
% 5.24/5.57 ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.24/5.57 => ( ( summable_real
% 5.24/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.24/5.57 => ( sums_real
% 5.24/5.57 @ ^ [K3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( B @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.24/5.57 @ ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Cauchy_product_sums
% 5.24/5.57 thf(fact_8890_complex__inverse,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.24/5.57 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_inverse
% 5.24/5.57 thf(fact_8891_sum_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.zero_middle
% 5.24/5.57 thf(fact_8892_sum_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.zero_middle
% 5.24/5.57 thf(fact_8893_sum_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.zero_middle
% 5.24/5.57 thf(fact_8894_sum_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.zero_middle
% 5.24/5.57 thf(fact_8895_sum_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum.zero_middle
% 5.24/5.57 thf(fact_8896_prod_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups6464643781859351333omplex
% 5.24/5.57 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ one_one_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups6464643781859351333omplex
% 5.24/5.57 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.zero_middle
% 5.24/5.57 thf(fact_8897_prod_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups129246275422532515t_real
% 5.24/5.57 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ one_one_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups129246275422532515t_real
% 5.24/5.57 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.zero_middle
% 5.24/5.57 thf(fact_8898_prod_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups73079841787564623at_rat
% 5.24/5.57 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups73079841787564623at_rat
% 5.24/5.57 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.zero_middle
% 5.24/5.57 thf(fact_8899_prod_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups708209901874060359at_nat
% 5.24/5.57 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.zero_middle
% 5.24/5.57 thf(fact_8900_prod_Ozero__middle,axiom,
% 5.24/5.57 ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.24/5.57 => ( ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [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 ) ) ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P6 ) )
% 5.24/5.57 = ( groups705719431365010083at_int
% 5.24/5.57 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % prod.zero_middle
% 5.24/5.57 thf(fact_8901_gbinomial__partial__sum__poly,axiom,
% 5.24/5.57 ! [M: nat,A: complex,X: complex,Y4: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y4 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_sum_poly
% 5.24/5.57 thf(fact_8902_gbinomial__partial__sum__poly,axiom,
% 5.24/5.57 ! [M: nat,A: rat,X: rat,Y4: rat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_sum_poly
% 5.24/5.57 thf(fact_8903_gbinomial__partial__sum__poly,axiom,
% 5.24/5.57 ! [M: nat,A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y4 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_sum_poly
% 5.24/5.57 thf(fact_8904_exp__first__term,axiom,
% 5.24/5.57 ( exp_real
% 5.24/5.57 = ( ^ [X2: real] :
% 5.24/5.57 ( plus_plus_real @ one_one_real
% 5.24/5.57 @ ( suminf_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_first_term
% 5.24/5.57 thf(fact_8905_exp__first__term,axiom,
% 5.24/5.57 ( exp_complex
% 5.24/5.57 = ( ^ [X2: complex] :
% 5.24/5.57 ( plus_plus_complex @ one_one_complex
% 5.24/5.57 @ ( suminf_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N2 ) ) ) @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_first_term
% 5.24/5.57 thf(fact_8906_root__polyfun,axiom,
% 5.24/5.57 ! [N: nat,Z2: int,A: int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( ( power_power_int @ Z2 @ N )
% 5.24/5.57 = A )
% 5.24/5.57 = ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( if_int @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I4 = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_polyfun
% 5.24/5.57 thf(fact_8907_root__polyfun,axiom,
% 5.24/5.57 ! [N: nat,Z2: complex,A: complex] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( ( power_power_complex @ Z2 @ N )
% 5.24/5.57 = A )
% 5.24/5.57 = ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( if_complex @ ( I4 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I4 = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_polyfun
% 5.24/5.57 thf(fact_8908_root__polyfun,axiom,
% 5.24/5.57 ! [N: nat,Z2: rat,A: rat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( ( power_power_rat @ Z2 @ N )
% 5.24/5.57 = A )
% 5.24/5.57 = ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( if_rat @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I4 = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_rat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_polyfun
% 5.24/5.57 thf(fact_8909_root__polyfun,axiom,
% 5.24/5.57 ! [N: nat,Z2: code_integer,A: code_integer] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( ( power_8256067586552552935nteger @ Z2 @ N )
% 5.24/5.57 = A )
% 5.24/5.57 = ( ( groups7501900531339628137nteger
% 5.24/5.57 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I4 = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_z3403309356797280102nteger ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_polyfun
% 5.24/5.57 thf(fact_8910_root__polyfun,axiom,
% 5.24/5.57 ! [N: nat,Z2: real,A: real] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( ( power_power_real @ Z2 @ N )
% 5.24/5.57 = A )
% 5.24/5.57 = ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( if_real @ ( I4 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I4 = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z2 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_polyfun
% 5.24/5.57 thf(fact_8911_sum__gp0,axiom,
% 5.24/5.57 ! [X: complex,N: nat] :
% 5.24/5.57 ( ( ( X = one_one_complex )
% 5.24/5.57 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.24/5.57 & ( ( X != one_one_complex )
% 5.24/5.57 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp0
% 5.24/5.57 thf(fact_8912_sum__gp0,axiom,
% 5.24/5.57 ! [X: rat,N: nat] :
% 5.24/5.57 ( ( ( X = one_one_rat )
% 5.24/5.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.24/5.57 & ( ( X != one_one_rat )
% 5.24/5.57 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp0
% 5.24/5.57 thf(fact_8913_sum__gp0,axiom,
% 5.24/5.57 ! [X: real,N: nat] :
% 5.24/5.57 ( ( ( X = one_one_real )
% 5.24/5.57 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.24/5.57 & ( ( X != one_one_real )
% 5.24/5.57 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sum_gp0
% 5.24/5.57 thf(fact_8914_choose__alternating__linear__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( N != one_one_nat )
% 5.24/5.57 => ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ I4 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_linear_sum
% 5.24/5.57 thf(fact_8915_choose__alternating__linear__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( N != one_one_nat )
% 5.24/5.57 => ( ( groups7501900531339628137nteger
% 5.24/5.57 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ I4 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_linear_sum
% 5.24/5.57 thf(fact_8916_choose__alternating__linear__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( N != one_one_nat )
% 5.24/5.57 => ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ I4 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_linear_sum
% 5.24/5.57 thf(fact_8917_choose__alternating__linear__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( N != one_one_nat )
% 5.24/5.57 => ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_rat ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_linear_sum
% 5.24/5.57 thf(fact_8918_choose__alternating__linear__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( N != one_one_nat )
% 5.24/5.57 => ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ I4 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_linear_sum
% 5.24/5.57 thf(fact_8919_gbinomial__sum__nat__pow2,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_nat_pow2
% 5.24/5.57 thf(fact_8920_gbinomial__sum__nat__pow2,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_nat_pow2
% 5.24/5.57 thf(fact_8921_gbinomial__sum__nat__pow2,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_sum_nat_pow2
% 5.24/5.57 thf(fact_8922_gbinomial__partial__sum__poly__xpos,axiom,
% 5.24/5.57 ! [M: nat,A: complex,X: complex,Y4: complex] :
% 5.24/5.57 ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y4 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_sum_poly_xpos
% 5.24/5.57 thf(fact_8923_gbinomial__partial__sum__poly__xpos,axiom,
% 5.24/5.57 ! [M: nat,A: rat,X: rat,Y4: rat] :
% 5.24/5.57 ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_sum_poly_xpos
% 5.24/5.57 thf(fact_8924_gbinomial__partial__sum__poly__xpos,axiom,
% 5.24/5.57 ! [M: nat,A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y4 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gbinomial_partial_sum_poly_xpos
% 5.24/5.57 thf(fact_8925_polyfun__diff__alt,axiom,
% 5.24/5.57 ! [N: nat,A: nat > complex,X: complex,Y4: complex] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_complex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_complex @ ( minus_minus_complex @ X @ Y4 )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y4 @ K3 ) ) @ ( power_power_complex @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff_alt
% 5.24/5.57 thf(fact_8926_polyfun__diff__alt,axiom,
% 5.24/5.57 ! [N: nat,A: nat > rat,X: rat,Y4: rat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_rat
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_rat @ ( minus_minus_rat @ X @ Y4 )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y4 @ K3 ) ) @ ( power_power_rat @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff_alt
% 5.24/5.57 thf(fact_8927_polyfun__diff__alt,axiom,
% 5.24/5.57 ! [N: nat,A: nat > int,X: int,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_int
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( minus_minus_int @ X @ Y4 )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y4 @ K3 ) ) @ ( power_power_int @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff_alt
% 5.24/5.57 thf(fact_8928_polyfun__diff__alt,axiom,
% 5.24/5.57 ! [N: nat,A: nat > real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_real @ ( minus_minus_real @ X @ Y4 )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y4 @ K3 ) ) @ ( power_power_real @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff_alt
% 5.24/5.57 thf(fact_8929_binomial__r__part__sum,axiom,
% 5.24/5.57 ! [M: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.24/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % binomial_r_part_sum
% 5.24/5.57 thf(fact_8930_choose__linear__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( groups3542108847815614940at_nat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_linear_sum
% 5.24/5.57 thf(fact_8931_exp__first__terms,axiom,
% 5.24/5.57 ! [K: nat] :
% 5.24/5.57 ( exp_real
% 5.24/5.57 = ( ^ [X2: real] :
% 5.24/5.57 ( plus_plus_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ K ) )
% 5.24/5.57 @ ( suminf_real
% 5.24/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N2 @ K ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ N2 @ K ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_first_terms
% 5.24/5.57 thf(fact_8932_exp__first__terms,axiom,
% 5.24/5.57 ! [K: nat] :
% 5.24/5.57 ( exp_complex
% 5.24/5.57 = ( ^ [X2: complex] :
% 5.24/5.57 ( plus_plus_complex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X2 @ N2 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ K ) )
% 5.24/5.57 @ ( suminf_complex
% 5.24/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N2 @ K ) ) ) @ ( power_power_complex @ X2 @ ( plus_plus_nat @ N2 @ K ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_first_terms
% 5.24/5.57 thf(fact_8933_choose__alternating__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_sum
% 5.24/5.57 thf(fact_8934_choose__alternating__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( groups7501900531339628137nteger
% 5.24/5.57 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_z3403309356797280102nteger ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_sum
% 5.24/5.57 thf(fact_8935_choose__alternating__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_sum
% 5.24/5.57 thf(fact_8936_choose__alternating__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_rat ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_sum
% 5.24/5.57 thf(fact_8937_choose__alternating__sum,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 = zero_zero_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % choose_alternating_sum
% 5.24/5.57 thf(fact_8938_polyfun__extremal__lemma,axiom,
% 5.24/5.57 ! [E: real,C: nat > complex,N: nat] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ E )
% 5.24/5.57 => ? [M8: real] :
% 5.24/5.57 ! [Z5: complex] :
% 5.24/5.57 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z5 ) )
% 5.24/5.57 => ( ord_less_eq_real
% 5.24/5.57 @ ( real_V1022390504157884413omplex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_extremal_lemma
% 5.24/5.57 thf(fact_8939_polyfun__extremal__lemma,axiom,
% 5.24/5.57 ! [E: real,C: nat > real,N: nat] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ E )
% 5.24/5.57 => ? [M8: real] :
% 5.24/5.57 ! [Z5: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z5 ) )
% 5.24/5.57 => ( ord_less_eq_real
% 5.24/5.57 @ ( real_V7735802525324610683m_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_extremal_lemma
% 5.24/5.57 thf(fact_8940_polyfun__diff,axiom,
% 5.24/5.57 ! [N: nat,A: nat > complex,X: complex,Y4: complex] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_complex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_complex @ ( minus_minus_complex @ X @ Y4 )
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( times_times_complex
% 5.24/5.57 @ ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_complex @ ( A @ I4 ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( power_power_complex @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff
% 5.24/5.57 thf(fact_8941_polyfun__diff,axiom,
% 5.24/5.57 ! [N: nat,A: nat > rat,X: rat,Y4: rat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_rat
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_rat @ ( minus_minus_rat @ X @ Y4 )
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( times_times_rat
% 5.24/5.57 @ ( groups2906978787729119204at_rat
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( power_power_rat @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff
% 5.24/5.57 thf(fact_8942_polyfun__diff,axiom,
% 5.24/5.57 ! [N: nat,A: nat > int,X: int,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_int
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( minus_minus_int @ X @ Y4 )
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( times_times_int
% 5.24/5.57 @ ( groups3539618377306564664at_int
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( power_power_int @ Y4 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( power_power_int @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff
% 5.24/5.57 thf(fact_8943_polyfun__diff,axiom,
% 5.24/5.57 ! [N: nat,A: nat > real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.24/5.57 => ( ( minus_minus_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ X @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y4 @ I4 ) )
% 5.24/5.57 @ ( set_ord_atMost_nat @ N ) ) )
% 5.24/5.57 = ( times_times_real @ ( minus_minus_real @ X @ Y4 )
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [J3: nat] :
% 5.24/5.57 ( times_times_real
% 5.24/5.57 @ ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [I4: nat] : ( times_times_real @ ( A @ I4 ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.24/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.24/5.57 @ ( power_power_real @ X @ J3 ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % polyfun_diff
% 5.24/5.57 thf(fact_8944_cos__x__cos__y,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [P4: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [N2: nat] :
% 5.24/5.57 ( if_real
% 5.24/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.24/5.57 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.24/5.57 @ ( 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 @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.24/5.57 @ zero_zero_real )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.24/5.57 @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_x_cos_y
% 5.24/5.57 thf(fact_8945_cos__x__cos__y,axiom,
% 5.24/5.57 ! [X: complex,Y4: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [P4: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [N2: nat] :
% 5.24/5.57 ( if_complex
% 5.24/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.24/5.57 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.24/5.57 @ ( 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 @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.24/5.57 @ zero_zero_complex )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.24/5.57 @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_x_cos_y
% 5.24/5.57 thf(fact_8946_sums__cos__x__plus__y,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [P4: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 ) @ ( 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 @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ P4 @ N2 ) ) ) @ zero_zero_real )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.24/5.57 @ ( cos_real @ ( plus_plus_real @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sums_cos_x_plus_y
% 5.24/5.57 thf(fact_8947_sums__cos__x__plus__y,axiom,
% 5.24/5.57 ! [X: complex,Y4: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [P4: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [N2: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 ) @ ( 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 @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ P4 @ N2 ) ) ) @ zero_zero_complex )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.24/5.57 @ ( cos_complex @ ( plus_plus_complex @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sums_cos_x_plus_y
% 5.24/5.57 thf(fact_8948_sin__x__sin__y,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [P4: nat] :
% 5.24/5.57 ( groups6591440286371151544t_real
% 5.24/5.57 @ ^ [N2: nat] :
% 5.24/5.57 ( if_real
% 5.24/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.24/5.57 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.24/5.57 @ ( 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 @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) ) @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.24/5.57 @ zero_zero_real )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.24/5.57 @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_x_sin_y
% 5.24/5.57 thf(fact_8949_sin__x__sin__y,axiom,
% 5.24/5.57 ! [X: complex,Y4: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [P4: nat] :
% 5.24/5.57 ( groups2073611262835488442omplex
% 5.24/5.57 @ ^ [N2: nat] :
% 5.24/5.57 ( if_complex
% 5.24/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.24/5.57 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.24/5.57 @ ( 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 @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) ) @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.24/5.57 @ zero_zero_complex )
% 5.24/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.24/5.57 @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_x_sin_y
% 5.24/5.57 thf(fact_8950_sinh__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) )
% 5.24/5.57 @ ( sinh_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_converges
% 5.24/5.57 thf(fact_8951_sinh__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.24/5.57 @ ( sinh_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_converges
% 5.24/5.57 thf(fact_8952_cosh__converges,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( sums_real
% 5.24/5.57 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) @ zero_zero_real )
% 5.24/5.57 @ ( cosh_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_converges
% 5.24/5.57 thf(fact_8953_cosh__converges,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( sums_complex
% 5.24/5.57 @ ^ [N2: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X @ N2 ) ) @ zero_zero_complex )
% 5.24/5.57 @ ( cosh_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_converges
% 5.24/5.57 thf(fact_8954_i__even__power,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % i_even_power
% 5.24/5.57 thf(fact_8955_log__base__10__eq1,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.57 = ( 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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_base_10_eq1
% 5.24/5.57 thf(fact_8956_arctan__def,axiom,
% 5.24/5.57 ( arctan
% 5.24/5.57 = ( ^ [Y: real] :
% 5.24/5.57 ( the_real
% 5.24/5.57 @ ^ [X2: real] :
% 5.24/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.24/5.57 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.57 & ( ( tan_real @ X2 )
% 5.24/5.57 = Y ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % arctan_def
% 5.24/5.57 thf(fact_8957_cosh__0,axiom,
% 5.24/5.57 ( ( cosh_complex @ zero_zero_complex )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_0
% 5.24/5.57 thf(fact_8958_cosh__0,axiom,
% 5.24/5.57 ( ( cosh_real @ zero_zero_real )
% 5.24/5.57 = one_one_real ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_0
% 5.24/5.57 thf(fact_8959_log__one,axiom,
% 5.24/5.57 ! [A: real] :
% 5.24/5.57 ( ( log @ A @ one_one_real )
% 5.24/5.57 = zero_zero_real ) ).
% 5.24/5.57
% 5.24/5.57 % log_one
% 5.24/5.57 thf(fact_8960_norm__ii,axiom,
% 5.24/5.57 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.24/5.57 = one_one_real ) ).
% 5.24/5.57
% 5.24/5.57 % norm_ii
% 5.24/5.57 thf(fact_8961_complex__i__mult__minus,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_i_mult_minus
% 5.24/5.57 thf(fact_8962_zero__less__log__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.24/5.57 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_less_log_cancel_iff
% 5.24/5.57 thf(fact_8963_log__less__zero__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.24/5.57 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_less_zero_cancel_iff
% 5.24/5.57 thf(fact_8964_one__less__log__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 5.24/5.57 = ( ord_less_real @ A @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_less_log_cancel_iff
% 5.24/5.57 thf(fact_8965_log__less__one__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 5.24/5.57 = ( ord_less_real @ X @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_less_one_cancel_iff
% 5.24/5.57 thf(fact_8966_log__less__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) )
% 5.24/5.57 = ( ord_less_real @ X @ Y4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_less_cancel_iff
% 5.24/5.57 thf(fact_8967_log__eq__one,axiom,
% 5.24/5.57 ! [A: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( log @ A @ A )
% 5.24/5.57 = one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_eq_one
% 5.24/5.57 thf(fact_8968_divide__numeral__i,axiom,
% 5.24/5.57 ! [Z2: complex,N: num] :
% 5.24/5.57 ( ( divide1717551699836669952omplex @ Z2 @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.24/5.57 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z2 ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % divide_numeral_i
% 5.24/5.57 thf(fact_8969_divide__i,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.24/5.57 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % divide_i
% 5.24/5.57 thf(fact_8970_i__squared,axiom,
% 5.24/5.57 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % i_squared
% 5.24/5.57 thf(fact_8971_log__le__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_le_cancel_iff
% 5.24/5.57 thf(fact_8972_log__le__one__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.24/5.57 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_le_one_cancel_iff
% 5.24/5.57 thf(fact_8973_one__le__log__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.24/5.57 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_le_log_cancel_iff
% 5.24/5.57 thf(fact_8974_log__le__zero__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.24/5.57 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_le_zero_cancel_iff
% 5.24/5.57 thf(fact_8975_zero__le__log__cancel__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.24/5.57 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_le_log_cancel_iff
% 5.24/5.57 thf(fact_8976_log__pow__cancel,axiom,
% 5.24/5.57 ! [A: real,B: nat] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.24/5.57 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_pow_cancel
% 5.24/5.57 thf(fact_8977_power2__i,axiom,
% 5.24/5.57 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % power2_i
% 5.24/5.57 thf(fact_8978_tanh__def,axiom,
% 5.24/5.57 ( tanh_complex
% 5.24/5.57 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ X2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tanh_def
% 5.24/5.57 thf(fact_8979_tanh__def,axiom,
% 5.24/5.57 ( tanh_real
% 5.24/5.57 = ( ^ [X2: real] : ( divide_divide_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tanh_def
% 5.24/5.57 thf(fact_8980_sinh__plus__cosh,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( plus_plus_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) )
% 5.24/5.57 = ( exp_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_plus_cosh
% 5.24/5.57 thf(fact_8981_sinh__plus__cosh,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( plus_plus_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) )
% 5.24/5.57 = ( exp_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_plus_cosh
% 5.24/5.57 thf(fact_8982_cosh__plus__sinh,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( plus_plus_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ X ) )
% 5.24/5.57 = ( exp_complex @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_plus_sinh
% 5.24/5.57 thf(fact_8983_cosh__plus__sinh,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( plus_plus_real @ ( cosh_real @ X ) @ ( sinh_real @ X ) )
% 5.24/5.57 = ( exp_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_plus_sinh
% 5.24/5.57 thf(fact_8984_cosh__add,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( cosh_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.57 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_add
% 5.24/5.57 thf(fact_8985_sinh__add,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( sinh_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.57 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_add
% 5.24/5.57 thf(fact_8986_cosh__diff,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( cosh_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.57 = ( minus_minus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_diff
% 5.24/5.57 thf(fact_8987_sinh__diff,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( sinh_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.24/5.57 = ( minus_minus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_diff
% 5.24/5.57 thf(fact_8988_complex__i__not__one,axiom,
% 5.24/5.57 imaginary_unit != one_one_complex ).
% 5.24/5.57
% 5.24/5.57 % complex_i_not_one
% 5.24/5.57 thf(fact_8989_cosh__real__ge__1,axiom,
% 5.24/5.57 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_real_ge_1
% 5.24/5.57 thf(fact_8990_sinh__double,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.57 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X ) ) @ ( cosh_complex @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_double
% 5.24/5.57 thf(fact_8991_sinh__double,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.57 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X ) ) @ ( cosh_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_double
% 5.24/5.57 thf(fact_8992_i__times__eq__iff,axiom,
% 5.24/5.57 ! [W2: complex,Z2: complex] :
% 5.24/5.57 ( ( ( times_times_complex @ imaginary_unit @ W2 )
% 5.24/5.57 = Z2 )
% 5.24/5.57 = ( W2
% 5.24/5.57 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % i_times_eq_iff
% 5.24/5.57 thf(fact_8993_log__ln,axiom,
% 5.24/5.57 ( ln_ln_real
% 5.24/5.57 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_ln
% 5.24/5.57 thf(fact_8994_cosh__square__eq,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_square_eq
% 5.24/5.57 thf(fact_8995_cosh__square__eq,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_square_eq
% 5.24/5.57 thf(fact_8996_sinh__square__eq,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_square_eq
% 5.24/5.57 thf(fact_8997_sinh__square__eq,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_square_eq
% 5.24/5.57 thf(fact_8998_hyperbolic__pythagoras,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % hyperbolic_pythagoras
% 5.24/5.57 thf(fact_8999_hyperbolic__pythagoras,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = one_one_real ) ).
% 5.24/5.57
% 5.24/5.57 % hyperbolic_pythagoras
% 5.24/5.57 thf(fact_9000_imaginary__unit_Ocode,axiom,
% 5.24/5.57 ( imaginary_unit
% 5.24/5.57 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % imaginary_unit.code
% 5.24/5.57 thf(fact_9001_Complex__eq__i,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( ( complex2 @ X @ Y4 )
% 5.24/5.57 = imaginary_unit )
% 5.24/5.57 = ( ( X = zero_zero_real )
% 5.24/5.57 & ( Y4 = one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Complex_eq_i
% 5.24/5.57 thf(fact_9002_cosh__double,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.57 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_double
% 5.24/5.57 thf(fact_9003_cosh__double,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.24/5.57 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_double
% 5.24/5.57 thf(fact_9004_i__mult__Complex,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.24/5.57 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % i_mult_Complex
% 5.24/5.57 thf(fact_9005_Complex__mult__i,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.24/5.57 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % Complex_mult_i
% 5.24/5.57 thf(fact_9006_log__base__change,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( log @ B @ X )
% 5.24/5.57 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_base_change
% 5.24/5.57 thf(fact_9007_less__log__of__power,axiom,
% 5.24/5.57 ! [B: real,N: nat,M: real] :
% 5.24/5.57 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % less_log_of_power
% 5.24/5.57 thf(fact_9008_log__of__power__eq,axiom,
% 5.24/5.57 ! [M: nat,B: real,N: nat] :
% 5.24/5.57 ( ( ( semiri5074537144036343181t_real @ M )
% 5.24/5.57 = ( power_power_real @ B @ N ) )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( semiri5074537144036343181t_real @ N )
% 5.24/5.57 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_of_power_eq
% 5.24/5.57 thf(fact_9009_log__mult,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ( log @ A @ ( times_times_real @ X @ Y4 ) )
% 5.24/5.57 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_mult
% 5.24/5.57 thf(fact_9010_log__divide,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ( log @ A @ ( divide_divide_real @ X @ Y4 ) )
% 5.24/5.57 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_divide
% 5.24/5.57 thf(fact_9011_le__log__of__power,axiom,
% 5.24/5.57 ! [B: real,N: nat,M: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_log_of_power
% 5.24/5.57 thf(fact_9012_log__nat__power,axiom,
% 5.24/5.57 ! [X: real,B: real,N: nat] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 5.24/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_nat_power
% 5.24/5.57 thf(fact_9013_log__inverse,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 5.24/5.57 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_inverse
% 5.24/5.57 thf(fact_9014_log2__of__power__eq,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( M
% 5.24/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( semiri5074537144036343181t_real @ N )
% 5.24/5.57 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log2_of_power_eq
% 5.24/5.57 thf(fact_9015_log__of__power__less,axiom,
% 5.24/5.57 ! [M: nat,B: real,N: nat] :
% 5.24/5.57 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.57 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_of_power_less
% 5.24/5.57 thf(fact_9016_log__eq__div__ln__mult__log,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( B != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( log @ A @ X )
% 5.24/5.57 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_eq_div_ln_mult_log
% 5.24/5.57 thf(fact_9017_log__of__power__le,axiom,
% 5.24/5.57 ! [M: nat,B: real,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.57 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_of_power_le
% 5.24/5.57 thf(fact_9018_tanh__add,axiom,
% 5.24/5.57 ! [X: complex,Y4: complex] :
% 5.24/5.57 ( ( ( cosh_complex @ X )
% 5.24/5.57 != zero_zero_complex )
% 5.24/5.57 => ( ( ( cosh_complex @ Y4 )
% 5.24/5.57 != zero_zero_complex )
% 5.24/5.57 => ( ( tanh_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.57 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y4 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tanh_add
% 5.24/5.57 thf(fact_9019_tanh__add,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( ( cosh_real @ X )
% 5.24/5.57 != zero_zero_real )
% 5.24/5.57 => ( ( ( cosh_real @ Y4 )
% 5.24/5.57 != zero_zero_real )
% 5.24/5.57 => ( ( tanh_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.24/5.57 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X ) @ ( tanh_real @ Y4 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X ) @ ( tanh_real @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % tanh_add
% 5.24/5.57 thf(fact_9020_less__log2__of__power,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.24/5.57 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % less_log2_of_power
% 5.24/5.57 thf(fact_9021_le__log2__of__power,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.24/5.57 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_log2_of_power
% 5.24/5.57 thf(fact_9022_cosh__field__def,axiom,
% 5.24/5.57 ( cosh_real
% 5.24/5.57 = ( ^ [Z4: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z4 ) @ ( exp_real @ ( uminus_uminus_real @ Z4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_field_def
% 5.24/5.57 thf(fact_9023_cosh__field__def,axiom,
% 5.24/5.57 ( cosh_complex
% 5.24/5.57 = ( ^ [Z4: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z4 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z4 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_field_def
% 5.24/5.57 thf(fact_9024_sinh__field__def,axiom,
% 5.24/5.57 ( sinh_real
% 5.24/5.57 = ( ^ [Z4: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z4 ) @ ( exp_real @ ( uminus_uminus_real @ Z4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_field_def
% 5.24/5.57 thf(fact_9025_sinh__field__def,axiom,
% 5.24/5.57 ( sinh_complex
% 5.24/5.57 = ( ^ [Z4: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z4 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z4 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_field_def
% 5.24/5.57 thf(fact_9026_log2__of__power__less,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.57 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log2_of_power_less
% 5.24/5.57 thf(fact_9027_cosh__zero__iff,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ( cosh_real @ X )
% 5.24/5.57 = zero_zero_real )
% 5.24/5.57 = ( ( power_power_real @ ( exp_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_zero_iff
% 5.24/5.57 thf(fact_9028_cosh__zero__iff,axiom,
% 5.24/5.57 ! [X: complex] :
% 5.24/5.57 ( ( ( cosh_complex @ X )
% 5.24/5.57 = zero_zero_complex )
% 5.24/5.57 = ( ( power_power_complex @ ( exp_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_zero_iff
% 5.24/5.57 thf(fact_9029_pi__half,axiom,
% 5.24/5.57 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( the_real
% 5.24/5.57 @ ^ [X2: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.24/5.57 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.57 & ( ( cos_real @ X2 )
% 5.24/5.57 = zero_zero_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pi_half
% 5.24/5.57 thf(fact_9030_pi__def,axiom,
% 5.24/5.57 ( pi
% 5.24/5.57 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.24/5.57 @ ( the_real
% 5.24/5.57 @ ^ [X2: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.24/5.57 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.24/5.57 & ( ( cos_real @ X2 )
% 5.24/5.57 = zero_zero_real ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % pi_def
% 5.24/5.57 thf(fact_9031_cosh__def,axiom,
% 5.24/5.57 ( cosh_real
% 5.24/5.57 = ( ^ [X2: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_def
% 5.24/5.57 thf(fact_9032_cosh__def,axiom,
% 5.24/5.57 ( cosh_complex
% 5.24/5.57 = ( ^ [X2: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_def
% 5.24/5.57 thf(fact_9033_cosh__ln__real,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.24/5.57 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cosh_ln_real
% 5.24/5.57 thf(fact_9034_log2__of__power__le,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.57 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log2_of_power_le
% 5.24/5.57 thf(fact_9035_sinh__def,axiom,
% 5.24/5.57 ( sinh_real
% 5.24/5.57 = ( ^ [X2: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_def
% 5.24/5.57 thf(fact_9036_sinh__def,axiom,
% 5.24/5.57 ( sinh_complex
% 5.24/5.57 = ( ^ [X2: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_def
% 5.24/5.57 thf(fact_9037_log__base__10__eq2,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.24/5.57 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_base_10_eq2
% 5.24/5.57 thf(fact_9038_sinh__ln__real,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.24/5.57 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sinh_ln_real
% 5.24/5.57 thf(fact_9039_arcsin__def,axiom,
% 5.24/5.57 ( arcsin
% 5.24/5.57 = ( ^ [Y: real] :
% 5.24/5.57 ( the_real
% 5.24/5.57 @ ^ [X2: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.24/5.57 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.57 & ( ( sin_real @ X2 )
% 5.24/5.57 = Y ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % arcsin_def
% 5.24/5.57 thf(fact_9040_Arg__minus__ii,axiom,
% 5.24/5.57 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.24/5.57 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Arg_minus_ii
% 5.24/5.57 thf(fact_9041_ceiling__log__nat__eq__powr__iff,axiom,
% 5.24/5.57 ! [B: nat,K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.24/5.57 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.24/5.57 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_log_nat_eq_powr_iff
% 5.24/5.57 thf(fact_9042_Arg__ii,axiom,
% 5.24/5.57 ( ( arg @ imaginary_unit )
% 5.24/5.57 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Arg_ii
% 5.24/5.57 thf(fact_9043_ceiling__log__nat__eq__if,axiom,
% 5.24/5.57 ! [B: nat,N: nat,K: nat] :
% 5.24/5.57 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.24/5.57 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.24/5.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.24/5.57 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_log_nat_eq_if
% 5.24/5.57 thf(fact_9044_ceiling__log2__div2,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.57 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_log2_div2
% 5.24/5.57 thf(fact_9045_ceiling__numeral,axiom,
% 5.24/5.57 ! [V: num] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.24/5.57 = ( numeral_numeral_int @ V ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_numeral
% 5.24/5.57 thf(fact_9046_ceiling__numeral,axiom,
% 5.24/5.57 ! [V: num] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.24/5.57 = ( numeral_numeral_int @ V ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_numeral
% 5.24/5.57 thf(fact_9047_ceiling__one,axiom,
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.24/5.57 = one_one_int ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_one
% 5.24/5.57 thf(fact_9048_ceiling__one,axiom,
% 5.24/5.57 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.24/5.57 = one_one_int ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_one
% 5.24/5.57 thf(fact_9049_ceiling__add__of__int,axiom,
% 5.24/5.57 ! [X: rat,Z2: int] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_add_of_int
% 5.24/5.57 thf(fact_9050_ceiling__add__of__int,axiom,
% 5.24/5.57 ! [X: real,Z2: int] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_add_of_int
% 5.24/5.57 thf(fact_9051_ceiling__le__zero,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.24/5.57 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_zero
% 5.24/5.57 thf(fact_9052_ceiling__le__zero,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_zero
% 5.24/5.57 thf(fact_9053_zero__less__ceiling,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_less_ceiling
% 5.24/5.57 thf(fact_9054_zero__less__ceiling,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_less_ceiling
% 5.24/5.57 thf(fact_9055_ceiling__le__numeral,axiom,
% 5.24/5.57 ! [X: real,V: num] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_numeral
% 5.24/5.57 thf(fact_9056_ceiling__le__numeral,axiom,
% 5.24/5.57 ! [X: rat,V: num] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_numeral
% 5.24/5.57 thf(fact_9057_ceiling__less__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.24/5.57 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_one
% 5.24/5.57 thf(fact_9058_ceiling__less__one,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_one
% 5.24/5.57 thf(fact_9059_one__le__ceiling,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_le_ceiling
% 5.24/5.57 thf(fact_9060_one__le__ceiling,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_le_ceiling
% 5.24/5.57 thf(fact_9061_numeral__less__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: real] :
% 5.24/5.57 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_less_ceiling
% 5.24/5.57 thf(fact_9062_numeral__less__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: rat] :
% 5.24/5.57 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_less_ceiling
% 5.24/5.57 thf(fact_9063_ceiling__le__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.24/5.57 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_one
% 5.24/5.57 thf(fact_9064_ceiling__le__one,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_one
% 5.24/5.57 thf(fact_9065_one__less__ceiling,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_less_ceiling
% 5.24/5.57 thf(fact_9066_one__less__ceiling,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ one_one_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_less_ceiling
% 5.24/5.57 thf(fact_9067_ceiling__add__numeral,axiom,
% 5.24/5.57 ! [X: real,V: num] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_add_numeral
% 5.24/5.57 thf(fact_9068_ceiling__add__numeral,axiom,
% 5.24/5.57 ! [X: rat,V: num] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.57 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_add_numeral
% 5.24/5.57 thf(fact_9069_ceiling__neg__numeral,axiom,
% 5.24/5.57 ! [V: num] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_neg_numeral
% 5.24/5.57 thf(fact_9070_ceiling__neg__numeral,axiom,
% 5.24/5.57 ! [V: num] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_neg_numeral
% 5.24/5.57 thf(fact_9071_ceiling__add__one,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 5.24/5.57 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_add_one
% 5.24/5.57 thf(fact_9072_ceiling__add__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 5.24/5.57 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_add_one
% 5.24/5.57 thf(fact_9073_ceiling__diff__numeral,axiom,
% 5.24/5.57 ! [X: real,V: num] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.24/5.57 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_diff_numeral
% 5.24/5.57 thf(fact_9074_ceiling__diff__numeral,axiom,
% 5.24/5.57 ! [X: rat,V: num] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.24/5.57 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_diff_numeral
% 5.24/5.57 thf(fact_9075_ceiling__diff__one,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.24/5.57 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_diff_one
% 5.24/5.57 thf(fact_9076_ceiling__diff__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.24/5.57 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_diff_one
% 5.24/5.57 thf(fact_9077_ceiling__numeral__power,axiom,
% 5.24/5.57 ! [X: num,N: nat] :
% 5.24/5.57 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.24/5.57 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_numeral_power
% 5.24/5.57 thf(fact_9078_ceiling__numeral__power,axiom,
% 5.24/5.57 ! [X: num,N: nat] :
% 5.24/5.57 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.24/5.57 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_numeral_power
% 5.24/5.57 thf(fact_9079_ceiling__less__zero,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_zero
% 5.24/5.57 thf(fact_9080_ceiling__less__zero,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_zero
% 5.24/5.57 thf(fact_9081_zero__le__ceiling,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_le_ceiling
% 5.24/5.57 thf(fact_9082_zero__le__ceiling,axiom,
% 5.24/5.57 ! [X: rat] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_le_ceiling
% 5.24/5.57 thf(fact_9083_ceiling__less__numeral,axiom,
% 5.24/5.57 ! [X: real,V: num] :
% 5.24/5.57 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_numeral
% 5.24/5.57 thf(fact_9084_ceiling__less__numeral,axiom,
% 5.24/5.57 ! [X: rat,V: num] :
% 5.24/5.57 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_numeral
% 5.24/5.57 thf(fact_9085_numeral__le__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: real] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_le_ceiling
% 5.24/5.57 thf(fact_9086_numeral__le__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: rat] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_le_ceiling
% 5.24/5.57 thf(fact_9087_ceiling__le__neg__numeral,axiom,
% 5.24/5.57 ! [X: real,V: num] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_neg_numeral
% 5.24/5.57 thf(fact_9088_ceiling__le__neg__numeral,axiom,
% 5.24/5.57 ! [X: rat,V: num] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_le_neg_numeral
% 5.24/5.57 thf(fact_9089_neg__numeral__less__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: real] :
% 5.24/5.57 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_numeral_less_ceiling
% 5.24/5.57 thf(fact_9090_neg__numeral__less__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: rat] :
% 5.24/5.57 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_numeral_less_ceiling
% 5.24/5.57 thf(fact_9091_ceiling__less__neg__numeral,axiom,
% 5.24/5.57 ! [X: real,V: num] :
% 5.24/5.57 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_neg_numeral
% 5.24/5.57 thf(fact_9092_ceiling__less__neg__numeral,axiom,
% 5.24/5.57 ! [X: rat,V: num] :
% 5.24/5.57 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.24/5.57 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_less_neg_numeral
% 5.24/5.57 thf(fact_9093_neg__numeral__le__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: real] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.24/5.57 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_numeral_le_ceiling
% 5.24/5.57 thf(fact_9094_neg__numeral__le__ceiling,axiom,
% 5.24/5.57 ! [V: num,X: rat] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.24/5.57 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % neg_numeral_le_ceiling
% 5.24/5.57 thf(fact_9095_ceiling__mono,axiom,
% 5.24/5.57 ! [Y4: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ Y4 @ X )
% 5.24/5.57 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y4 ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_mono
% 5.24/5.57 thf(fact_9096_ceiling__mono,axiom,
% 5.24/5.57 ! [Y4: rat,X: rat] :
% 5.24/5.57 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.24/5.57 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y4 ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_mono
% 5.24/5.57 thf(fact_9097_le__of__int__ceiling,axiom,
% 5.24/5.57 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_of_int_ceiling
% 5.24/5.57 thf(fact_9098_le__of__int__ceiling,axiom,
% 5.24/5.57 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_of_int_ceiling
% 5.24/5.57 thf(fact_9099_cis__minus__pi__half,axiom,
% 5.24/5.57 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.24/5.57
% 5.24/5.57 % cis_minus_pi_half
% 5.24/5.57 thf(fact_9100_ceiling__log__eq__powr__iff,axiom,
% 5.24/5.57 ! [X: real,B: real,K: nat] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.24/5.57 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.24/5.57 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.24/5.57 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ceiling_log_eq_powr_iff
% 5.24/5.57 thf(fact_9101_floor__log__nat__eq__powr__iff,axiom,
% 5.24/5.57 ! [B: nat,K: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.24/5.57 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.24/5.57 = ( semiri1314217659103216013at_int @ N ) )
% 5.24/5.57 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.24/5.57 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_log_nat_eq_powr_iff
% 5.24/5.57 thf(fact_9102_floor__log__nat__eq__if,axiom,
% 5.24/5.57 ! [B: nat,N: nat,K: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.24/5.57 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.24/5.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.24/5.57 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.24/5.57 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_log_nat_eq_if
% 5.24/5.57 thf(fact_9103_even__set__encode__iff,axiom,
% 5.24/5.57 ! [A2: set_nat] :
% 5.24/5.57 ( ( finite_finite_nat @ A2 )
% 5.24/5.57 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.24/5.57 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % even_set_encode_iff
% 5.24/5.57 thf(fact_9104_powr__less__cancel__iff,axiom,
% 5.24/5.57 ! [X: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.24/5.57 = ( ord_less_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_less_cancel_iff
% 5.24/5.57 thf(fact_9105_norm__cis,axiom,
% 5.24/5.57 ! [A: real] :
% 5.24/5.57 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.24/5.57 = one_one_real ) ).
% 5.24/5.57
% 5.24/5.57 % norm_cis
% 5.24/5.57 thf(fact_9106_cis__zero,axiom,
% 5.24/5.57 ( ( cis @ zero_zero_real )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % cis_zero
% 5.24/5.57 thf(fact_9107_set__encode__empty,axiom,
% 5.24/5.57 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.24/5.57 = zero_zero_nat ) ).
% 5.24/5.57
% 5.24/5.57 % set_encode_empty
% 5.24/5.57 thf(fact_9108_powr__eq__one__iff,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ A )
% 5.24/5.57 => ( ( ( powr_real @ A @ X )
% 5.24/5.57 = one_one_real )
% 5.24/5.57 = ( X = zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_eq_one_iff
% 5.24/5.57 thf(fact_9109_powr__one__gt__zero__iff,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ( powr_real @ X @ one_one_real )
% 5.24/5.57 = X )
% 5.24/5.57 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_one_gt_zero_iff
% 5.24/5.57 thf(fact_9110_powr__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( powr_real @ X @ one_one_real )
% 5.24/5.57 = X ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_one
% 5.24/5.57 thf(fact_9111_powr__le__cancel__iff,axiom,
% 5.24/5.57 ! [X: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.24/5.57 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_le_cancel_iff
% 5.24/5.57 thf(fact_9112_numeral__powr__numeral__real,axiom,
% 5.24/5.57 ! [M: num,N: num] :
% 5.24/5.57 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.24/5.57 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_powr_numeral_real
% 5.24/5.57 thf(fact_9113_cis__pi,axiom,
% 5.24/5.57 ( ( cis @ pi )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % cis_pi
% 5.24/5.57 thf(fact_9114_log__powr__cancel,axiom,
% 5.24/5.57 ! [A: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( log @ A @ ( powr_real @ A @ Y4 ) )
% 5.24/5.57 = Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_powr_cancel
% 5.24/5.57 thf(fact_9115_powr__log__cancel,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 5.24/5.57 = X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_log_cancel
% 5.24/5.57 thf(fact_9116_powr__numeral,axiom,
% 5.24/5.57 ! [X: real,N: num] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 5.24/5.57 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_numeral
% 5.24/5.57 thf(fact_9117_cis__pi__half,axiom,
% 5.24/5.57 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = imaginary_unit ) ).
% 5.24/5.57
% 5.24/5.57 % cis_pi_half
% 5.24/5.57 thf(fact_9118_floor__one__divide__eq__div__numeral,axiom,
% 5.24/5.57 ! [B: num] :
% 5.24/5.57 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.24/5.57 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_one_divide_eq_div_numeral
% 5.24/5.57 thf(fact_9119_cis__2pi,axiom,
% 5.24/5.57 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % cis_2pi
% 5.24/5.57 thf(fact_9120_square__powr__half,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = ( abs_abs_real @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % square_powr_half
% 5.24/5.57 thf(fact_9121_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.24/5.57 ! [B: num] :
% 5.24/5.57 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.24/5.57 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_minus_one_divide_eq_div_numeral
% 5.24/5.57 thf(fact_9122_powr__powr,axiom,
% 5.24/5.57 ! [X: real,A: real,B: real] :
% 5.24/5.57 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.24/5.57 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_powr
% 5.24/5.57 thf(fact_9123_powr__less__mono,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( ord_less_real @ A @ B )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_less_mono
% 5.24/5.57 thf(fact_9124_powr__less__cancel,axiom,
% 5.24/5.57 ! [X: real,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ord_less_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_less_cancel
% 5.24/5.57 thf(fact_9125_powr__mono,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.24/5.57 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_mono
% 5.24/5.57 thf(fact_9126_cis__mult,axiom,
% 5.24/5.57 ! [A: real,B: real] :
% 5.24/5.57 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.24/5.57 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cis_mult
% 5.24/5.57 thf(fact_9127_gr__one__powr,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % gr_one_powr
% 5.24/5.57 thf(fact_9128_powr__inj,axiom,
% 5.24/5.57 ! [A: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( A != one_one_real )
% 5.24/5.57 => ( ( ( powr_real @ A @ X )
% 5.24/5.57 = ( powr_real @ A @ Y4 ) )
% 5.24/5.57 = ( X = Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_inj
% 5.24/5.57 thf(fact_9129_ge__one__powr__ge__zero,axiom,
% 5.24/5.57 ! [X: real,A: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ge_one_powr_ge_zero
% 5.24/5.57 thf(fact_9130_powr__mono__both,axiom,
% 5.24/5.57 ! [A: real,B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ A @ B )
% 5.24/5.57 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.57 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_mono_both
% 5.24/5.57 thf(fact_9131_powr__le1,axiom,
% 5.24/5.57 ! [A: real,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.57 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_le1
% 5.24/5.57 thf(fact_9132_powr__mult,axiom,
% 5.24/5.57 ! [X: real,Y4: real,A: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ( powr_real @ ( times_times_real @ X @ Y4 ) @ A )
% 5.24/5.57 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_mult
% 5.24/5.57 thf(fact_9133_divide__powr__uminus,axiom,
% 5.24/5.57 ! [A: real,B: real,C: real] :
% 5.24/5.57 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.24/5.57 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % divide_powr_uminus
% 5.24/5.57 thf(fact_9134_ln__powr,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( X != zero_zero_real )
% 5.24/5.57 => ( ( ln_ln_real @ ( powr_real @ X @ Y4 ) )
% 5.24/5.57 = ( times_times_real @ Y4 @ ( ln_ln_real @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ln_powr
% 5.24/5.57 thf(fact_9135_log__powr,axiom,
% 5.24/5.57 ! [X: real,B: real,Y4: real] :
% 5.24/5.57 ( ( X != zero_zero_real )
% 5.24/5.57 => ( ( log @ B @ ( powr_real @ X @ Y4 ) )
% 5.24/5.57 = ( times_times_real @ Y4 @ ( log @ B @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_powr
% 5.24/5.57 thf(fact_9136_floor__log__eq__powr__iff,axiom,
% 5.24/5.57 ! [X: real,B: real,K: int] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.24/5.57 = K )
% 5.24/5.57 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.24/5.57 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_log_eq_powr_iff
% 5.24/5.57 thf(fact_9137_powr__less__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ ( powr_real @ B @ Y4 ) @ X )
% 5.24/5.57 = ( ord_less_real @ Y4 @ ( log @ B @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_less_iff
% 5.24/5.57 thf(fact_9138_less__powr__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y4 ) )
% 5.24/5.57 = ( ord_less_real @ ( log @ B @ X ) @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % less_powr_iff
% 5.24/5.57 thf(fact_9139_log__less__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ ( log @ B @ X ) @ Y4 )
% 5.24/5.57 = ( ord_less_real @ X @ ( powr_real @ B @ Y4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_less_iff
% 5.24/5.57 thf(fact_9140_less__log__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ Y4 @ ( log @ B @ X ) )
% 5.24/5.57 = ( ord_less_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % less_log_iff
% 5.24/5.57 thf(fact_9141_real__of__int__floor__add__one__gt,axiom,
% 5.24/5.57 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_of_int_floor_add_one_gt
% 5.24/5.57 thf(fact_9142_floor__eq,axiom,
% 5.24/5.57 ! [N: int,X: real] :
% 5.24/5.57 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.24/5.57 => ( ( archim6058952711729229775r_real @ X )
% 5.24/5.57 = N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_eq
% 5.24/5.57 thf(fact_9143_real__of__int__floor__add__one__ge,axiom,
% 5.24/5.57 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_of_int_floor_add_one_ge
% 5.24/5.57 thf(fact_9144_real__of__int__floor__gt__diff__one,axiom,
% 5.24/5.57 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_of_int_floor_gt_diff_one
% 5.24/5.57 thf(fact_9145_real__of__int__floor__ge__diff__one,axiom,
% 5.24/5.57 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_of_int_floor_ge_diff_one
% 5.24/5.57 thf(fact_9146_DeMoivre,axiom,
% 5.24/5.57 ! [A: real,N: nat] :
% 5.24/5.57 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.24/5.57 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % DeMoivre
% 5.24/5.57 thf(fact_9147_powr__neg__one,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.24/5.57 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_neg_one
% 5.24/5.57 thf(fact_9148_powr__mult__base,axiom,
% 5.24/5.57 ! [X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( times_times_real @ X @ ( powr_real @ X @ Y4 ) )
% 5.24/5.57 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_mult_base
% 5.24/5.57 thf(fact_9149_powr__le__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y4 ) @ X )
% 5.24/5.57 = ( ord_less_eq_real @ Y4 @ ( log @ B @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_le_iff
% 5.24/5.57 thf(fact_9150_le__powr__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_powr_iff
% 5.24/5.57 thf(fact_9151_log__le__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y4 )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_le_iff
% 5.24/5.57 thf(fact_9152_le__log__iff,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ Y4 @ ( log @ B @ X ) )
% 5.24/5.57 = ( ord_less_eq_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_log_iff
% 5.24/5.57 thf(fact_9153_floor__eq2,axiom,
% 5.24/5.57 ! [N: int,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.24/5.57 => ( ( archim6058952711729229775r_real @ X )
% 5.24/5.57 = N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_eq2
% 5.24/5.57 thf(fact_9154_ln__powr__bound,axiom,
% 5.24/5.57 ! [X: real,A: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ln_powr_bound
% 5.24/5.57 thf(fact_9155_ln__powr__bound2,axiom,
% 5.24/5.57 ! [X: real,A: real] :
% 5.24/5.57 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ln_powr_bound2
% 5.24/5.57 thf(fact_9156_log__add__eq__powr,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( B != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y4 )
% 5.24/5.57 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_add_eq_powr
% 5.24/5.57 thf(fact_9157_add__log__eq__powr,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( B != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( plus_plus_real @ Y4 @ ( log @ B @ X ) )
% 5.24/5.57 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % add_log_eq_powr
% 5.24/5.57 thf(fact_9158_minus__log__eq__powr,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( B != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( minus_minus_real @ Y4 @ ( log @ B @ X ) )
% 5.24/5.57 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % minus_log_eq_powr
% 5.24/5.57 thf(fact_9159_log__minus__eq__powr,axiom,
% 5.24/5.57 ! [B: real,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( B != one_one_real )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y4 )
% 5.24/5.57 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_minus_eq_powr
% 5.24/5.57 thf(fact_9160_powr__half__sqrt,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.57 = ( sqrt @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_half_sqrt
% 5.24/5.57 thf(fact_9161_powr__neg__numeral,axiom,
% 5.24/5.57 ! [X: real,N: num] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.24/5.57 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_neg_numeral
% 5.24/5.57 thf(fact_9162_set__encode__def,axiom,
% 5.24/5.57 ( nat_set_encode
% 5.24/5.57 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % set_encode_def
% 5.24/5.57 thf(fact_9163_floor__log2__div2,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.57 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_log2_div2
% 5.24/5.57 thf(fact_9164_bij__betw__roots__unity,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( bij_betw_nat_complex
% 5.24/5.57 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.24/5.57 @ ( set_ord_lessThan_nat @ N )
% 5.24/5.57 @ ( collect_complex
% 5.24/5.57 @ ^ [Z4: complex] :
% 5.24/5.57 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.57 = one_one_complex ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bij_betw_roots_unity
% 5.24/5.57 thf(fact_9165_exp__pi__i_H,axiom,
% 5.24/5.57 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_pi_i'
% 5.24/5.57 thf(fact_9166_exp__pi__i,axiom,
% 5.24/5.57 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.24/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % exp_pi_i
% 5.24/5.57 thf(fact_9167_exp__two__pi__i_H,axiom,
% 5.24/5.57 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % exp_two_pi_i'
% 5.24/5.57 thf(fact_9168_exp__two__pi__i,axiom,
% 5.24/5.57 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % exp_two_pi_i
% 5.24/5.57 thf(fact_9169_complex__exp__exists,axiom,
% 5.24/5.57 ! [Z2: complex] :
% 5.24/5.57 ? [A3: complex,R3: real] :
% 5.24/5.57 ( Z2
% 5.24/5.57 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_exp_exists
% 5.24/5.57 thf(fact_9170_complex__of__real__mult__Complex,axiom,
% 5.24/5.57 ! [R2: real,X: real,Y4: real] :
% 5.24/5.57 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y4 ) )
% 5.24/5.57 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_of_real_mult_Complex
% 5.24/5.57 thf(fact_9171_Complex__mult__complex__of__real,axiom,
% 5.24/5.57 ! [X: real,Y4: real,R2: real] :
% 5.24/5.57 ( ( times_times_complex @ ( complex2 @ X @ Y4 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.24/5.57 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y4 @ R2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Complex_mult_complex_of_real
% 5.24/5.57 thf(fact_9172_Complex__add__complex__of__real,axiom,
% 5.24/5.57 ! [X: real,Y4: real,R2: real] :
% 5.24/5.57 ( ( plus_plus_complex @ ( complex2 @ X @ Y4 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.24/5.57 = ( complex2 @ ( plus_plus_real @ X @ R2 ) @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % Complex_add_complex_of_real
% 5.24/5.57 thf(fact_9173_complex__of__real__add__Complex,axiom,
% 5.24/5.57 ! [R2: real,X: real,Y4: real] :
% 5.24/5.57 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y4 ) )
% 5.24/5.57 = ( complex2 @ ( plus_plus_real @ R2 @ X ) @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_of_real_add_Complex
% 5.24/5.57 thf(fact_9174_cis__conv__exp,axiom,
% 5.24/5.57 ( cis
% 5.24/5.57 = ( ^ [B3: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % cis_conv_exp
% 5.24/5.57 thf(fact_9175_i__complex__of__real,axiom,
% 5.24/5.57 ! [R2: real] :
% 5.24/5.57 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.24/5.57 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % i_complex_of_real
% 5.24/5.57 thf(fact_9176_complex__of__real__i,axiom,
% 5.24/5.57 ! [R2: real] :
% 5.24/5.57 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.24/5.57 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_of_real_i
% 5.24/5.57 thf(fact_9177_Complex__eq,axiom,
% 5.24/5.57 ( complex2
% 5.24/5.57 = ( ^ [A4: real,B3: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A4 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Complex_eq
% 5.24/5.57 thf(fact_9178_complex__split__polar,axiom,
% 5.24/5.57 ! [Z2: complex] :
% 5.24/5.57 ? [R3: real,A3: real] :
% 5.24/5.57 ( Z2
% 5.24/5.57 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % complex_split_polar
% 5.24/5.57 thf(fact_9179_cmod__unit__one,axiom,
% 5.24/5.57 ! [A: real] :
% 5.24/5.57 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.24/5.57 = one_one_real ) ).
% 5.24/5.57
% 5.24/5.57 % cmod_unit_one
% 5.24/5.57 thf(fact_9180_cmod__complex__polar,axiom,
% 5.24/5.57 ! [R2: real,A: real] :
% 5.24/5.57 ( ( 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 ) ) ) ) ) )
% 5.24/5.57 = ( abs_abs_real @ R2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % cmod_complex_polar
% 5.24/5.57 thf(fact_9181_csqrt__ii,axiom,
% 5.24/5.57 ( ( csqrt @ imaginary_unit )
% 5.24/5.57 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % csqrt_ii
% 5.24/5.57 thf(fact_9182_modulo__int__unfold,axiom,
% 5.24/5.57 ! [L2: int,K: int,N: nat,M: nat] :
% 5.24/5.57 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( ( sgn_sgn_int @ K )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( N = zero_zero_nat ) )
% 5.24/5.57 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.24/5.57 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( ( sgn_sgn_int @ K )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( N = zero_zero_nat ) )
% 5.24/5.57 => ( ( ( ( sgn_sgn_int @ K )
% 5.24/5.57 = ( sgn_sgn_int @ L2 ) )
% 5.24/5.57 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.24/5.57 & ( ( ( sgn_sgn_int @ K )
% 5.24/5.57 != ( sgn_sgn_int @ L2 ) )
% 5.24/5.57 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.57 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.24/5.57 @ ( minus_minus_int
% 5.24/5.57 @ ( semiri1314217659103216013at_int
% 5.24/5.57 @ ( times_times_nat @ N
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.24/5.57 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % modulo_int_unfold
% 5.24/5.57 thf(fact_9183_num_Osize__gen_I3_J,axiom,
% 5.24/5.57 ! [X32: num] :
% 5.24/5.57 ( ( size_num @ ( bit1 @ X32 ) )
% 5.24/5.57 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % num.size_gen(3)
% 5.24/5.57 thf(fact_9184_mask__nat__positive__iff,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.24/5.57 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % mask_nat_positive_iff
% 5.24/5.57 thf(fact_9185_csqrt__eq__1,axiom,
% 5.24/5.57 ! [Z2: complex] :
% 5.24/5.57 ( ( ( csqrt @ Z2 )
% 5.24/5.57 = one_one_complex )
% 5.24/5.57 = ( Z2 = one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % csqrt_eq_1
% 5.24/5.57 thf(fact_9186_csqrt__1,axiom,
% 5.24/5.57 ( ( csqrt @ one_one_complex )
% 5.24/5.57 = one_one_complex ) ).
% 5.24/5.57
% 5.24/5.57 % csqrt_1
% 5.24/5.57 thf(fact_9187_dvd__mult__sgn__iff,axiom,
% 5.24/5.57 ! [L2: int,K: int,R2: int] :
% 5.24/5.57 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.24/5.57 = ( ( dvd_dvd_int @ L2 @ K )
% 5.24/5.57 | ( R2 = zero_zero_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % dvd_mult_sgn_iff
% 5.24/5.57 thf(fact_9188_dvd__sgn__mult__iff,axiom,
% 5.24/5.57 ! [L2: int,R2: int,K: int] :
% 5.24/5.57 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.24/5.57 = ( ( dvd_dvd_int @ L2 @ K )
% 5.24/5.57 | ( R2 = zero_zero_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % dvd_sgn_mult_iff
% 5.24/5.57 thf(fact_9189_mult__sgn__dvd__iff,axiom,
% 5.24/5.57 ! [L2: int,R2: int,K: int] :
% 5.24/5.57 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.24/5.57 = ( ( dvd_dvd_int @ L2 @ K )
% 5.24/5.57 & ( ( R2 = zero_zero_int )
% 5.24/5.57 => ( K = zero_zero_int ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mult_sgn_dvd_iff
% 5.24/5.57 thf(fact_9190_sgn__mult__dvd__iff,axiom,
% 5.24/5.57 ! [R2: int,L2: int,K: int] :
% 5.24/5.57 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L2 ) @ K )
% 5.24/5.57 = ( ( dvd_dvd_int @ L2 @ K )
% 5.24/5.57 & ( ( R2 = zero_zero_int )
% 5.24/5.57 => ( K = zero_zero_int ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sgn_mult_dvd_iff
% 5.24/5.57 thf(fact_9191_power2__csqrt,axiom,
% 5.24/5.57 ! [Z2: complex] :
% 5.24/5.57 ( ( power_power_complex @ ( csqrt @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.57 = Z2 ) ).
% 5.24/5.57
% 5.24/5.57 % power2_csqrt
% 5.24/5.57 thf(fact_9192_less__eq__mask,axiom,
% 5.24/5.57 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % less_eq_mask
% 5.24/5.57 thf(fact_9193_int__sgnE,axiom,
% 5.24/5.57 ! [K: int] :
% 5.24/5.57 ~ ! [N3: nat,L4: int] :
% 5.24/5.57 ( K
% 5.24/5.57 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % int_sgnE
% 5.24/5.57 thf(fact_9194_sgn__mod,axiom,
% 5.24/5.57 ! [L2: int,K: int] :
% 5.24/5.57 ( ( L2 != zero_zero_int )
% 5.24/5.57 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.24/5.57 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.24/5.57 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sgn_mod
% 5.24/5.57 thf(fact_9195_less__mask,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.57 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % less_mask
% 5.24/5.57 thf(fact_9196_zsgn__def,axiom,
% 5.24/5.57 ( sgn_sgn_int
% 5.24/5.57 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zsgn_def
% 5.24/5.57 thf(fact_9197_div__sgn__abs__cancel,axiom,
% 5.24/5.57 ! [V: int,K: int,L2: int] :
% 5.24/5.57 ( ( V != zero_zero_int )
% 5.24/5.57 => ( ( 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 ) ) )
% 5.24/5.57 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % div_sgn_abs_cancel
% 5.24/5.57 thf(fact_9198_div__dvd__sgn__abs,axiom,
% 5.24/5.57 ! [L2: int,K: int] :
% 5.24/5.57 ( ( dvd_dvd_int @ L2 @ K )
% 5.24/5.57 => ( ( divide_divide_int @ K @ L2 )
% 5.24/5.57 = ( 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 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % div_dvd_sgn_abs
% 5.24/5.57 thf(fact_9199_num_Osize__gen_I1_J,axiom,
% 5.24/5.57 ( ( size_num @ one )
% 5.24/5.57 = zero_zero_nat ) ).
% 5.24/5.57
% 5.24/5.57 % num.size_gen(1)
% 5.24/5.57 thf(fact_9200_Suc__mask__eq__exp,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.24/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % Suc_mask_eq_exp
% 5.24/5.57 thf(fact_9201_mask__nat__less__exp,axiom,
% 5.24/5.57 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % mask_nat_less_exp
% 5.24/5.57 thf(fact_9202_eucl__rel__int__remainderI,axiom,
% 5.24/5.57 ! [R2: int,L2: int,K: int,Q2: int] :
% 5.24/5.57 ( ( ( sgn_sgn_int @ R2 )
% 5.24/5.57 = ( sgn_sgn_int @ L2 ) )
% 5.24/5.57 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 5.24/5.57 => ( ( K
% 5.24/5.57 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R2 ) )
% 5.24/5.57 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % eucl_rel_int_remainderI
% 5.24/5.57 thf(fact_9203_mask__nat__def,axiom,
% 5.24/5.57 ( bit_se2002935070580805687sk_nat
% 5.24/5.57 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mask_nat_def
% 5.24/5.57 thf(fact_9204_mask__half__int,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mask_half_int
% 5.24/5.57 thf(fact_9205_mask__int__def,axiom,
% 5.24/5.57 ( bit_se2000444600071755411sk_int
% 5.24/5.57 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % mask_int_def
% 5.24/5.57 thf(fact_9206_eucl__rel__int_Ocases,axiom,
% 5.24/5.57 ! [A12: int,A23: int,A32: product_prod_int_int] :
% 5.24/5.57 ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 5.24/5.57 => ( ( ( A23 = zero_zero_int )
% 5.24/5.57 => ( A32
% 5.24/5.57 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.24/5.57 => ( ! [Q3: int] :
% 5.24/5.57 ( ( A32
% 5.24/5.57 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.24/5.57 => ( ( A23 != zero_zero_int )
% 5.24/5.57 => ( A12
% 5.24/5.57 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.24/5.57 => ~ ! [R3: int,Q3: int] :
% 5.24/5.57 ( ( A32
% 5.24/5.57 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.24/5.57 => ( ( ( sgn_sgn_int @ R3 )
% 5.24/5.57 = ( sgn_sgn_int @ A23 ) )
% 5.24/5.57 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.24/5.57 => ( A12
% 5.24/5.57 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % eucl_rel_int.cases
% 5.24/5.57 thf(fact_9207_eucl__rel__int_Osimps,axiom,
% 5.24/5.57 ( eucl_rel_int
% 5.24/5.57 = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 5.24/5.57 ( ? [K3: int] :
% 5.24/5.57 ( ( A1 = K3 )
% 5.24/5.57 & ( A22 = zero_zero_int )
% 5.24/5.57 & ( A33
% 5.24/5.57 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.24/5.57 | ? [L: int,K3: int,Q4: int] :
% 5.24/5.57 ( ( A1 = K3 )
% 5.24/5.57 & ( A22 = L )
% 5.24/5.57 & ( A33
% 5.24/5.57 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.24/5.57 & ( L != zero_zero_int )
% 5.24/5.57 & ( K3
% 5.24/5.57 = ( times_times_int @ Q4 @ L ) ) )
% 5.24/5.57 | ? [R5: int,L: int,K3: int,Q4: int] :
% 5.24/5.57 ( ( A1 = K3 )
% 5.24/5.57 & ( A22 = L )
% 5.24/5.57 & ( A33
% 5.24/5.57 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.24/5.57 & ( ( sgn_sgn_int @ R5 )
% 5.24/5.57 = ( sgn_sgn_int @ L ) )
% 5.24/5.57 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.24/5.57 & ( K3
% 5.24/5.57 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % eucl_rel_int.simps
% 5.24/5.57 thf(fact_9208_num_Osize__gen_I2_J,axiom,
% 5.24/5.57 ! [X22: num] :
% 5.24/5.57 ( ( size_num @ ( bit0 @ X22 ) )
% 5.24/5.57 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % num.size_gen(2)
% 5.24/5.57 thf(fact_9209_divide__int__unfold,axiom,
% 5.24/5.57 ! [L2: int,K: int,N: nat,M: nat] :
% 5.24/5.57 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( ( sgn_sgn_int @ K )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( N = zero_zero_nat ) )
% 5.24/5.57 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.57 = zero_zero_int ) )
% 5.24/5.57 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( ( sgn_sgn_int @ K )
% 5.24/5.57 = zero_zero_int )
% 5.24/5.57 | ( N = zero_zero_nat ) )
% 5.24/5.57 => ( ( ( ( sgn_sgn_int @ K )
% 5.24/5.57 = ( sgn_sgn_int @ L2 ) )
% 5.24/5.57 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.57 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.24/5.57 & ( ( ( sgn_sgn_int @ K )
% 5.24/5.57 != ( sgn_sgn_int @ L2 ) )
% 5.24/5.57 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.24/5.57 = ( uminus_uminus_int
% 5.24/5.57 @ ( semiri1314217659103216013at_int
% 5.24/5.57 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % divide_int_unfold
% 5.24/5.57 thf(fact_9210_bij__betw__nth__root__unity,axiom,
% 5.24/5.57 ! [C: complex,N: nat] :
% 5.24/5.57 ( ( C != zero_zero_complex )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.24/5.57 @ ( collect_complex
% 5.24/5.57 @ ^ [Z4: complex] :
% 5.24/5.57 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.57 = one_one_complex ) )
% 5.24/5.57 @ ( collect_complex
% 5.24/5.57 @ ^ [Z4: complex] :
% 5.24/5.57 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.57 = C ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bij_betw_nth_root_unity
% 5.24/5.57 thf(fact_9211_modulo__int__def,axiom,
% 5.24/5.57 ( modulo_modulo_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( if_int @ ( L = zero_zero_int ) @ K3
% 5.24/5.57 @ ( if_int
% 5.24/5.57 @ ( ( sgn_sgn_int @ K3 )
% 5.24/5.57 = ( sgn_sgn_int @ L ) )
% 5.24/5.57 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.24/5.57 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.24/5.57 @ ( minus_minus_int
% 5.24/5.57 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 5.24/5.57 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % modulo_int_def
% 5.24/5.57 thf(fact_9212_divide__int__def,axiom,
% 5.24/5.57 ( divide_divide_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.24/5.57 @ ( if_int
% 5.24/5.57 @ ( ( sgn_sgn_int @ K3 )
% 5.24/5.57 = ( sgn_sgn_int @ L ) )
% 5.24/5.57 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.24/5.57 @ ( uminus_uminus_int
% 5.24/5.57 @ ( semiri1314217659103216013at_int
% 5.24/5.57 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % divide_int_def
% 5.24/5.57 thf(fact_9213_powr__int,axiom,
% 5.24/5.57 ! [X: real,I2: int] :
% 5.24/5.57 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.24/5.57 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.24/5.57 = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 5.24/5.57 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.24/5.57 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.24/5.57 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % powr_int
% 5.24/5.57 thf(fact_9214_nat__numeral,axiom,
% 5.24/5.57 ! [K: num] :
% 5.24/5.57 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.24/5.57 = ( numeral_numeral_nat @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_numeral
% 5.24/5.57 thf(fact_9215_real__root__Suc__0,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.24/5.57 = X ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_Suc_0
% 5.24/5.57 thf(fact_9216_real__root__eq__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ( root @ N @ X )
% 5.24/5.57 = ( root @ N @ Y4 ) )
% 5.24/5.57 = ( X = Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_eq_iff
% 5.24/5.57 thf(fact_9217_nat__1,axiom,
% 5.24/5.57 ( ( nat2 @ one_one_int )
% 5.24/5.57 = ( suc @ zero_zero_nat ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_1
% 5.24/5.57 thf(fact_9218_real__root__eq__0__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ( root @ N @ X )
% 5.24/5.57 = zero_zero_real )
% 5.24/5.57 = ( X = zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_eq_0_iff
% 5.24/5.57 thf(fact_9219_real__root__less__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) )
% 5.24/5.57 = ( ord_less_real @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_less_iff
% 5.24/5.57 thf(fact_9220_real__root__le__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_le_iff
% 5.24/5.57 thf(fact_9221_zless__nat__conj,axiom,
% 5.24/5.57 ! [W2: int,Z2: int] :
% 5.24/5.57 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.57 & ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % zless_nat_conj
% 5.24/5.57 thf(fact_9222_real__root__one,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( root @ N @ one_one_real )
% 5.24/5.57 = one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_one
% 5.24/5.57 thf(fact_9223_real__root__eq__1__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ( root @ N @ X )
% 5.24/5.57 = one_one_real )
% 5.24/5.57 = ( X = one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_eq_1_iff
% 5.24/5.57 thf(fact_9224_real__root__gt__0__iff,axiom,
% 5.24/5.57 ! [N: nat,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y4 ) )
% 5.24/5.57 = ( ord_less_real @ zero_zero_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_gt_0_iff
% 5.24/5.57 thf(fact_9225_real__root__lt__0__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.24/5.57 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_lt_0_iff
% 5.24/5.57 thf(fact_9226_real__root__ge__0__iff,axiom,
% 5.24/5.57 ! [N: nat,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_ge_0_iff
% 5.24/5.57 thf(fact_9227_real__root__le__0__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.24/5.57 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_le_0_iff
% 5.24/5.57 thf(fact_9228_zero__less__nat__eq,axiom,
% 5.24/5.57 ! [Z2: int] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % zero_less_nat_eq
% 5.24/5.57 thf(fact_9229_real__root__gt__1__iff,axiom,
% 5.24/5.57 ! [N: nat,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y4 ) )
% 5.24/5.57 = ( ord_less_real @ one_one_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_gt_1_iff
% 5.24/5.57 thf(fact_9230_real__root__lt__1__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 5.24/5.57 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_lt_1_iff
% 5.24/5.57 thf(fact_9231_real__root__ge__1__iff,axiom,
% 5.24/5.57 ! [N: nat,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y4 ) )
% 5.24/5.57 = ( ord_less_eq_real @ one_one_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_ge_1_iff
% 5.24/5.57 thf(fact_9232_real__root__le__1__iff,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 5.24/5.57 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_le_1_iff
% 5.24/5.57 thf(fact_9233_diff__nat__numeral,axiom,
% 5.24/5.57 ! [V: num,V3: num] :
% 5.24/5.57 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.24/5.57 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % diff_nat_numeral
% 5.24/5.57 thf(fact_9234_numeral__power__eq__nat__cancel__iff,axiom,
% 5.24/5.57 ! [X: num,N: nat,Y4: int] :
% 5.24/5.57 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.24/5.57 = ( nat2 @ Y4 ) )
% 5.24/5.57 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.24/5.57 = Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_power_eq_nat_cancel_iff
% 5.24/5.57 thf(fact_9235_nat__eq__numeral__power__cancel__iff,axiom,
% 5.24/5.57 ! [Y4: int,X: num,N: nat] :
% 5.24/5.57 ( ( ( nat2 @ Y4 )
% 5.24/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.24/5.57 = ( Y4
% 5.24/5.57 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_eq_numeral_power_cancel_iff
% 5.24/5.57 thf(fact_9236_nat__ceiling__le__eq,axiom,
% 5.24/5.57 ! [X: real,A: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.24/5.57 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_ceiling_le_eq
% 5.24/5.57 thf(fact_9237_one__less__nat__eq,axiom,
% 5.24/5.57 ! [Z2: int] :
% 5.24/5.57 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % one_less_nat_eq
% 5.24/5.57 thf(fact_9238_real__root__pow__pos2,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.24/5.57 = X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_pow_pos2
% 5.24/5.57 thf(fact_9239_nat__numeral__diff__1,axiom,
% 5.24/5.57 ! [V: num] :
% 5.24/5.57 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.24/5.57 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_numeral_diff_1
% 5.24/5.57 thf(fact_9240_numeral__power__less__nat__cancel__iff,axiom,
% 5.24/5.57 ! [X: num,N: nat,A: int] :
% 5.24/5.57 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.24/5.57 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_power_less_nat_cancel_iff
% 5.24/5.57 thf(fact_9241_nat__less__numeral__power__cancel__iff,axiom,
% 5.24/5.57 ! [A: int,X: num,N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.24/5.57 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_less_numeral_power_cancel_iff
% 5.24/5.57 thf(fact_9242_nat__le__numeral__power__cancel__iff,axiom,
% 5.24/5.57 ! [A: int,X: num,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.24/5.57 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_le_numeral_power_cancel_iff
% 5.24/5.57 thf(fact_9243_numeral__power__le__nat__cancel__iff,axiom,
% 5.24/5.57 ! [X: num,N: nat,A: int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.24/5.57 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.24/5.57
% 5.24/5.57 % numeral_power_le_nat_cancel_iff
% 5.24/5.57 thf(fact_9244_sgn__root,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 5.24/5.57 = ( sgn_sgn_real @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sgn_root
% 5.24/5.57 thf(fact_9245_real__root__mult,axiom,
% 5.24/5.57 ! [N: nat,X: real,Y4: real] :
% 5.24/5.57 ( ( root @ N @ ( times_times_real @ X @ Y4 ) )
% 5.24/5.57 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_mult
% 5.24/5.57 thf(fact_9246_real__root__mult__exp,axiom,
% 5.24/5.57 ! [M: nat,N: nat,X: real] :
% 5.24/5.57 ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 5.24/5.57 = ( root @ M @ ( root @ N @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_mult_exp
% 5.24/5.57 thf(fact_9247_nat__zero__as__int,axiom,
% 5.24/5.57 ( zero_zero_nat
% 5.24/5.57 = ( nat2 @ zero_zero_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_zero_as_int
% 5.24/5.57 thf(fact_9248_nat__numeral__as__int,axiom,
% 5.24/5.57 ( numeral_numeral_nat
% 5.24/5.57 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_numeral_as_int
% 5.24/5.57 thf(fact_9249_nat__mono,axiom,
% 5.24/5.57 ! [X: int,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ X @ Y4 )
% 5.24/5.57 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_mono
% 5.24/5.57 thf(fact_9250_nat__one__as__int,axiom,
% 5.24/5.57 ( one_one_nat
% 5.24/5.57 = ( nat2 @ one_one_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_one_as_int
% 5.24/5.57 thf(fact_9251_root__sgn__power,axiom,
% 5.24/5.57 ! [N: nat,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) ) )
% 5.24/5.57 = Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_sgn_power
% 5.24/5.57 thf(fact_9252_sgn__power__root,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 5.24/5.57 = X ) ) ).
% 5.24/5.57
% 5.24/5.57 % sgn_power_root
% 5.24/5.57 thf(fact_9253_split__root,axiom,
% 5.24/5.57 ! [P: real > $o,N: nat,X: real] :
% 5.24/5.57 ( ( P @ ( root @ N @ X ) )
% 5.24/5.57 = ( ( ( N = zero_zero_nat )
% 5.24/5.57 => ( P @ zero_zero_real ) )
% 5.24/5.57 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ! [Y: real] :
% 5.24/5.57 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.24/5.57 = X )
% 5.24/5.57 => ( P @ Y ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % split_root
% 5.24/5.57 thf(fact_9254_real__root__less__mono,axiom,
% 5.24/5.57 ! [N: nat,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ X @ Y4 )
% 5.24/5.57 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_less_mono
% 5.24/5.57 thf(fact_9255_real__root__le__mono,axiom,
% 5.24/5.57 ! [N: nat,X: real,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.24/5.57 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_le_mono
% 5.24/5.57 thf(fact_9256_real__root__power,axiom,
% 5.24/5.57 ! [N: nat,X: real,K: nat] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 5.24/5.57 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_power
% 5.24/5.57 thf(fact_9257_real__root__abs,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 5.24/5.57 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_abs
% 5.24/5.57 thf(fact_9258_nat__mono__iff,axiom,
% 5.24/5.57 ! [Z2: int,W2: int] :
% 5.24/5.57 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.24/5.57 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_mono_iff
% 5.24/5.57 thf(fact_9259_zless__nat__eq__int__zless,axiom,
% 5.24/5.57 ! [M: nat,Z2: int] :
% 5.24/5.57 ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z2 ) ) ).
% 5.24/5.57
% 5.24/5.57 % zless_nat_eq_int_zless
% 5.24/5.57 thf(fact_9260_nat__le__iff,axiom,
% 5.24/5.57 ! [X: int,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 5.24/5.57 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_le_iff
% 5.24/5.57 thf(fact_9261_nat__int__add,axiom,
% 5.24/5.57 ! [A: nat,B: nat] :
% 5.24/5.57 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.24/5.57 = ( plus_plus_nat @ A @ B ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_int_add
% 5.24/5.57 thf(fact_9262_int__minus,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.24/5.57 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % int_minus
% 5.24/5.57 thf(fact_9263_nat__abs__mult__distrib,axiom,
% 5.24/5.57 ! [W2: int,Z2: int] :
% 5.24/5.57 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z2 ) ) )
% 5.24/5.57 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_abs_mult_distrib
% 5.24/5.57 thf(fact_9264_nat__plus__as__int,axiom,
% 5.24/5.57 ( plus_plus_nat
% 5.24/5.57 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_plus_as_int
% 5.24/5.57 thf(fact_9265_nat__times__as__int,axiom,
% 5.24/5.57 ( times_times_nat
% 5.24/5.57 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_times_as_int
% 5.24/5.57 thf(fact_9266_nat__minus__as__int,axiom,
% 5.24/5.57 ( minus_minus_nat
% 5.24/5.57 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_minus_as_int
% 5.24/5.57 thf(fact_9267_nat__div__as__int,axiom,
% 5.24/5.57 ( divide_divide_nat
% 5.24/5.57 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_div_as_int
% 5.24/5.57 thf(fact_9268_nat__mod__as__int,axiom,
% 5.24/5.57 ( modulo_modulo_nat
% 5.24/5.57 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_mod_as_int
% 5.24/5.57 thf(fact_9269_real__root__gt__zero,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_gt_zero
% 5.24/5.57 thf(fact_9270_real__root__strict__decreasing,axiom,
% 5.24/5.57 ! [N: nat,N4: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_nat @ N @ N4 )
% 5.24/5.57 => ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.57 => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_strict_decreasing
% 5.24/5.57 thf(fact_9271_sqrt__def,axiom,
% 5.24/5.57 ( sqrt
% 5.24/5.57 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sqrt_def
% 5.24/5.57 thf(fact_9272_sgn__real__def,axiom,
% 5.24/5.57 ( sgn_sgn_real
% 5.24/5.57 = ( ^ [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 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sgn_real_def
% 5.24/5.57 thf(fact_9273_root__abs__power,axiom,
% 5.24/5.57 ! [N: nat,Y4: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y4 @ N ) ) )
% 5.24/5.57 = ( abs_abs_real @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_abs_power
% 5.24/5.57 thf(fact_9274_nat__less__eq__zless,axiom,
% 5.24/5.57 ! [W2: int,Z2: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.24/5.57 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_less_eq_zless
% 5.24/5.57 thf(fact_9275_nat__le__eq__zle,axiom,
% 5.24/5.57 ! [W2: int,Z2: int] :
% 5.24/5.57 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 5.24/5.57 | ( ord_less_eq_int @ zero_zero_int @ Z2 ) )
% 5.24/5.57 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( ord_less_eq_int @ W2 @ Z2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_le_eq_zle
% 5.24/5.57 thf(fact_9276_le__nat__iff,axiom,
% 5.24/5.57 ! [K: int,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.57 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.24/5.57 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_nat_iff
% 5.24/5.57 thf(fact_9277_nat__add__distrib,axiom,
% 5.24/5.57 ! [Z2: int,Z6: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.57 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.24/5.57 => ( ( nat2 @ ( plus_plus_int @ Z2 @ Z6 ) )
% 5.24/5.57 = ( plus_plus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_add_distrib
% 5.24/5.57 thf(fact_9278_nat__mult__distrib,axiom,
% 5.24/5.57 ! [Z2: int,Z6: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.57 => ( ( nat2 @ ( times_times_int @ Z2 @ Z6 ) )
% 5.24/5.57 = ( times_times_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_mult_distrib
% 5.24/5.57 thf(fact_9279_Suc__as__int,axiom,
% 5.24/5.57 ( suc
% 5.24/5.57 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Suc_as_int
% 5.24/5.57 thf(fact_9280_nat__abs__triangle__ineq,axiom,
% 5.24/5.57 ! [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_abs_triangle_ineq
% 5.24/5.57 thf(fact_9281_nat__div__distrib_H,axiom,
% 5.24/5.57 ! [Y4: int,X: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.24/5.57 => ( ( nat2 @ ( divide_divide_int @ X @ Y4 ) )
% 5.24/5.57 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_div_distrib'
% 5.24/5.57 thf(fact_9282_nat__div__distrib,axiom,
% 5.24/5.57 ! [X: int,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.24/5.57 => ( ( nat2 @ ( divide_divide_int @ X @ Y4 ) )
% 5.24/5.57 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_div_distrib
% 5.24/5.57 thf(fact_9283_nat__power__eq,axiom,
% 5.24/5.57 ! [Z2: int,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.57 => ( ( nat2 @ ( power_power_int @ Z2 @ N ) )
% 5.24/5.57 = ( power_power_nat @ ( nat2 @ Z2 ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_power_eq
% 5.24/5.57 thf(fact_9284_nat__mod__distrib,axiom,
% 5.24/5.57 ! [X: int,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.24/5.57 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.24/5.57 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y4 ) )
% 5.24/5.57 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_mod_distrib
% 5.24/5.57 thf(fact_9285_div__abs__eq__div__nat,axiom,
% 5.24/5.57 ! [K: int,L2: int] :
% 5.24/5.57 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.24/5.57 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % div_abs_eq_div_nat
% 5.24/5.57 thf(fact_9286_floor__eq3,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.24/5.57 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.24/5.57 = N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_eq3
% 5.24/5.57 thf(fact_9287_le__nat__floor,axiom,
% 5.24/5.57 ! [X: nat,A: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.24/5.57 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % le_nat_floor
% 5.24/5.57 thf(fact_9288_real__root__pos__pos,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_pos_pos
% 5.24/5.57 thf(fact_9289_real__root__strict__increasing,axiom,
% 5.24/5.57 ! [N: nat,N4: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_nat @ N @ N4 )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.57 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_strict_increasing
% 5.24/5.57 thf(fact_9290_real__root__decreasing,axiom,
% 5.24/5.57 ! [N: nat,N4: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.24/5.57 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.24/5.57 => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_decreasing
% 5.24/5.57 thf(fact_9291_real__root__pow__pos,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.24/5.57 = X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_pow_pos
% 5.24/5.57 thf(fact_9292_real__root__power__cancel,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.24/5.57 = X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_power_cancel
% 5.24/5.57 thf(fact_9293_real__root__pos__unique,axiom,
% 5.24/5.57 ! [N: nat,Y4: real,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.24/5.57 => ( ( ( power_power_real @ Y4 @ N )
% 5.24/5.57 = X )
% 5.24/5.57 => ( ( root @ N @ X )
% 5.24/5.57 = Y4 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_pos_unique
% 5.24/5.57 thf(fact_9294_odd__real__root__power__cancel,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.57 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.24/5.57 = X ) ) ).
% 5.24/5.57
% 5.24/5.57 % odd_real_root_power_cancel
% 5.24/5.57 thf(fact_9295_odd__real__root__unique,axiom,
% 5.24/5.57 ! [N: nat,Y4: real,X: real] :
% 5.24/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.57 => ( ( ( power_power_real @ Y4 @ N )
% 5.24/5.57 = X )
% 5.24/5.57 => ( ( root @ N @ X )
% 5.24/5.57 = Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % odd_real_root_unique
% 5.24/5.57 thf(fact_9296_odd__real__root__pow,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.57 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.24/5.57 = X ) ) ).
% 5.24/5.57
% 5.24/5.57 % odd_real_root_pow
% 5.24/5.57 thf(fact_9297_nat__2,axiom,
% 5.24/5.57 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.57 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_2
% 5.24/5.57 thf(fact_9298_sgn__power__injE,axiom,
% 5.24/5.57 ! [A: real,N: nat,X: real,B: real] :
% 5.24/5.57 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.24/5.57 = X )
% 5.24/5.57 => ( ( X
% 5.24/5.57 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( A = B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % sgn_power_injE
% 5.24/5.57 thf(fact_9299_Suc__nat__eq__nat__zadd1,axiom,
% 5.24/5.57 ! [Z2: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.24/5.57 => ( ( suc @ ( nat2 @ Z2 ) )
% 5.24/5.57 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Suc_nat_eq_nat_zadd1
% 5.24/5.57 thf(fact_9300_nat__less__iff,axiom,
% 5.24/5.57 ! [W2: int,M: nat] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.24/5.57 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 5.24/5.57 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_less_iff
% 5.24/5.57 thf(fact_9301_nat__mult__distrib__neg,axiom,
% 5.24/5.57 ! [Z2: int,Z6: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 5.24/5.57 => ( ( nat2 @ ( times_times_int @ Z2 @ Z6 ) )
% 5.24/5.57 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z2 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_mult_distrib_neg
% 5.24/5.57 thf(fact_9302_nat__abs__int__diff,axiom,
% 5.24/5.57 ! [A: nat,B: nat] :
% 5.24/5.57 ( ( ( ord_less_eq_nat @ A @ B )
% 5.24/5.57 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.24/5.57 = ( minus_minus_nat @ B @ A ) ) )
% 5.24/5.57 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.24/5.57 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.24/5.57 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % nat_abs_int_diff
% 5.24/5.57 thf(fact_9303_floor__eq4,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.24/5.57 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.24/5.57 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.24/5.57 = N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % floor_eq4
% 5.24/5.57 thf(fact_9304_real__root__increasing,axiom,
% 5.24/5.57 ! [N: nat,N4: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.24/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.57 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % real_root_increasing
% 5.24/5.57 thf(fact_9305_ln__root,axiom,
% 5.24/5.57 ! [N: nat,B: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.24/5.57 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % ln_root
% 5.24/5.57 thf(fact_9306_log__root,axiom,
% 5.24/5.57 ! [N: nat,A: real,B: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.24/5.57 => ( ( log @ B @ ( root @ N @ A ) )
% 5.24/5.57 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_root
% 5.24/5.57 thf(fact_9307_log__base__root,axiom,
% 5.24/5.57 ! [N: nat,B: real,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.24/5.57 => ( ( log @ ( root @ N @ B ) @ X )
% 5.24/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % log_base_root
% 5.24/5.57 thf(fact_9308_root__powr__inverse,axiom,
% 5.24/5.57 ! [N: nat,X: real] :
% 5.24/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.57 => ( ( root @ N @ X )
% 5.24/5.57 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % root_powr_inverse
% 5.24/5.57 thf(fact_9309_even__nat__iff,axiom,
% 5.24/5.57 ! [K: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.57 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.24/5.57 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % even_nat_iff
% 5.24/5.57 thf(fact_9310_arctan__inverse,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( X != zero_zero_real )
% 5.24/5.57 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.24/5.57 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % arctan_inverse
% 5.24/5.57 thf(fact_9311_and__int__unfold,axiom,
% 5.24/5.57 ( bit_se725231765392027082nd_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( if_int
% 5.24/5.57 @ ( ( K3 = zero_zero_int )
% 5.24/5.57 | ( L = zero_zero_int ) )
% 5.24/5.57 @ zero_zero_int
% 5.24/5.57 @ ( if_int
% 5.24/5.57 @ ( K3
% 5.24/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.57 @ L
% 5.24/5.57 @ ( if_int
% 5.24/5.57 @ ( L
% 5.24/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.57 @ K3
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int_unfold
% 5.24/5.57 thf(fact_9312_take__bit__of__Suc__0,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_of_Suc_0
% 5.24/5.57 thf(fact_9313_and__minus__numerals_I6_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.24/5.57 = one_one_int ) ).
% 5.24/5.57
% 5.24/5.57 % and_minus_numerals(6)
% 5.24/5.57 thf(fact_9314_and__minus__numerals_I2_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.57 = one_one_int ) ).
% 5.24/5.57
% 5.24/5.57 % and_minus_numerals(2)
% 5.24/5.57 thf(fact_9315_and__minus__numerals_I5_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.24/5.57 = zero_zero_int ) ).
% 5.24/5.57
% 5.24/5.57 % and_minus_numerals(5)
% 5.24/5.57 thf(fact_9316_and__minus__numerals_I1_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.57 = zero_zero_int ) ).
% 5.24/5.57
% 5.24/5.57 % and_minus_numerals(1)
% 5.24/5.57 thf(fact_9317_take__bit__mult,axiom,
% 5.24/5.57 ! [N: nat,K: int,L2: int] :
% 5.24/5.57 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.24/5.57 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_mult
% 5.24/5.57 thf(fact_9318_take__bit__tightened__less__eq__nat,axiom,
% 5.24/5.57 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_tightened_less_eq_nat
% 5.24/5.57 thf(fact_9319_take__bit__nat__less__eq__self,axiom,
% 5.24/5.57 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_nat_less_eq_self
% 5.24/5.57 thf(fact_9320_take__bit__tightened__less__eq__int,axiom,
% 5.24/5.57 ! [M: nat,N: nat,K: int] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_tightened_less_eq_int
% 5.24/5.57 thf(fact_9321_pow_Osimps_I1_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( pow @ X @ one )
% 5.24/5.57 = X ) ).
% 5.24/5.57
% 5.24/5.57 % pow.simps(1)
% 5.24/5.57 thf(fact_9322_take__bit__decr__eq,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.24/5.57 != zero_zero_int )
% 5.24/5.57 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.24/5.57 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_decr_eq
% 5.24/5.57 thf(fact_9323_even__and__iff__int,axiom,
% 5.24/5.57 ! [K: int,L2: int] :
% 5.24/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.24/5.57 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.24/5.57 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % even_and_iff_int
% 5.24/5.57 thf(fact_9324_take__bit__eq__mask__iff,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.24/5.57 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.24/5.57 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.24/5.57 = zero_zero_int ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_eq_mask_iff
% 5.24/5.57 thf(fact_9325_take__bit__nat__eq__self,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.24/5.57 = M ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_nat_eq_self
% 5.24/5.57 thf(fact_9326_take__bit__nat__less__exp,axiom,
% 5.24/5.57 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_nat_less_exp
% 5.24/5.57 thf(fact_9327_take__bit__nat__eq__self__iff,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.24/5.57 = M )
% 5.24/5.57 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_nat_eq_self_iff
% 5.24/5.57 thf(fact_9328_take__bit__nat__def,axiom,
% 5.24/5.57 ( bit_se2925701944663578781it_nat
% 5.24/5.57 = ( ^ [N2: nat,M2: nat] : ( modulo_modulo_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_nat_def
% 5.24/5.57 thf(fact_9329_take__bit__int__less__exp,axiom,
% 5.24/5.57 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_less_exp
% 5.24/5.57 thf(fact_9330_take__bit__int__def,axiom,
% 5.24/5.57 ( bit_se2923211474154528505it_int
% 5.24/5.57 = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_def
% 5.24/5.57 thf(fact_9331_take__bit__nat__less__self__iff,axiom,
% 5.24/5.57 ! [N: nat,M: nat] :
% 5.24/5.57 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.24/5.57 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_nat_less_self_iff
% 5.24/5.57 thf(fact_9332_take__bit__Suc__minus__bit0,axiom,
% 5.24/5.57 ! [N: nat,K: num] :
% 5.24/5.57 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.24/5.57 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_Suc_minus_bit0
% 5.24/5.57 thf(fact_9333_take__bit__int__greater__eq__self__iff,axiom,
% 5.24/5.57 ! [K: int,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.24/5.57 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_greater_eq_self_iff
% 5.24/5.57 thf(fact_9334_take__bit__int__less__self__iff,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.24/5.57 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_less_self_iff
% 5.24/5.57 thf(fact_9335_take__bit__int__eq__self,axiom,
% 5.24/5.57 ! [K: int,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.57 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.24/5.57 = K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_eq_self
% 5.24/5.57 thf(fact_9336_take__bit__int__eq__self__iff,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.24/5.57 = K )
% 5.24/5.57 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.24/5.57 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_eq_self_iff
% 5.24/5.57 thf(fact_9337_take__bit__numeral__minus__bit0,axiom,
% 5.24/5.57 ! [L2: num,K: num] :
% 5.24/5.57 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.24/5.57 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_numeral_minus_bit0
% 5.24/5.57 thf(fact_9338_take__bit__incr__eq,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.24/5.57 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.24/5.57 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.24/5.57 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_incr_eq
% 5.24/5.57 thf(fact_9339_take__bit__int__less__eq,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.24/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.57 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_less_eq
% 5.24/5.57 thf(fact_9340_take__bit__int__greater__eq,axiom,
% 5.24/5.57 ! [K: int,N: nat] :
% 5.24/5.57 ( ( ord_less_int @ K @ zero_zero_int )
% 5.24/5.57 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_int_greater_eq
% 5.24/5.57 thf(fact_9341_signed__take__bit__eq__take__bit__shift,axiom,
% 5.24/5.57 ( bit_ri631733984087533419it_int
% 5.24/5.57 = ( ^ [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 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % signed_take_bit_eq_take_bit_shift
% 5.24/5.57 thf(fact_9342_and__int__rec,axiom,
% 5.24/5.57 ( bit_se725231765392027082nd_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( plus_plus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int_rec
% 5.24/5.57 thf(fact_9343_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.24/5.57 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.24/5.57 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_eq_mask_iff_exp_dvd
% 5.24/5.57 thf(fact_9344_take__bit__minus__small__eq,axiom,
% 5.24/5.57 ! [K: int,N: nat] :
% 5.24/5.57 ( ( ord_less_int @ zero_zero_int @ K )
% 5.24/5.57 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.24/5.57 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_minus_small_eq
% 5.24/5.57 thf(fact_9345_take__bit__numeral__minus__bit1,axiom,
% 5.24/5.57 ! [L2: num,K: num] :
% 5.24/5.57 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.24/5.57 = ( 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 ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_numeral_minus_bit1
% 5.24/5.57 thf(fact_9346_and__int_Oelims,axiom,
% 5.24/5.57 ! [X: int,Xa2: int,Y4: int] :
% 5.24/5.57 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.24/5.57 = Y4 )
% 5.24/5.57 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( Y4
% 5.24/5.57 = ( uminus_uminus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.24/5.57 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( Y4
% 5.24/5.57 = ( plus_plus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int.elims
% 5.24/5.57 thf(fact_9347_and__int_Osimps,axiom,
% 5.24/5.57 ( bit_se725231765392027082nd_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( if_int
% 5.24/5.57 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 @ ( uminus_uminus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.24/5.57 @ ( plus_plus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int.simps
% 5.24/5.57 thf(fact_9348_take__bit__Suc__minus__bit1,axiom,
% 5.24/5.57 ! [N: nat,K: num] :
% 5.24/5.57 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.24/5.57 = ( 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 ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_Suc_minus_bit1
% 5.24/5.57 thf(fact_9349_pred__numeral__inc,axiom,
% 5.24/5.57 ! [K: num] :
% 5.24/5.57 ( ( pred_numeral @ ( inc @ K ) )
% 5.24/5.57 = ( numeral_numeral_nat @ K ) ) ).
% 5.24/5.57
% 5.24/5.57 % pred_numeral_inc
% 5.24/5.57 thf(fact_9350_and__nat__numerals_I1_J,axiom,
% 5.24/5.57 ! [Y4: num] :
% 5.24/5.57 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.24/5.57 = zero_zero_nat ) ).
% 5.24/5.57
% 5.24/5.57 % and_nat_numerals(1)
% 5.24/5.57 thf(fact_9351_and__nat__numerals_I3_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = zero_zero_nat ) ).
% 5.24/5.57
% 5.24/5.57 % and_nat_numerals(3)
% 5.24/5.57 thf(fact_9352_and__nat__numerals_I2_J,axiom,
% 5.24/5.57 ! [Y4: num] :
% 5.24/5.57 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.24/5.57 = one_one_nat ) ).
% 5.24/5.57
% 5.24/5.57 % and_nat_numerals(2)
% 5.24/5.57 thf(fact_9353_and__nat__numerals_I4_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = one_one_nat ) ).
% 5.24/5.57
% 5.24/5.57 % and_nat_numerals(4)
% 5.24/5.57 thf(fact_9354_and__Suc__0__eq,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_Suc_0_eq
% 5.24/5.57 thf(fact_9355_Suc__0__and__eq,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.57 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Suc_0_and_eq
% 5.24/5.57 thf(fact_9356_num__induct,axiom,
% 5.24/5.57 ! [P: num > $o,X: num] :
% 5.24/5.57 ( ( P @ one )
% 5.24/5.57 => ( ! [X3: num] :
% 5.24/5.57 ( ( P @ X3 )
% 5.24/5.57 => ( P @ ( inc @ X3 ) ) )
% 5.24/5.57 => ( P @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % num_induct
% 5.24/5.57 thf(fact_9357_add__inc,axiom,
% 5.24/5.57 ! [X: num,Y4: num] :
% 5.24/5.57 ( ( plus_plus_num @ X @ ( inc @ Y4 ) )
% 5.24/5.57 = ( inc @ ( plus_plus_num @ X @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % add_inc
% 5.24/5.57 thf(fact_9358_inc_Osimps_I1_J,axiom,
% 5.24/5.57 ( ( inc @ one )
% 5.24/5.57 = ( bit0 @ one ) ) ).
% 5.24/5.57
% 5.24/5.57 % inc.simps(1)
% 5.24/5.57 thf(fact_9359_inc_Osimps_I2_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( inc @ ( bit0 @ X ) )
% 5.24/5.57 = ( bit1 @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % inc.simps(2)
% 5.24/5.57 thf(fact_9360_inc_Osimps_I3_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( inc @ ( bit1 @ X ) )
% 5.24/5.57 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % inc.simps(3)
% 5.24/5.57 thf(fact_9361_add__One,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( plus_plus_num @ X @ one )
% 5.24/5.57 = ( inc @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % add_One
% 5.24/5.57 thf(fact_9362_inc__BitM__eq,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( inc @ ( bitM @ N ) )
% 5.24/5.57 = ( bit0 @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % inc_BitM_eq
% 5.24/5.57 thf(fact_9363_BitM__inc__eq,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bitM @ ( inc @ N ) )
% 5.24/5.57 = ( bit1 @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % BitM_inc_eq
% 5.24/5.57 thf(fact_9364_mult__inc,axiom,
% 5.24/5.57 ! [X: num,Y4: num] :
% 5.24/5.57 ( ( times_times_num @ X @ ( inc @ Y4 ) )
% 5.24/5.57 = ( plus_plus_num @ ( times_times_num @ X @ Y4 ) @ X ) ) ).
% 5.24/5.57
% 5.24/5.57 % mult_inc
% 5.24/5.57 thf(fact_9365_atLeastAtMostPlus1__int__conv,axiom,
% 5.24/5.57 ! [M: int,N: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.24/5.57 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.24/5.57 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atLeastAtMostPlus1_int_conv
% 5.24/5.57 thf(fact_9366_simp__from__to,axiom,
% 5.24/5.57 ( set_or1266510415728281911st_int
% 5.24/5.57 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % simp_from_to
% 5.24/5.57 thf(fact_9367_and__nat__unfold,axiom,
% 5.24/5.57 ( bit_se727722235901077358nd_nat
% 5.24/5.57 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.57 ( if_nat
% 5.24/5.57 @ ( ( M2 = zero_zero_nat )
% 5.24/5.57 | ( N2 = zero_zero_nat ) )
% 5.24/5.57 @ zero_zero_nat
% 5.24/5.57 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M2 @ ( 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 @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_nat_unfold
% 5.24/5.57 thf(fact_9368_and__nat__rec,axiom,
% 5.24/5.57 ( bit_se727722235901077358nd_nat
% 5.24/5.57 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.57 ( plus_plus_nat
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.24/5.57 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.24/5.57 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_nat_rec
% 5.24/5.57 thf(fact_9369_and__int_Opsimps,axiom,
% 5.24/5.57 ! [K: int,L2: int] :
% 5.24/5.57 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.24/5.57 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.24/5.57 = ( uminus_uminus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.24/5.57 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.24/5.57 = ( plus_plus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int.psimps
% 5.24/5.57 thf(fact_9370_and__int_Opelims,axiom,
% 5.24/5.57 ! [X: int,Xa2: int,Y4: int] :
% 5.24/5.57 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.24/5.57 = Y4 )
% 5.24/5.57 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.24/5.57 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( Y4
% 5.24/5.57 = ( uminus_uminus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.24/5.57 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( Y4
% 5.24/5.57 = ( plus_plus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.24/5.57 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) )
% 5.24/5.57 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int.pelims
% 5.24/5.57 thf(fact_9371_signed__take__bit__eq__take__bit__minus,axiom,
% 5.24/5.57 ( bit_ri631733984087533419it_int
% 5.24/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % signed_take_bit_eq_take_bit_minus
% 5.24/5.57 thf(fact_9372_atMost__0,axiom,
% 5.24/5.57 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.24/5.57 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_0
% 5.24/5.57 thf(fact_9373_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.24/5.57 ! [W2: num,N: nat] :
% 5.24/5.57 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N ) )
% 5.24/5.57 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_minus_numeral_Bit0_Suc_iff
% 5.24/5.57 thf(fact_9374_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.24/5.57 ! [W2: num,N: nat] :
% 5.24/5.57 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N ) )
% 5.24/5.57 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_minus_numeral_Bit1_Suc_iff
% 5.24/5.57 thf(fact_9375_bit__minus__numeral__int_I1_J,axiom,
% 5.24/5.57 ! [W2: num,N: num] :
% 5.24/5.57 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.57 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_minus_numeral_int(1)
% 5.24/5.57 thf(fact_9376_bit__minus__numeral__int_I2_J,axiom,
% 5.24/5.57 ! [W2: num,N: num] :
% 5.24/5.57 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.57 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_minus_numeral_int(2)
% 5.24/5.57 thf(fact_9377_set__encode__insert,axiom,
% 5.24/5.57 ! [A2: set_nat,N: nat] :
% 5.24/5.57 ( ( finite_finite_nat @ A2 )
% 5.24/5.57 => ( ~ ( member_nat @ N @ A2 )
% 5.24/5.57 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.24/5.57 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % set_encode_insert
% 5.24/5.57 thf(fact_9378_lessThan__Suc,axiom,
% 5.24/5.57 ! [K: nat] :
% 5.24/5.57 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.24/5.57 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % lessThan_Suc
% 5.24/5.57 thf(fact_9379_atMost__Suc,axiom,
% 5.24/5.57 ! [K: nat] :
% 5.24/5.57 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.24/5.57 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_Suc
% 5.24/5.57 thf(fact_9380_bit__not__int__iff_H,axiom,
% 5.24/5.57 ! [K: int,N: nat] :
% 5.24/5.57 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.24/5.57 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_not_int_iff'
% 5.24/5.57 thf(fact_9381_atLeast0__atMost__Suc,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.24/5.57 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atLeast0_atMost_Suc
% 5.24/5.57 thf(fact_9382_atLeastAtMost__insertL,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.24/5.57 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atLeastAtMost_insertL
% 5.24/5.57 thf(fact_9383_atLeastAtMostSuc__conv,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.24/5.57 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.24/5.57 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atLeastAtMostSuc_conv
% 5.24/5.57 thf(fact_9384_Icc__eq__insert__lb__nat,axiom,
% 5.24/5.57 ! [M: nat,N: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.24/5.57 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Icc_eq_insert_lb_nat
% 5.24/5.57 thf(fact_9385_lessThan__nat__numeral,axiom,
% 5.24/5.57 ! [K: num] :
% 5.24/5.57 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.24/5.57 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % lessThan_nat_numeral
% 5.24/5.57 thf(fact_9386_atMost__nat__numeral,axiom,
% 5.24/5.57 ! [K: num] :
% 5.24/5.57 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.24/5.57 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atMost_nat_numeral
% 5.24/5.57 thf(fact_9387_bit__imp__take__bit__positive,axiom,
% 5.24/5.57 ! [N: nat,M: nat,K: int] :
% 5.24/5.57 ( ( ord_less_nat @ N @ M )
% 5.24/5.57 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.24/5.57 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_imp_take_bit_positive
% 5.24/5.57 thf(fact_9388_bit__concat__bit__iff,axiom,
% 5.24/5.57 ! [M: nat,K: int,L2: int,N: nat] :
% 5.24/5.57 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 5.24/5.57 = ( ( ( ord_less_nat @ N @ M )
% 5.24/5.57 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.24/5.57 | ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.57 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_concat_bit_iff
% 5.24/5.57 thf(fact_9389_int__bit__bound,axiom,
% 5.24/5.57 ! [K: int] :
% 5.24/5.57 ~ ! [N3: nat] :
% 5.24/5.57 ( ! [M3: nat] :
% 5.24/5.57 ( ( ord_less_eq_nat @ N3 @ M3 )
% 5.24/5.57 => ( ( bit_se1146084159140164899it_int @ K @ M3 )
% 5.24/5.57 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.24/5.57 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.24/5.57 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.24/5.57 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % int_bit_bound
% 5.24/5.57 thf(fact_9390_atLeast1__atMost__eq__remove0,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.57 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % atLeast1_atMost_eq_remove0
% 5.24/5.57 thf(fact_9391_bit__int__def,axiom,
% 5.24/5.57 ( bit_se1146084159140164899it_int
% 5.24/5.57 = ( ^ [K3: int,N2: nat] :
% 5.24/5.57 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_int_def
% 5.24/5.57 thf(fact_9392_set__decode__plus__power__2,axiom,
% 5.24/5.57 ! [N: nat,Z2: nat] :
% 5.24/5.57 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z2 ) )
% 5.24/5.57 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z2 ) )
% 5.24/5.57 = ( insert_nat @ N @ ( nat_set_decode @ Z2 ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % set_decode_plus_power_2
% 5.24/5.57 thf(fact_9393_set__bit__eq,axiom,
% 5.24/5.57 ( bit_se7879613467334960850it_int
% 5.24/5.57 = ( ^ [N2: nat,K3: int] :
% 5.24/5.57 ( plus_plus_int @ K3
% 5.24/5.57 @ ( times_times_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 5.24/5.57 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % set_bit_eq
% 5.24/5.57 thf(fact_9394_unset__bit__eq,axiom,
% 5.24/5.57 ( bit_se4203085406695923979it_int
% 5.24/5.57 = ( ^ [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 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % unset_bit_eq
% 5.24/5.57 thf(fact_9395_and__int_Opinduct,axiom,
% 5.24/5.57 ! [A0: int,A12: int,P: int > int > $o] :
% 5.24/5.57 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.24/5.57 => ( ! [K2: int,L4: int] :
% 5.24/5.57 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.24/5.57 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.24/5.57 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.24/5.57 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.57 => ( P @ K2 @ L4 ) ) )
% 5.24/5.57 => ( P @ A0 @ A12 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % and_int.pinduct
% 5.24/5.57 thf(fact_9396_take__bit__Suc__from__most,axiom,
% 5.24/5.57 ! [N: nat,K: int] :
% 5.24/5.57 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.24/5.57 = ( 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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % take_bit_Suc_from_most
% 5.24/5.57 thf(fact_9397_upto_Opinduct,axiom,
% 5.24/5.57 ! [A0: int,A12: int,P: int > int > $o] :
% 5.24/5.57 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.24/5.57 => ( ! [I3: int,J2: int] :
% 5.24/5.57 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.24/5.57 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.24/5.57 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.24/5.57 => ( P @ I3 @ J2 ) ) )
% 5.24/5.57 => ( P @ A0 @ A12 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % upto.pinduct
% 5.24/5.57 thf(fact_9398_or__int__unfold,axiom,
% 5.24/5.57 ( bit_se1409905431419307370or_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( if_int
% 5.24/5.57 @ ( ( K3
% 5.24/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.57 | ( L
% 5.24/5.57 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.24/5.57 @ ( uminus_uminus_int @ one_one_int )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_int_unfold
% 5.24/5.57 thf(fact_9399_cis__multiple__2pi,axiom,
% 5.24/5.57 ! [N: real] :
% 5.24/5.57 ( ( member_real @ N @ ring_1_Ints_real )
% 5.24/5.57 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.24/5.57 = one_one_complex ) ) ).
% 5.24/5.57
% 5.24/5.57 % cis_multiple_2pi
% 5.24/5.57 thf(fact_9400_xor__Suc__0__eq,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_Suc_0_eq
% 5.24/5.57 thf(fact_9401_or__minus__numerals_I2_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(2)
% 5.24/5.57 thf(fact_9402_or__minus__numerals_I6_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(6)
% 5.24/5.57 thf(fact_9403_xor__nat__numerals_I4_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_nat_numerals(4)
% 5.24/5.57 thf(fact_9404_xor__nat__numerals_I3_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_nat_numerals(3)
% 5.24/5.57 thf(fact_9405_xor__nat__numerals_I2_J,axiom,
% 5.24/5.57 ! [Y4: num] :
% 5.24/5.57 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_nat_numerals(2)
% 5.24/5.57 thf(fact_9406_xor__nat__numerals_I1_J,axiom,
% 5.24/5.57 ! [Y4: num] :
% 5.24/5.57 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_nat_numerals(1)
% 5.24/5.57 thf(fact_9407_bit__Suc__0__iff,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.57 = ( N = zero_zero_nat ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_Suc_0_iff
% 5.24/5.57 thf(fact_9408_not__bit__Suc__0__Suc,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % not_bit_Suc_0_Suc
% 5.24/5.57 thf(fact_9409_plus__and__or,axiom,
% 5.24/5.57 ! [X: int,Y4: int] :
% 5.24/5.57 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ ( bit_se1409905431419307370or_int @ X @ Y4 ) )
% 5.24/5.57 = ( plus_plus_int @ X @ Y4 ) ) ).
% 5.24/5.57
% 5.24/5.57 % plus_and_or
% 5.24/5.57 thf(fact_9410_not__bit__Suc__0__numeral,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.24/5.57
% 5.24/5.57 % not_bit_Suc_0_numeral
% 5.24/5.57 thf(fact_9411_sin__times__pi__eq__0,axiom,
% 5.24/5.57 ! [X: real] :
% 5.24/5.57 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.24/5.57 = zero_zero_real )
% 5.24/5.57 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_times_pi_eq_0
% 5.24/5.57 thf(fact_9412_bit__nat__def,axiom,
% 5.24/5.57 ( bit_se1148574629649215175it_nat
% 5.24/5.57 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.57 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % bit_nat_def
% 5.24/5.57 thf(fact_9413_OR__upper,axiom,
% 5.24/5.57 ! [X: int,N: nat,Y4: int] :
% 5.24/5.57 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.24/5.57 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ( ord_less_int @ Y4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.57 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y4 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % OR_upper
% 5.24/5.57 thf(fact_9414_sin__integer__2pi,axiom,
% 5.24/5.57 ! [N: real] :
% 5.24/5.57 ( ( member_real @ N @ ring_1_Ints_real )
% 5.24/5.57 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.24/5.57 = zero_zero_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % sin_integer_2pi
% 5.24/5.57 thf(fact_9415_cos__integer__2pi,axiom,
% 5.24/5.57 ! [N: real] :
% 5.24/5.57 ( ( member_real @ N @ ring_1_Ints_real )
% 5.24/5.57 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.24/5.57 = one_one_real ) ) ).
% 5.24/5.57
% 5.24/5.57 % cos_integer_2pi
% 5.24/5.57 thf(fact_9416_xor__nat__unfold,axiom,
% 5.24/5.57 ( bit_se6528837805403552850or_nat
% 5.24/5.57 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M2 @ ( 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 @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_nat_unfold
% 5.24/5.57 thf(fact_9417_or__int__rec,axiom,
% 5.24/5.57 ( bit_se1409905431419307370or_int
% 5.24/5.57 = ( ^ [K3: int,L: int] :
% 5.24/5.57 ( plus_plus_int
% 5.24/5.57 @ ( zero_n2684676970156552555ol_int
% 5.24/5.57 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.24/5.57 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.24/5.57 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_int_rec
% 5.24/5.57 thf(fact_9418_xor__nat__rec,axiom,
% 5.24/5.57 ( bit_se6528837805403552850or_nat
% 5.24/5.57 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.57 ( plus_plus_nat
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.24/5.57 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.24/5.57 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % xor_nat_rec
% 5.24/5.57 thf(fact_9419_Suc__0__xor__eq,axiom,
% 5.24/5.57 ! [N: nat] :
% 5.24/5.57 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.57 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.57 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % Suc_0_xor_eq
% 5.24/5.57 thf(fact_9420_or__minus__numerals_I1_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(1)
% 5.24/5.57 thf(fact_9421_or__minus__numerals_I5_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(5)
% 5.24/5.57 thf(fact_9422_horner__sum__of__bool__2__less,axiom,
% 5.24/5.57 ! [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 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % horner_sum_of_bool_2_less
% 5.24/5.57 thf(fact_9423_or__nat__numerals_I2_J,axiom,
% 5.24/5.57 ! [Y4: num] :
% 5.24/5.57 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_nat_numerals(2)
% 5.24/5.57 thf(fact_9424_or__nat__numerals_I4_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_nat_numerals(4)
% 5.24/5.57 thf(fact_9425_or__nat__numerals_I1_J,axiom,
% 5.24/5.57 ! [Y4: num] :
% 5.24/5.57 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_nat_numerals(1)
% 5.24/5.57 thf(fact_9426_or__nat__numerals_I3_J,axiom,
% 5.24/5.57 ! [X: num] :
% 5.24/5.57 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.24/5.57 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_nat_numerals(3)
% 5.24/5.57 thf(fact_9427_or__minus__numerals_I4_J,axiom,
% 5.24/5.57 ! [M: num,N: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(4)
% 5.24/5.57 thf(fact_9428_or__minus__numerals_I8_J,axiom,
% 5.24/5.57 ! [N: num,M: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(8)
% 5.24/5.57 thf(fact_9429_or__minus__numerals_I3_J,axiom,
% 5.24/5.57 ! [M: num,N: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(3)
% 5.24/5.57 thf(fact_9430_or__minus__numerals_I7_J,axiom,
% 5.24/5.57 ! [N: num,M: num] :
% 5.24/5.57 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.24/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_minus_numerals(7)
% 5.24/5.57 thf(fact_9431_or__not__num__neg_Osimps_I1_J,axiom,
% 5.24/5.57 ( ( bit_or_not_num_neg @ one @ one )
% 5.24/5.57 = one ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(1)
% 5.24/5.57 thf(fact_9432_or__not__num__neg_Osimps_I4_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.24/5.57 = ( bit0 @ one ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(4)
% 5.24/5.57 thf(fact_9433_or__not__num__neg_Osimps_I6_J,axiom,
% 5.24/5.57 ! [N: num,M: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.24/5.57 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(6)
% 5.24/5.57 thf(fact_9434_or__not__num__neg_Osimps_I7_J,axiom,
% 5.24/5.57 ! [N: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.24/5.57 = one ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(7)
% 5.24/5.57 thf(fact_9435_or__not__num__neg_Osimps_I3_J,axiom,
% 5.24/5.57 ! [M: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.24/5.57 = ( bit1 @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(3)
% 5.24/5.57 thf(fact_9436_or__not__num__neg_Osimps_I5_J,axiom,
% 5.24/5.57 ! [N: num,M: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.24/5.57 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(5)
% 5.24/5.57 thf(fact_9437_or__not__num__neg_Osimps_I2_J,axiom,
% 5.24/5.57 ! [M: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.24/5.57 = ( bit1 @ M ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(2)
% 5.24/5.57 thf(fact_9438_or__not__num__neg_Osimps_I8_J,axiom,
% 5.24/5.57 ! [N: num,M: num] :
% 5.24/5.57 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.24/5.57 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.24/5.57
% 5.24/5.57 % or_not_num_neg.simps(8)
% 5.24/5.57 thf(fact_9439_or__not__num__neg_Oelims,axiom,
% 5.24/5.57 ! [X: num,Xa2: num,Y4: num] :
% 5.24/5.57 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.24/5.57 = Y4 )
% 5.24/5.57 => ( ( ( X = one )
% 5.24/5.57 => ( ( Xa2 = one )
% 5.24/5.57 => ( Y4 != one ) ) )
% 5.24/5.57 => ( ( ( X = one )
% 5.24/5.57 => ! [M4: num] :
% 5.24/5.57 ( ( Xa2
% 5.24/5.57 = ( bit0 @ M4 ) )
% 5.24/5.57 => ( Y4
% 5.24/5.57 != ( bit1 @ M4 ) ) ) )
% 5.24/5.57 => ( ( ( X = one )
% 5.24/5.57 => ! [M4: num] :
% 5.24/5.57 ( ( Xa2
% 5.24/5.57 = ( bit1 @ M4 ) )
% 5.24/5.57 => ( Y4
% 5.24/5.57 != ( bit1 @ M4 ) ) ) )
% 5.24/5.57 => ( ( ? [N3: num] :
% 5.24/5.57 ( X
% 5.24/5.57 = ( bit0 @ N3 ) )
% 5.24/5.57 => ( ( Xa2 = one )
% 5.24/5.57 => ( Y4
% 5.24/5.57 != ( bit0 @ one ) ) ) )
% 5.24/5.57 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.24/5.58 => ( ( ? [N3: num] :
% 5.24/5.58 ( X
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4 != one ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.24/5.58 => ~ ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_num_neg.elims
% 5.24/5.58 thf(fact_9440_XOR__upper,axiom,
% 5.24/5.58 ! [X: int,N: nat,Y4: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.24/5.58 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.58 => ( ( ord_less_int @ Y4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.24/5.58 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y4 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % XOR_upper
% 5.24/5.58 thf(fact_9441_floor__real__def,axiom,
% 5.24/5.58 ( archim6058952711729229775r_real
% 5.24/5.58 = ( ^ [X2: real] :
% 5.24/5.58 ( the_int
% 5.24/5.58 @ ^ [Z4: int] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X2 )
% 5.24/5.58 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % floor_real_def
% 5.24/5.58 thf(fact_9442_or__Suc__0__eq,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.58 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_Suc_0_eq
% 5.24/5.58 thf(fact_9443_Suc__0__or__eq,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.58 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Suc_0_or_eq
% 5.24/5.58 thf(fact_9444_or__nat__rec,axiom,
% 5.24/5.58 ( bit_se1412395901928357646or_nat
% 5.24/5.58 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.58 ( plus_plus_nat
% 5.24/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.24/5.58 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.24/5.58 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.24/5.58 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_nat_rec
% 5.24/5.58 thf(fact_9445_xor__int__rec,axiom,
% 5.24/5.58 ( bit_se6526347334894502574or_int
% 5.24/5.58 = ( ^ [K3: int,L: int] :
% 5.24/5.58 ( plus_plus_int
% 5.24/5.58 @ ( zero_n2684676970156552555ol_int
% 5.24/5.58 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.24/5.58 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.24/5.58 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_int_rec
% 5.24/5.58 thf(fact_9446_or__nat__unfold,axiom,
% 5.24/5.58 ( bit_se1412395901928357646or_nat
% 5.24/5.58 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M2 @ ( 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 @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_nat_unfold
% 5.24/5.58 thf(fact_9447_xor__int__unfold,axiom,
% 5.24/5.58 ( bit_se6526347334894502574or_int
% 5.24/5.58 = ( ^ [K3: int,L: int] :
% 5.24/5.58 ( if_int
% 5.24/5.58 @ ( K3
% 5.24/5.58 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.58 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.24/5.58 @ ( if_int
% 5.24/5.58 @ ( L
% 5.24/5.58 = ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.58 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.24/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_int_unfold
% 5.24/5.58 thf(fact_9448_floor__rat__def,axiom,
% 5.24/5.58 ( archim3151403230148437115or_rat
% 5.24/5.58 = ( ^ [X2: rat] :
% 5.24/5.58 ( the_int
% 5.24/5.58 @ ^ [Z4: int] :
% 5.24/5.58 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 )
% 5.24/5.58 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % floor_rat_def
% 5.24/5.58 thf(fact_9449_push__bit__of__Suc__0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % push_bit_of_Suc_0
% 5.24/5.58 thf(fact_9450_or__minus__minus__numerals,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_minus_minus_numerals
% 5.24/5.58 thf(fact_9451_and__minus__minus__numerals,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_minus_minus_numerals
% 5.24/5.58 thf(fact_9452_set__bit__nat__def,axiom,
% 5.24/5.58 ( bit_se7882103937844011126it_nat
% 5.24/5.58 = ( ^ [M2: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % set_bit_nat_def
% 5.24/5.58 thf(fact_9453_flip__bit__int__def,axiom,
% 5.24/5.58 ( bit_se2159334234014336723it_int
% 5.24/5.58 = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % flip_bit_int_def
% 5.24/5.58 thf(fact_9454_sgn__rat__def,axiom,
% 5.24/5.58 ( sgn_sgn_rat
% 5.24/5.58 = ( ^ [A4: rat] : ( if_rat @ ( A4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sgn_rat_def
% 5.24/5.58 thf(fact_9455_obtain__pos__sum,axiom,
% 5.24/5.58 ! [R2: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.24/5.58 => ~ ! [S: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ S )
% 5.24/5.58 => ! [T3: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.24/5.58 => ( R2
% 5.24/5.58 != ( plus_plus_rat @ S @ T3 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % obtain_pos_sum
% 5.24/5.58 thf(fact_9456_unset__bit__int__def,axiom,
% 5.24/5.58 ( bit_se4203085406695923979it_int
% 5.24/5.58 = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % unset_bit_int_def
% 5.24/5.58 thf(fact_9457_flip__bit__nat__def,axiom,
% 5.24/5.58 ( bit_se2161824704523386999it_nat
% 5.24/5.58 = ( ^ [M2: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % flip_bit_nat_def
% 5.24/5.58 thf(fact_9458_not__int__def,axiom,
% 5.24/5.58 ( bit_ri7919022796975470100ot_int
% 5.24/5.58 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % not_int_def
% 5.24/5.58 thf(fact_9459_and__not__numerals_I1_J,axiom,
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.24/5.58 = zero_zero_int ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(1)
% 5.24/5.58 thf(fact_9460_or__not__numerals_I1_J,axiom,
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(1)
% 5.24/5.58 thf(fact_9461_bit__push__bit__iff__int,axiom,
% 5.24/5.58 ! [M: nat,K: int,N: nat] :
% 5.24/5.58 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.24/5.58 = ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.58 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bit_push_bit_iff_int
% 5.24/5.58 thf(fact_9462_bit__push__bit__iff__nat,axiom,
% 5.24/5.58 ! [M: nat,Q2: nat,N: nat] :
% 5.24/5.58 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.24/5.58 = ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.58 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bit_push_bit_iff_nat
% 5.24/5.58 thf(fact_9463_concat__bit__eq,axiom,
% 5.24/5.58 ( bit_concat_bit
% 5.24/5.58 = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % concat_bit_eq
% 5.24/5.58 thf(fact_9464_set__bit__int__def,axiom,
% 5.24/5.58 ( bit_se7879613467334960850it_int
% 5.24/5.58 = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % set_bit_int_def
% 5.24/5.58 thf(fact_9465_not__int__div__2,axiom,
% 5.24/5.58 ! [K: int] :
% 5.24/5.58 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % not_int_div_2
% 5.24/5.58 thf(fact_9466_even__not__iff__int,axiom,
% 5.24/5.58 ! [K: int] :
% 5.24/5.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.24/5.58 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % even_not_iff_int
% 5.24/5.58 thf(fact_9467_and__not__numerals_I4_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.24/5.58 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(4)
% 5.24/5.58 thf(fact_9468_and__not__numerals_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = one_one_int ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(2)
% 5.24/5.58 thf(fact_9469_or__not__numerals_I4_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(4)
% 5.24/5.58 thf(fact_9470_or__not__numerals_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(2)
% 5.24/5.58 thf(fact_9471_bit__minus__int__iff,axiom,
% 5.24/5.58 ! [K: int,N: nat] :
% 5.24/5.58 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.24/5.58 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % bit_minus_int_iff
% 5.24/5.58 thf(fact_9472_and__not__numerals_I5_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(5)
% 5.24/5.58 thf(fact_9473_and__not__numerals_I7_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.24/5.58 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(7)
% 5.24/5.58 thf(fact_9474_or__not__numerals_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(3)
% 5.24/5.58 thf(fact_9475_and__not__numerals_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = zero_zero_int ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(3)
% 5.24/5.58 thf(fact_9476_or__not__numerals_I7_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(7)
% 5.24/5.58 thf(fact_9477_push__bit__int__def,axiom,
% 5.24/5.58 ( bit_se545348938243370406it_int
% 5.24/5.58 = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % push_bit_int_def
% 5.24/5.58 thf(fact_9478_push__bit__nat__def,axiom,
% 5.24/5.58 ( bit_se547839408752420682it_nat
% 5.24/5.58 = ( ^ [N2: nat,M2: nat] : ( times_times_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % push_bit_nat_def
% 5.24/5.58 thf(fact_9479_and__not__numerals_I9_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(9)
% 5.24/5.58 thf(fact_9480_and__not__numerals_I6_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(6)
% 5.24/5.58 thf(fact_9481_or__not__numerals_I6_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(6)
% 5.24/5.58 thf(fact_9482_push__bit__minus__one,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.58 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % push_bit_minus_one
% 5.24/5.58 thf(fact_9483_or__not__numerals_I5_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(5)
% 5.24/5.58 thf(fact_9484_and__not__numerals_I8_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_numerals(8)
% 5.24/5.58 thf(fact_9485_or__not__numerals_I8_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(8)
% 5.24/5.58 thf(fact_9486_or__not__numerals_I9_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_numerals(9)
% 5.24/5.58 thf(fact_9487_not__int__rec,axiom,
% 5.24/5.58 ( bit_ri7919022796975470100ot_int
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % not_int_rec
% 5.24/5.58 thf(fact_9488_rat__inverse__code,axiom,
% 5.24/5.58 ! [P6: rat] :
% 5.24/5.58 ( ( quotient_of @ ( inverse_inverse_rat @ P6 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_inverse_code
% 5.24/5.58 thf(fact_9489_normalize__negative,axiom,
% 5.24/5.58 ! [Q2: int,P6: int] :
% 5.24/5.58 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.24/5.58 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.24/5.58 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P6 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % normalize_negative
% 5.24/5.58 thf(fact_9490_quotient__of__number_I3_J,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.24/5.58 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_number(3)
% 5.24/5.58 thf(fact_9491_normalize__denom__zero,axiom,
% 5.24/5.58 ! [P6: int] :
% 5.24/5.58 ( ( normalize @ ( product_Pair_int_int @ P6 @ zero_zero_int ) )
% 5.24/5.58 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % normalize_denom_zero
% 5.24/5.58 thf(fact_9492_rat__one__code,axiom,
% 5.24/5.58 ( ( quotient_of @ one_one_rat )
% 5.24/5.58 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_one_code
% 5.24/5.58 thf(fact_9493_rat__zero__code,axiom,
% 5.24/5.58 ( ( quotient_of @ zero_zero_rat )
% 5.24/5.58 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_zero_code
% 5.24/5.58 thf(fact_9494_quotient__of__number_I5_J,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.24/5.58 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_number(5)
% 5.24/5.58 thf(fact_9495_quotient__of__number_I4_J,axiom,
% 5.24/5.58 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.24/5.58 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_number(4)
% 5.24/5.58 thf(fact_9496_divide__rat__def,axiom,
% 5.24/5.58 ( divide_divide_rat
% 5.24/5.58 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divide_rat_def
% 5.24/5.58 thf(fact_9497_diff__rat__def,axiom,
% 5.24/5.58 ( minus_minus_rat
% 5.24/5.58 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % diff_rat_def
% 5.24/5.58 thf(fact_9498_rat__times__code,axiom,
% 5.24/5.58 ! [P6: rat,Q2: rat] :
% 5.24/5.58 ( ( quotient_of @ ( times_times_rat @ P6 @ Q2 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [A4: int,C2: int] :
% 5.24/5.58 ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ B3 ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.24/5.58 @ ( quotient_of @ Q2 ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_times_code
% 5.24/5.58 thf(fact_9499_rat__divide__code,axiom,
% 5.24/5.58 ! [P6: rat,Q2: rat] :
% 5.24/5.58 ( ( quotient_of @ ( divide_divide_rat @ P6 @ Q2 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [A4: int,C2: int] :
% 5.24/5.58 ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C2 @ B3 ) ) )
% 5.24/5.58 @ ( quotient_of @ Q2 ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_divide_code
% 5.24/5.58 thf(fact_9500_quotient__of__div,axiom,
% 5.24/5.58 ! [R2: rat,N: int,D: int] :
% 5.24/5.58 ( ( ( quotient_of @ R2 )
% 5.24/5.58 = ( product_Pair_int_int @ N @ D ) )
% 5.24/5.58 => ( R2
% 5.24/5.58 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_div
% 5.24/5.58 thf(fact_9501_rat__plus__code,axiom,
% 5.24/5.58 ! [P6: rat,Q2: rat] :
% 5.24/5.58 ( ( quotient_of @ ( plus_plus_rat @ P6 @ Q2 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [A4: int,C2: int] :
% 5.24/5.58 ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B3 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.24/5.58 @ ( quotient_of @ Q2 ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_plus_code
% 5.24/5.58 thf(fact_9502_rat__minus__code,axiom,
% 5.24/5.58 ! [P6: rat,Q2: rat] :
% 5.24/5.58 ( ( quotient_of @ ( minus_minus_rat @ P6 @ Q2 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [A4: int,C2: int] :
% 5.24/5.58 ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B3 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.24/5.58 @ ( quotient_of @ Q2 ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_minus_code
% 5.24/5.58 thf(fact_9503_quotient__of__denom__pos,axiom,
% 5.24/5.58 ! [R2: rat,P6: int,Q2: int] :
% 5.24/5.58 ( ( ( quotient_of @ R2 )
% 5.24/5.58 = ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.24/5.58 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_denom_pos
% 5.24/5.58 thf(fact_9504_rat__less__code,axiom,
% 5.24/5.58 ( ord_less_rat
% 5.24/5.58 = ( ^ [P4: rat,Q4: rat] :
% 5.24/5.58 ( produc4947309494688390418_int_o
% 5.24/5.58 @ ^ [A4: int,C2: int] :
% 5.24/5.58 ( produc4947309494688390418_int_o
% 5.24/5.58 @ ^ [B3: int,D2: int] : ( ord_less_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.24/5.58 @ ( quotient_of @ Q4 ) )
% 5.24/5.58 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_less_code
% 5.24/5.58 thf(fact_9505_rat__less__eq__code,axiom,
% 5.24/5.58 ( ord_less_eq_rat
% 5.24/5.58 = ( ^ [P4: rat,Q4: rat] :
% 5.24/5.58 ( produc4947309494688390418_int_o
% 5.24/5.58 @ ^ [A4: int,C2: int] :
% 5.24/5.58 ( produc4947309494688390418_int_o
% 5.24/5.58 @ ^ [B3: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.24/5.58 @ ( quotient_of @ Q4 ) )
% 5.24/5.58 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_less_eq_code
% 5.24/5.58 thf(fact_9506_rat__uminus__code,axiom,
% 5.24/5.58 ! [P6: rat] :
% 5.24/5.58 ( ( quotient_of @ ( uminus_uminus_rat @ P6 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [A4: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A4 ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_uminus_code
% 5.24/5.58 thf(fact_9507_rat__abs__code,axiom,
% 5.24/5.58 ! [P6: rat] :
% 5.24/5.58 ( ( quotient_of @ ( abs_abs_rat @ P6 ) )
% 5.24/5.58 = ( produc4245557441103728435nt_int
% 5.24/5.58 @ ^ [A4: int] : ( product_Pair_int_int @ ( abs_abs_int @ A4 ) )
% 5.24/5.58 @ ( quotient_of @ P6 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_abs_code
% 5.24/5.58 thf(fact_9508_normalize__denom__pos,axiom,
% 5.24/5.58 ! [R2: product_prod_int_int,P6: int,Q2: int] :
% 5.24/5.58 ( ( ( normalize @ R2 )
% 5.24/5.58 = ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.24/5.58 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % normalize_denom_pos
% 5.24/5.58 thf(fact_9509_normalize__crossproduct,axiom,
% 5.24/5.58 ! [Q2: int,S2: int,P6: int,R2: int] :
% 5.24/5.58 ( ( Q2 != zero_zero_int )
% 5.24/5.58 => ( ( S2 != zero_zero_int )
% 5.24/5.58 => ( ( ( normalize @ ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.24/5.58 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 5.24/5.58 => ( ( times_times_int @ P6 @ S2 )
% 5.24/5.58 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % normalize_crossproduct
% 5.24/5.58 thf(fact_9510_quotient__of__int,axiom,
% 5.24/5.58 ! [A: int] :
% 5.24/5.58 ( ( quotient_of @ ( of_int @ A ) )
% 5.24/5.58 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_int
% 5.24/5.58 thf(fact_9511_Sum__Ico__nat,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( groups3542108847815614940at_nat
% 5.24/5.58 @ ^ [X2: nat] : X2
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.24/5.58 = ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Sum_Ico_nat
% 5.24/5.58 thf(fact_9512_Cauchy__iff2,axiom,
% 5.24/5.58 ( topolo4055970368930404560y_real
% 5.24/5.58 = ( ^ [X6: nat > real] :
% 5.24/5.58 ! [J3: nat] :
% 5.24/5.58 ? [M9: nat] :
% 5.24/5.58 ! [M2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ M9 @ M2 )
% 5.24/5.58 => ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ M9 @ N2 )
% 5.24/5.58 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Cauchy_iff2
% 5.24/5.58 thf(fact_9513_VEBT_Osize_I3_J,axiom,
% 5.24/5.58 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.24/5.58 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.24/5.58 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT.size(3)
% 5.24/5.58 thf(fact_9514_atLeastLessThan__singleton,axiom,
% 5.24/5.58 ! [M: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.24/5.58 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThan_singleton
% 5.24/5.58 thf(fact_9515_all__nat__less__eq,axiom,
% 5.24/5.58 ! [N: nat,P: nat > $o] :
% 5.24/5.58 ( ( ! [M2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ M2 @ N )
% 5.24/5.58 => ( P @ M2 ) ) )
% 5.24/5.58 = ( ! [X2: nat] :
% 5.24/5.58 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.24/5.58 => ( P @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % all_nat_less_eq
% 5.24/5.58 thf(fact_9516_ex__nat__less__eq,axiom,
% 5.24/5.58 ! [N: nat,P: nat > $o] :
% 5.24/5.58 ( ( ? [M2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ M2 @ N )
% 5.24/5.58 & ( P @ M2 ) ) )
% 5.24/5.58 = ( ? [X2: nat] :
% 5.24/5.58 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.24/5.58 & ( P @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % ex_nat_less_eq
% 5.24/5.58 thf(fact_9517_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.24/5.58 ! [L2: nat,U2: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U2 ) )
% 5.24/5.58 = ( set_or1269000886237332187st_nat @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThanSuc_atLeastAtMost
% 5.24/5.58 thf(fact_9518_atLeastLessThan0,axiom,
% 5.24/5.58 ! [M: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.24/5.58 = bot_bot_set_nat ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThan0
% 5.24/5.58 thf(fact_9519_atLeast0__lessThan__Suc,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.24/5.58 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast0_lessThan_Suc
% 5.24/5.58 thf(fact_9520_atLeastLessThanSuc,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.24/5.58 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.24/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.24/5.58 = bot_bot_set_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThanSuc
% 5.24/5.58 thf(fact_9521_prod__Suc__fact,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.24/5.58 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_Suc_fact
% 5.24/5.58 thf(fact_9522_prod__Suc__Suc__fact,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.24/5.58 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_Suc_Suc_fact
% 5.24/5.58 thf(fact_9523_atLeastLessThan__nat__numeral,axiom,
% 5.24/5.58 ! [M: nat,K: num] :
% 5.24/5.58 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.24/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.24/5.58 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.24/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.24/5.58 = bot_bot_set_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThan_nat_numeral
% 5.24/5.58 thf(fact_9524_atLeast1__lessThan__eq__remove0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.24/5.58 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast1_lessThan_eq_remove0
% 5.24/5.58 thf(fact_9525_sum__power2,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.24/5.58 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % sum_power2
% 5.24/5.58 thf(fact_9526_Chebyshev__sum__upper__nat,axiom,
% 5.24/5.58 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.24/5.58 ( ! [I3: nat,J2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.24/5.58 => ( ( ord_less_nat @ J2 @ N )
% 5.24/5.58 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 5.24/5.58 => ( ! [I3: nat,J2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.24/5.58 => ( ( ord_less_nat @ J2 @ N )
% 5.24/5.58 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 5.24/5.58 => ( ord_less_eq_nat
% 5.24/5.58 @ ( times_times_nat @ N
% 5.24/5.58 @ ( groups3542108847815614940at_nat
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.24/5.58 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Chebyshev_sum_upper_nat
% 5.24/5.58 thf(fact_9527_VEBT_Osize__gen_I1_J,axiom,
% 5.24/5.58 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.24/5.58 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.24/5.58 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT.size_gen(1)
% 5.24/5.58 thf(fact_9528_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.24/5.58 ! [L2: int,U2: int] :
% 5.24/5.58 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U2 @ one_one_int ) )
% 5.24/5.58 = ( set_or1266510415728281911st_int @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.24/5.58 thf(fact_9529_VEBT_Osize__gen_I2_J,axiom,
% 5.24/5.58 ! [X21: $o,X222: $o] :
% 5.24/5.58 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.24/5.58 = zero_zero_nat ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT.size_gen(2)
% 5.24/5.58 thf(fact_9530_Frct__code__post_I5_J,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.24/5.58 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(5)
% 5.24/5.58 thf(fact_9531_valid__eq,axiom,
% 5.24/5.58 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.24/5.58
% 5.24/5.58 % valid_eq
% 5.24/5.58 thf(fact_9532_valid__eq2,axiom,
% 5.24/5.58 ! [T: vEBT_VEBT,D: nat] :
% 5.24/5.58 ( ( vEBT_VEBT_valid @ T @ D )
% 5.24/5.58 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.24/5.58
% 5.24/5.58 % valid_eq2
% 5.24/5.58 thf(fact_9533_valid__eq1,axiom,
% 5.24/5.58 ! [T: vEBT_VEBT,D: nat] :
% 5.24/5.58 ( ( vEBT_invar_vebt @ T @ D )
% 5.24/5.58 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.24/5.58
% 5.24/5.58 % valid_eq1
% 5.24/5.58 thf(fact_9534_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.24/5.58 ! [Uu: $o,Uv: $o,D: nat] :
% 5.24/5.58 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.24/5.58 = ( D = one_one_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.simps(1)
% 5.24/5.58 thf(fact_9535_Frct__code__post_I1_J,axiom,
% 5.24/5.58 ! [A: int] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.24/5.58 = zero_zero_rat ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(1)
% 5.24/5.58 thf(fact_9536_Frct__code__post_I2_J,axiom,
% 5.24/5.58 ! [A: int] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.24/5.58 = zero_zero_rat ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(2)
% 5.24/5.58 thf(fact_9537_Frct__code__post_I8_J,axiom,
% 5.24/5.58 ! [A: int,B: int] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.24/5.58 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(8)
% 5.24/5.58 thf(fact_9538_Frct__code__post_I7_J,axiom,
% 5.24/5.58 ! [A: int,B: int] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.24/5.58 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(7)
% 5.24/5.58 thf(fact_9539_Frct__code__post_I3_J,axiom,
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.24/5.58 = one_one_rat ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(3)
% 5.24/5.58 thf(fact_9540_Frct__code__post_I4_J,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.24/5.58 = ( numeral_numeral_rat @ K ) ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(4)
% 5.24/5.58 thf(fact_9541_Frct__code__post_I6_J,axiom,
% 5.24/5.58 ! [K: num,L2: num] :
% 5.24/5.58 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.24/5.58 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Frct_code_post(6)
% 5.24/5.58 thf(fact_9542_divmod__step__integer__def,axiom,
% 5.24/5.58 ( unique4921790084139445826nteger
% 5.24/5.58 = ( ^ [L: num] :
% 5.24/5.58 ( produc6916734918728496179nteger
% 5.24/5.58 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_step_integer_def
% 5.24/5.58 thf(fact_9543_csqrt_Osimps_I1_J,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( re @ ( csqrt @ Z2 ) )
% 5.24/5.58 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt.simps(1)
% 5.24/5.58 thf(fact_9544_times__integer__code_I1_J,axiom,
% 5.24/5.58 ! [K: code_integer] :
% 5.24/5.58 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.24/5.58 = zero_z3403309356797280102nteger ) ).
% 5.24/5.58
% 5.24/5.58 % times_integer_code(1)
% 5.24/5.58 thf(fact_9545_times__integer__code_I2_J,axiom,
% 5.24/5.58 ! [L2: code_integer] :
% 5.24/5.58 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.24/5.58 = zero_z3403309356797280102nteger ) ).
% 5.24/5.58
% 5.24/5.58 % times_integer_code(2)
% 5.24/5.58 thf(fact_9546_divmod__integer_H__def,axiom,
% 5.24/5.58 ( unique3479559517661332726nteger
% 5.24/5.58 = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_integer'_def
% 5.24/5.58 thf(fact_9547_full__exhaustive__integer_H_Ocases,axiom,
% 5.24/5.58 ! [X: produc1908205239877642774nteger] :
% 5.24/5.58 ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D3: code_integer,I3: code_integer] :
% 5.24/5.58 ( X
% 5.24/5.58 != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I3 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % full_exhaustive_integer'.cases
% 5.24/5.58 thf(fact_9548_exhaustive__integer_H_Ocases,axiom,
% 5.24/5.58 ! [X: produc8763457246119570046nteger] :
% 5.24/5.58 ~ ! [F2: code_integer > option6357759511663192854e_term,D3: code_integer,I3: code_integer] :
% 5.24/5.58 ( X
% 5.24/5.58 != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I3 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % exhaustive_integer'.cases
% 5.24/5.58 thf(fact_9549_plus__integer__code_I2_J,axiom,
% 5.24/5.58 ! [L2: code_integer] :
% 5.24/5.58 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.24/5.58 = L2 ) ).
% 5.24/5.58
% 5.24/5.58 % plus_integer_code(2)
% 5.24/5.58 thf(fact_9550_plus__integer__code_I1_J,axiom,
% 5.24/5.58 ! [K: code_integer] :
% 5.24/5.58 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.24/5.58 = K ) ).
% 5.24/5.58
% 5.24/5.58 % plus_integer_code(1)
% 5.24/5.58 thf(fact_9551_sgn__integer__code,axiom,
% 5.24/5.58 ( sgn_sgn_Code_integer
% 5.24/5.58 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sgn_integer_code
% 5.24/5.58 thf(fact_9552_one__complex_Osimps_I1_J,axiom,
% 5.24/5.58 ( ( re @ one_one_complex )
% 5.24/5.58 = one_one_real ) ).
% 5.24/5.58
% 5.24/5.58 % one_complex.simps(1)
% 5.24/5.58 thf(fact_9553_plus__complex_Osimps_I1_J,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( re @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.58 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y4 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_complex.simps(1)
% 5.24/5.58 thf(fact_9554_scaleR__complex_Osimps_I1_J,axiom,
% 5.24/5.58 ! [R2: real,X: complex] :
% 5.24/5.58 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.24/5.58 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % scaleR_complex.simps(1)
% 5.24/5.58 thf(fact_9555_one__integer_Orsp,axiom,
% 5.24/5.58 one_one_int = one_one_int ).
% 5.24/5.58
% 5.24/5.58 % one_integer.rsp
% 5.24/5.58 thf(fact_9556_one__natural_Orsp,axiom,
% 5.24/5.58 one_one_nat = one_one_nat ).
% 5.24/5.58
% 5.24/5.58 % one_natural.rsp
% 5.24/5.58 thf(fact_9557_cmod__plus__Re__le__0__iff,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ zero_zero_real )
% 5.24/5.58 = ( ( re @ Z2 )
% 5.24/5.58 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cmod_plus_Re_le_0_iff
% 5.24/5.58 thf(fact_9558_cos__n__Re__cis__pow__n,axiom,
% 5.24/5.58 ! [N: nat,A: real] :
% 5.24/5.58 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.24/5.58 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cos_n_Re_cis_pow_n
% 5.24/5.58 thf(fact_9559_csqrt_Ocode,axiom,
% 5.24/5.58 ( csqrt
% 5.24/5.58 = ( ^ [Z4: complex] :
% 5.24/5.58 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.58 @ ( times_times_real
% 5.24/5.58 @ ( if_real
% 5.24/5.58 @ ( ( im @ Z4 )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 @ one_one_real
% 5.24/5.58 @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 5.24/5.58 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt.code
% 5.24/5.58 thf(fact_9560_csqrt_Osimps_I2_J,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( im @ ( csqrt @ Z2 ) )
% 5.24/5.58 = ( times_times_real
% 5.24/5.58 @ ( if_real
% 5.24/5.58 @ ( ( im @ Z2 )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 @ one_one_real
% 5.24/5.58 @ ( sgn_sgn_real @ ( im @ Z2 ) ) )
% 5.24/5.58 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt.simps(2)
% 5.24/5.58 thf(fact_9561_integer__of__int__code,axiom,
% 5.24/5.58 ( code_integer_of_int
% 5.24/5.58 = ( ^ [K3: int] :
% 5.24/5.58 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.24/5.58 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.24/5.58 @ ( if_Code_integer
% 5.24/5.58 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_int_code
% 5.24/5.58 thf(fact_9562_csqrt__of__real__nonpos,axiom,
% 5.24/5.58 ! [X: complex] :
% 5.24/5.58 ( ( ( im @ X )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.24/5.58 => ( ( csqrt @ X )
% 5.24/5.58 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt_of_real_nonpos
% 5.24/5.58 thf(fact_9563_Im__i__times,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( im @ ( times_times_complex @ imaginary_unit @ Z2 ) )
% 5.24/5.58 = ( re @ Z2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_i_times
% 5.24/5.58 thf(fact_9564_Re__i__times,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( re @ ( times_times_complex @ imaginary_unit @ Z2 ) )
% 5.24/5.58 = ( uminus_uminus_real @ ( im @ Z2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_i_times
% 5.24/5.58 thf(fact_9565_csqrt__minus,axiom,
% 5.24/5.58 ! [X: complex] :
% 5.24/5.58 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.24/5.58 | ( ( ( im @ X )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.24/5.58 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.24/5.58 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt_minus
% 5.24/5.58 thf(fact_9566_imaginary__unit_Osimps_I2_J,axiom,
% 5.24/5.58 ( ( im @ imaginary_unit )
% 5.24/5.58 = one_one_real ) ).
% 5.24/5.58
% 5.24/5.58 % imaginary_unit.simps(2)
% 5.24/5.58 thf(fact_9567_one__complex_Osimps_I2_J,axiom,
% 5.24/5.58 ( ( im @ one_one_complex )
% 5.24/5.58 = zero_zero_real ) ).
% 5.24/5.58
% 5.24/5.58 % one_complex.simps(2)
% 5.24/5.58 thf(fact_9568_plus__integer_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: int,X: int] :
% 5.24/5.58 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.24/5.58 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_integer.abs_eq
% 5.24/5.58 thf(fact_9569_times__integer_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: int,X: int] :
% 5.24/5.58 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.24/5.58 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_integer.abs_eq
% 5.24/5.58 thf(fact_9570_one__integer__def,axiom,
% 5.24/5.58 ( one_one_Code_integer
% 5.24/5.58 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_integer_def
% 5.24/5.58 thf(fact_9571_plus__complex_Osimps_I2_J,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( im @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.58 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y4 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_complex.simps(2)
% 5.24/5.58 thf(fact_9572_scaleR__complex_Osimps_I2_J,axiom,
% 5.24/5.58 ! [R2: real,X: complex] :
% 5.24/5.58 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.24/5.58 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % scaleR_complex.simps(2)
% 5.24/5.58 thf(fact_9573_times__complex_Osimps_I2_J,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( im @ ( times_times_complex @ X @ Y4 ) )
% 5.24/5.58 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_complex.simps(2)
% 5.24/5.58 thf(fact_9574_times__complex_Osimps_I1_J,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( re @ ( times_times_complex @ X @ Y4 ) )
% 5.24/5.58 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_complex.simps(1)
% 5.24/5.58 thf(fact_9575_plus__complex_Ocode,axiom,
% 5.24/5.58 ( plus_plus_complex
% 5.24/5.58 = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_complex.code
% 5.24/5.58 thf(fact_9576_scaleR__complex_Ocode,axiom,
% 5.24/5.58 ( real_V2046097035970521341omplex
% 5.24/5.58 = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % scaleR_complex.code
% 5.24/5.58 thf(fact_9577_cmod__le,axiom,
% 5.24/5.58 ! [Z2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z2 ) ) @ ( abs_abs_real @ ( im @ Z2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cmod_le
% 5.24/5.58 thf(fact_9578_sin__n__Im__cis__pow__n,axiom,
% 5.24/5.58 ! [N: nat,A: real] :
% 5.24/5.58 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.24/5.58 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sin_n_Im_cis_pow_n
% 5.24/5.58 thf(fact_9579_Re__exp,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( re @ ( exp_complex @ Z2 ) )
% 5.24/5.58 = ( times_times_real @ ( exp_real @ ( re @ Z2 ) ) @ ( cos_real @ ( im @ Z2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_exp
% 5.24/5.58 thf(fact_9580_Im__exp,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( im @ ( exp_complex @ Z2 ) )
% 5.24/5.58 = ( times_times_real @ ( exp_real @ ( re @ Z2 ) ) @ ( sin_real @ ( im @ Z2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_exp
% 5.24/5.58 thf(fact_9581_complex__eq,axiom,
% 5.24/5.58 ! [A: complex] :
% 5.24/5.58 ( A
% 5.24/5.58 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_eq
% 5.24/5.58 thf(fact_9582_times__complex_Ocode,axiom,
% 5.24/5.58 ( times_times_complex
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_complex.code
% 5.24/5.58 thf(fact_9583_exp__eq__polar,axiom,
% 5.24/5.58 ( exp_complex
% 5.24/5.58 = ( ^ [Z4: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z4 ) ) ) @ ( cis @ ( im @ Z4 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % exp_eq_polar
% 5.24/5.58 thf(fact_9584_cmod__power2,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.58 = ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cmod_power2
% 5.24/5.58 thf(fact_9585_Im__power2,axiom,
% 5.24/5.58 ! [X: complex] :
% 5.24/5.58 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_power2
% 5.24/5.58 thf(fact_9586_Re__power2,axiom,
% 5.24/5.58 ! [X: complex] :
% 5.24/5.58 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_power2
% 5.24/5.58 thf(fact_9587_complex__eq__0,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( Z2 = zero_zero_complex )
% 5.24/5.58 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_eq_0
% 5.24/5.58 thf(fact_9588_norm__complex__def,axiom,
% 5.24/5.58 ( real_V1022390504157884413omplex
% 5.24/5.58 = ( ^ [Z4: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % norm_complex_def
% 5.24/5.58 thf(fact_9589_inverse__complex_Osimps_I1_J,axiom,
% 5.24/5.58 ! [X: complex] :
% 5.24/5.58 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_complex.simps(1)
% 5.24/5.58 thf(fact_9590_complex__neq__0,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( Z2 != zero_zero_complex )
% 5.24/5.58 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_neq_0
% 5.24/5.58 thf(fact_9591_Re__divide,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( re @ ( divide1717551699836669952omplex @ X @ Y4 ) )
% 5.24/5.58 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_divide
% 5.24/5.58 thf(fact_9592_csqrt__unique,axiom,
% 5.24/5.58 ! [W2: complex,Z2: complex] :
% 5.24/5.58 ( ( ( power_power_complex @ W2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.24/5.58 = Z2 )
% 5.24/5.58 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W2 ) )
% 5.24/5.58 | ( ( ( re @ W2 )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W2 ) ) ) )
% 5.24/5.58 => ( ( csqrt @ Z2 )
% 5.24/5.58 = W2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt_unique
% 5.24/5.58 thf(fact_9593_csqrt__square,axiom,
% 5.24/5.58 ! [B: complex] :
% 5.24/5.58 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.24/5.58 | ( ( ( re @ B )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.24/5.58 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = B ) ) ).
% 5.24/5.58
% 5.24/5.58 % csqrt_square
% 5.24/5.58 thf(fact_9594_inverse__complex_Osimps_I2_J,axiom,
% 5.24/5.58 ! [X: complex] :
% 5.24/5.58 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_complex.simps(2)
% 5.24/5.58 thf(fact_9595_Im__divide,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( im @ ( divide1717551699836669952omplex @ X @ Y4 ) )
% 5.24/5.58 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_divide
% 5.24/5.58 thf(fact_9596_complex__abs__le__norm,axiom,
% 5.24/5.58 ! [Z2: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z2 ) ) @ ( abs_abs_real @ ( im @ Z2 ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_abs_le_norm
% 5.24/5.58 thf(fact_9597_complex__unit__circle,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( Z2 != zero_zero_complex )
% 5.24/5.58 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z2 ) @ ( real_V1022390504157884413omplex @ Z2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z2 ) @ ( real_V1022390504157884413omplex @ Z2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = one_one_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_unit_circle
% 5.24/5.58 thf(fact_9598_inverse__complex_Ocode,axiom,
% 5.24/5.58 ( invers8013647133539491842omplex
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_complex.code
% 5.24/5.58 thf(fact_9599_Complex__divide,axiom,
% 5.24/5.58 ( divide1717551699836669952omplex
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Complex_divide
% 5.24/5.58 thf(fact_9600_Im__Reals__divide,axiom,
% 5.24/5.58 ! [R2: complex,Z2: complex] :
% 5.24/5.58 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.24/5.58 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z2 ) )
% 5.24/5.58 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_Reals_divide
% 5.24/5.58 thf(fact_9601_Re__Reals__divide,axiom,
% 5.24/5.58 ! [R2: complex,Z2: complex] :
% 5.24/5.58 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.24/5.58 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z2 ) )
% 5.24/5.58 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_Reals_divide
% 5.24/5.58 thf(fact_9602_real__eq__imaginary__iff,axiom,
% 5.24/5.58 ! [Y4: complex,X: complex] :
% 5.24/5.58 ( ( member_complex @ Y4 @ real_V2521375963428798218omplex )
% 5.24/5.58 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.24/5.58 => ( ( X
% 5.24/5.58 = ( times_times_complex @ imaginary_unit @ Y4 ) )
% 5.24/5.58 = ( ( X = zero_zero_complex )
% 5.24/5.58 & ( Y4 = zero_zero_complex ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % real_eq_imaginary_iff
% 5.24/5.58 thf(fact_9603_imaginary__eq__real__iff,axiom,
% 5.24/5.58 ! [Y4: complex,X: complex] :
% 5.24/5.58 ( ( member_complex @ Y4 @ real_V2521375963428798218omplex )
% 5.24/5.58 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.24/5.58 => ( ( ( times_times_complex @ imaginary_unit @ Y4 )
% 5.24/5.58 = X )
% 5.24/5.58 = ( ( X = zero_zero_complex )
% 5.24/5.58 & ( Y4 = zero_zero_complex ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % imaginary_eq_real_iff
% 5.24/5.58 thf(fact_9604_complex__mult__cnj,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( times_times_complex @ Z2 @ ( cnj @ Z2 ) )
% 5.24/5.58 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_mult_cnj
% 5.24/5.58 thf(fact_9605_integer__of__num_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.24/5.58 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_num(3)
% 5.24/5.58 thf(fact_9606_int__of__integer__code,axiom,
% 5.24/5.58 ( code_int_of_integer
% 5.24/5.58 = ( ^ [K3: code_integer] :
% 5.24/5.58 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.24/5.58 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.24/5.58 @ ( produc1553301316500091796er_int
% 5.24/5.58 @ ^ [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 ) )
% 5.24/5.58 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % int_of_integer_code
% 5.24/5.58 thf(fact_9607_complex__cnj__mult,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( cnj @ ( times_times_complex @ X @ Y4 ) )
% 5.24/5.58 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y4 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_cnj_mult
% 5.24/5.58 thf(fact_9608_complex__cnj__one__iff,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( ( cnj @ Z2 )
% 5.24/5.58 = one_one_complex )
% 5.24/5.58 = ( Z2 = one_one_complex ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_cnj_one_iff
% 5.24/5.58 thf(fact_9609_complex__cnj__one,axiom,
% 5.24/5.58 ( ( cnj @ one_one_complex )
% 5.24/5.58 = one_one_complex ) ).
% 5.24/5.58
% 5.24/5.58 % complex_cnj_one
% 5.24/5.58 thf(fact_9610_complex__cnj__add,axiom,
% 5.24/5.58 ! [X: complex,Y4: complex] :
% 5.24/5.58 ( ( cnj @ ( plus_plus_complex @ X @ Y4 ) )
% 5.24/5.58 = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y4 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_cnj_add
% 5.24/5.58 thf(fact_9611_plus__integer_Orep__eq,axiom,
% 5.24/5.58 ! [X: code_integer,Xa2: code_integer] :
% 5.24/5.58 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 5.24/5.58 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_integer.rep_eq
% 5.24/5.58 thf(fact_9612_times__integer_Orep__eq,axiom,
% 5.24/5.58 ! [X: code_integer,Xa2: code_integer] :
% 5.24/5.58 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 5.24/5.58 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_integer.rep_eq
% 5.24/5.58 thf(fact_9613_one__integer_Orep__eq,axiom,
% 5.24/5.58 ( ( code_int_of_integer @ one_one_Code_integer )
% 5.24/5.58 = one_one_int ) ).
% 5.24/5.58
% 5.24/5.58 % one_integer.rep_eq
% 5.24/5.58 thf(fact_9614_complex__In__mult__cnj__zero,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( im @ ( times_times_complex @ Z2 @ ( cnj @ Z2 ) ) )
% 5.24/5.58 = zero_zero_real ) ).
% 5.24/5.58
% 5.24/5.58 % complex_In_mult_cnj_zero
% 5.24/5.58 thf(fact_9615_Re__complex__div__eq__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.24/5.58 = zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_complex_div_eq_0
% 5.24/5.58 thf(fact_9616_Im__complex__div__eq__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.24/5.58 = zero_zero_real )
% 5.24/5.58 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.24/5.58 = zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_complex_div_eq_0
% 5.24/5.58 thf(fact_9617_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.24/5.58 ( real_V1022390504157884413omplex
% 5.24/5.58 = ( ^ [Z4: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z4 @ ( cnj @ Z4 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_mod_sqrt_Re_mult_cnj
% 5.24/5.58 thf(fact_9618_integer__of__num__triv_I1_J,axiom,
% 5.24/5.58 ( ( code_integer_of_num @ one )
% 5.24/5.58 = one_one_Code_integer ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_num_triv(1)
% 5.24/5.58 thf(fact_9619_Re__complex__div__gt__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.58 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_complex_div_gt_0
% 5.24/5.58 thf(fact_9620_Re__complex__div__lt__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.24/5.58 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_complex_div_lt_0
% 5.24/5.58 thf(fact_9621_Re__complex__div__le__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.24/5.58 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_complex_div_le_0
% 5.24/5.58 thf(fact_9622_Re__complex__div__ge__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.58 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_complex_div_ge_0
% 5.24/5.58 thf(fact_9623_Im__complex__div__gt__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.58 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_complex_div_gt_0
% 5.24/5.58 thf(fact_9624_Im__complex__div__lt__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.24/5.58 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_complex_div_lt_0
% 5.24/5.58 thf(fact_9625_Im__complex__div__le__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.24/5.58 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_complex_div_le_0
% 5.24/5.58 thf(fact_9626_Im__complex__div__ge__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.58 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_complex_div_ge_0
% 5.24/5.58 thf(fact_9627_integer__of__num_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.24/5.58 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_num(2)
% 5.24/5.58 thf(fact_9628_complex__mod__mult__cnj,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z2 @ ( cnj @ Z2 ) ) )
% 5.24/5.58 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_mod_mult_cnj
% 5.24/5.58 thf(fact_9629_complex__div__gt__0,axiom,
% 5.24/5.58 ! [A: complex,B: complex] :
% 5.24/5.58 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.58 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.24/5.58 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.24/5.58 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_div_gt_0
% 5.24/5.58 thf(fact_9630_integer__of__num__triv_I2_J,axiom,
% 5.24/5.58 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.24/5.58 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_num_triv(2)
% 5.24/5.58 thf(fact_9631_complex__norm__square,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = ( times_times_complex @ Z2 @ ( cnj @ Z2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_norm_square
% 5.24/5.58 thf(fact_9632_complex__add__cnj,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( plus_plus_complex @ Z2 @ ( cnj @ Z2 ) )
% 5.24/5.58 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_add_cnj
% 5.24/5.58 thf(fact_9633_complex__diff__cnj,axiom,
% 5.24/5.58 ! [Z2: complex] :
% 5.24/5.58 ( ( minus_minus_complex @ Z2 @ ( cnj @ Z2 ) )
% 5.24/5.58 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z2 ) ) ) @ imaginary_unit ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_diff_cnj
% 5.24/5.58 thf(fact_9634_complex__div__cnj,axiom,
% 5.24/5.58 ( divide1717551699836669952omplex
% 5.24/5.58 = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % complex_div_cnj
% 5.24/5.58 thf(fact_9635_cnj__add__mult__eq__Re,axiom,
% 5.24/5.58 ! [Z2: complex,W2: complex] :
% 5.24/5.58 ( ( plus_plus_complex @ ( times_times_complex @ Z2 @ ( cnj @ W2 ) ) @ ( times_times_complex @ ( cnj @ Z2 ) @ W2 ) )
% 5.24/5.58 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z2 @ ( cnj @ W2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cnj_add_mult_eq_Re
% 5.24/5.58 thf(fact_9636_divmod__integer__def,axiom,
% 5.24/5.58 ( code_divmod_integer
% 5.24/5.58 = ( ^ [K3: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L ) @ ( modulo364778990260209775nteger @ K3 @ L ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_integer_def
% 5.24/5.58 thf(fact_9637_num__of__integer__code,axiom,
% 5.24/5.58 ( code_num_of_integer
% 5.24/5.58 = ( ^ [K3: code_integer] :
% 5.24/5.58 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.24/5.58 @ ( produc7336495610019696514er_num
% 5.24/5.58 @ ^ [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 ) )
% 5.24/5.58 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_integer_code
% 5.24/5.58 thf(fact_9638_nat__of__integer__code,axiom,
% 5.24/5.58 ( code_nat_of_integer
% 5.24/5.58 = ( ^ [K3: code_integer] :
% 5.24/5.58 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.24/5.58 @ ( produc1555791787009142072er_nat
% 5.24/5.58 @ ^ [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 ) )
% 5.24/5.58 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nat_of_integer_code
% 5.24/5.58 thf(fact_9639_bit__cut__integer__def,axiom,
% 5.24/5.58 ( code_bit_cut_integer
% 5.24/5.58 = ( ^ [K3: code_integer] :
% 5.24/5.58 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.24/5.58 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bit_cut_integer_def
% 5.24/5.58 thf(fact_9640_nat__of__integer__code__post_I3_J,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.24/5.58 = ( numeral_numeral_nat @ K ) ) ).
% 5.24/5.58
% 5.24/5.58 % nat_of_integer_code_post(3)
% 5.24/5.58 thf(fact_9641_nat__of__integer__code__post_I2_J,axiom,
% 5.24/5.58 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.24/5.58 = one_one_nat ) ).
% 5.24/5.58
% 5.24/5.58 % nat_of_integer_code_post(2)
% 5.24/5.58 thf(fact_9642_bit__cut__integer__code,axiom,
% 5.24/5.58 ( code_bit_cut_integer
% 5.24/5.58 = ( ^ [K3: code_integer] :
% 5.24/5.58 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.24/5.58 @ ( produc9125791028180074456eger_o
% 5.24/5.58 @ ^ [R5: code_integer,S5: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S5 ) ) @ ( S5 = one_one_Code_integer ) )
% 5.24/5.58 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bit_cut_integer_code
% 5.24/5.58 thf(fact_9643_vebt__maxt_Opelims,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Y4: option_nat] :
% 5.24/5.58 ( ( ( vEBT_vebt_maxt @ X )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.24/5.58 => ( ! [A3: $o,B2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.58 => ( ( ( B2
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( some_nat @ one_one_nat ) ) )
% 5.24/5.58 & ( ~ B2
% 5.24/5.58 => ( ( A3
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( some_nat @ zero_zero_nat ) ) )
% 5.24/5.58 & ( ~ A3
% 5.24/5.58 => ( Y4 = none_nat ) ) ) ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.24/5.58 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.24/5.58 => ( ( Y4 = none_nat )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) ) ) )
% 5.24/5.58 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_nat @ Ma2 ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vebt_maxt.pelims
% 5.24/5.58 thf(fact_9644_card__Collect__less__nat,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.24/5.58 = N ) ).
% 5.24/5.58
% 5.24/5.58 % card_Collect_less_nat
% 5.24/5.58 thf(fact_9645_card__atMost,axiom,
% 5.24/5.58 ! [U2: nat] :
% 5.24/5.58 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U2 ) )
% 5.24/5.58 = ( suc @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_atMost
% 5.24/5.58 thf(fact_9646_card__Collect__le__nat,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.24/5.58 = ( suc @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_Collect_le_nat
% 5.24/5.58 thf(fact_9647_card__atLeastAtMost,axiom,
% 5.24/5.58 ! [L2: nat,U2: nat] :
% 5.24/5.58 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U2 ) )
% 5.24/5.58 = ( minus_minus_nat @ ( suc @ U2 ) @ L2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_atLeastAtMost
% 5.24/5.58 thf(fact_9648_card__atLeastAtMost__int,axiom,
% 5.24/5.58 ! [L2: int,U2: int] :
% 5.24/5.58 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U2 ) )
% 5.24/5.58 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U2 @ L2 ) @ one_one_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_atLeastAtMost_int
% 5.24/5.58 thf(fact_9649_card__less,axiom,
% 5.24/5.58 ! [M7: set_nat,I2: nat] :
% 5.24/5.58 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.24/5.58 => ( ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [K3: nat] :
% 5.24/5.58 ( ( member_nat @ K3 @ M7 )
% 5.24/5.58 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.24/5.58 != zero_zero_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_less
% 5.24/5.58 thf(fact_9650_card__less__Suc,axiom,
% 5.24/5.58 ! [M7: set_nat,I2: nat] :
% 5.24/5.58 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.24/5.58 => ( ( suc
% 5.24/5.58 @ ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [K3: nat] :
% 5.24/5.58 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.24/5.58 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.24/5.58 = ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [K3: nat] :
% 5.24/5.58 ( ( member_nat @ K3 @ M7 )
% 5.24/5.58 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_less_Suc
% 5.24/5.58 thf(fact_9651_card__less__Suc2,axiom,
% 5.24/5.58 ! [M7: set_nat,I2: nat] :
% 5.24/5.58 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.24/5.58 => ( ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [K3: nat] :
% 5.24/5.58 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.24/5.58 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.24/5.58 = ( finite_card_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [K3: nat] :
% 5.24/5.58 ( ( member_nat @ K3 @ M7 )
% 5.24/5.58 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_less_Suc2
% 5.24/5.58 thf(fact_9652_subset__card__intvl__is__intvl,axiom,
% 5.24/5.58 ! [A2: set_nat,K: nat] :
% 5.24/5.58 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.24/5.58 => ( A2
% 5.24/5.58 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % subset_card_intvl_is_intvl
% 5.24/5.58 thf(fact_9653_divmod__abs__code_I6_J,axiom,
% 5.24/5.58 ! [J: code_integer] :
% 5.24/5.58 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.24/5.58 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_abs_code(6)
% 5.24/5.58 thf(fact_9654_divmod__abs__code_I5_J,axiom,
% 5.24/5.58 ! [J: code_integer] :
% 5.24/5.58 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.24/5.58 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_abs_code(5)
% 5.24/5.58 thf(fact_9655_subset__eq__atLeast0__lessThan__card,axiom,
% 5.24/5.58 ! [N4: set_nat,N: nat] :
% 5.24/5.58 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.24/5.58 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % subset_eq_atLeast0_lessThan_card
% 5.24/5.58 thf(fact_9656_card__sum__le__nat__sum,axiom,
% 5.24/5.58 ! [S3: set_nat] :
% 5.24/5.58 ( ord_less_eq_nat
% 5.24/5.58 @ ( groups3542108847815614940at_nat
% 5.24/5.58 @ ^ [X2: nat] : X2
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.24/5.58 @ ( groups3542108847815614940at_nat
% 5.24/5.58 @ ^ [X2: nat] : X2
% 5.24/5.58 @ S3 ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_sum_le_nat_sum
% 5.24/5.58 thf(fact_9657_card__nth__roots,axiom,
% 5.24/5.58 ! [C: complex,N: nat] :
% 5.24/5.58 ( ( C != zero_zero_complex )
% 5.24/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( finite_card_complex
% 5.24/5.58 @ ( collect_complex
% 5.24/5.58 @ ^ [Z4: complex] :
% 5.24/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.58 = C ) ) )
% 5.24/5.58 = N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_nth_roots
% 5.24/5.58 thf(fact_9658_card__roots__unity__eq,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( finite_card_complex
% 5.24/5.58 @ ( collect_complex
% 5.24/5.58 @ ^ [Z4: complex] :
% 5.24/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.24/5.58 = one_one_complex ) ) )
% 5.24/5.58 = N ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_roots_unity_eq
% 5.24/5.58 thf(fact_9659_divmod__abs__def,axiom,
% 5.24/5.58 ( code_divmod_abs
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_abs_def
% 5.24/5.58 thf(fact_9660_vebt__mint_Opelims,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Y4: option_nat] :
% 5.24/5.58 ( ( ( vEBT_vebt_mint @ X )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.24/5.58 => ( ! [A3: $o,B2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.24/5.58 => ( ( ( A3
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( some_nat @ zero_zero_nat ) ) )
% 5.24/5.58 & ( ~ A3
% 5.24/5.58 => ( ( B2
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( some_nat @ one_one_nat ) ) )
% 5.24/5.58 & ( ~ B2
% 5.24/5.58 => ( Y4 = none_nat ) ) ) ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.24/5.58 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.24/5.58 => ( ( Y4 = none_nat )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) ) ) )
% 5.24/5.58 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_nat @ Mi2 ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vebt_mint.pelims
% 5.24/5.58 thf(fact_9661_divmod__integer__code,axiom,
% 5.24/5.58 ( code_divmod_integer
% 5.24/5.58 = ( ^ [K3: code_integer,L: code_integer] :
% 5.24/5.58 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 5.24/5.58 @ ( produc6916734918728496179nteger
% 5.24/5.58 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S5 ) ) )
% 5.24/5.58 @ ( code_divmod_abs @ K3 @ L ) ) )
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.24/5.58 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 5.24/5.58 @ ( produc6916734918728496179nteger
% 5.24/5.58 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S5 ) ) )
% 5.24/5.58 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_integer_code
% 5.24/5.58 thf(fact_9662_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Y4: $o] :
% 5.24/5.58 ( ( ( vEBT_VEBT_minNull @ X )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.24/5.58 => ( ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ $false @ $false ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.24/5.58 => ( ! [Uv2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.24/5.58 => ( ~ Y4
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.24/5.58 => ( ! [Uu3: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.24/5.58 => ( ~ Y4
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu3 @ $true ) ) ) )
% 5.24/5.58 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.24/5.58 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.24/5.58 => ( ~ Y4
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.minNull.pelims(1)
% 5.24/5.58 thf(fact_9663_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT] :
% 5.24/5.58 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.24/5.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.24/5.58 => ( ! [Uv2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.24/5.58 => ( ! [Uu3: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu3 @ $true ) ) )
% 5.24/5.58 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.minNull.pelims(3)
% 5.24/5.58 thf(fact_9664_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT] :
% 5.24/5.58 ( ( vEBT_VEBT_minNull @ X )
% 5.24/5.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.24/5.58 => ( ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ $false @ $false ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.24/5.58 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.24/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.minNull.pelims(2)
% 5.24/5.58 thf(fact_9665_bezw__0,axiom,
% 5.24/5.58 ! [X: nat] :
% 5.24/5.58 ( ( bezw @ X @ zero_zero_nat )
% 5.24/5.58 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezw_0
% 5.24/5.58 thf(fact_9666_less__eq__nat_Osimps_I2_J,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.24/5.58 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq_nat.simps(2)
% 5.24/5.58 thf(fact_9667_max__Suc1,axiom,
% 5.24/5.58 ! [N: nat,M: nat] :
% 5.24/5.58 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.24/5.58 = ( case_nat_nat @ ( suc @ N )
% 5.24/5.58 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 5.24/5.58 @ M ) ) ).
% 5.24/5.58
% 5.24/5.58 % max_Suc1
% 5.24/5.58 thf(fact_9668_max__Suc2,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.24/5.58 = ( case_nat_nat @ ( suc @ N )
% 5.24/5.58 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 5.24/5.58 @ M ) ) ).
% 5.24/5.58
% 5.24/5.58 % max_Suc2
% 5.24/5.58 thf(fact_9669_diff__Suc,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.24/5.58 = ( case_nat_nat @ zero_zero_nat
% 5.24/5.58 @ ^ [K3: nat] : K3
% 5.24/5.58 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % diff_Suc
% 5.24/5.58 thf(fact_9670_prod__decode__aux_Oelims,axiom,
% 5.24/5.58 ! [X: nat,Xa2: nat,Y4: product_prod_nat_nat] :
% 5.24/5.58 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_decode_aux.elims
% 5.24/5.58 thf(fact_9671_prod__decode__aux_Osimps,axiom,
% 5.24/5.58 ( nat_prod_decode_aux
% 5.24/5.58 = ( ^ [K3: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K3 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K3 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M2 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_decode_aux.simps
% 5.24/5.58 thf(fact_9672_drop__bit__numeral__minus__bit1,axiom,
% 5.24/5.58 ! [L2: num,K: num] :
% 5.24/5.58 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.24/5.58 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_numeral_minus_bit1
% 5.24/5.58 thf(fact_9673_drop__bit__minus__one,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.24/5.58 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_minus_one
% 5.24/5.58 thf(fact_9674_drop__bit__Suc__minus__bit0,axiom,
% 5.24/5.58 ! [N: nat,K: num] :
% 5.24/5.58 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.24/5.58 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_Suc_minus_bit0
% 5.24/5.58 thf(fact_9675_drop__bit__numeral__minus__bit0,axiom,
% 5.24/5.58 ! [L2: num,K: num] :
% 5.24/5.58 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.24/5.58 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_numeral_minus_bit0
% 5.24/5.58 thf(fact_9676_drop__bit__Suc__minus__bit1,axiom,
% 5.24/5.58 ! [N: nat,K: num] :
% 5.24/5.58 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.24/5.58 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_Suc_minus_bit1
% 5.24/5.58 thf(fact_9677_drop__bit__int__def,axiom,
% 5.24/5.58 ( bit_se8568078237143864401it_int
% 5.24/5.58 = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_int_def
% 5.24/5.58 thf(fact_9678_Suc__0__mod__numeral,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.58 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Suc_0_mod_numeral
% 5.24/5.58 thf(fact_9679_Suc__0__div__numeral,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.58 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Suc_0_div_numeral
% 5.24/5.58 thf(fact_9680_divmod__integer__eq__cases,axiom,
% 5.24/5.58 ( code_divmod_integer
% 5.24/5.58 = ( ^ [K3: code_integer,L: code_integer] :
% 5.24/5.58 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.24/5.58 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger
% 5.24/5.58 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.24/5.58 = ( sgn_sgn_Code_integer @ L ) )
% 5.24/5.58 @ ( code_divmod_abs @ K3 @ L )
% 5.24/5.58 @ ( produc6916734918728496179nteger
% 5.24/5.58 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S5 ) ) )
% 5.24/5.58 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_integer_eq_cases
% 5.24/5.58 thf(fact_9681_drop__bit__of__Suc__0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.24/5.58 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_of_Suc_0
% 5.24/5.58 thf(fact_9682_fst__divmod__nat,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.24/5.58 = ( divide_divide_nat @ M @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % fst_divmod_nat
% 5.24/5.58 thf(fact_9683_drop__bit__nat__def,axiom,
% 5.24/5.58 ( bit_se8570568707652914677it_nat
% 5.24/5.58 = ( ^ [N2: nat,M2: nat] : ( divide_divide_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_bit_nat_def
% 5.24/5.58 thf(fact_9684_card_Ocomp__fun__commute__on,axiom,
% 5.24/5.58 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.24/5.58 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.24/5.58
% 5.24/5.58 % card.comp_fun_commute_on
% 5.24/5.58 thf(fact_9685_bezw__non__0,axiom,
% 5.24/5.58 ! [Y4: nat,X: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ Y4 )
% 5.24/5.58 => ( ( bezw @ X @ Y4 )
% 5.24/5.58 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezw_non_0
% 5.24/5.58 thf(fact_9686_bezw_Osimps,axiom,
% 5.24/5.58 ( bezw
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezw.simps
% 5.24/5.58 thf(fact_9687_bezw_Oelims,axiom,
% 5.24/5.58 ! [X: nat,Xa2: nat,Y4: product_prod_int_int] :
% 5.24/5.58 ( ( ( bezw @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.24/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezw.elims
% 5.24/5.58 thf(fact_9688_rat__sgn__code,axiom,
% 5.24/5.58 ! [P6: rat] :
% 5.24/5.58 ( ( quotient_of @ ( sgn_sgn_rat @ P6 ) )
% 5.24/5.58 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P6 ) ) ) @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_sgn_code
% 5.24/5.58 thf(fact_9689_minus__one__mod__numeral,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % minus_one_mod_numeral
% 5.24/5.58 thf(fact_9690_one__mod__minus__numeral,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_mod_minus_numeral
% 5.24/5.58 thf(fact_9691_bezw_Opelims,axiom,
% 5.24/5.58 ! [X: nat,Xa2: nat,Y4: product_prod_int_int] :
% 5.24/5.58 ( ( ( bezw @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.24/5.58 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.24/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ) )
% 5.24/5.58 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezw.pelims
% 5.24/5.58 thf(fact_9692_normalize__def,axiom,
% 5.24/5.58 ( normalize
% 5.24/5.58 = ( ^ [P4: product_prod_int_int] :
% 5.24/5.58 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P4 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) )
% 5.24/5.58 @ ( if_Pro3027730157355071871nt_int
% 5.24/5.58 @ ( ( product_snd_int_int @ P4 )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.24/5.58 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % normalize_def
% 5.24/5.58 thf(fact_9693_gcd__1__int,axiom,
% 5.24/5.58 ! [M: int] :
% 5.24/5.58 ( ( gcd_gcd_int @ M @ one_one_int )
% 5.24/5.58 = one_one_int ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_1_int
% 5.24/5.58 thf(fact_9694_bezout__int,axiom,
% 5.24/5.58 ! [X: int,Y4: int] :
% 5.24/5.58 ? [U4: int,V2: int] :
% 5.24/5.58 ( ( plus_plus_int @ ( times_times_int @ U4 @ X ) @ ( times_times_int @ V2 @ Y4 ) )
% 5.24/5.58 = ( gcd_gcd_int @ X @ Y4 ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezout_int
% 5.24/5.58 thf(fact_9695_gcd__mult__distrib__int,axiom,
% 5.24/5.58 ! [K: int,M: int,N: int] :
% 5.24/5.58 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.24/5.58 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_mult_distrib_int
% 5.24/5.58 thf(fact_9696_nat__descend__induct,axiom,
% 5.24/5.58 ! [N: nat,P: nat > $o,M: nat] :
% 5.24/5.58 ( ! [K2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ N @ K2 )
% 5.24/5.58 => ( P @ K2 ) )
% 5.24/5.58 => ( ! [K2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ N )
% 5.24/5.58 => ( ! [I: nat] :
% 5.24/5.58 ( ( ord_less_nat @ K2 @ I )
% 5.24/5.58 => ( P @ I ) )
% 5.24/5.58 => ( P @ K2 ) ) )
% 5.24/5.58 => ( P @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nat_descend_induct
% 5.24/5.58 thf(fact_9697_prod__decode__aux_Opelims,axiom,
% 5.24/5.58 ! [X: nat,Xa2: nat,Y4: product_prod_nat_nat] :
% 5.24/5.58 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.24/5.58 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.24/5.58 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_decode_aux.pelims
% 5.24/5.58 thf(fact_9698_gcd__1__nat,axiom,
% 5.24/5.58 ! [M: nat] :
% 5.24/5.58 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.24/5.58 = one_one_nat ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_1_nat
% 5.24/5.58 thf(fact_9699_gcd__Suc__0,axiom,
% 5.24/5.58 ! [M: nat] :
% 5.24/5.58 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.24/5.58 = ( suc @ zero_zero_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_Suc_0
% 5.24/5.58 thf(fact_9700_gcd__pos__nat,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.24/5.58 = ( ( M != zero_zero_nat )
% 5.24/5.58 | ( N != zero_zero_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_pos_nat
% 5.24/5.58 thf(fact_9701_gcd__mult__distrib__nat,axiom,
% 5.24/5.58 ! [K: nat,M: nat,N: nat] :
% 5.24/5.58 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.24/5.58 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_mult_distrib_nat
% 5.24/5.58 thf(fact_9702_gcd__le2__nat,axiom,
% 5.24/5.58 ! [B: nat,A: nat] :
% 5.24/5.58 ( ( B != zero_zero_nat )
% 5.24/5.58 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_le2_nat
% 5.24/5.58 thf(fact_9703_gcd__le1__nat,axiom,
% 5.24/5.58 ! [A: nat,B: nat] :
% 5.24/5.58 ( ( A != zero_zero_nat )
% 5.24/5.58 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_le1_nat
% 5.24/5.58 thf(fact_9704_gcd__diff1__nat,axiom,
% 5.24/5.58 ! [N: nat,M: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ N @ M )
% 5.24/5.58 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.24/5.58 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_diff1_nat
% 5.24/5.58 thf(fact_9705_gcd__diff2__nat,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.58 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.24/5.58 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_diff2_nat
% 5.24/5.58 thf(fact_9706_bezout__nat,axiom,
% 5.24/5.58 ! [A: nat,B: nat] :
% 5.24/5.58 ( ( A != zero_zero_nat )
% 5.24/5.58 => ? [X3: nat,Y3: nat] :
% 5.24/5.58 ( ( times_times_nat @ A @ X3 )
% 5.24/5.58 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezout_nat
% 5.24/5.58 thf(fact_9707_bezout__gcd__nat_H,axiom,
% 5.24/5.58 ! [B: nat,A: nat] :
% 5.24/5.58 ? [X3: nat,Y3: nat] :
% 5.24/5.58 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.24/5.58 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.24/5.58 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.24/5.58 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.24/5.58 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.24/5.58 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezout_gcd_nat'
% 5.24/5.58 thf(fact_9708_bezw__aux,axiom,
% 5.24/5.58 ! [X: nat,Y4: nat] :
% 5.24/5.58 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y4 ) )
% 5.24/5.58 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y4 ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y4 ) ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % bezw_aux
% 5.24/5.58 thf(fact_9709_gcd__nat_Opelims,axiom,
% 5.24/5.58 ! [X: nat,Xa2: nat,Y4: nat] :
% 5.24/5.58 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.24/5.58 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.24/5.58 => ( Y4 = X ) )
% 5.24/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 5.24/5.58 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_nat.pelims
% 5.24/5.58 thf(fact_9710_card__greaterThanLessThan__int,axiom,
% 5.24/5.58 ! [L2: int,U2: int] :
% 5.24/5.58 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U2 ) )
% 5.24/5.58 = ( nat2 @ ( minus_minus_int @ U2 @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_greaterThanLessThan_int
% 5.24/5.58 thf(fact_9711_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.24/5.58 ! [L2: int,U2: int] :
% 5.24/5.58 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U2 )
% 5.24/5.58 = ( set_or5832277885323065728an_int @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.24/5.58 thf(fact_9712_infinite__nat__iff__unbounded__le,axiom,
% 5.24/5.58 ! [S3: set_nat] :
% 5.24/5.58 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.24/5.58 = ( ! [M2: nat] :
% 5.24/5.58 ? [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.24/5.58 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % infinite_nat_iff_unbounded_le
% 5.24/5.58 thf(fact_9713_xor__minus__numerals_I2_J,axiom,
% 5.24/5.58 ! [K: int,N: num] :
% 5.24/5.58 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_minus_numerals(2)
% 5.24/5.58 thf(fact_9714_xor__minus__numerals_I1_J,axiom,
% 5.24/5.58 ! [N: num,K: int] :
% 5.24/5.58 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.24/5.58 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_minus_numerals(1)
% 5.24/5.58 thf(fact_9715_card__greaterThanLessThan,axiom,
% 5.24/5.58 ! [L2: nat,U2: nat] :
% 5.24/5.58 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U2 ) )
% 5.24/5.58 = ( minus_minus_nat @ U2 @ ( suc @ L2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_greaterThanLessThan
% 5.24/5.58 thf(fact_9716_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.24/5.58 ! [L2: nat,U2: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U2 )
% 5.24/5.58 = ( set_or5834768355832116004an_nat @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastSucLessThan_greaterThanLessThan
% 5.24/5.58 thf(fact_9717_tanh__real__bounds,axiom,
% 5.24/5.58 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % tanh_real_bounds
% 5.24/5.58 thf(fact_9718_sub__BitM__One__eq,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.24/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sub_BitM_One_eq
% 5.24/5.58 thf(fact_9719_unbounded__k__infinite,axiom,
% 5.24/5.58 ! [K: nat,S3: set_nat] :
% 5.24/5.58 ( ! [M4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ K @ M4 )
% 5.24/5.58 => ? [N9: nat] :
% 5.24/5.58 ( ( ord_less_nat @ M4 @ N9 )
% 5.24/5.58 & ( member_nat @ N9 @ S3 ) ) )
% 5.24/5.58 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.24/5.58
% 5.24/5.58 % unbounded_k_infinite
% 5.24/5.58 thf(fact_9720_infinite__nat__iff__unbounded,axiom,
% 5.24/5.58 ! [S3: set_nat] :
% 5.24/5.58 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.24/5.58 = ( ! [M2: nat] :
% 5.24/5.58 ? [N2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ M2 @ N2 )
% 5.24/5.58 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % infinite_nat_iff_unbounded
% 5.24/5.58 thf(fact_9721_finite__enumerate,axiom,
% 5.24/5.58 ! [S3: set_nat] :
% 5.24/5.58 ( ( finite_finite_nat @ S3 )
% 5.24/5.58 => ? [R3: nat > nat] :
% 5.24/5.58 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.24/5.58 & ! [N9: nat] :
% 5.24/5.58 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S3 ) )
% 5.24/5.58 => ( member_nat @ ( R3 @ N9 ) @ S3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % finite_enumerate
% 5.24/5.58 thf(fact_9722_Suc__funpow,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( compow_nat_nat @ N @ suc )
% 5.24/5.58 = ( plus_plus_nat @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % Suc_funpow
% 5.24/5.58 thf(fact_9723_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.24/5.58 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X2 )
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( ord_less_nat @ Y @ X2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % max_nat.semilattice_neutr_order_axioms
% 5.24/5.58 thf(fact_9724_times__int_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.24/5.58 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.24/5.58 = ( abs_Integ
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U3 ) ) ) )
% 5.24/5.58 @ Xa2
% 5.24/5.58 @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_int.abs_eq
% 5.24/5.58 thf(fact_9725_eq__Abs__Integ,axiom,
% 5.24/5.58 ! [Z2: int] :
% 5.24/5.58 ~ ! [X3: nat,Y3: nat] :
% 5.24/5.58 ( Z2
% 5.24/5.58 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % eq_Abs_Integ
% 5.24/5.58 thf(fact_9726_zero__int__def,axiom,
% 5.24/5.58 ( zero_zero_int
% 5.24/5.58 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % zero_int_def
% 5.24/5.58 thf(fact_9727_int__def,axiom,
% 5.24/5.58 ( semiri1314217659103216013at_int
% 5.24/5.58 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % int_def
% 5.24/5.58 thf(fact_9728_uminus__int_Oabs__eq,axiom,
% 5.24/5.58 ! [X: product_prod_nat_nat] :
% 5.24/5.58 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.24/5.58 = ( abs_Integ
% 5.24/5.58 @ ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 )
% 5.24/5.58 @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_int.abs_eq
% 5.24/5.58 thf(fact_9729_one__int__def,axiom,
% 5.24/5.58 ( one_one_int
% 5.24/5.58 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_int_def
% 5.24/5.58 thf(fact_9730_less__int_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.24/5.58 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.24/5.58 = ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) )
% 5.24/5.58 @ Xa2
% 5.24/5.58 @ X ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_int.abs_eq
% 5.24/5.58 thf(fact_9731_less__eq__int_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.24/5.58 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.24/5.58 = ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) )
% 5.24/5.58 @ Xa2
% 5.24/5.58 @ X ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq_int.abs_eq
% 5.24/5.58 thf(fact_9732_plus__int_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.24/5.58 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.24/5.58 = ( abs_Integ
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U3 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 5.24/5.58 @ Xa2
% 5.24/5.58 @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_int.abs_eq
% 5.24/5.58 thf(fact_9733_minus__int_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.24/5.58 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.24/5.58 = ( abs_Integ
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U3 ) ) )
% 5.24/5.58 @ Xa2
% 5.24/5.58 @ X ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % minus_int.abs_eq
% 5.24/5.58 thf(fact_9734_Gcd__remove0__nat,axiom,
% 5.24/5.58 ! [M7: set_nat] :
% 5.24/5.58 ( ( finite_finite_nat @ M7 )
% 5.24/5.58 => ( ( gcd_Gcd_nat @ M7 )
% 5.24/5.58 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Gcd_remove0_nat
% 5.24/5.58 thf(fact_9735_Gcd__nat__eq__one,axiom,
% 5.24/5.58 ! [N4: set_nat] :
% 5.24/5.58 ( ( member_nat @ one_one_nat @ N4 )
% 5.24/5.58 => ( ( gcd_Gcd_nat @ N4 )
% 5.24/5.58 = one_one_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % Gcd_nat_eq_one
% 5.24/5.58 thf(fact_9736_Gcd__in,axiom,
% 5.24/5.58 ! [A2: set_nat] :
% 5.24/5.58 ( ! [A3: nat,B2: nat] :
% 5.24/5.58 ( ( member_nat @ A3 @ A2 )
% 5.24/5.58 => ( ( member_nat @ B2 @ A2 )
% 5.24/5.58 => ( member_nat @ ( gcd_gcd_nat @ A3 @ B2 ) @ A2 ) ) )
% 5.24/5.58 => ( ( A2 != bot_bot_set_nat )
% 5.24/5.58 => ( member_nat @ ( gcd_Gcd_nat @ A2 ) @ A2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Gcd_in
% 5.24/5.58 thf(fact_9737_less__eq__int_Orep__eq,axiom,
% 5.24/5.58 ( ord_less_eq_int
% 5.24/5.58 = ( ^ [X2: int,Xa4: int] :
% 5.24/5.58 ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [Y: nat,Z4: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U3 @ Z4 ) ) )
% 5.24/5.58 @ ( rep_Integ @ X2 )
% 5.24/5.58 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq_int.rep_eq
% 5.24/5.58 thf(fact_9738_less__int_Orep__eq,axiom,
% 5.24/5.58 ( ord_less_int
% 5.24/5.58 = ( ^ [X2: int,Xa4: int] :
% 5.24/5.58 ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [Y: nat,Z4: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U3 @ Z4 ) ) )
% 5.24/5.58 @ ( rep_Integ @ X2 )
% 5.24/5.58 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_int.rep_eq
% 5.24/5.58 thf(fact_9739_uminus__int__def,axiom,
% 5.24/5.58 ( uminus_uminus_int
% 5.24/5.58 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.24/5.58 @ ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_int_def
% 5.24/5.58 thf(fact_9740_num__of__nat_Osimps_I2_J,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( num_of_nat @ ( suc @ N ) )
% 5.24/5.58 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( num_of_nat @ ( suc @ N ) )
% 5.24/5.58 = one ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_nat.simps(2)
% 5.24/5.58 thf(fact_9741_num__of__nat__numeral__eq,axiom,
% 5.24/5.58 ! [Q2: num] :
% 5.24/5.58 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.24/5.58 = Q2 ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_nat_numeral_eq
% 5.24/5.58 thf(fact_9742_num__of__nat_Osimps_I1_J,axiom,
% 5.24/5.58 ( ( num_of_nat @ zero_zero_nat )
% 5.24/5.58 = one ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_nat.simps(1)
% 5.24/5.58 thf(fact_9743_numeral__num__of__nat,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.24/5.58 = N ) ) ).
% 5.24/5.58
% 5.24/5.58 % numeral_num_of_nat
% 5.24/5.58 thf(fact_9744_num__of__nat__One,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.24/5.58 => ( ( num_of_nat @ N )
% 5.24/5.58 = one ) ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_nat_One
% 5.24/5.58 thf(fact_9745_num__of__nat__double,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.24/5.58 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_nat_double
% 5.24/5.58 thf(fact_9746_num__of__nat__plus__distrib,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.24/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.24/5.58 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % num_of_nat_plus_distrib
% 5.24/5.58 thf(fact_9747_times__int__def,axiom,
% 5.24/5.58 ( times_times_int
% 5.24/5.58 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U3 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_int_def
% 5.24/5.58 thf(fact_9748_minus__int__def,axiom,
% 5.24/5.58 ( minus_minus_int
% 5.24/5.58 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U3 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % minus_int_def
% 5.24/5.58 thf(fact_9749_plus__int__def,axiom,
% 5.24/5.58 ( plus_plus_int
% 5.24/5.58 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U3 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_int_def
% 5.24/5.58 thf(fact_9750_pow_Osimps_I3_J,axiom,
% 5.24/5.58 ! [X: num,Y4: num] :
% 5.24/5.58 ( ( pow @ X @ ( bit1 @ Y4 ) )
% 5.24/5.58 = ( times_times_num @ ( sqr @ ( pow @ X @ Y4 ) ) @ X ) ) ).
% 5.24/5.58
% 5.24/5.58 % pow.simps(3)
% 5.24/5.58 thf(fact_9751_sqr_Osimps_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( sqr @ ( bit0 @ N ) )
% 5.24/5.58 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sqr.simps(2)
% 5.24/5.58 thf(fact_9752_sqr_Osimps_I1_J,axiom,
% 5.24/5.58 ( ( sqr @ one )
% 5.24/5.58 = one ) ).
% 5.24/5.58
% 5.24/5.58 % sqr.simps(1)
% 5.24/5.58 thf(fact_9753_sqr__conv__mult,axiom,
% 5.24/5.58 ( sqr
% 5.24/5.58 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sqr_conv_mult
% 5.24/5.58 thf(fact_9754_pow_Osimps_I2_J,axiom,
% 5.24/5.58 ! [X: num,Y4: num] :
% 5.24/5.58 ( ( pow @ X @ ( bit0 @ Y4 ) )
% 5.24/5.58 = ( sqr @ ( pow @ X @ Y4 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % pow.simps(2)
% 5.24/5.58 thf(fact_9755_sqr_Osimps_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( sqr @ ( bit1 @ N ) )
% 5.24/5.58 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sqr.simps(3)
% 5.24/5.58 thf(fact_9756_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.24/5.58 ! [N: nat,J: nat,I2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 5.24/5.58 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N )
% 5.24/5.58 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nth_sorted_list_of_set_greaterThanLessThan
% 5.24/5.58 thf(fact_9757_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.58 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.24/5.58 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.24/5.58 ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.58 => ( Xa2 = one_one_nat ) )
% 5.24/5.58 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.24/5.58 => ( ( Deg2 = Xa2 )
% 5.24/5.58 & ! [X3: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.elims(3)
% 5.24/5.58 thf(fact_9758_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.24/5.58 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.24/5.58 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 5.24/5.58 = ( ( Deg = Deg4 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.simps(2)
% 5.24/5.58 thf(fact_9759_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.58 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.24/5.58 ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( Xa2 != one_one_nat ) ) )
% 5.24/5.58 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( ~ ( ( Deg2 = Xa2 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.elims(1)
% 5.24/5.58 thf(fact_9760_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.58 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.24/5.58 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.24/5.58 ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.58 => ( Xa2 != one_one_nat ) )
% 5.24/5.58 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.24/5.58 => ~ ( ( Deg2 = Xa2 )
% 5.24/5.58 & ! [X5: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.elims(2)
% 5.24/5.58 thf(fact_9761_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.24/5.58 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.58 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( Xa2 = one_one_nat ) )
% 5.24/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) ) ) )
% 5.24/5.58 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( ( Deg2 = Xa2 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima ) ) )
% 5.24/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.pelims(1)
% 5.24/5.58 thf(fact_9762_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.58 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.58 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) )
% 5.24/5.58 => ( Xa2 != one_one_nat ) ) )
% 5.24/5.58 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.24/5.58 => ~ ( ( Deg2 = Xa2 )
% 5.24/5.58 & ! [X5: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.pelims(2)
% 5.24/5.58 thf(fact_9763_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.24/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.24/5.58 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.24/5.58 => ( ! [Uu3: $o,Uv2: $o] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) )
% 5.24/5.58 => ( Xa2 = one_one_nat ) ) )
% 5.24/5.58 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.24/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.24/5.58 => ( ( Deg2 = Xa2 )
% 5.24/5.58 & ! [X3: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.24/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 & ( case_o184042715313410164at_nat
% 5.24/5.58 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.24/5.58 & ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [Mi3: nat,Ma3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.24/5.58 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 & ! [I4: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.24/5.58 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.24/5.58 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.24/5.58 & ( ( Mi3 = Ma3 )
% 5.24/5.58 => ! [X2: vEBT_VEBT] :
% 5.24/5.58 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.24/5.58 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.24/5.58 & ( ( Mi3 != Ma3 )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.24/5.58 & ! [X2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.24/5.58 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.24/5.58 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.24/5.58 @ Mima ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % VEBT_internal.valid'.pelims(3)
% 5.24/5.58 thf(fact_9764_take__bit__numeral__minus__numeral__int,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( case_option_int_num @ zero_zero_int
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_numeral_minus_numeral_int
% 5.24/5.58 thf(fact_9765_and__minus__numerals_I3_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.24/5.58 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_minus_numerals(3)
% 5.24/5.58 thf(fact_9766_take__bit__num__simps_I1_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.24/5.58 = none_num ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(1)
% 5.24/5.58 thf(fact_9767_take__bit__num__simps_I2_J,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.24/5.58 = ( some_num @ one ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(2)
% 5.24/5.58 thf(fact_9768_take__bit__num__simps_I5_J,axiom,
% 5.24/5.58 ! [R2: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.24/5.58 = ( some_num @ one ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(5)
% 5.24/5.58 thf(fact_9769_take__bit__num__simps_I3_J,axiom,
% 5.24/5.58 ! [N: nat,M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.24/5.58 = ( case_o6005452278849405969um_num @ none_num
% 5.24/5.58 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.24/5.58 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(3)
% 5.24/5.58 thf(fact_9770_take__bit__num__simps_I4_J,axiom,
% 5.24/5.58 ! [N: nat,M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.24/5.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(4)
% 5.24/5.58 thf(fact_9771_take__bit__num__simps_I6_J,axiom,
% 5.24/5.58 ! [R2: num,M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.24/5.58 = ( case_o6005452278849405969um_num @ none_num
% 5.24/5.58 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.24/5.58 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(6)
% 5.24/5.58 thf(fact_9772_take__bit__num__simps_I7_J,axiom,
% 5.24/5.58 ! [R2: num,M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.24/5.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_simps(7)
% 5.24/5.58 thf(fact_9773_and__minus__numerals_I8_J,axiom,
% 5.24/5.58 ! [N: num,M: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.24/5.58 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_minus_numerals(8)
% 5.24/5.58 thf(fact_9774_and__minus__numerals_I4_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.24/5.58 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_minus_numerals(4)
% 5.24/5.58 thf(fact_9775_and__minus__numerals_I7_J,axiom,
% 5.24/5.58 ! [N: num,M: num] :
% 5.24/5.58 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.24/5.58 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_minus_numerals(7)
% 5.24/5.58 thf(fact_9776_and__not__num_Osimps_I1_J,axiom,
% 5.24/5.58 ( ( bit_and_not_num @ one @ one )
% 5.24/5.58 = none_num ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(1)
% 5.24/5.58 thf(fact_9777_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.24/5.58 ! [N: nat,M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.24/5.58 = ( case_nat_option_num @ none_num
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( case_o6005452278849405969um_num @ none_num
% 5.24/5.58 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.24/5.58 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.24/5.58 @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.24/5.58 thf(fact_9778_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( bit_take_bit_num @ N @ one )
% 5.24/5.58 = ( case_nat_option_num @ none_num
% 5.24/5.58 @ ^ [N2: nat] : ( some_num @ one )
% 5.24/5.58 @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.24/5.58 thf(fact_9779_and__not__num_Osimps_I4_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.24/5.58 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(4)
% 5.24/5.58 thf(fact_9780_and__not__num_Osimps_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.24/5.58 = ( some_num @ one ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(2)
% 5.24/5.58 thf(fact_9781_GreatestI__nat,axiom,
% 5.24/5.58 ! [P: nat > $o,K: nat,B: nat] :
% 5.24/5.58 ( ( P @ K )
% 5.24/5.58 => ( ! [Y3: nat] :
% 5.24/5.58 ( ( P @ Y3 )
% 5.24/5.58 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.24/5.58 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % GreatestI_nat
% 5.24/5.58 thf(fact_9782_Greatest__le__nat,axiom,
% 5.24/5.58 ! [P: nat > $o,K: nat,B: nat] :
% 5.24/5.58 ( ( P @ K )
% 5.24/5.58 => ( ! [Y3: nat] :
% 5.24/5.58 ( ( P @ Y3 )
% 5.24/5.58 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.24/5.58 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Greatest_le_nat
% 5.24/5.58 thf(fact_9783_GreatestI__ex__nat,axiom,
% 5.24/5.58 ! [P: nat > $o,B: nat] :
% 5.24/5.58 ( ? [X_12: nat] : ( P @ X_12 )
% 5.24/5.58 => ( ! [Y3: nat] :
% 5.24/5.58 ( ( P @ Y3 )
% 5.24/5.58 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.24/5.58 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % GreatestI_ex_nat
% 5.24/5.58 thf(fact_9784_and__not__num_Osimps_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.24/5.58 = none_num ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(3)
% 5.24/5.58 thf(fact_9785_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.24/5.58 ! [N: nat,M: num] :
% 5.24/5.58 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.24/5.58 = ( case_nat_option_num @ none_num
% 5.24/5.58 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.24/5.58 @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.24/5.58 thf(fact_9786_and__not__num_Osimps_I7_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.24/5.58 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(7)
% 5.24/5.58 thf(fact_9787_and__not__num__eq__Some__iff,axiom,
% 5.24/5.58 ! [M: num,N: num,Q2: num] :
% 5.24/5.58 ( ( ( bit_and_not_num @ M @ N )
% 5.24/5.58 = ( some_num @ Q2 ) )
% 5.24/5.58 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num_eq_Some_iff
% 5.24/5.58 thf(fact_9788_and__not__num_Osimps_I8_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.58 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.24/5.58 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(8)
% 5.24/5.58 thf(fact_9789_and__not__num__eq__None__iff,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( ( bit_and_not_num @ M @ N )
% 5.24/5.58 = none_num )
% 5.24/5.58 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = zero_zero_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num_eq_None_iff
% 5.24/5.58 thf(fact_9790_take__bit__num__def,axiom,
% 5.24/5.58 ( bit_take_bit_num
% 5.24/5.58 = ( ^ [N2: nat,M2: num] :
% 5.24/5.58 ( if_option_num
% 5.24/5.58 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M2 ) )
% 5.24/5.58 = zero_zero_nat )
% 5.24/5.58 @ none_num
% 5.24/5.58 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_bit_num_def
% 5.24/5.58 thf(fact_9791_Bit__Operations_Otake__bit__num__code,axiom,
% 5.24/5.58 ( bit_take_bit_num
% 5.24/5.58 = ( ^ [N2: nat,M2: num] :
% 5.24/5.58 ( produc478579273971653890on_num
% 5.24/5.58 @ ^ [A4: nat,X2: num] :
% 5.24/5.58 ( case_nat_option_num @ none_num
% 5.24/5.58 @ ^ [O: nat] :
% 5.24/5.58 ( case_num_option_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [P4: num] :
% 5.24/5.58 ( case_o6005452278849405969um_num @ none_num
% 5.24/5.58 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.24/5.58 @ ( bit_take_bit_num @ O @ P4 ) )
% 5.24/5.58 @ ^ [P4: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P4 ) ) )
% 5.24/5.58 @ X2 )
% 5.24/5.58 @ A4 )
% 5.24/5.58 @ ( product_Pair_nat_num @ N2 @ M2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Bit_Operations.take_bit_num_code
% 5.24/5.58 thf(fact_9792_and__not__num_Oelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: option_num] :
% 5.24/5.58 ( ( ( bit_and_not_num @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4 != none_num ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ? [N3: num] :
% 5.24/5.58 ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ one ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ? [N3: num] :
% 5.24/5.58 ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4 != none_num ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.24/5.58 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ~ ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.elims
% 5.24/5.58 thf(fact_9793_and__not__num_Osimps_I5_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(5)
% 5.24/5.58 thf(fact_9794_and__not__num_Osimps_I6_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(6)
% 5.24/5.58 thf(fact_9795_and__not__num_Osimps_I9_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.simps(9)
% 5.24/5.58 thf(fact_9796_and__num_Oelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: option_num] :
% 5.24/5.58 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ one ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ? [N3: num] :
% 5.24/5.58 ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4 != none_num ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ? [N3: num] :
% 5.24/5.58 ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ one ) ) ) )
% 5.24/5.58 => ( ( ? [M4: num] :
% 5.24/5.58 ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4 != none_num ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ( ? [M4: num] :
% 5.24/5.58 ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ one ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ~ ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.24/5.58 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.elims
% 5.24/5.58 thf(fact_9797_xor__num_Oelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: option_num] :
% 5.24/5.58 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4 != none_num ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ~ ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.elims
% 5.24/5.58 thf(fact_9798_and__num_Osimps_I1_J,axiom,
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.24/5.58 = ( some_num @ one ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(1)
% 5.24/5.58 thf(fact_9799_xor__num_Osimps_I1_J,axiom,
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.24/5.58 = none_num ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(1)
% 5.24/5.58 thf(fact_9800_xor__num_Osimps_I5_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(5)
% 5.24/5.58 thf(fact_9801_and__num_Osimps_I5_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(5)
% 5.24/5.58 thf(fact_9802_and__num_Osimps_I7_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.24/5.58 = ( some_num @ one ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(7)
% 5.24/5.58 thf(fact_9803_and__num_Osimps_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.24/5.58 = ( some_num @ one ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(3)
% 5.24/5.58 thf(fact_9804_and__num_Osimps_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.24/5.58 = none_num ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(2)
% 5.24/5.58 thf(fact_9805_and__num_Osimps_I4_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.24/5.58 = none_num ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(4)
% 5.24/5.58 thf(fact_9806_and__num_Osimps_I8_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(8)
% 5.24/5.58 thf(fact_9807_and__num_Osimps_I6_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(6)
% 5.24/5.58 thf(fact_9808_xor__num_Osimps_I9_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(9)
% 5.24/5.58 thf(fact_9809_xor__num_Osimps_I2_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.24/5.58 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(2)
% 5.24/5.58 thf(fact_9810_xor__num_Osimps_I3_J,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.24/5.58 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(3)
% 5.24/5.58 thf(fact_9811_xor__num_Osimps_I4_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.24/5.58 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(4)
% 5.24/5.58 thf(fact_9812_xor__num_Osimps_I7_J,axiom,
% 5.24/5.58 ! [M: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.24/5.58 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(7)
% 5.24/5.58 thf(fact_9813_and__num_Osimps_I9_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.24/5.58 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.24/5.58 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.simps(9)
% 5.24/5.58 thf(fact_9814_xor__num_Osimps_I8_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.24/5.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(8)
% 5.24/5.58 thf(fact_9815_xor__num_Osimps_I6_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.24/5.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.simps(6)
% 5.24/5.58 thf(fact_9816_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.24/5.58 ! [N: nat,J: nat,I2: nat] :
% 5.24/5.58 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I2 ) )
% 5.24/5.58 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N )
% 5.24/5.58 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nth_sorted_list_of_set_greaterThanAtMost
% 5.24/5.58 thf(fact_9817_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.24/5.58 ! [L2: nat,U2: nat] :
% 5.24/5.58 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U2 )
% 5.24/5.58 = ( set_or6659071591806873216st_nat @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastSucAtMost_greaterThanAtMost
% 5.24/5.58 thf(fact_9818_Rats__eq__int__div__nat,axiom,
% 5.24/5.58 ( field_5140801741446780682s_real
% 5.24/5.58 = ( collect_real
% 5.24/5.58 @ ^ [Uu2: real] :
% 5.24/5.58 ? [I4: int,N2: nat] :
% 5.24/5.58 ( ( Uu2
% 5.24/5.58 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.24/5.58 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rats_eq_int_div_nat
% 5.24/5.58 thf(fact_9819_rat__floor__lemma,axiom,
% 5.24/5.58 ! [A: int,B: int] :
% 5.24/5.58 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.24/5.58 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_floor_lemma
% 5.24/5.58 thf(fact_9820_image__minus__const__atLeastLessThan__nat,axiom,
% 5.24/5.58 ! [C: nat,Y4: nat,X: nat] :
% 5.24/5.58 ( ( ( ord_less_nat @ C @ Y4 )
% 5.24/5.58 => ( ( image_nat_nat
% 5.24/5.58 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ X @ Y4 ) )
% 5.24/5.58 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y4 @ C ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_nat @ C @ Y4 )
% 5.24/5.58 => ( ( ( ord_less_nat @ X @ Y4 )
% 5.24/5.58 => ( ( image_nat_nat
% 5.24/5.58 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ X @ Y4 ) )
% 5.24/5.58 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.24/5.58 & ( ~ ( ord_less_nat @ X @ Y4 )
% 5.24/5.58 => ( ( image_nat_nat
% 5.24/5.58 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ X @ Y4 ) )
% 5.24/5.58 = bot_bot_set_nat ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % image_minus_const_atLeastLessThan_nat
% 5.24/5.58 thf(fact_9821_bij__betw__Suc,axiom,
% 5.24/5.58 ! [M7: set_nat,N4: set_nat] :
% 5.24/5.58 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 5.24/5.58 = ( ( image_nat_nat @ suc @ M7 )
% 5.24/5.58 = N4 ) ) ).
% 5.24/5.58
% 5.24/5.58 % bij_betw_Suc
% 5.24/5.58 thf(fact_9822_image__Suc__atLeastAtMost,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.24/5.58 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % image_Suc_atLeastAtMost
% 5.24/5.58 thf(fact_9823_image__Suc__atLeastLessThan,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 5.24/5.58 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % image_Suc_atLeastLessThan
% 5.24/5.58 thf(fact_9824_mult__rat,axiom,
% 5.24/5.58 ! [A: int,B: int,C: int,D: int] :
% 5.24/5.58 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.24/5.58 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % mult_rat
% 5.24/5.58 thf(fact_9825_divide__rat,axiom,
% 5.24/5.58 ! [A: int,B: int,C: int,D: int] :
% 5.24/5.58 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.24/5.58 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divide_rat
% 5.24/5.58 thf(fact_9826_less__rat,axiom,
% 5.24/5.58 ! [B: int,D: int,A: int,C: int] :
% 5.24/5.58 ( ( B != zero_zero_int )
% 5.24/5.58 => ( ( D != zero_zero_int )
% 5.24/5.58 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_rat
% 5.24/5.58 thf(fact_9827_add__rat,axiom,
% 5.24/5.58 ! [B: int,D: int,A: int,C: int] :
% 5.24/5.58 ( ( B != zero_zero_int )
% 5.24/5.58 => ( ( D != zero_zero_int )
% 5.24/5.58 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.24/5.58 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % add_rat
% 5.24/5.58 thf(fact_9828_le__rat,axiom,
% 5.24/5.58 ! [B: int,D: int,A: int,C: int] :
% 5.24/5.58 ( ( B != zero_zero_int )
% 5.24/5.58 => ( ( D != zero_zero_int )
% 5.24/5.58 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % le_rat
% 5.24/5.58 thf(fact_9829_diff__rat,axiom,
% 5.24/5.58 ! [B: int,D: int,A: int,C: int] :
% 5.24/5.58 ( ( B != zero_zero_int )
% 5.24/5.58 => ( ( D != zero_zero_int )
% 5.24/5.58 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.24/5.58 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % diff_rat
% 5.24/5.58 thf(fact_9830_sgn__rat,axiom,
% 5.24/5.58 ! [A: int,B: int] :
% 5.24/5.58 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.24/5.58 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sgn_rat
% 5.24/5.58 thf(fact_9831_zero__notin__Suc__image,axiom,
% 5.24/5.58 ! [A2: set_nat] :
% 5.24/5.58 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % zero_notin_Suc_image
% 5.24/5.58 thf(fact_9832_eq__rat_I2_J,axiom,
% 5.24/5.58 ! [A: int] :
% 5.24/5.58 ( ( fract @ A @ zero_zero_int )
% 5.24/5.58 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % eq_rat(2)
% 5.24/5.58 thf(fact_9833_eq__rat_I1_J,axiom,
% 5.24/5.58 ! [B: int,D: int,A: int,C: int] :
% 5.24/5.58 ( ( B != zero_zero_int )
% 5.24/5.58 => ( ( D != zero_zero_int )
% 5.24/5.58 => ( ( ( fract @ A @ B )
% 5.24/5.58 = ( fract @ C @ D ) )
% 5.24/5.58 = ( ( times_times_int @ A @ D )
% 5.24/5.58 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % eq_rat(1)
% 5.24/5.58 thf(fact_9834_mult__rat__cancel,axiom,
% 5.24/5.58 ! [C: int,A: int,B: int] :
% 5.24/5.58 ( ( C != zero_zero_int )
% 5.24/5.58 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.24/5.58 = ( fract @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % mult_rat_cancel
% 5.24/5.58 thf(fact_9835_Fract__of__nat__eq,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 5.24/5.58 = ( semiri681578069525770553at_rat @ K ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract_of_nat_eq
% 5.24/5.58 thf(fact_9836_One__rat__def,axiom,
% 5.24/5.58 ( one_one_rat
% 5.24/5.58 = ( fract @ one_one_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % One_rat_def
% 5.24/5.58 thf(fact_9837_quotient__of__eq,axiom,
% 5.24/5.58 ! [A: int,B: int,P6: int,Q2: int] :
% 5.24/5.58 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 5.24/5.58 = ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.24/5.58 => ( ( fract @ P6 @ Q2 )
% 5.24/5.58 = ( fract @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_eq
% 5.24/5.58 thf(fact_9838_Fract__of__int__eq,axiom,
% 5.24/5.58 ! [K: int] :
% 5.24/5.58 ( ( fract @ K @ one_one_int )
% 5.24/5.58 = ( ring_1_of_int_rat @ K ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract_of_int_eq
% 5.24/5.58 thf(fact_9839_normalize__eq,axiom,
% 5.24/5.58 ! [A: int,B: int,P6: int,Q2: int] :
% 5.24/5.58 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 5.24/5.58 = ( product_Pair_int_int @ P6 @ Q2 ) )
% 5.24/5.58 => ( ( fract @ P6 @ Q2 )
% 5.24/5.58 = ( fract @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % normalize_eq
% 5.24/5.58 thf(fact_9840_Zero__rat__def,axiom,
% 5.24/5.58 ( zero_zero_rat
% 5.24/5.58 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % Zero_rat_def
% 5.24/5.58 thf(fact_9841_rat__number__expand_I3_J,axiom,
% 5.24/5.58 ( numeral_numeral_rat
% 5.24/5.58 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_number_expand(3)
% 5.24/5.58 thf(fact_9842_rat__number__collapse_I3_J,axiom,
% 5.24/5.58 ! [W2: num] :
% 5.24/5.58 ( ( fract @ ( numeral_numeral_int @ W2 ) @ one_one_int )
% 5.24/5.58 = ( numeral_numeral_rat @ W2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_number_collapse(3)
% 5.24/5.58 thf(fact_9843_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.24/5.58 ! [L2: int,U2: int] :
% 5.24/5.58 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U2 )
% 5.24/5.58 = ( set_or6656581121297822940st_int @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.24/5.58 thf(fact_9844_quotient__of__Fract,axiom,
% 5.24/5.58 ! [A: int,B: int] :
% 5.24/5.58 ( ( quotient_of @ ( fract @ A @ B ) )
% 5.24/5.58 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % quotient_of_Fract
% 5.24/5.58 thf(fact_9845_image__Suc__lessThan,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % image_Suc_lessThan
% 5.24/5.58 thf(fact_9846_image__Suc__atMost,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.24/5.58 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % image_Suc_atMost
% 5.24/5.58 thf(fact_9847_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.24/5.58 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast0_atMost_Suc_eq_insert_0
% 5.24/5.58 thf(fact_9848_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.24/5.58 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast0_lessThan_Suc_eq_insert_0
% 5.24/5.58 thf(fact_9849_lessThan__Suc__eq__insert__0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.24/5.58 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % lessThan_Suc_eq_insert_0
% 5.24/5.58 thf(fact_9850_atMost__Suc__eq__insert__0,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.24/5.58 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atMost_Suc_eq_insert_0
% 5.24/5.58 thf(fact_9851_one__less__Fract__iff,axiom,
% 5.24/5.58 ! [B: int,A: int] :
% 5.24/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.58 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.24/5.58 = ( ord_less_int @ B @ A ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_less_Fract_iff
% 5.24/5.58 thf(fact_9852_Fract__less__one__iff,axiom,
% 5.24/5.58 ! [B: int,A: int] :
% 5.24/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.58 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.24/5.58 = ( ord_less_int @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract_less_one_iff
% 5.24/5.58 thf(fact_9853_rat__number__collapse_I5_J,axiom,
% 5.24/5.58 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.24/5.58 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_number_collapse(5)
% 5.24/5.58 thf(fact_9854_Fract__add__one,axiom,
% 5.24/5.58 ! [N: int,M: int] :
% 5.24/5.58 ( ( N != zero_zero_int )
% 5.24/5.58 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 5.24/5.58 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract_add_one
% 5.24/5.58 thf(fact_9855_Fract__le__one__iff,axiom,
% 5.24/5.58 ! [B: int,A: int] :
% 5.24/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.58 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.24/5.58 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract_le_one_iff
% 5.24/5.58 thf(fact_9856_one__le__Fract__iff,axiom,
% 5.24/5.58 ! [B: int,A: int] :
% 5.24/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.24/5.58 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.24/5.58 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_le_Fract_iff
% 5.24/5.58 thf(fact_9857_rat__number__collapse_I4_J,axiom,
% 5.24/5.58 ! [W2: num] :
% 5.24/5.58 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ one_one_int )
% 5.24/5.58 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_number_collapse(4)
% 5.24/5.58 thf(fact_9858_rat__number__expand_I5_J,axiom,
% 5.24/5.58 ! [K: num] :
% 5.24/5.58 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.24/5.58 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % rat_number_expand(5)
% 5.24/5.58 thf(fact_9859_positive__rat,axiom,
% 5.24/5.58 ! [A: int,B: int] :
% 5.24/5.58 ( ( positive @ ( fract @ A @ B ) )
% 5.24/5.58 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % positive_rat
% 5.24/5.58 thf(fact_9860_Rat_Opositive__add,axiom,
% 5.24/5.58 ! [X: rat,Y4: rat] :
% 5.24/5.58 ( ( positive @ X )
% 5.24/5.58 => ( ( positive @ Y4 )
% 5.24/5.58 => ( positive @ ( plus_plus_rat @ X @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive_add
% 5.24/5.58 thf(fact_9861_Rat_Opositive__mult,axiom,
% 5.24/5.58 ! [X: rat,Y4: rat] :
% 5.24/5.58 ( ( positive @ X )
% 5.24/5.58 => ( ( positive @ Y4 )
% 5.24/5.58 => ( positive @ ( times_times_rat @ X @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive_mult
% 5.24/5.58 thf(fact_9862_image__add__int__atLeastLessThan,axiom,
% 5.24/5.58 ! [L2: int,U2: int] :
% 5.24/5.58 ( ( image_int_int
% 5.24/5.58 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L2 )
% 5.24/5.58 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U2 @ L2 ) ) )
% 5.24/5.58 = ( set_or4662586982721622107an_int @ L2 @ U2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % image_add_int_atLeastLessThan
% 5.24/5.58 thf(fact_9863_Rat_Opositive_Orep__eq,axiom,
% 5.24/5.58 ( positive
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive.rep_eq
% 5.24/5.58 thf(fact_9864_Sup__nat__empty,axiom,
% 5.24/5.58 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.24/5.58 = zero_zero_nat ) ).
% 5.24/5.58
% 5.24/5.58 % Sup_nat_empty
% 5.24/5.58 thf(fact_9865_Inf__nat__def1,axiom,
% 5.24/5.58 ! [K5: set_nat] :
% 5.24/5.58 ( ( K5 != bot_bot_set_nat )
% 5.24/5.58 => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 5.24/5.58
% 5.24/5.58 % Inf_nat_def1
% 5.24/5.58 thf(fact_9866_UNIV__nat__eq,axiom,
% 5.24/5.58 ( top_top_set_nat
% 5.24/5.58 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % UNIV_nat_eq
% 5.24/5.58 thf(fact_9867_range__mod,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( image_nat_nat
% 5.24/5.58 @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 5.24/5.58 @ top_top_set_nat )
% 5.24/5.58 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % range_mod
% 5.24/5.58 thf(fact_9868_card__UNIV__unit,axiom,
% 5.24/5.58 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.24/5.58 = one_one_nat ) ).
% 5.24/5.58
% 5.24/5.58 % card_UNIV_unit
% 5.24/5.58 thf(fact_9869_range__mult,axiom,
% 5.24/5.58 ! [A: real] :
% 5.24/5.58 ( ( ( A = zero_zero_real )
% 5.24/5.58 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.24/5.58 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.24/5.58 & ( ( A != zero_zero_real )
% 5.24/5.58 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.24/5.58 = top_top_set_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % range_mult
% 5.24/5.58 thf(fact_9870_card__UNIV__bool,axiom,
% 5.24/5.58 ( ( finite_card_o @ top_top_set_o )
% 5.24/5.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_UNIV_bool
% 5.24/5.58 thf(fact_9871_root__def,axiom,
% 5.24/5.58 ( root
% 5.24/5.58 = ( ^ [N2: nat,X2: real] :
% 5.24/5.58 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.24/5.58 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.24/5.58 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 5.24/5.58 @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % root_def
% 5.24/5.58 thf(fact_9872_card__UNIV__char,axiom,
% 5.24/5.58 ( ( finite_card_char @ top_top_set_char )
% 5.24/5.58 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_UNIV_char
% 5.24/5.58 thf(fact_9873_UNIV__char__of__nat,axiom,
% 5.24/5.58 ( top_top_set_char
% 5.24/5.58 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % UNIV_char_of_nat
% 5.24/5.58 thf(fact_9874_char_Osize_I2_J,axiom,
% 5.24/5.58 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X8: $o] :
% 5.24/5.58 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X8 ) )
% 5.24/5.58 = zero_zero_nat ) ).
% 5.24/5.58
% 5.24/5.58 % char.size(2)
% 5.24/5.58 thf(fact_9875_nat__of__char__less__256,axiom,
% 5.24/5.58 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nat_of_char_less_256
% 5.24/5.58 thf(fact_9876_range__nat__of__char,axiom,
% 5.24/5.58 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.24/5.58 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % range_nat_of_char
% 5.24/5.58 thf(fact_9877_integer__of__char__code,axiom,
% 5.24/5.58 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.24/5.58 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.24/5.58 = ( 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 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_char_code
% 5.24/5.58 thf(fact_9878_String_Ochar__of__ascii__of,axiom,
% 5.24/5.58 ! [C: char] :
% 5.24/5.58 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.24/5.58 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % String.char_of_ascii_of
% 5.24/5.58 thf(fact_9879_DERIV__real__root__generic,axiom,
% 5.24/5.58 ! [N: nat,X: real,D4: real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( X != zero_zero_real )
% 5.24/5.58 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.58 => ( D4
% 5.24/5.58 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.24/5.58 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.58 => ( D4
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ) ) )
% 5.24/5.58 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( D4
% 5.24/5.58 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_real_root_generic
% 5.24/5.58 thf(fact_9880_DERIV__even__real__root,axiom,
% 5.24/5.58 ! [N: nat,X: real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.58 => ( 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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_even_real_root
% 5.24/5.58 thf(fact_9881_sorted__list__of__set__lessThan__Suc,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.24/5.58 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_list_of_set_lessThan_Suc
% 5.24/5.58 thf(fact_9882_sorted__list__of__set__atMost__Suc,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.24/5.58 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_list_of_set_atMost_Suc
% 5.24/5.58 thf(fact_9883_has__real__derivative__pos__inc__right,axiom,
% 5.24/5.58 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.24/5.58 => ? [D3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.24/5.58 & ! [H4: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.24/5.58 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.24/5.58 => ( ( ord_less_real @ H4 @ D3 )
% 5.24/5.58 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % has_real_derivative_pos_inc_right
% 5.24/5.58 thf(fact_9884_has__real__derivative__neg__dec__right,axiom,
% 5.24/5.58 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.24/5.58 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.24/5.58 => ? [D3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.24/5.58 & ! [H4: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.24/5.58 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.24/5.58 => ( ( ord_less_real @ H4 @ D3 )
% 5.24/5.58 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % has_real_derivative_neg_dec_right
% 5.24/5.58 thf(fact_9885_DERIV__pos__inc__right,axiom,
% 5.24/5.58 ! [F: real > real,L2: real,X: real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.24/5.58 => ? [D3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.24/5.58 & ! [H4: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.24/5.58 => ( ( ord_less_real @ H4 @ D3 )
% 5.24/5.58 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_pos_inc_right
% 5.24/5.58 thf(fact_9886_DERIV__neg__dec__right,axiom,
% 5.24/5.58 ! [F: real > real,L2: real,X: real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.24/5.58 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.24/5.58 => ? [D3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.24/5.58 & ! [H4: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.24/5.58 => ( ( ord_less_real @ H4 @ D3 )
% 5.24/5.58 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_neg_dec_right
% 5.24/5.58 thf(fact_9887_DERIV__const__ratio__const,axiom,
% 5.24/5.58 ! [A: real,B: real,F: real > real,K: real] :
% 5.24/5.58 ( ( A != B )
% 5.24/5.58 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.24/5.58 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.24/5.58 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_const_ratio_const
% 5.24/5.58 thf(fact_9888_MVT2,axiom,
% 5.24/5.58 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.24/5.58 ( ( ord_less_real @ A @ B )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ A @ X3 )
% 5.24/5.58 => ( ( ord_less_eq_real @ X3 @ B )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.24/5.58 => ? [Z: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ Z )
% 5.24/5.58 & ( ord_less_real @ Z @ B )
% 5.24/5.58 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.24/5.58 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % MVT2
% 5.24/5.58 thf(fact_9889_DERIV__const__average,axiom,
% 5.24/5.58 ! [A: real,B: real,V: real > real,K: real] :
% 5.24/5.58 ( ( A != B )
% 5.24/5.58 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.24/5.58 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.24/5.58 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_const_average
% 5.24/5.58 thf(fact_9890_DERIV__ln__divide,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_ln_divide
% 5.24/5.58 thf(fact_9891_DERIV__pow,axiom,
% 5.24/5.58 ! [N: nat,X: real,S2: set_real] :
% 5.24/5.58 ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 5.24/5.58 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_pow
% 5.24/5.58 thf(fact_9892_DERIV__fun__pow,axiom,
% 5.24/5.58 ! [G: real > real,M: real,X: real,N: nat] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 5.24/5.58 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_fun_pow
% 5.24/5.58 thf(fact_9893_has__real__derivative__powr,axiom,
% 5.24/5.58 ! [Z2: real,R2: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [Z4: real] : ( powr_real @ Z4 @ R2 )
% 5.24/5.58 @ ( times_times_real @ R2 @ ( powr_real @ Z2 @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % has_real_derivative_powr
% 5.24/5.58 thf(fact_9894_DERIV__log,axiom,
% 5.24/5.58 ! [X: real,B: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.58 => ( 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 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_log
% 5.24/5.58 thf(fact_9895_DERIV__fun__powr,axiom,
% 5.24/5.58 ! [G: real > real,M: real,X: real,R2: real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 5.24/5.58 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_fun_powr
% 5.24/5.58 thf(fact_9896_DERIV__powr,axiom,
% 5.24/5.58 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.24/5.58 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.24/5.58 @ ( 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 ) ) ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_powr
% 5.24/5.58 thf(fact_9897_DERIV__real__sqrt,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_real_sqrt
% 5.24/5.58 thf(fact_9898_DERIV__series_H,axiom,
% 5.24/5.58 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.24/5.58 ( ! [N3: nat] :
% 5.24/5.58 ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] : ( F @ X2 @ N3 )
% 5.24/5.58 @ ( F4 @ X0 @ N3 )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.24/5.58 => ( summable_real @ ( F @ X3 ) ) )
% 5.24/5.58 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.24/5.58 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.24/5.58 => ( ( summable_real @ L5 )
% 5.24/5.58 => ( ! [N3: nat,X3: real,Y3: real] :
% 5.24/5.58 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.24/5.58 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.24/5.58 => ( 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 ) ) ) ) ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.24/5.58 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_series'
% 5.24/5.58 thf(fact_9899_DERIV__arctan,axiom,
% 5.24/5.58 ! [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 ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_arctan
% 5.24/5.58 thf(fact_9900_arsinh__real__has__field__derivative,axiom,
% 5.24/5.58 ! [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 ) ) ).
% 5.24/5.58
% 5.24/5.58 % arsinh_real_has_field_derivative
% 5.24/5.58 thf(fact_9901_DERIV__real__sqrt__generic,axiom,
% 5.24/5.58 ! [X: real,D4: real] :
% 5.24/5.58 ( ( X != zero_zero_real )
% 5.24/5.58 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.58 => ( D4
% 5.24/5.58 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.24/5.58 => ( D4
% 5.24/5.58 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_real_sqrt_generic
% 5.24/5.58 thf(fact_9902_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 5.24/5.58 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 5.24/5.58 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_list_of_set_greaterThanAtMost
% 5.24/5.58 thf(fact_9903_arcosh__real__has__field__derivative,axiom,
% 5.24/5.58 ! [X: real,A2: set_real] :
% 5.24/5.58 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.58 => ( 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 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % arcosh_real_has_field_derivative
% 5.24/5.58 thf(fact_9904_artanh__real__has__field__derivative,axiom,
% 5.24/5.58 ! [X: real,A2: set_real] :
% 5.24/5.58 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.58 => ( 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 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % artanh_real_has_field_derivative
% 5.24/5.58 thf(fact_9905_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 5.24/5.58 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 5.24/5.58 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_list_of_set_greaterThanLessThan
% 5.24/5.58 thf(fact_9906_DERIV__power__series_H,axiom,
% 5.24/5.58 ! [R: real,F: nat > real,X0: real] :
% 5.24/5.58 ( ! [X3: real] :
% 5.24/5.58 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.24/5.58 => ( summable_real
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.24/5.58 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X2: real] :
% 5.24/5.58 ( suminf_real
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) )
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_power_series'
% 5.24/5.58 thf(fact_9907_DERIV__real__root,axiom,
% 5.24/5.58 ! [N: nat,X: real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.24/5.58 => ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_real_root
% 5.24/5.58 thf(fact_9908_DERIV__arccos,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.58 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.58 => ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_arccos
% 5.24/5.58 thf(fact_9909_DERIV__arcsin,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.58 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.58 => ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_arcsin
% 5.24/5.58 thf(fact_9910_Maclaurin__all__le,axiom,
% 5.24/5.58 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.24/5.58 ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.58 & ( ( F @ X )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin_all_le
% 5.24/5.58 thf(fact_9911_Maclaurin__all__le__objl,axiom,
% 5.24/5.58 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.24/5.58 ( ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 & ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.58 & ( ( F @ X )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin_all_le_objl
% 5.24/5.58 thf(fact_9912_DERIV__odd__real__root,axiom,
% 5.24/5.58 ! [N: nat,X: real] :
% 5.24/5.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( ( X != zero_zero_real )
% 5.24/5.58 => ( 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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_odd_real_root
% 5.24/5.58 thf(fact_9913_Maclaurin,axiom,
% 5.24/5.58 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.24/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.24/5.58 & ( ord_less_real @ T3 @ H2 )
% 5.24/5.58 & ( ( F @ H2 )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin
% 5.24/5.58 thf(fact_9914_Maclaurin2,axiom,
% 5.24/5.58 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.24/5.58 => ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ H2 )
% 5.24/5.58 & ( ( F @ H2 )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin2
% 5.24/5.58 thf(fact_9915_Maclaurin__minus,axiom,
% 5.24/5.58 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.24/5.58 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.24/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ H2 @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_real @ H2 @ T3 )
% 5.24/5.58 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.24/5.58 & ( ( F @ H2 )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin_minus
% 5.24/5.58 thf(fact_9916_Maclaurin__all__lt,axiom,
% 5.24/5.58 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.24/5.58 ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( X != zero_zero_real )
% 5.24/5.58 => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.24/5.58 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.58 & ( ( F @ X )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin_all_lt
% 5.24/5.58 thf(fact_9917_Maclaurin__bi__le,axiom,
% 5.24/5.58 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.24/5.58 ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.24/5.58 & ( ( F @ X )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin_bi_le
% 5.24/5.58 thf(fact_9918_Taylor,axiom,
% 5.24/5.58 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ A @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ B ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ( ( ord_less_eq_real @ A @ C )
% 5.24/5.58 => ( ( ord_less_eq_real @ C @ B )
% 5.24/5.58 => ( ( ord_less_eq_real @ A @ X )
% 5.24/5.58 => ( ( ord_less_eq_real @ X @ B )
% 5.24/5.58 => ( ( X != C )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ( ord_less_real @ X @ C )
% 5.24/5.58 => ( ( ord_less_real @ X @ T3 )
% 5.24/5.58 & ( ord_less_real @ T3 @ C ) ) )
% 5.24/5.58 & ( ~ ( ord_less_real @ X @ C )
% 5.24/5.58 => ( ( ord_less_real @ C @ T3 )
% 5.24/5.58 & ( ord_less_real @ T3 @ X ) ) )
% 5.24/5.58 & ( ( F @ X )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Taylor
% 5.24/5.58 thf(fact_9919_Taylor__up,axiom,
% 5.24/5.58 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ A @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ B ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ( ( ord_less_eq_real @ A @ C )
% 5.24/5.58 => ( ( ord_less_real @ C @ B )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_real @ C @ T3 )
% 5.24/5.58 & ( ord_less_real @ T3 @ B )
% 5.24/5.58 & ( ( F @ B )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Taylor_up
% 5.24/5.58 thf(fact_9920_Taylor__down,axiom,
% 5.24/5.58 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( ( Diff @ zero_zero_nat )
% 5.24/5.58 = F )
% 5.24/5.58 => ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ A @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ B ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ( ( ord_less_real @ A @ C )
% 5.24/5.58 => ( ( ord_less_eq_real @ C @ B )
% 5.24/5.58 => ? [T3: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ T3 )
% 5.24/5.58 & ( ord_less_real @ T3 @ C )
% 5.24/5.58 & ( ( F @ A )
% 5.24/5.58 = ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M2 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.24/5.58 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Taylor_down
% 5.24/5.58 thf(fact_9921_Maclaurin__lemma2,axiom,
% 5.24/5.58 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B5: real] :
% 5.24/5.58 ( ! [M4: nat,T3: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M4 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.24/5.58 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.24/5.58 => ( ( N
% 5.24/5.58 = ( suc @ K ) )
% 5.24/5.58 => ! [M3: nat,T6: real] :
% 5.24/5.58 ( ( ( ord_less_nat @ M3 @ N )
% 5.24/5.58 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.24/5.58 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [U3: real] :
% 5.24/5.58 ( minus_minus_real @ ( Diff @ M3 @ U3 )
% 5.24/5.58 @ ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ U3 @ P4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 5.24/5.58 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U3 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 5.24/5.58 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T6 )
% 5.24/5.58 @ ( plus_plus_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T6 @ P4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 5.24/5.58 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T6 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Maclaurin_lemma2
% 5.24/5.58 thf(fact_9922_DERIV__arctan__series,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.58 => ( has_fi5821293074295781190e_real
% 5.24/5.58 @ ^ [X9: real] :
% 5.24/5.58 ( suminf_real
% 5.24/5.58 @ ^ [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 ) ) ) ) )
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [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 ) ) ) ) ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DERIV_arctan_series
% 5.24/5.58 thf(fact_9923_upto__aux__rec,axiom,
% 5.24/5.58 ( upto_aux
% 5.24/5.58 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_aux_rec
% 5.24/5.58 thf(fact_9924_isCont__arcosh,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % isCont_arcosh
% 5.24/5.58 thf(fact_9925_isCont__arccos,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.58 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % isCont_arccos
% 5.24/5.58 thf(fact_9926_isCont__arcsin,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.58 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % isCont_arcsin
% 5.24/5.58 thf(fact_9927_isCont__artanh,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.24/5.58 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % isCont_artanh
% 5.24/5.58 thf(fact_9928_GMVT_H,axiom,
% 5.24/5.58 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.24/5.58 ( ( ord_less_real @ A @ B )
% 5.24/5.58 => ( ! [Z: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ A @ Z )
% 5.24/5.58 => ( ( ord_less_eq_real @ Z @ B )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ F ) ) )
% 5.24/5.58 => ( ! [Z: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ A @ Z )
% 5.24/5.58 => ( ( ord_less_eq_real @ Z @ B )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ G ) ) )
% 5.24/5.58 => ( ! [Z: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ Z )
% 5.24/5.58 => ( ( ord_less_real @ Z @ B )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 5.24/5.58 => ( ! [Z: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ Z )
% 5.24/5.58 => ( ( ord_less_real @ Z @ B )
% 5.24/5.58 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 5.24/5.58 => ? [C3: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ C3 )
% 5.24/5.58 & ( ord_less_real @ C3 @ B )
% 5.24/5.58 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.24/5.58 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % GMVT'
% 5.24/5.58 thf(fact_9929_upto_Opsimps,axiom,
% 5.24/5.58 ! [I2: int,J: int] :
% 5.24/5.58 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 5.24/5.58 => ( ( ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( upto @ I2 @ J )
% 5.24/5.58 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( upto @ I2 @ J )
% 5.24/5.58 = nil_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto.psimps
% 5.24/5.58 thf(fact_9930_upto_Opelims,axiom,
% 5.24/5.58 ! [X: int,Xa2: int,Y4: list_int] :
% 5.24/5.58 ( ( ( upto @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.24/5.58 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.24/5.58 => ( Y4 = nil_int ) ) )
% 5.24/5.58 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto.pelims
% 5.24/5.58 thf(fact_9931_nth__upto,axiom,
% 5.24/5.58 ! [I2: int,K: nat,J: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.24/5.58 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 5.24/5.58 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nth_upto
% 5.24/5.58 thf(fact_9932_length__upto,axiom,
% 5.24/5.58 ! [I2: int,J: int] :
% 5.24/5.58 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 5.24/5.58 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % length_upto
% 5.24/5.58 thf(fact_9933_upto__rec__numeral_I1_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 = nil_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_rec_numeral(1)
% 5.24/5.58 thf(fact_9934_upto__rec__numeral_I4_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = nil_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_rec_numeral(4)
% 5.24/5.58 thf(fact_9935_upto__rec__numeral_I3_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 = ( 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 ) ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.24/5.58 = nil_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_rec_numeral(3)
% 5.24/5.58 thf(fact_9936_upto__rec__numeral_I2_J,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.24/5.58 = nil_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_rec_numeral(2)
% 5.24/5.58 thf(fact_9937_atLeastAtMost__upto,axiom,
% 5.24/5.58 ( set_or1266510415728281911st_int
% 5.24/5.58 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ J3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastAtMost_upto
% 5.24/5.58 thf(fact_9938_upto__split2,axiom,
% 5.24/5.58 ! [I2: int,J: int,K: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( ord_less_eq_int @ J @ K )
% 5.24/5.58 => ( ( upto @ I2 @ K )
% 5.24/5.58 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_split2
% 5.24/5.58 thf(fact_9939_upto__split1,axiom,
% 5.24/5.58 ! [I2: int,J: int,K: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( ord_less_eq_int @ J @ K )
% 5.24/5.58 => ( ( upto @ I2 @ K )
% 5.24/5.58 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_split1
% 5.24/5.58 thf(fact_9940_atLeastLessThan__upto,axiom,
% 5.24/5.58 ( set_or4662586982721622107an_int
% 5.24/5.58 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThan_upto
% 5.24/5.58 thf(fact_9941_greaterThanAtMost__upto,axiom,
% 5.24/5.58 ( set_or6656581121297822940st_int
% 5.24/5.58 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % greaterThanAtMost_upto
% 5.24/5.58 thf(fact_9942_upto__rec1,axiom,
% 5.24/5.58 ! [I2: int,J: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( upto @ I2 @ J )
% 5.24/5.58 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_rec1
% 5.24/5.58 thf(fact_9943_upto_Osimps,axiom,
% 5.24/5.58 ( upto
% 5.24/5.58 = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto.simps
% 5.24/5.58 thf(fact_9944_upto_Oelims,axiom,
% 5.24/5.58 ! [X: int,Xa2: int,Y4: list_int] :
% 5.24/5.58 ( ( ( upto @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.24/5.58 => ( Y4
% 5.24/5.58 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.24/5.58 => ( Y4 = nil_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto.elims
% 5.24/5.58 thf(fact_9945_upto__rec2,axiom,
% 5.24/5.58 ! [I2: int,J: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( upto @ I2 @ J )
% 5.24/5.58 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_rec2
% 5.24/5.58 thf(fact_9946_greaterThanLessThan__upto,axiom,
% 5.24/5.58 ( set_or5832277885323065728an_int
% 5.24/5.58 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % greaterThanLessThan_upto
% 5.24/5.58 thf(fact_9947_upto__split3,axiom,
% 5.24/5.58 ! [I2: int,J: int,K: int] :
% 5.24/5.58 ( ( ord_less_eq_int @ I2 @ J )
% 5.24/5.58 => ( ( ord_less_eq_int @ J @ K )
% 5.24/5.58 => ( ( upto @ I2 @ K )
% 5.24/5.58 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upto_split3
% 5.24/5.58 thf(fact_9948_GMVT,axiom,
% 5.24/5.58 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.24/5.58 ( ( ord_less_real @ A @ B )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.24/5.58 & ( ord_less_eq_real @ X3 @ B ) )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( ( ord_less_real @ A @ X3 )
% 5.24/5.58 & ( ord_less_real @ X3 @ B ) )
% 5.24/5.58 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.24/5.58 & ( ord_less_eq_real @ X3 @ B ) )
% 5.24/5.58 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( ( ord_less_real @ A @ X3 )
% 5.24/5.58 & ( ord_less_real @ X3 @ B ) )
% 5.24/5.58 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.24/5.58 => ? [G_c: real,F_c: real,C3: real] :
% 5.24/5.58 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.24/5.58 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.24/5.58 & ( ord_less_real @ A @ C3 )
% 5.24/5.58 & ( ord_less_real @ C3 @ B )
% 5.24/5.58 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.24/5.58 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % GMVT
% 5.24/5.58 thf(fact_9949_LIM__cos__div__sin,axiom,
% 5.24/5.58 ( filterlim_real_real
% 5.24/5.58 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIM_cos_div_sin
% 5.24/5.58 thf(fact_9950_summable__Leibniz_I2_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ( topolo6980174941875973593q_real @ A )
% 5.24/5.58 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.24/5.58 => ! [N9: nat] :
% 5.24/5.58 ( member_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.24/5.58 @ ( set_or1222579329274155063t_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz(2)
% 5.24/5.58 thf(fact_9951_summable__Leibniz_I3_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ( topolo6980174941875973593q_real @ A )
% 5.24/5.58 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.24/5.58 => ! [N9: nat] :
% 5.24/5.58 ( member_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.24/5.58 @ ( set_or1222579329274155063t_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz(3)
% 5.24/5.58 thf(fact_9952_filterlim__Suc,axiom,
% 5.24/5.58 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.24/5.58
% 5.24/5.58 % filterlim_Suc
% 5.24/5.58 thf(fact_9953_mult__nat__left__at__top,axiom,
% 5.24/5.58 ! [C: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.24/5.58 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % mult_nat_left_at_top
% 5.24/5.58 thf(fact_9954_mult__nat__right__at__top,axiom,
% 5.24/5.58 ! [C: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.24/5.58 => ( filterlim_nat_nat
% 5.24/5.58 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.24/5.58 @ at_top_nat
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % mult_nat_right_at_top
% 5.24/5.58 thf(fact_9955_LIMSEQ__root,axiom,
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_root
% 5.24/5.58 thf(fact_9956_nested__sequence__unique,axiom,
% 5.24/5.58 ! [F: nat > real,G: nat > real] :
% 5.24/5.58 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.24/5.58 => ( ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat )
% 5.24/5.58 => ? [L4: real] :
% 5.24/5.58 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 5.24/5.58 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.24/5.58 & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 5.24/5.58 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nested_sequence_unique
% 5.24/5.58 thf(fact_9957_LIMSEQ__inverse__zero,axiom,
% 5.24/5.58 ! [X7: nat > real] :
% 5.24/5.58 ( ! [R3: real] :
% 5.24/5.58 ? [N7: nat] :
% 5.24/5.58 ! [N3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.24/5.58 => ( ord_less_real @ R3 @ ( X7 @ N3 ) ) )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X7 @ N2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_inverse_zero
% 5.24/5.58 thf(fact_9958_lim__inverse__n_H,axiom,
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % lim_inverse_n'
% 5.24/5.58 thf(fact_9959_LIMSEQ__root__const,axiom,
% 5.24/5.58 ! [C: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ C )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_root_const
% 5.24/5.58 thf(fact_9960_LIMSEQ__inverse__real__of__nat,axiom,
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_inverse_real_of_nat
% 5.24/5.58 thf(fact_9961_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.24/5.58 ! [R2: real] :
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ R2 )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_inverse_real_of_nat_add
% 5.24/5.58 thf(fact_9962_increasing__LIMSEQ,axiom,
% 5.24/5.58 ! [F: nat > real,L2: real] :
% 5.24/5.58 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 5.24/5.58 => ( ! [E2: real] :
% 5.24/5.58 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.24/5.58 => ? [N9: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 5.24/5.58 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % increasing_LIMSEQ
% 5.24/5.58 thf(fact_9963_LIMSEQ__realpow__zero,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.58 => ( ( ord_less_real @ X @ one_one_real )
% 5.24/5.58 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_realpow_zero
% 5.24/5.58 thf(fact_9964_LIMSEQ__divide__realpow__zero,axiom,
% 5.24/5.58 ! [X: real,A: real] :
% 5.24/5.58 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_divide_realpow_zero
% 5.24/5.58 thf(fact_9965_LIMSEQ__abs__realpow__zero,axiom,
% 5.24/5.58 ! [C: real] :
% 5.24/5.58 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.24/5.58 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_abs_realpow_zero
% 5.24/5.58 thf(fact_9966_LIMSEQ__abs__realpow__zero2,axiom,
% 5.24/5.58 ! [C: real] :
% 5.24/5.58 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.24/5.58 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_abs_realpow_zero2
% 5.24/5.58 thf(fact_9967_LIMSEQ__inverse__realpow__zero,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_real @ one_one_real @ X )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_inverse_realpow_zero
% 5.24/5.58 thf(fact_9968_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.24/5.58 ! [R2: real] :
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ R2 )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.24/5.58 thf(fact_9969_tendsto__exp__limit__sequentially,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % tendsto_exp_limit_sequentially
% 5.24/5.58 thf(fact_9970_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.24/5.58 ! [R2: real] :
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ R2 )
% 5.24/5.58 @ at_top_nat ) ).
% 5.24/5.58
% 5.24/5.58 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.24/5.58 thf(fact_9971_summable__Leibniz_I1_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ( topolo6980174941875973593q_real @ A )
% 5.24/5.58 => ( summable_real
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz(1)
% 5.24/5.58 thf(fact_9972_summable,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.24/5.58 => ( summable_real
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable
% 5.24/5.58 thf(fact_9973_cos__diff__limit__1,axiom,
% 5.24/5.58 ! [Theta: nat > real,Theta2: real] :
% 5.24/5.58 ( ( filterlim_nat_real
% 5.24/5.58 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.24/5.58 @ at_top_nat )
% 5.24/5.58 => ~ ! [K2: nat > int] :
% 5.24/5.58 ~ ( filterlim_nat_real
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % cos_diff_limit_1
% 5.24/5.58 thf(fact_9974_cos__limit__1,axiom,
% 5.24/5.58 ! [Theta: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real
% 5.24/5.58 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.24/5.58 @ at_top_nat )
% 5.24/5.58 => ? [K2: nat > int] :
% 5.24/5.58 ( filterlim_nat_real
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % cos_limit_1
% 5.24/5.58 thf(fact_9975_summable__Leibniz_I4_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ( topolo6980174941875973593q_real @ A )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.24/5.58 @ at_top_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz(4)
% 5.24/5.58 thf(fact_9976_zeroseq__arctan__series,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % zeroseq_arctan_series
% 5.24/5.58 thf(fact_9977_summable__Leibniz_H_I2_J,axiom,
% 5.24/5.58 ! [A: nat > real,N: nat] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.24/5.58 => ( ord_less_eq_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz'(2)
% 5.24/5.58 thf(fact_9978_summable__Leibniz_H_I3_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.24/5.58 @ at_top_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz'(3)
% 5.24/5.58 thf(fact_9979_sums__alternating__upper__lower,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.58 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ? [L4: real] :
% 5.24/5.58 ( ! [N9: nat] :
% 5.24/5.58 ( ord_less_eq_real
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.24/5.58 @ L4 )
% 5.24/5.58 & ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ L4 )
% 5.24/5.58 @ at_top_nat )
% 5.24/5.58 & ! [N9: nat] :
% 5.24/5.58 ( ord_less_eq_real @ L4
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 5.24/5.58 & ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ L4 )
% 5.24/5.58 @ at_top_nat ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sums_alternating_upper_lower
% 5.24/5.58 thf(fact_9980_summable__Leibniz_I5_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ( topolo6980174941875973593q_real @ A )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.24/5.58 @ at_top_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz(5)
% 5.24/5.58 thf(fact_9981_summable__Leibniz_H_I5_J,axiom,
% 5.24/5.58 ! [A: nat > real] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.24/5.58 => ( filterlim_nat_real
% 5.24/5.58 @ ^ [N2: nat] :
% 5.24/5.58 ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.24/5.58 @ at_top_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz'(5)
% 5.24/5.58 thf(fact_9982_summable__Leibniz_H_I4_J,axiom,
% 5.24/5.58 ! [A: nat > real,N: nat] :
% 5.24/5.58 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.24/5.58 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.24/5.58 => ( ord_less_eq_real
% 5.24/5.58 @ ( suminf_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.24/5.58 @ ( groups6591440286371151544t_real
% 5.24/5.58 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.24/5.58 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % summable_Leibniz'(4)
% 5.24/5.58 thf(fact_9983_eventually__sequentially__Suc,axiom,
% 5.24/5.58 ! [P: nat > $o] :
% 5.24/5.58 ( ( eventually_nat
% 5.24/5.58 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 5.24/5.58 @ at_top_nat )
% 5.24/5.58 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % eventually_sequentially_Suc
% 5.24/5.58 thf(fact_9984_eventually__sequentially__seg,axiom,
% 5.24/5.58 ! [P: nat > $o,K: nat] :
% 5.24/5.58 ( ( eventually_nat
% 5.24/5.58 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.24/5.58 @ at_top_nat )
% 5.24/5.58 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % eventually_sequentially_seg
% 5.24/5.58 thf(fact_9985_eventually__sequentially,axiom,
% 5.24/5.58 ! [P: nat > $o] :
% 5.24/5.58 ( ( eventually_nat @ P @ at_top_nat )
% 5.24/5.58 = ( ? [N6: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.24/5.58 => ( P @ N2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % eventually_sequentially
% 5.24/5.58 thf(fact_9986_eventually__sequentiallyI,axiom,
% 5.24/5.58 ! [C: nat,P: nat > $o] :
% 5.24/5.58 ( ! [X3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ C @ X3 )
% 5.24/5.58 => ( P @ X3 ) )
% 5.24/5.58 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % eventually_sequentiallyI
% 5.24/5.58 thf(fact_9987_real__bounded__linear,axiom,
% 5.24/5.58 ( real_V5970128139526366754l_real
% 5.24/5.58 = ( ^ [F3: real > real] :
% 5.24/5.58 ? [C2: real] :
% 5.24/5.58 ( F3
% 5.24/5.58 = ( ^ [X2: real] : ( times_times_real @ X2 @ C2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % real_bounded_linear
% 5.24/5.58 thf(fact_9988_le__sequentially,axiom,
% 5.24/5.58 ! [F5: filter_nat] :
% 5.24/5.58 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.24/5.58 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % le_sequentially
% 5.24/5.58 thf(fact_9989_sequentially__offset,axiom,
% 5.24/5.58 ! [P: nat > $o,K: nat] :
% 5.24/5.58 ( ( eventually_nat @ P @ at_top_nat )
% 5.24/5.58 => ( eventually_nat
% 5.24/5.58 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 5.24/5.58 @ at_top_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % sequentially_offset
% 5.24/5.58 thf(fact_9990_tanh__real__at__top,axiom,
% 5.24/5.58 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.24/5.58
% 5.24/5.58 % tanh_real_at_top
% 5.24/5.58 thf(fact_9991_artanh__real__at__left__1,axiom,
% 5.24/5.58 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % artanh_real_at_left_1
% 5.24/5.58 thf(fact_9992_tendsto__exp__limit__at__top,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( filterlim_real_real
% 5.24/5.58 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y ) ) @ Y )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.24/5.58 @ at_top_real ) ).
% 5.24/5.58
% 5.24/5.58 % tendsto_exp_limit_at_top
% 5.24/5.58 thf(fact_9993_filterlim__tan__at__left,axiom,
% 5.24/5.58 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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % filterlim_tan_at_left
% 5.24/5.58 thf(fact_9994_tendsto__arctan__at__top,axiom,
% 5.24/5.58 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.24/5.58
% 5.24/5.58 % tendsto_arctan_at_top
% 5.24/5.58 thf(fact_9995_tendsto__exp__limit__at__right,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( filterlim_real_real
% 5.24/5.58 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 5.24/5.58 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % tendsto_exp_limit_at_right
% 5.24/5.58 thf(fact_9996_tendsto__arctan__at__bot,axiom,
% 5.24/5.58 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.24/5.58
% 5.24/5.58 % tendsto_arctan_at_bot
% 5.24/5.58 thf(fact_9997_artanh__real__at__right__1,axiom,
% 5.24/5.58 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % artanh_real_at_right_1
% 5.24/5.58 thf(fact_9998_eventually__at__right__to__0,axiom,
% 5.24/5.58 ! [P: real > $o,A: real] :
% 5.24/5.58 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.24/5.58 = ( eventually_real
% 5.24/5.58 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % eventually_at_right_to_0
% 5.24/5.58 thf(fact_9999_filterlim__tan__at__right,axiom,
% 5.24/5.58 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 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % filterlim_tan_at_right
% 5.24/5.58 thf(fact_10000_tanh__real__at__bot,axiom,
% 5.24/5.58 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.24/5.58
% 5.24/5.58 % tanh_real_at_bot
% 5.24/5.58 thf(fact_10001_tendsto__arcosh__at__left__1,axiom,
% 5.24/5.58 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % tendsto_arcosh_at_left_1
% 5.24/5.58 thf(fact_10002_filterlim__pow__at__bot__odd,axiom,
% 5.24/5.58 ! [N: nat,F: real > real,F5: filter_real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.24/5.58 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( filterlim_real_real
% 5.24/5.58 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.24/5.58 @ at_bot_real
% 5.24/5.58 @ F5 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % filterlim_pow_at_bot_odd
% 5.24/5.58 thf(fact_10003_filterlim__pow__at__bot__even,axiom,
% 5.24/5.58 ! [N: nat,F: real > real,F5: filter_real] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.24/5.58 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.24/5.58 => ( filterlim_real_real
% 5.24/5.58 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.24/5.58 @ at_top_real
% 5.24/5.58 @ F5 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % filterlim_pow_at_bot_even
% 5.24/5.58 thf(fact_10004_atLeast__Suc__greaterThan,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.24/5.58 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast_Suc_greaterThan
% 5.24/5.58 thf(fact_10005_INT__greaterThan__UNIV,axiom,
% 5.24/5.58 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.24/5.58 = bot_bot_set_nat ) ).
% 5.24/5.58
% 5.24/5.58 % INT_greaterThan_UNIV
% 5.24/5.58 thf(fact_10006_greaterThan__0,axiom,
% 5.24/5.58 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.24/5.58 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % greaterThan_0
% 5.24/5.58 thf(fact_10007_greaterThan__Suc,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.24/5.58 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % greaterThan_Suc
% 5.24/5.58 thf(fact_10008_atLeast__Suc,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.24/5.58 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast_Suc
% 5.24/5.58 thf(fact_10009_Gcd__eq__Max,axiom,
% 5.24/5.58 ! [M7: set_nat] :
% 5.24/5.58 ( ( finite_finite_nat @ M7 )
% 5.24/5.58 => ( ( M7 != bot_bot_set_nat )
% 5.24/5.58 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.24/5.58 => ( ( gcd_Gcd_nat @ M7 )
% 5.24/5.58 = ( lattic8265883725875713057ax_nat
% 5.24/5.58 @ ( comple7806235888213564991et_nat
% 5.24/5.58 @ ( image_nat_set_nat
% 5.24/5.58 @ ^ [M2: nat] :
% 5.24/5.58 ( collect_nat
% 5.24/5.58 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M2 ) )
% 5.24/5.58 @ M7 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Gcd_eq_Max
% 5.24/5.58 thf(fact_10010_card__le__Suc__Max,axiom,
% 5.24/5.58 ! [S3: set_nat] :
% 5.24/5.58 ( ( finite_finite_nat @ S3 )
% 5.24/5.58 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_le_Suc_Max
% 5.24/5.58 thf(fact_10011_Sup__nat__def,axiom,
% 5.24/5.58 ( complete_Sup_Sup_nat
% 5.24/5.58 = ( ^ [X6: set_nat] : ( if_nat @ ( X6 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X6 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Sup_nat_def
% 5.24/5.58 thf(fact_10012_divide__nat__def,axiom,
% 5.24/5.58 ( divide_divide_nat
% 5.24/5.58 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.58 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.24/5.58 @ ( lattic8265883725875713057ax_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divide_nat_def
% 5.24/5.58 thf(fact_10013_gcd__is__Max__divisors__nat,axiom,
% 5.24/5.58 ! [N: nat,M: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( ( gcd_gcd_nat @ M @ N )
% 5.24/5.58 = ( lattic8265883725875713057ax_nat
% 5.24/5.58 @ ( collect_nat
% 5.24/5.58 @ ^ [D2: nat] :
% 5.24/5.58 ( ( dvd_dvd_nat @ D2 @ M )
% 5.24/5.58 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % gcd_is_Max_divisors_nat
% 5.24/5.58 thf(fact_10014_MVT,axiom,
% 5.24/5.58 ! [A: real,B: real,F: real > real] :
% 5.24/5.58 ( ( ord_less_real @ A @ B )
% 5.24/5.58 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ X3 )
% 5.24/5.58 => ( ( ord_less_real @ X3 @ B )
% 5.24/5.58 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.24/5.58 => ? [L4: real,Z: real] :
% 5.24/5.58 ( ( ord_less_real @ A @ Z )
% 5.24/5.58 & ( ord_less_real @ Z @ B )
% 5.24/5.58 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) )
% 5.24/5.58 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.24/5.58 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % MVT
% 5.24/5.58 thf(fact_10015_continuous__on__arcosh,axiom,
% 5.24/5.58 ! [A2: set_real] :
% 5.24/5.58 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.24/5.58 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % continuous_on_arcosh
% 5.24/5.58 thf(fact_10016_continuous__on__arcosh_H,axiom,
% 5.24/5.58 ! [A2: set_real,F: real > real] :
% 5.24/5.58 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( member_real @ X3 @ A2 )
% 5.24/5.58 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.24/5.58 => ( topolo5044208981011980120l_real @ A2
% 5.24/5.58 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % continuous_on_arcosh'
% 5.24/5.58 thf(fact_10017_continuous__on__arccos_H,axiom,
% 5.24/5.58 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.24/5.58
% 5.24/5.58 % continuous_on_arccos'
% 5.24/5.58 thf(fact_10018_continuous__on__arcsin_H,axiom,
% 5.24/5.58 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.24/5.58
% 5.24/5.58 % continuous_on_arcsin'
% 5.24/5.58 thf(fact_10019_continuous__on__artanh,axiom,
% 5.24/5.58 ! [A2: set_real] :
% 5.24/5.58 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.24/5.58 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % continuous_on_artanh
% 5.24/5.58 thf(fact_10020_continuous__on__artanh_H,axiom,
% 5.24/5.58 ! [A2: set_real,F: real > real] :
% 5.24/5.58 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.24/5.58 => ( ! [X3: real] :
% 5.24/5.58 ( ( member_real @ X3 @ A2 )
% 5.24/5.58 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.24/5.58 => ( topolo5044208981011980120l_real @ A2
% 5.24/5.58 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % continuous_on_artanh'
% 5.24/5.58 thf(fact_10021_mono__Suc,axiom,
% 5.24/5.58 order_mono_nat_nat @ suc ).
% 5.24/5.58
% 5.24/5.58 % mono_Suc
% 5.24/5.58 thf(fact_10022_mono__times__nat,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % mono_times_nat
% 5.24/5.58 thf(fact_10023_mono__ge2__power__minus__self,axiom,
% 5.24/5.58 ! [K: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.24/5.58 => ( order_mono_nat_nat
% 5.24/5.58 @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % mono_ge2_power_minus_self
% 5.24/5.58 thf(fact_10024_Bseq__realpow,axiom,
% 5.24/5.58 ! [X: real] :
% 5.24/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.24/5.58 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.24/5.58 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Bseq_realpow
% 5.24/5.58 thf(fact_10025_inj__sgn__power,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.24/5.58 => ( inj_on_real_real
% 5.24/5.58 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.24/5.58 @ top_top_set_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % inj_sgn_power
% 5.24/5.58 thf(fact_10026_log__inj,axiom,
% 5.24/5.58 ! [B: real] :
% 5.24/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.24/5.58 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % log_inj
% 5.24/5.58 thf(fact_10027_inj__on__diff__nat,axiom,
% 5.24/5.58 ! [N4: set_nat,K: nat] :
% 5.24/5.58 ( ! [N3: nat] :
% 5.24/5.58 ( ( member_nat @ N3 @ N4 )
% 5.24/5.58 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.24/5.58 => ( inj_on_nat_nat
% 5.24/5.58 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.24/5.58 @ N4 ) ) ).
% 5.24/5.58
% 5.24/5.58 % inj_on_diff_nat
% 5.24/5.58 thf(fact_10028_inj__Suc,axiom,
% 5.24/5.58 ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 5.24/5.58
% 5.24/5.58 % inj_Suc
% 5.24/5.58 thf(fact_10029_inj__on__char__of__nat,axiom,
% 5.24/5.58 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inj_on_char_of_nat
% 5.24/5.58 thf(fact_10030_min__Suc__Suc,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.24/5.58 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % min_Suc_Suc
% 5.24/5.58 thf(fact_10031_min__numeral__Suc,axiom,
% 5.24/5.58 ! [K: num,N: nat] :
% 5.24/5.58 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.24/5.58 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % min_numeral_Suc
% 5.24/5.58 thf(fact_10032_min__Suc__numeral,axiom,
% 5.24/5.58 ! [N: nat,K: num] :
% 5.24/5.58 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.24/5.58 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % min_Suc_numeral
% 5.24/5.58 thf(fact_10033_nat__mult__min__left,axiom,
% 5.24/5.58 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.58 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.24/5.58 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nat_mult_min_left
% 5.24/5.58 thf(fact_10034_nat__mult__min__right,axiom,
% 5.24/5.58 ! [M: nat,N: nat,Q2: nat] :
% 5.24/5.58 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.24/5.58 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nat_mult_min_right
% 5.24/5.58 thf(fact_10035_min__Suc1,axiom,
% 5.24/5.58 ! [N: nat,M: nat] :
% 5.24/5.58 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.24/5.58 = ( case_nat_nat @ zero_zero_nat
% 5.24/5.58 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 5.24/5.58 @ M ) ) ).
% 5.24/5.58
% 5.24/5.58 % min_Suc1
% 5.24/5.58 thf(fact_10036_min__Suc2,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.24/5.58 = ( case_nat_nat @ zero_zero_nat
% 5.24/5.58 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 5.24/5.58 @ M ) ) ).
% 5.24/5.58
% 5.24/5.58 % min_Suc2
% 5.24/5.58 thf(fact_10037_pred__nat__def,axiom,
% 5.24/5.58 ( pred_nat
% 5.24/5.58 = ( collec3392354462482085612at_nat
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [M2: nat,N2: nat] :
% 5.24/5.58 ( N2
% 5.24/5.58 = ( suc @ M2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % pred_nat_def
% 5.24/5.58 thf(fact_10038_min__enat__simps_I2_J,axiom,
% 5.24/5.58 ! [Q2: extended_enat] :
% 5.24/5.58 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.24/5.58 = zero_z5237406670263579293d_enat ) ).
% 5.24/5.58
% 5.24/5.58 % min_enat_simps(2)
% 5.24/5.58 thf(fact_10039_min__enat__simps_I3_J,axiom,
% 5.24/5.58 ! [Q2: extended_enat] :
% 5.24/5.58 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.24/5.58 = zero_z5237406670263579293d_enat ) ).
% 5.24/5.58
% 5.24/5.58 % min_enat_simps(3)
% 5.24/5.58 thf(fact_10040_inf__enat__def,axiom,
% 5.24/5.58 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.24/5.58
% 5.24/5.58 % inf_enat_def
% 5.24/5.58 thf(fact_10041_sup__enat__def,axiom,
% 5.24/5.58 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.24/5.58
% 5.24/5.58 % sup_enat_def
% 5.24/5.58 thf(fact_10042_atLeastLessThan__add__Un,axiom,
% 5.24/5.58 ! [I2: nat,J: nat,K: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.58 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.24/5.58 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThan_add_Un
% 5.24/5.58 thf(fact_10043_less__eq,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.24/5.58 = ( ord_less_nat @ M @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq
% 5.24/5.58 thf(fact_10044_pred__nat__trancl__eq__le,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.24/5.58 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % pred_nat_trancl_eq_le
% 5.24/5.58 thf(fact_10045_tl__upt,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.24/5.58 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % tl_upt
% 5.24/5.58 thf(fact_10046_hd__upt,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I2 @ J )
% 5.24/5.58 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 5.24/5.58 = I2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % hd_upt
% 5.24/5.58 thf(fact_10047_drop__upt,axiom,
% 5.24/5.58 ! [M: nat,I2: nat,J: nat] :
% 5.24/5.58 ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 5.24/5.58 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 5.24/5.58
% 5.24/5.58 % drop_upt
% 5.24/5.58 thf(fact_10048_length__upt,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 5.24/5.58 = ( minus_minus_nat @ J @ I2 ) ) ).
% 5.24/5.58
% 5.24/5.58 % length_upt
% 5.24/5.58 thf(fact_10049_take__upt,axiom,
% 5.24/5.58 ! [I2: nat,M: nat,N: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N )
% 5.24/5.58 => ( ( take_nat @ M @ ( upt @ I2 @ N ) )
% 5.24/5.58 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % take_upt
% 5.24/5.58 thf(fact_10050_upt__conv__Nil,axiom,
% 5.24/5.58 ! [J: nat,I2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ J @ I2 )
% 5.24/5.58 => ( ( upt @ I2 @ J )
% 5.24/5.58 = nil_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_conv_Nil
% 5.24/5.58 thf(fact_10051_upt__eq__Nil__conv,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ( upt @ I2 @ J )
% 5.24/5.58 = nil_nat )
% 5.24/5.58 = ( ( J = zero_zero_nat )
% 5.24/5.58 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_eq_Nil_conv
% 5.24/5.58 thf(fact_10052_nth__upt,axiom,
% 5.24/5.58 ! [I2: nat,K: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 5.24/5.58 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 5.24/5.58 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % nth_upt
% 5.24/5.58 thf(fact_10053_upt__rec__numeral,axiom,
% 5.24/5.58 ! [M: num,N: num] :
% 5.24/5.58 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.58 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.58 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.58 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.24/5.58 = nil_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_rec_numeral
% 5.24/5.58 thf(fact_10054_map__add__upt,axiom,
% 5.24/5.58 ! [N: nat,M: nat] :
% 5.24/5.58 ( ( map_nat_nat
% 5.24/5.58 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 5.24/5.58 @ ( upt @ zero_zero_nat @ M ) )
% 5.24/5.58 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % map_add_upt
% 5.24/5.58 thf(fact_10055_map__Suc__upt,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.24/5.58 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % map_Suc_upt
% 5.24/5.58 thf(fact_10056_upt__conv__Cons__Cons,axiom,
% 5.24/5.58 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.24/5.58 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.24/5.58 = ( upt @ M @ Q2 ) )
% 5.24/5.58 = ( ( cons_nat @ N @ Ns )
% 5.24/5.58 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_conv_Cons_Cons
% 5.24/5.58 thf(fact_10057_greaterThanLessThan__upt,axiom,
% 5.24/5.58 ( set_or5834768355832116004an_nat
% 5.24/5.58 = ( ^ [N2: nat,M2: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % greaterThanLessThan_upt
% 5.24/5.58 thf(fact_10058_atLeastAtMost__upt,axiom,
% 5.24/5.58 ( set_or1269000886237332187st_nat
% 5.24/5.58 = ( ^ [N2: nat,M2: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastAtMost_upt
% 5.24/5.58 thf(fact_10059_atLeastLessThan__upt,axiom,
% 5.24/5.58 ( set_or4665077453230672383an_nat
% 5.24/5.58 = ( ^ [I4: nat,J3: nat] : ( set_nat2 @ ( upt @ I4 @ J3 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeastLessThan_upt
% 5.24/5.58 thf(fact_10060_greaterThanAtMost__upt,axiom,
% 5.24/5.58 ( set_or6659071591806873216st_nat
% 5.24/5.58 = ( ^ [N2: nat,M2: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % greaterThanAtMost_upt
% 5.24/5.58 thf(fact_10061_atLeast__upt,axiom,
% 5.24/5.58 ( set_ord_lessThan_nat
% 5.24/5.58 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atLeast_upt
% 5.24/5.58 thf(fact_10062_atMost__upto,axiom,
% 5.24/5.58 ( set_ord_atMost_nat
% 5.24/5.58 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % atMost_upto
% 5.24/5.58 thf(fact_10063_upt__conv__Cons,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I2 @ J )
% 5.24/5.58 => ( ( upt @ I2 @ J )
% 5.24/5.58 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_conv_Cons
% 5.24/5.58 thf(fact_10064_map__decr__upt,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( map_nat_nat
% 5.24/5.58 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.24/5.58 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.24/5.58 = ( upt @ M @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % map_decr_upt
% 5.24/5.58 thf(fact_10065_upt__add__eq__append,axiom,
% 5.24/5.58 ! [I2: nat,J: nat,K: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.58 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.24/5.58 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_add_eq_append
% 5.24/5.58 thf(fact_10066_upt__eq__Cons__conv,axiom,
% 5.24/5.58 ! [I2: nat,J: nat,X: nat,Xs2: list_nat] :
% 5.24/5.58 ( ( ( upt @ I2 @ J )
% 5.24/5.58 = ( cons_nat @ X @ Xs2 ) )
% 5.24/5.58 = ( ( ord_less_nat @ I2 @ J )
% 5.24/5.58 & ( I2 = X )
% 5.24/5.58 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 5.24/5.58 = Xs2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_eq_Cons_conv
% 5.24/5.58 thf(fact_10067_upt__rec,axiom,
% 5.24/5.58 ( upt
% 5.24/5.58 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_rec
% 5.24/5.58 thf(fact_10068_upt__Suc,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.58 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.24/5.58 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.24/5.58 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.58 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.24/5.58 = nil_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_Suc
% 5.24/5.58 thf(fact_10069_upt__Suc__append,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ I2 @ J )
% 5.24/5.58 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.24/5.58 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % upt_Suc_append
% 5.24/5.58 thf(fact_10070_sum__list__upt,axiom,
% 5.24/5.58 ! [M: nat,N: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ M @ N )
% 5.24/5.58 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.24/5.58 = ( groups3542108847815614940at_nat
% 5.24/5.58 @ ^ [X2: nat] : X2
% 5.24/5.58 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sum_list_upt
% 5.24/5.58 thf(fact_10071_card__length__sum__list__rec,axiom,
% 5.24/5.58 ! [M: nat,N4: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.24/5.58 => ( ( finite_card_list_nat
% 5.24/5.58 @ ( collect_list_nat
% 5.24/5.58 @ ^ [L: list_nat] :
% 5.24/5.58 ( ( ( size_size_list_nat @ L )
% 5.24/5.58 = M )
% 5.24/5.58 & ( ( groups4561878855575611511st_nat @ L )
% 5.24/5.58 = N4 ) ) ) )
% 5.24/5.58 = ( plus_plus_nat
% 5.24/5.58 @ ( finite_card_list_nat
% 5.24/5.58 @ ( collect_list_nat
% 5.24/5.58 @ ^ [L: list_nat] :
% 5.24/5.58 ( ( ( size_size_list_nat @ L )
% 5.24/5.58 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.24/5.58 & ( ( groups4561878855575611511st_nat @ L )
% 5.24/5.58 = N4 ) ) ) )
% 5.24/5.58 @ ( finite_card_list_nat
% 5.24/5.58 @ ( collect_list_nat
% 5.24/5.58 @ ^ [L: list_nat] :
% 5.24/5.58 ( ( ( size_size_list_nat @ L )
% 5.24/5.58 = M )
% 5.24/5.58 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 5.24/5.58 = N4 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_length_sum_list_rec
% 5.24/5.58 thf(fact_10072_card__length__sum__list,axiom,
% 5.24/5.58 ! [M: nat,N4: nat] :
% 5.24/5.58 ( ( finite_card_list_nat
% 5.24/5.58 @ ( collect_list_nat
% 5.24/5.58 @ ^ [L: list_nat] :
% 5.24/5.58 ( ( ( size_size_list_nat @ L )
% 5.24/5.58 = M )
% 5.24/5.58 & ( ( groups4561878855575611511st_nat @ L )
% 5.24/5.58 = N4 ) ) ) )
% 5.24/5.58 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 5.24/5.58
% 5.24/5.58 % card_length_sum_list
% 5.24/5.58 thf(fact_10073_sorted__wrt__upt,axiom,
% 5.24/5.58 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_wrt_upt
% 5.24/5.58 thf(fact_10074_sorted__upt,axiom,
% 5.24/5.58 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_upt
% 5.24/5.58 thf(fact_10075_sorted__wrt__less__idx,axiom,
% 5.24/5.58 ! [Ns: list_nat,I2: nat] :
% 5.24/5.58 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.24/5.58 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.24/5.58 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % sorted_wrt_less_idx
% 5.24/5.58 thf(fact_10076_prod__encode__prod__decode__aux,axiom,
% 5.24/5.58 ! [K: nat,M: nat] :
% 5.24/5.58 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.24/5.58 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_encode_prod_decode_aux
% 5.24/5.58 thf(fact_10077_le__prod__encode__1,axiom,
% 5.24/5.58 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % le_prod_encode_1
% 5.24/5.58 thf(fact_10078_le__prod__encode__2,axiom,
% 5.24/5.58 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % le_prod_encode_2
% 5.24/5.58 thf(fact_10079_prod__encode__def,axiom,
% 5.24/5.58 ( nat_prod_encode
% 5.24/5.58 = ( produc6842872674320459806at_nat
% 5.24/5.58 @ ^ [M2: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M2 @ N2 ) ) @ M2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % prod_encode_def
% 5.24/5.58 thf(fact_10080_list__encode_Oelims,axiom,
% 5.24/5.58 ! [X: list_nat,Y4: nat] :
% 5.24/5.58 ( ( ( nat_list_encode @ X )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( ( X = nil_nat )
% 5.24/5.58 => ( Y4 != zero_zero_nat ) )
% 5.24/5.58 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( cons_nat @ X3 @ Xs3 ) )
% 5.24/5.58 => ( Y4
% 5.24/5.58 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % list_encode.elims
% 5.24/5.58 thf(fact_10081_list__encode_Osimps_I2_J,axiom,
% 5.24/5.58 ! [X: nat,Xs2: list_nat] :
% 5.24/5.58 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 5.24/5.58 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % list_encode.simps(2)
% 5.24/5.58 thf(fact_10082_list__encode_Opelims,axiom,
% 5.24/5.58 ! [X: list_nat,Y4: nat] :
% 5.24/5.58 ( ( ( nat_list_encode @ X )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.24/5.58 => ( ( ( X = nil_nat )
% 5.24/5.58 => ( ( Y4 = zero_zero_nat )
% 5.24/5.58 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.24/5.58 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( cons_nat @ X3 @ Xs3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.24/5.58 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % list_encode.pelims
% 5.24/5.58 thf(fact_10083_Gcd__int__set__eq__fold,axiom,
% 5.24/5.58 ! [Xs2: list_int] :
% 5.24/5.58 ( ( gcd_Gcd_int @ ( set_int2 @ Xs2 ) )
% 5.24/5.58 = ( fold_int_int @ gcd_gcd_int @ Xs2 @ zero_zero_int ) ) ).
% 5.24/5.58
% 5.24/5.58 % Gcd_int_set_eq_fold
% 5.24/5.58 thf(fact_10084_Gcd__nat__set__eq__fold,axiom,
% 5.24/5.58 ! [Xs2: list_nat] :
% 5.24/5.58 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 5.24/5.58 = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % Gcd_nat_set_eq_fold
% 5.24/5.58 thf(fact_10085_vanishes__mult__bounded,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ? [A6: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ A6 )
% 5.24/5.58 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N3 ) ) @ A6 ) )
% 5.24/5.58 => ( ( vanishes @ Y7 )
% 5.24/5.58 => ( vanishes
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_rat @ ( X7 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vanishes_mult_bounded
% 5.24/5.58 thf(fact_10086_vanishes__add,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ( vanishes @ X7 )
% 5.24/5.58 => ( ( vanishes @ Y7 )
% 5.24/5.58 => ( vanishes
% 5.24/5.58 @ ^ [N2: nat] : ( plus_plus_rat @ ( X7 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vanishes_add
% 5.24/5.58 thf(fact_10087_vanishes__def,axiom,
% 5.24/5.58 ( vanishes
% 5.24/5.58 = ( ^ [X6: nat > rat] :
% 5.24/5.58 ! [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 => ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N2 ) ) @ R5 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vanishes_def
% 5.24/5.58 thf(fact_10088_vanishesI,axiom,
% 5.24/5.58 ! [X7: nat > rat] :
% 5.24/5.58 ( ! [R3: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.24/5.58 => ? [K4: nat] :
% 5.24/5.58 ! [N3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.24/5.58 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N3 ) ) @ R3 ) ) )
% 5.24/5.58 => ( vanishes @ X7 ) ) ).
% 5.24/5.58
% 5.24/5.58 % vanishesI
% 5.24/5.58 thf(fact_10089_vanishesD,axiom,
% 5.24/5.58 ! [X7: nat > rat,R2: rat] :
% 5.24/5.58 ( ( vanishes @ X7 )
% 5.24/5.58 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.24/5.58 => ? [K2: nat] :
% 5.24/5.58 ! [N9: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ N9 )
% 5.24/5.58 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N9 ) ) @ R2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vanishesD
% 5.24/5.58 thf(fact_10090_and__not__num_Opelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: option_num] :
% 5.24/5.58 ( ( ( bit_and_not_num @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4 = none_num )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ one ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4 = none_num )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.24/5.58 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ~ ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_not_num.pelims
% 5.24/5.58 thf(fact_10091_and__num_Opelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: option_num] :
% 5.24/5.58 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ one ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4 = none_num )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ one ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4 = none_num )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ one ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ~ ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.24/5.58 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.24/5.58 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % and_num.pelims
% 5.24/5.58 thf(fact_10092_xor__num_Opelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: option_num] :
% 5.24/5.58 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4 = none_num )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( bit1 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( bit0 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( bit1 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.24/5.58 => ~ ! [M4: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ! [N3: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % xor_num.pelims
% 5.24/5.58 thf(fact_10093_or__not__num__neg_Opelims,axiom,
% 5.24/5.58 ! [X: num,Xa2: num,Y4: num] :
% 5.24/5.58 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.24/5.58 = Y4 )
% 5.24/5.58 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4 = one )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.24/5.58 => ( ( ( X = one )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bit0 @ one ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit0 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ( ( Xa2 = one )
% 5.24/5.58 => ( ( Y4 = one )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.24/5.58 => ( ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit0 @ M4 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.24/5.58 => ~ ! [N3: num] :
% 5.24/5.58 ( ( X
% 5.24/5.58 = ( bit1 @ N3 ) )
% 5.24/5.58 => ! [M4: num] :
% 5.24/5.58 ( ( Xa2
% 5.24/5.58 = ( bit1 @ M4 ) )
% 5.24/5.58 => ( ( Y4
% 5.24/5.58 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.24/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % or_not_num_neg.pelims
% 5.24/5.58 thf(fact_10094_rcis__inverse,axiom,
% 5.24/5.58 ! [R2: real,A: real] :
% 5.24/5.58 ( ( invers8013647133539491842omplex @ ( rcis @ R2 @ A ) )
% 5.24/5.58 = ( rcis @ ( divide_divide_real @ one_one_real @ R2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rcis_inverse
% 5.24/5.58 thf(fact_10095_Re__rcis,axiom,
% 5.24/5.58 ! [R2: real,A: real] :
% 5.24/5.58 ( ( re @ ( rcis @ R2 @ A ) )
% 5.24/5.58 = ( times_times_real @ R2 @ ( cos_real @ A ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Re_rcis
% 5.24/5.58 thf(fact_10096_Im__rcis,axiom,
% 5.24/5.58 ! [R2: real,A: real] :
% 5.24/5.58 ( ( im @ ( rcis @ R2 @ A ) )
% 5.24/5.58 = ( times_times_real @ R2 @ ( sin_real @ A ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Im_rcis
% 5.24/5.58 thf(fact_10097_cis__rcis__eq,axiom,
% 5.24/5.58 ( cis
% 5.24/5.58 = ( rcis @ one_one_real ) ) ).
% 5.24/5.58
% 5.24/5.58 % cis_rcis_eq
% 5.24/5.58 thf(fact_10098_rcis__mult,axiom,
% 5.24/5.58 ! [R1: real,A: real,R22: real,B: real] :
% 5.24/5.58 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.24/5.58 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rcis_mult
% 5.24/5.58 thf(fact_10099_rcis__def,axiom,
% 5.24/5.58 ( rcis
% 5.24/5.58 = ( ^ [R5: real,A4: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R5 ) @ ( cis @ A4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % rcis_def
% 5.24/5.58 thf(fact_10100_DeMoivre2,axiom,
% 5.24/5.58 ! [R2: real,A: real,N: nat] :
% 5.24/5.58 ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 5.24/5.58 = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % DeMoivre2
% 5.24/5.58 thf(fact_10101_Field__natLeq__on,axiom,
% 5.24/5.58 ! [N: nat] :
% 5.24/5.58 ( ( field_nat
% 5.24/5.58 @ ( collec3392354462482085612at_nat
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( ( ord_less_nat @ X2 @ N )
% 5.24/5.58 & ( ord_less_nat @ Y @ N )
% 5.24/5.58 & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) )
% 5.24/5.58 = ( collect_nat
% 5.24/5.58 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Field_natLeq_on
% 5.24/5.58 thf(fact_10102_natLess__def,axiom,
% 5.24/5.58 ( bNF_Ca8459412986667044542atLess
% 5.24/5.58 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % natLess_def
% 5.24/5.58 thf(fact_10103_wf__less,axiom,
% 5.24/5.58 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.24/5.58
% 5.24/5.58 % wf_less
% 5.24/5.58 thf(fact_10104_strict__mono__imp__increasing,axiom,
% 5.24/5.58 ! [F: nat > nat,N: nat] :
% 5.24/5.58 ( ( order_5726023648592871131at_nat @ F )
% 5.24/5.58 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % strict_mono_imp_increasing
% 5.24/5.58 thf(fact_10105_cauchy__def,axiom,
% 5.24/5.58 ( cauchy
% 5.24/5.58 = ( ^ [X6: nat > rat] :
% 5.24/5.58 ! [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 => ? [K3: nat] :
% 5.24/5.58 ! [M2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ M2 )
% 5.24/5.58 => ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M2 ) @ ( X6 @ N2 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchy_def
% 5.24/5.58 thf(fact_10106_cauchy__add,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( cauchy @ Y7 )
% 5.24/5.58 => ( cauchy
% 5.24/5.58 @ ^ [N2: nat] : ( plus_plus_rat @ ( X7 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchy_add
% 5.24/5.58 thf(fact_10107_cauchy__mult,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( cauchy @ Y7 )
% 5.24/5.58 => ( cauchy
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_rat @ ( X7 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchy_mult
% 5.24/5.58 thf(fact_10108_cauchy__not__vanishes__cases,axiom,
% 5.24/5.58 ! [X7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ~ ( vanishes @ X7 )
% 5.24/5.58 => ? [B2: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.24/5.58 & ? [K2: nat] :
% 5.24/5.58 ( ! [N9: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ N9 )
% 5.24/5.58 => ( ord_less_rat @ B2 @ ( uminus_uminus_rat @ ( X7 @ N9 ) ) ) )
% 5.24/5.58 | ! [N9: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ N9 )
% 5.24/5.58 => ( ord_less_rat @ B2 @ ( X7 @ N9 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchy_not_vanishes_cases
% 5.24/5.58 thf(fact_10109_cauchy__not__vanishes,axiom,
% 5.24/5.58 ! [X7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ~ ( vanishes @ X7 )
% 5.24/5.58 => ? [B2: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.24/5.58 & ? [K2: nat] :
% 5.24/5.58 ! [N9: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ N9 )
% 5.24/5.58 => ( ord_less_rat @ B2 @ ( abs_abs_rat @ ( X7 @ N9 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchy_not_vanishes
% 5.24/5.58 thf(fact_10110_cauchyD,axiom,
% 5.24/5.58 ! [X7: nat > rat,R2: rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.24/5.58 => ? [K2: nat] :
% 5.24/5.58 ! [M3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ M3 )
% 5.24/5.58 => ! [N9: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K2 @ N9 )
% 5.24/5.58 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M3 ) @ ( X7 @ N9 ) ) ) @ R2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchyD
% 5.24/5.58 thf(fact_10111_cauchyI,axiom,
% 5.24/5.58 ! [X7: nat > rat] :
% 5.24/5.58 ( ! [R3: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.24/5.58 => ? [K4: nat] :
% 5.24/5.58 ! [M4: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K4 @ M4 )
% 5.24/5.58 => ! [N3: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.24/5.58 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) ) @ R3 ) ) ) )
% 5.24/5.58 => ( cauchy @ X7 ) ) ).
% 5.24/5.58
% 5.24/5.58 % cauchyI
% 5.24/5.58 thf(fact_10112_le__Real,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( cauchy @ Y7 )
% 5.24/5.58 => ( ( ord_less_eq_real @ ( real2 @ X7 ) @ ( real2 @ Y7 ) )
% 5.24/5.58 = ( ! [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 => ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_eq_rat @ ( X7 @ N2 ) @ ( plus_plus_rat @ ( Y7 @ N2 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % le_Real
% 5.24/5.58 thf(fact_10113_one__real__def,axiom,
% 5.24/5.58 ( one_one_real
% 5.24/5.58 = ( real2
% 5.24/5.58 @ ^ [N2: nat] : one_one_rat ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_real_def
% 5.24/5.58 thf(fact_10114_add__Real,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( cauchy @ Y7 )
% 5.24/5.58 => ( ( plus_plus_real @ ( real2 @ X7 ) @ ( real2 @ Y7 ) )
% 5.24/5.58 = ( real2
% 5.24/5.58 @ ^ [N2: nat] : ( plus_plus_rat @ ( X7 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % add_Real
% 5.24/5.58 thf(fact_10115_mult__Real,axiom,
% 5.24/5.58 ! [X7: nat > rat,Y7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( cauchy @ Y7 )
% 5.24/5.58 => ( ( times_times_real @ ( real2 @ X7 ) @ ( real2 @ Y7 ) )
% 5.24/5.58 = ( real2
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_rat @ ( X7 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % mult_Real
% 5.24/5.58 thf(fact_10116_not__positive__Real,axiom,
% 5.24/5.58 ! [X7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( ~ ( positive2 @ ( real2 @ X7 ) ) )
% 5.24/5.58 = ( ! [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 => ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_eq_rat @ ( X7 @ N2 ) @ R5 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % not_positive_Real
% 5.24/5.58 thf(fact_10117_positive__Real,axiom,
% 5.24/5.58 ! [X7: nat > rat] :
% 5.24/5.58 ( ( cauchy @ X7 )
% 5.24/5.58 => ( ( positive2 @ ( real2 @ X7 ) )
% 5.24/5.58 = ( ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( X7 @ N2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % positive_Real
% 5.24/5.58 thf(fact_10118_Real_Opositive__mult,axiom,
% 5.24/5.58 ! [X: real,Y4: real] :
% 5.24/5.58 ( ( positive2 @ X )
% 5.24/5.58 => ( ( positive2 @ Y4 )
% 5.24/5.58 => ( positive2 @ ( times_times_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive_mult
% 5.24/5.58 thf(fact_10119_Real_Opositive__add,axiom,
% 5.24/5.58 ! [X: real,Y4: real] :
% 5.24/5.58 ( ( positive2 @ X )
% 5.24/5.58 => ( ( positive2 @ Y4 )
% 5.24/5.58 => ( positive2 @ ( plus_plus_real @ X @ Y4 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive_add
% 5.24/5.58 thf(fact_10120_Real_Opositive_Orep__eq,axiom,
% 5.24/5.58 ( positive2
% 5.24/5.58 = ( ^ [X2: real] :
% 5.24/5.58 ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( rep_real @ X2 @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive.rep_eq
% 5.24/5.58 thf(fact_10121_le__enumerate,axiom,
% 5.24/5.58 ! [S3: set_nat,N: nat] :
% 5.24/5.58 ( ~ ( finite_finite_nat @ S3 )
% 5.24/5.58 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % le_enumerate
% 5.24/5.58 thf(fact_10122_finite__le__enumerate,axiom,
% 5.24/5.58 ! [S3: set_nat,N: nat] :
% 5.24/5.58 ( ( finite_finite_nat @ S3 )
% 5.24/5.58 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 5.24/5.58 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % finite_le_enumerate
% 5.24/5.58 thf(fact_10123_Least__Suc2,axiom,
% 5.24/5.58 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.24/5.58 ( ( P @ N )
% 5.24/5.58 => ( ( Q @ M )
% 5.24/5.58 => ( ~ ( P @ zero_zero_nat )
% 5.24/5.58 => ( ! [K2: nat] :
% 5.24/5.58 ( ( P @ ( suc @ K2 ) )
% 5.24/5.58 = ( Q @ K2 ) )
% 5.24/5.58 => ( ( ord_Least_nat @ P )
% 5.24/5.58 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Least_Suc2
% 5.24/5.58 thf(fact_10124_Least__Suc,axiom,
% 5.24/5.58 ! [P: nat > $o,N: nat] :
% 5.24/5.58 ( ( P @ N )
% 5.24/5.58 => ( ~ ( P @ zero_zero_nat )
% 5.24/5.58 => ( ( ord_Least_nat @ P )
% 5.24/5.58 = ( suc
% 5.24/5.58 @ ( ord_Least_nat
% 5.24/5.58 @ ^ [M2: nat] : ( P @ ( suc @ M2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Least_Suc
% 5.24/5.58 thf(fact_10125_divmod__nat__code,axiom,
% 5.24/5.58 ( divmod_nat
% 5.24/5.58 = ( ^ [M2: nat,N2: nat] :
% 5.24/5.58 ( produc8678311845419106900er_nat @ code_nat_of_integer @ code_nat_of_integer
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger
% 5.24/5.58 @ ( ( code_integer_of_nat @ M2 )
% 5.24/5.58 = zero_z3403309356797280102nteger )
% 5.24/5.58 @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.24/5.58 @ ( if_Pro6119634080678213985nteger
% 5.24/5.58 @ ( ( code_integer_of_nat @ N2 )
% 5.24/5.58 = zero_z3403309356797280102nteger )
% 5.24/5.58 @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( code_integer_of_nat @ M2 ) )
% 5.24/5.58 @ ( code_divmod_abs @ ( code_integer_of_nat @ M2 ) @ ( code_integer_of_nat @ N2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % divmod_nat_code
% 5.24/5.58 thf(fact_10126_integer__of__nat__numeral,axiom,
% 5.24/5.58 ! [N: num] :
% 5.24/5.58 ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 5.24/5.58 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_nat_numeral
% 5.24/5.58 thf(fact_10127_integer__of__nat__1,axiom,
% 5.24/5.58 ( ( code_integer_of_nat @ one_one_nat )
% 5.24/5.58 = one_one_Code_integer ) ).
% 5.24/5.58
% 5.24/5.58 % integer_of_nat_1
% 5.24/5.58 thf(fact_10128_eventually__prod__sequentially,axiom,
% 5.24/5.58 ! [P: product_prod_nat_nat > $o] :
% 5.24/5.58 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.24/5.58 = ( ? [N6: nat] :
% 5.24/5.58 ! [M2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ N6 @ M2 )
% 5.24/5.58 => ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.24/5.58 => ( P @ ( product_Pair_nat_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % eventually_prod_sequentially
% 5.24/5.58 thf(fact_10129_at__right__to__0,axiom,
% 5.24/5.58 ! [A: real] :
% 5.24/5.58 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.24/5.58 = ( filtermap_real_real
% 5.24/5.58 @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 5.24/5.58 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % at_right_to_0
% 5.24/5.58 thf(fact_10130_last__upt,axiom,
% 5.24/5.58 ! [I2: nat,J: nat] :
% 5.24/5.58 ( ( ord_less_nat @ I2 @ J )
% 5.24/5.58 => ( ( last_nat @ ( upt @ I2 @ J ) )
% 5.24/5.58 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % last_upt
% 5.24/5.58 thf(fact_10131_Real_Opositive_Oabs__eq,axiom,
% 5.24/5.58 ! [X: nat > rat] :
% 5.24/5.58 ( ( realrel @ X @ X )
% 5.24/5.58 => ( ( positive2 @ ( real2 @ X ) )
% 5.24/5.58 = ( ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( X @ N2 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive.abs_eq
% 5.24/5.58 thf(fact_10132_one__real_Orsp,axiom,
% 5.24/5.58 ( realrel
% 5.24/5.58 @ ^ [N2: nat] : one_one_rat
% 5.24/5.58 @ ^ [N2: nat] : one_one_rat ) ).
% 5.24/5.58
% 5.24/5.58 % one_real.rsp
% 5.24/5.58 thf(fact_10133_plus__real_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: nat > rat,X: nat > rat] :
% 5.24/5.58 ( ( realrel @ Xa2 @ Xa2 )
% 5.24/5.58 => ( ( realrel @ X @ X )
% 5.24/5.58 => ( ( plus_plus_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 5.24/5.58 = ( real2
% 5.24/5.58 @ ^ [N2: nat] : ( plus_plus_rat @ ( Xa2 @ N2 ) @ ( X @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_real.abs_eq
% 5.24/5.58 thf(fact_10134_times__real_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: nat > rat,X: nat > rat] :
% 5.24/5.58 ( ( realrel @ Xa2 @ Xa2 )
% 5.24/5.58 => ( ( realrel @ X @ X )
% 5.24/5.58 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 5.24/5.58 = ( real2
% 5.24/5.58 @ ^ [N2: nat] : ( times_times_rat @ ( Xa2 @ N2 ) @ ( X @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_real.abs_eq
% 5.24/5.58 thf(fact_10135_Real_Opositive_Orsp,axiom,
% 5.24/5.58 ( bNF_re728719798268516973at_o_o @ realrel
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [X6: nat > rat] :
% 5.24/5.58 ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) )
% 5.24/5.58 @ ^ [X6: nat > rat] :
% 5.24/5.58 ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive.rsp
% 5.24/5.58 thf(fact_10136_times__real_Orsp,axiom,
% 5.24/5.58 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.24/5.58 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.24/5.58 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_real.rsp
% 5.24/5.58 thf(fact_10137_plus__real_Orsp,axiom,
% 5.24/5.58 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.24/5.58 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.24/5.58 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_real.rsp
% 5.24/5.58 thf(fact_10138_less__eq__natural_Orsp,axiom,
% 5.24/5.58 ( bNF_re578469030762574527_nat_o
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re4705727531993890431at_o_o
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.24/5.58 @ ord_less_eq_nat
% 5.24/5.58 @ ord_less_eq_nat ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq_natural.rsp
% 5.24/5.58 thf(fact_10139_times__natural_Orsp,axiom,
% 5.24/5.58 ( bNF_re1345281282404953727at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re5653821019739307937at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.24/5.58 @ times_times_nat
% 5.24/5.58 @ times_times_nat ) ).
% 5.24/5.58
% 5.24/5.58 % times_natural.rsp
% 5.24/5.58 thf(fact_10140_times__integer_Orsp,axiom,
% 5.24/5.58 ( bNF_re711492959462206631nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re4712519889275205905nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.24/5.58 @ times_times_int
% 5.24/5.58 @ times_times_int ) ).
% 5.24/5.58
% 5.24/5.58 % times_integer.rsp
% 5.24/5.58 thf(fact_10141_Suc_Orsp,axiom,
% 5.24/5.58 ( bNF_re5653821019739307937at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ suc
% 5.24/5.58 @ suc ) ).
% 5.24/5.58
% 5.24/5.58 % Suc.rsp
% 5.24/5.58 thf(fact_10142_plus__integer_Orsp,axiom,
% 5.24/5.58 ( bNF_re711492959462206631nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re4712519889275205905nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.24/5.58 @ plus_plus_int
% 5.24/5.58 @ plus_plus_int ) ).
% 5.24/5.58
% 5.24/5.58 % plus_integer.rsp
% 5.24/5.58 thf(fact_10143_plus__natural_Orsp,axiom,
% 5.24/5.58 ( bNF_re1345281282404953727at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re5653821019739307937at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.24/5.58 @ plus_plus_nat
% 5.24/5.58 @ plus_plus_nat ) ).
% 5.24/5.58
% 5.24/5.58 % plus_natural.rsp
% 5.24/5.58 thf(fact_10144_less__natural_Orsp,axiom,
% 5.24/5.58 ( bNF_re578469030762574527_nat_o
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re4705727531993890431at_o_o
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.24/5.58 @ ord_less_nat
% 5.24/5.58 @ ord_less_nat ) ).
% 5.24/5.58
% 5.24/5.58 % less_natural.rsp
% 5.24/5.58 thf(fact_10145_divide__natural_Orsp,axiom,
% 5.24/5.58 ( bNF_re1345281282404953727at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re5653821019739307937at_nat
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.24/5.58 @ divide_divide_nat
% 5.24/5.58 @ divide_divide_nat ) ).
% 5.24/5.58
% 5.24/5.58 % divide_natural.rsp
% 5.24/5.58 thf(fact_10146_dup_Orsp,axiom,
% 5.24/5.58 ( bNF_re4712519889275205905nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 5.24/5.58 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 5.24/5.58
% 5.24/5.58 % dup.rsp
% 5.24/5.58 thf(fact_10147_Real_Opositive_Otransfer,axiom,
% 5.24/5.58 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [X6: nat > rat] :
% 5.24/5.58 ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) )
% 5.24/5.58 @ positive2 ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive.transfer
% 5.24/5.58 thf(fact_10148_plus__rat_Otransfer,axiom,
% 5.24/5.58 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ plus_plus_rat ) ).
% 5.24/5.58
% 5.24/5.58 % plus_rat.transfer
% 5.24/5.58 thf(fact_10149_one__real_Otransfer,axiom,
% 5.24/5.58 ( pcr_real
% 5.24/5.58 @ ^ [N2: nat] : one_one_rat
% 5.24/5.58 @ one_one_real ) ).
% 5.24/5.58
% 5.24/5.58 % one_real.transfer
% 5.24/5.58 thf(fact_10150_plus__real_Otransfer,axiom,
% 5.24/5.58 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.24/5.58 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.24/5.58 @ plus_plus_real ) ).
% 5.24/5.58
% 5.24/5.58 % plus_real.transfer
% 5.24/5.58 thf(fact_10151_times__real_Otransfer,axiom,
% 5.24/5.58 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.24/5.58 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.24/5.58 @ times_times_real ) ).
% 5.24/5.58
% 5.24/5.58 % times_real.transfer
% 5.24/5.58 thf(fact_10152_one__rat_Otransfer,axiom,
% 5.24/5.58 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 5.24/5.58
% 5.24/5.58 % one_rat.transfer
% 5.24/5.58 thf(fact_10153_zero__rat_Otransfer,axiom,
% 5.24/5.58 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 5.24/5.58
% 5.24/5.58 % zero_rat.transfer
% 5.24/5.58 thf(fact_10154_Fract_Otransfer,axiom,
% 5.24/5.58 ( bNF_re3461391660133120880nt_rat
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re2214769303045360666nt_rat
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ pcr_rat )
% 5.24/5.58 @ ^ [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 ) )
% 5.24/5.58 @ fract ) ).
% 5.24/5.58
% 5.24/5.58 % Fract.transfer
% 5.24/5.58 thf(fact_10155_uminus__rat_Otransfer,axiom,
% 5.24/5.58 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 5.24/5.58 @ uminus_uminus_rat ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_rat.transfer
% 5.24/5.58 thf(fact_10156_times__rat_Otransfer,axiom,
% 5.24/5.58 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ times_times_rat ) ).
% 5.24/5.58
% 5.24/5.58 % times_rat.transfer
% 5.24/5.58 thf(fact_10157_Rat_Opositive_Otransfer,axiom,
% 5.24/5.58 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 5.24/5.58 @ positive ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive.transfer
% 5.24/5.58 thf(fact_10158_inverse__rat_Otransfer,axiom,
% 5.24/5.58 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.24/5.58 @ ^ [X2: product_prod_int_int] :
% 5.24/5.58 ( if_Pro3027730157355071871nt_int
% 5.24/5.58 @ ( ( product_fst_int_int @ X2 )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.24/5.58 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 5.24/5.58 @ inverse_inverse_rat ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_rat.transfer
% 5.24/5.58 thf(fact_10159_times__int_Otransfer,axiom,
% 5.24/5.58 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U3 ) ) ) ) )
% 5.24/5.58 @ times_times_int ) ).
% 5.24/5.58
% 5.24/5.58 % times_int.transfer
% 5.24/5.58 thf(fact_10160_minus__int_Otransfer,axiom,
% 5.24/5.58 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U3 ) ) ) )
% 5.24/5.58 @ minus_minus_int ) ).
% 5.24/5.58
% 5.24/5.58 % minus_int.transfer
% 5.24/5.58 thf(fact_10161_zero__int_Otransfer,axiom,
% 5.24/5.58 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.24/5.58
% 5.24/5.58 % zero_int.transfer
% 5.24/5.58 thf(fact_10162_int__transfer,axiom,
% 5.24/5.58 ( bNF_re6830278522597306478at_int
% 5.24/5.58 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.24/5.58 @ pcr_int
% 5.24/5.58 @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 5.24/5.58 @ semiri1314217659103216013at_int ) ).
% 5.24/5.58
% 5.24/5.58 % int_transfer
% 5.24/5.58 thf(fact_10163_uminus__int_Otransfer,axiom,
% 5.24/5.58 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.24/5.58 @ ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) )
% 5.24/5.58 @ uminus_uminus_int ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_int.transfer
% 5.24/5.58 thf(fact_10164_one__int_Otransfer,axiom,
% 5.24/5.58 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.24/5.58
% 5.24/5.58 % one_int.transfer
% 5.24/5.58 thf(fact_10165_less__int_Otransfer,axiom,
% 5.24/5.58 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.24/5.58 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.24/5.58 @ ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) ) )
% 5.24/5.58 @ ord_less_int ) ).
% 5.24/5.58
% 5.24/5.58 % less_int.transfer
% 5.24/5.58 thf(fact_10166_less__eq__int_Otransfer,axiom,
% 5.24/5.58 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.24/5.58 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.24/5.58 @ ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) ) )
% 5.24/5.58 @ ord_less_eq_int ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq_int.transfer
% 5.24/5.58 thf(fact_10167_plus__int_Otransfer,axiom,
% 5.24/5.58 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U3 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.24/5.58 @ plus_plus_int ) ).
% 5.24/5.58
% 5.24/5.58 % plus_int.transfer
% 5.24/5.58 thf(fact_10168_times__int_Orsp,axiom,
% 5.24/5.58 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U3 ) ) ) ) )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U3 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_int.rsp
% 5.24/5.58 thf(fact_10169_intrel__iff,axiom,
% 5.24/5.58 ! [X: nat,Y4: nat,U2: nat,V: nat] :
% 5.24/5.58 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( product_Pair_nat_nat @ U2 @ V ) )
% 5.24/5.58 = ( ( plus_plus_nat @ X @ V )
% 5.24/5.58 = ( plus_plus_nat @ U2 @ Y4 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % intrel_iff
% 5.24/5.58 thf(fact_10170_uminus__int_Orsp,axiom,
% 5.24/5.58 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.24/5.58 @ ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) )
% 5.24/5.58 @ ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_int.rsp
% 5.24/5.58 thf(fact_10171_zero__int_Orsp,axiom,
% 5.24/5.58 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.24/5.58
% 5.24/5.58 % zero_int.rsp
% 5.24/5.58 thf(fact_10172_one__int_Orsp,axiom,
% 5.24/5.58 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.24/5.58
% 5.24/5.58 % one_int.rsp
% 5.24/5.58 thf(fact_10173_intrel__def,axiom,
% 5.24/5.58 ( intrel
% 5.24/5.58 = ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] :
% 5.24/5.58 ( ( plus_plus_nat @ X2 @ V4 )
% 5.24/5.58 = ( plus_plus_nat @ U3 @ Y ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % intrel_def
% 5.24/5.58 thf(fact_10174_less__int_Orsp,axiom,
% 5.24/5.58 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.24/5.58 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.24/5.58 @ ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) ) )
% 5.24/5.58 @ ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_int.rsp
% 5.24/5.58 thf(fact_10175_less__eq__int_Orsp,axiom,
% 5.24/5.58 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.24/5.58 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.24/5.58 @ ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) ) )
% 5.24/5.58 @ ( produc8739625826339149834_nat_o
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U3 @ Y ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % less_eq_int.rsp
% 5.24/5.58 thf(fact_10176_plus__int_Orsp,axiom,
% 5.24/5.58 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U3 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U3 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_int.rsp
% 5.24/5.58 thf(fact_10177_minus__int_Orsp,axiom,
% 5.24/5.58 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U3 ) ) ) )
% 5.24/5.58 @ ( produc27273713700761075at_nat
% 5.24/5.58 @ ^ [X2: nat,Y: nat] :
% 5.24/5.58 ( produc2626176000494625587at_nat
% 5.24/5.58 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U3 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % minus_int.rsp
% 5.24/5.58 thf(fact_10178_plus__rat_Orsp,axiom,
% 5.24/5.58 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ^ [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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_rat.rsp
% 5.24/5.58 thf(fact_10179_ratrel__iff,axiom,
% 5.24/5.58 ( ratrel
% 5.24/5.58 = ( ^ [X2: product_prod_int_int,Y: product_prod_int_int] :
% 5.24/5.58 ( ( ( product_snd_int_int @ X2 )
% 5.24/5.58 != zero_zero_int )
% 5.24/5.58 & ( ( product_snd_int_int @ Y )
% 5.24/5.58 != zero_zero_int )
% 5.24/5.58 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) )
% 5.24/5.58 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % ratrel_iff
% 5.24/5.58 thf(fact_10180_zero__rat_Orsp,axiom,
% 5.24/5.58 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 5.24/5.58
% 5.24/5.58 % zero_rat.rsp
% 5.24/5.58 thf(fact_10181_one__rat_Orsp,axiom,
% 5.24/5.58 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 5.24/5.58
% 5.24/5.58 % one_rat.rsp
% 5.24/5.58 thf(fact_10182_Fract_Orsp,axiom,
% 5.24/5.58 ( bNF_re157797125943740599nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ( bNF_re6250860962936578807nt_int
% 5.24/5.58 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.24/5.58 @ ratrel )
% 5.24/5.58 @ ^ [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 ) )
% 5.24/5.58 @ ^ [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 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract.rsp
% 5.24/5.58 thf(fact_10183_ratrel__def,axiom,
% 5.24/5.58 ( ratrel
% 5.24/5.58 = ( ^ [X2: product_prod_int_int,Y: product_prod_int_int] :
% 5.24/5.58 ( ( ( product_snd_int_int @ X2 )
% 5.24/5.58 != zero_zero_int )
% 5.24/5.58 & ( ( product_snd_int_int @ Y )
% 5.24/5.58 != zero_zero_int )
% 5.24/5.58 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) )
% 5.24/5.58 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % ratrel_def
% 5.24/5.58 thf(fact_10184_uminus__rat_Orsp,axiom,
% 5.24/5.58 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_rat.rsp
% 5.24/5.58 thf(fact_10185_times__rat_Orsp,axiom,
% 5.24/5.58 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.24/5.58 @ ^ [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 ) ) )
% 5.24/5.58 @ ^ [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 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_rat.rsp
% 5.24/5.58 thf(fact_10186_Rat_Opositive_Orsp,axiom,
% 5.24/5.58 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.24/5.58 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive.rsp
% 5.24/5.58 thf(fact_10187_inverse__rat_Orsp,axiom,
% 5.24/5.58 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.24/5.58 @ ^ [X2: product_prod_int_int] :
% 5.24/5.58 ( if_Pro3027730157355071871nt_int
% 5.24/5.58 @ ( ( product_fst_int_int @ X2 )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.24/5.58 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 5.24/5.58 @ ^ [X2: product_prod_int_int] :
% 5.24/5.58 ( if_Pro3027730157355071871nt_int
% 5.24/5.58 @ ( ( product_fst_int_int @ X2 )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.24/5.58 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_rat.rsp
% 5.24/5.58 thf(fact_10188_plus__rat_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 5.24/5.58 ( ( ratrel @ Xa2 @ Xa2 )
% 5.24/5.58 => ( ( ratrel @ X @ X )
% 5.24/5.58 => ( ( plus_plus_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_rat.abs_eq
% 5.24/5.58 thf(fact_10189_inverse__rat_Oabs__eq,axiom,
% 5.24/5.58 ! [X: product_prod_int_int] :
% 5.24/5.58 ( ( ratrel @ X @ X )
% 5.24/5.58 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 5.24/5.58 = ( abs_Rat
% 5.24/5.58 @ ( if_Pro3027730157355071871nt_int
% 5.24/5.58 @ ( ( product_fst_int_int @ X )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.24/5.58 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_rat.abs_eq
% 5.24/5.58 thf(fact_10190_one__rat__def,axiom,
% 5.24/5.58 ( one_one_rat
% 5.24/5.58 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % one_rat_def
% 5.24/5.58 thf(fact_10191_Fract_Oabs__eq,axiom,
% 5.24/5.58 ( fract
% 5.24/5.58 = ( ^ [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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Fract.abs_eq
% 5.24/5.58 thf(fact_10192_zero__rat__def,axiom,
% 5.24/5.58 ( zero_zero_rat
% 5.24/5.58 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % zero_rat_def
% 5.24/5.58 thf(fact_10193_uminus__rat_Oabs__eq,axiom,
% 5.24/5.58 ! [X: product_prod_int_int] :
% 5.24/5.58 ( ( ratrel @ X @ X )
% 5.24/5.58 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 5.24/5.58 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_rat.abs_eq
% 5.24/5.58 thf(fact_10194_times__rat_Oabs__eq,axiom,
% 5.24/5.58 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 5.24/5.58 ( ( ratrel @ Xa2 @ Xa2 )
% 5.24/5.58 => ( ( ratrel @ X @ X )
% 5.24/5.58 => ( ( times_times_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 5.24/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_rat.abs_eq
% 5.24/5.58 thf(fact_10195_Rat_Opositive_Oabs__eq,axiom,
% 5.24/5.58 ! [X: product_prod_int_int] :
% 5.24/5.58 ( ( ratrel @ X @ X )
% 5.24/5.58 => ( ( positive @ ( abs_Rat @ X ) )
% 5.24/5.58 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive.abs_eq
% 5.24/5.58 thf(fact_10196_inverse__rat__def,axiom,
% 5.24/5.58 ( inverse_inverse_rat
% 5.24/5.58 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.24/5.58 @ ^ [X2: product_prod_int_int] :
% 5.24/5.58 ( if_Pro3027730157355071871nt_int
% 5.24/5.58 @ ( ( product_fst_int_int @ X2 )
% 5.24/5.58 = zero_zero_int )
% 5.24/5.58 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.24/5.58 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % inverse_rat_def
% 5.24/5.58 thf(fact_10197_uminus__rat__def,axiom,
% 5.24/5.58 ( uminus_uminus_rat
% 5.24/5.58 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % uminus_rat_def
% 5.24/5.58 thf(fact_10198_plus__rat__def,axiom,
% 5.24/5.58 ( plus_plus_rat
% 5.24/5.58 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.24/5.58 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % plus_rat_def
% 5.24/5.58 thf(fact_10199_times__rat__def,axiom,
% 5.24/5.58 ( times_times_rat
% 5.24/5.58 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.24/5.58 @ ^ [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 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % times_rat_def
% 5.24/5.58 thf(fact_10200_Rat_Opositive__def,axiom,
% 5.24/5.58 ( positive
% 5.24/5.58 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.24/5.58 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Rat.positive_def
% 5.24/5.58 thf(fact_10201_Real_Opositive__def,axiom,
% 5.24/5.58 ( positive2
% 5.24/5.58 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.24/5.58 @ ^ [X6: nat > rat] :
% 5.24/5.58 ? [R5: rat] :
% 5.24/5.58 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.24/5.58 & ? [K3: nat] :
% 5.24/5.58 ! [N2: nat] :
% 5.24/5.58 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.24/5.58 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % Real.positive_def
% 5.24/5.58 thf(fact_10202_pairs__le__eq__Sigma,axiom,
% 5.24/5.58 ! [M: nat] :
% 5.24/5.58 ( ( collec3392354462482085612at_nat
% 5.24/5.58 @ ( produc6081775807080527818_nat_o
% 5.24/5.58 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 5.24/5.58 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.24/5.58 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % pairs_le_eq_Sigma
% 5.24/5.58 thf(fact_10203_finite__vimage__Suc__iff,axiom,
% 5.24/5.58 ! [F5: set_nat] :
% 5.24/5.58 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F5 ) )
% 5.24/5.58 = ( finite_finite_nat @ F5 ) ) ).
% 5.24/5.58
% 5.24/5.58 % finite_vimage_Suc_iff
% 5.24/5.58 thf(fact_10204_vimage__Suc__insert__Suc,axiom,
% 5.24/5.58 ! [N: nat,A2: set_nat] :
% 5.24/5.58 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A2 ) )
% 5.24/5.58 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 5.24/5.58
% 5.24/5.58 % vimage_Suc_insert_Suc
% 5.24/5.58
% 5.24/5.58 % Helper facts (39)
% 5.24/5.58 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.24/5.58 ! [X: int,Y4: int] :
% 5.24/5.58 ( ( if_int @ $false @ X @ Y4 )
% 5.24/5.58 = Y4 ) ).
% 5.24/5.58
% 5.24/5.58 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.24/5.58 ! [X: int,Y4: int] :
% 5.24/5.58 ( ( if_int @ $true @ X @ Y4 )
% 5.24/5.58 = X ) ).
% 5.24/5.58
% 5.24/5.58 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.24/5.58 ! [X: nat,Y4: nat] :
% 5.24/5.58 ( ( if_nat @ $false @ X @ Y4 )
% 5.24/5.58 = Y4 ) ).
% 5.24/5.58
% 5.24/5.58 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.24/5.59 ! [X: nat,Y4: nat] :
% 5.24/5.59 ( ( if_nat @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.24/5.59 ! [X: num,Y4: num] :
% 5.24/5.59 ( ( if_num @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.24/5.59 ! [X: num,Y4: num] :
% 5.24/5.59 ( ( if_num @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.24/5.59 ! [X: rat,Y4: rat] :
% 5.24/5.59 ( ( if_rat @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.24/5.59 ! [X: rat,Y4: rat] :
% 5.24/5.59 ( ( if_rat @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.24/5.59 ! [X: real,Y4: real] :
% 5.24/5.59 ( ( if_real @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.24/5.59 ! [X: real,Y4: real] :
% 5.24/5.59 ( ( if_real @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.24/5.59 ! [X: complex,Y4: complex] :
% 5.24/5.59 ( ( if_complex @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.24/5.59 ! [X: complex,Y4: complex] :
% 5.24/5.59 ( ( if_complex @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.24/5.59 ! [X: extended_enat,Y4: extended_enat] :
% 5.24/5.59 ( ( if_Extended_enat @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.24/5.59 ! [X: extended_enat,Y4: extended_enat] :
% 5.24/5.59 ( ( if_Extended_enat @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.24/5.59 ! [X: code_integer,Y4: code_integer] :
% 5.24/5.59 ( ( if_Code_integer @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.24/5.59 ! [X: code_integer,Y4: code_integer] :
% 5.24/5.59 ( ( if_Code_integer @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.24/5.59 ! [X: set_int,Y4: set_int] :
% 5.24/5.59 ( ( if_set_int @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.24/5.59 ! [X: set_int,Y4: set_int] :
% 5.24/5.59 ( ( if_set_int @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.24/5.59 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.59 ( ( if_set_nat @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.24/5.59 ! [X: set_nat,Y4: set_nat] :
% 5.24/5.59 ( ( if_set_nat @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.24/5.59 ! [X: vEBT_VEBT,Y4: vEBT_VEBT] :
% 5.24/5.59 ( ( if_VEBT_VEBT @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.24/5.59 ! [X: vEBT_VEBT,Y4: vEBT_VEBT] :
% 5.24/5.59 ( ( if_VEBT_VEBT @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.24/5.59 ! [X: list_int,Y4: list_int] :
% 5.24/5.59 ( ( if_list_int @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.24/5.59 ! [X: list_int,Y4: list_int] :
% 5.24/5.59 ( ( if_list_int @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.24/5.59 ! [X: list_nat,Y4: list_nat] :
% 5.24/5.59 ( ( if_list_nat @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.24/5.59 ! [X: list_nat,Y4: list_nat] :
% 5.24/5.59 ( ( if_list_nat @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.24/5.59 ! [X: option_nat,Y4: option_nat] :
% 5.24/5.59 ( ( if_option_nat @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.24/5.59 ! [X: option_nat,Y4: option_nat] :
% 5.24/5.59 ( ( if_option_nat @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.24/5.59 ! [X: option_num,Y4: option_num] :
% 5.24/5.59 ( ( if_option_num @ $false @ X @ Y4 )
% 5.24/5.59 = Y4 ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.24/5.59 ! [X: option_num,Y4: option_num] :
% 5.24/5.59 ( ( if_option_num @ $true @ X @ Y4 )
% 5.24/5.59 = X ) ).
% 5.24/5.59
% 5.24/5.59 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.24/5.59 ! [X: product_prod_int_int,Y4: product_prod_int_int] :
% 6.51/6.85 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y4 )
% 6.51/6.85 = Y4 ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.51/6.85 ! [X: product_prod_int_int,Y4: product_prod_int_int] :
% 6.51/6.85 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y4 )
% 6.51/6.85 = X ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.51/6.85 ! [X: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 6.51/6.85 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y4 )
% 6.51/6.85 = Y4 ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.51/6.85 ! [X: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 6.51/6.85 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y4 )
% 6.51/6.85 = X ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.51/6.85 ! [X: produc6271795597528267376eger_o,Y4: produc6271795597528267376eger_o] :
% 6.51/6.85 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y4 )
% 6.51/6.85 = Y4 ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.51/6.85 ! [X: produc6271795597528267376eger_o,Y4: produc6271795597528267376eger_o] :
% 6.51/6.85 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y4 )
% 6.51/6.85 = X ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.51/6.85 ! [P: $o] :
% 6.51/6.85 ( ( P = $true )
% 6.51/6.85 | ( P = $false ) ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.51/6.85 ! [X: produc8923325533196201883nteger,Y4: produc8923325533196201883nteger] :
% 6.51/6.85 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y4 )
% 6.51/6.85 = Y4 ) ).
% 6.51/6.85
% 6.51/6.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.51/6.85 ! [X: produc8923325533196201883nteger,Y4: produc8923325533196201883nteger] :
% 6.51/6.85 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y4 )
% 6.51/6.85 = X ) ).
% 6.51/6.85
% 6.51/6.85 % Conjectures (1)
% 6.51/6.85 thf(conj_0,conjecture,
% 6.51/6.85 ord_less_eq_nat @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ maxy ).
% 6.51/6.85
% 6.51/6.85 %------------------------------------------------------------------------------
% 6.51/6.85 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.kr6uF4UZrw/cvc5---1.0.5_12079.p...
% 6.51/6.85 (declare-sort $$unsorted 0)
% 6.51/6.85 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.51/6.85 (declare-sort tptp.produc1908205239877642774nteger 0)
% 6.51/6.85 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.51/6.85 (declare-sort tptp.produc2285326912895808259nt_int 0)
% 6.51/6.85 (declare-sort tptp.produc8763457246119570046nteger 0)
% 6.51/6.85 (declare-sort tptp.produc7773217078559923341nt_int 0)
% 6.51/6.85 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.51/6.85 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.51/6.85 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.51/6.85 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.51/6.85 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.51/6.85 (declare-sort tptp.produc6241069584506657477e_term 0)
% 6.51/6.85 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.51/6.85 (declare-sort tptp.produc8551481072490612790e_term 0)
% 6.51/6.85 (declare-sort tptp.option6357759511663192854e_term 0)
% 6.51/6.85 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.51/6.85 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.51/6.85 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.51/6.85 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.51/6.85 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.51/6.85 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.51/6.85 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.51/6.85 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.51/6.85 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.51/6.85 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.51/6.85 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.51/6.85 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.51/6.85 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.51/6.85 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.51/6.85 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.51/6.85 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.51/6.85 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.51/6.85 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.51/6.85 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.51/6.85 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.51/6.85 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.51/6.85 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.51/6.85 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.51/6.85 (declare-sort tptp.product_prod_num_num 0)
% 6.51/6.85 (declare-sort tptp.product_prod_nat_num 0)
% 6.51/6.85 (declare-sort tptp.product_prod_nat_nat 0)
% 6.51/6.85 (declare-sort tptp.product_prod_int_int 0)
% 6.51/6.85 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.51/6.85 (declare-sort tptp.set_list_complex 0)
% 6.51/6.85 (declare-sort tptp.list_list_nat 0)
% 6.51/6.85 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.51/6.85 (declare-sort tptp.set_list_nat 0)
% 6.51/6.85 (declare-sort tptp.set_list_int 0)
% 6.51/6.85 (declare-sort tptp.product_prod_nat_o 0)
% 6.51/6.85 (declare-sort tptp.product_prod_o_nat 0)
% 6.51/6.85 (declare-sort tptp.product_prod_o_int 0)
% 6.51/6.85 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.51/6.85 (declare-sort tptp.set_set_nat 0)
% 6.51/6.85 (declare-sort tptp.set_Product_unit 0)
% 6.51/6.85 (declare-sort tptp.set_Extended_enat 0)
% 6.51/6.85 (declare-sort tptp.list_complex 0)
% 6.51/6.85 (declare-sort tptp.set_list_o 0)
% 6.51/6.85 (declare-sort tptp.product_prod_o_o 0)
% 6.51/6.85 (declare-sort tptp.set_complex 0)
% 6.51/6.85 (declare-sort tptp.filter_real 0)
% 6.51/6.85 (declare-sort tptp.option_num 0)
% 6.51/6.85 (declare-sort tptp.option_nat 0)
% 6.51/6.85 (declare-sort tptp.filter_nat 0)
% 6.51/6.85 (declare-sort tptp.set_char 0)
% 6.51/6.85 (declare-sort tptp.list_real 0)
% 6.51/6.85 (declare-sort tptp.set_real 0)
% 6.51/6.85 (declare-sort tptp.list_nat 0)
% 6.51/6.85 (declare-sort tptp.list_int 0)
% 6.51/6.85 (declare-sort tptp.vEBT_VEBT 0)
% 6.51/6.85 (declare-sort tptp.set_rat 0)
% 6.51/6.85 (declare-sort tptp.set_num 0)
% 6.51/6.85 (declare-sort tptp.set_nat 0)
% 6.51/6.85 (declare-sort tptp.set_int 0)
% 6.51/6.85 (declare-sort tptp.code_integer 0)
% 6.51/6.85 (declare-sort tptp.extended_enat 0)
% 6.51/6.85 (declare-sort tptp.list_o 0)
% 6.51/6.85 (declare-sort tptp.complex 0)
% 6.51/6.85 (declare-sort tptp.set_o 0)
% 6.51/6.85 (declare-sort tptp.char 0)
% 6.51/6.85 (declare-sort tptp.real 0)
% 6.51/6.85 (declare-sort tptp.rat 0)
% 6.51/6.85 (declare-sort tptp.num 0)
% 6.51/6.85 (declare-sort tptp.nat 0)
% 6.51/6.85 (declare-sort tptp.int 0)
% 6.51/6.85 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.51/6.85 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.51/6.85 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.51/6.85 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.51/6.85 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.51/6.85 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.51/6.85 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.51/6.85 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.51/6.85 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.51/6.85 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.51/6.85 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.51/6.85 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.51/6.85 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.code_integer_of_nat (tptp.nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.51/6.85 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.51/6.85 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.51/6.85 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.51/6.85 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.51/6.85 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.51/6.85 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.51/6.85 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.51/6.85 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.51/6.85 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.51/6.85 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.51/6.85 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.51/6.85 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.51/6.85 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.51/6.85 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.51/6.85 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.51/6.85 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.51/6.85 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.51/6.85 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.51/6.85 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.51/6.85 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.51/6.85 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.51/6.85 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.51/6.85 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.51/6.85 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.51/6.85 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.51/6.85 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.51/6.85 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.51/6.85 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.51/6.85 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.51/6.85 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.51/6.85 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.51/6.85 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.51/6.85 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.51/6.85 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.51/6.85 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.51/6.85 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.id_o (Bool) Bool)
% 6.51/6.85 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.51/6.85 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.one_one_int () tptp.int)
% 6.51/6.85 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.51/6.85 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.51/6.85 (declare-fun tptp.one_one_real () tptp.real)
% 6.51/6.85 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.51/6.85 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.51/6.85 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.51/6.85 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.51/6.85 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.51/6.85 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups8682486955453173170nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups8110221916422527690omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups6036352826371341000t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.51/6.85 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.51/6.85 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.51/6.85 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.51/6.85 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.51/6.85 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.51/6.85 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.51/6.85 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.51/6.85 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.51/6.85 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.51/6.85 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.51/6.85 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.51/6.85 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.51/6.85 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.51/6.85 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.fold_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.nil_int () tptp.list_int)
% 6.51/6.85 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.51/6.85 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 6.51/6.85 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.51/6.85 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.51/6.85 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.51/6.85 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.51/6.85 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.nth_list_nat (tptp.list_list_nat tptp.nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.51/6.85 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.51/6.85 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.51/6.85 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.51/6.85 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.51/6.85 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.51/6.85 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.51/6.85 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.51/6.85 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.51/6.85 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.51/6.85 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.51/6.85 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.51/6.85 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.51/6.85 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.51/6.85 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.51/6.85 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.51/6.85 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.51/6.85 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.51/6.85 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.51/6.85 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.51/6.85 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.51/6.85 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.51/6.85 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.51/6.85 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.51/6.85 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.51/6.85 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.51/6.85 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.51/6.85 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.51/6.85 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.51/6.85 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.one () tptp.num)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.51/6.85 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.51/6.85 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.51/6.85 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.51/6.85 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.51/6.85 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.51/6.85 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.51/6.85 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.51/6.85 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.none_num () tptp.option_num)
% 6.51/6.85 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.51/6.85 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.51/6.85 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.51/6.85 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.51/6.85 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.51/6.85 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.51/6.85 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.51/6.85 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.bot_bot_complex_o (tptp.complex) Bool)
% 6.51/6.85 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 6.51/6.85 (declare-fun tptp.bot_bot_list_nat_o (tptp.list_nat) Bool)
% 6.51/6.85 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.bot_bo482883023278783056_nat_o (tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.bot_bot_real_o (tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.51/6.85 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.51/6.85 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.51/6.85 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.51/6.85 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.51/6.85 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.51/6.85 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.51/6.85 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.51/6.85 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.51/6.85 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.51/6.85 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.51/6.85 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.51/6.85 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.51/6.85 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.produc6137756002093451184nteger ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc8763457246119570046nteger)
% 6.51/6.85 (declare-fun tptp.produc4305682042979456191nt_int ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc7773217078559923341nt_int)
% 6.51/6.85 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.51/6.85 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.51/6.85 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.51/6.85 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.51/6.85 (declare-fun tptp.produc8603105652947943368nteger ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc1908205239877642774nteger)
% 6.51/6.85 (declare-fun tptp.produc5700946648718959541nt_int ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc2285326912895808259nt_int)
% 6.51/6.85 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.51/6.85 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.51/6.85 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.51/6.85 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.51/6.85 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.51/6.85 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.51/6.85 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.51/6.85 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.51/6.85 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.51/6.85 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.51/6.85 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.51/6.85 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.51/6.85 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.51/6.85 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.51/6.85 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.51/6.85 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.51/6.85 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.produc8678311845419106900er_nat ((-> tptp.code_integer tptp.nat) (-> tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.produc127349428274296955eger_o ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) tptp.produc8763457246119570046nteger) Bool)
% 6.51/6.85 (declare-fun tptp.produc2592262431452330817omplex ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex) tptp.produc8763457246119570046nteger) tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.produc8604463032469472703et_int ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int) tptp.produc8763457246119570046nteger) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.produc3558942015123893603et_nat ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat) tptp.produc8763457246119570046nteger) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.produc815715089573277247t_real ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real) tptp.produc8763457246119570046nteger) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.produc2558449545302689196_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc7773217078559923341nt_int) Bool)
% 6.51/6.85 (declare-fun tptp.produc8289552606927098482et_nat ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat) tptp.produc7773217078559923341nt_int) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.produc6253627499356882019eger_o ((-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) tptp.produc1908205239877642774nteger) Bool)
% 6.51/6.85 (declare-fun tptp.produc1573362020775583542_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc2285326912895808259nt_int) Bool)
% 6.51/6.85 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.51/6.85 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.51/6.85 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.51/6.85 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.51/6.85 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.51/6.85 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.produc8580519160106071146omplex ((-> tptp.int tptp.int tptp.set_complex) tptp.product_prod_int_int) tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.produc73460835934605544et_int ((-> tptp.int tptp.int tptp.set_int) tptp.product_prod_int_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.produc4251311855443802252et_nat ((-> tptp.int tptp.int tptp.set_nat) tptp.product_prod_int_int) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.produc1656060378719767003at_nat ((-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat) tptp.product_prod_int_int) tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.produc6452406959799940328t_real ((-> tptp.int tptp.int tptp.set_real) tptp.product_prod_int_int) tptp.set_real)
% 6.51/6.85 (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)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.51/6.85 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.51/6.85 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.51/6.85 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.51/6.85 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.51/6.85 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.51/6.85 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.51/6.85 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.51/6.85 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.51/6.85 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.51/6.85 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.51/6.85 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.51/6.85 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.51/6.85 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.51/6.85 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.51/6.85 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.51/6.85 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.51/6.85 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.51/6.85 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.51/6.85 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.51/6.85 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.51/6.85 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.51/6.85 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.51/6.85 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.51/6.85 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.51/6.85 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.51/6.85 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.51/6.85 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.51/6.85 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.51/6.85 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.51/6.85 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.51/6.85 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.51/6.85 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.51/6.85 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.51/6.85 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.51/6.85 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.51/6.85 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.51/6.85 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.51/6.85 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.51/6.85 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.51/6.85 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.51/6.85 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.51/6.85 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.51/6.85 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.51/6.85 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.51/6.85 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.51/6.85 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.51/6.85 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.51/6.85 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.51/6.85 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.51/6.85 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.51/6.85 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.51/6.85 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.51/6.85 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.set_or8419480210114673929d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 6.51/6.85 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.51/6.85 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.51/6.85 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.51/6.85 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.51/6.85 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.51/6.85 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.51/6.85 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.51/6.85 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.51/6.85 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.51/6.85 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 6.51/6.85 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.51/6.85 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.51/6.85 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.51/6.85 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.51/6.85 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.51/6.85 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.51/6.85 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.pi () tptp.real)
% 6.51/6.85 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.51/6.85 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.51/6.85 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.51/6.85 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.51/6.85 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.51/6.85 (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)
% 6.51/6.85 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.51/6.85 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.51/6.85 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.51/6.85 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.51/6.85 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.51/6.85 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.51/6.85 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.51/6.85 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.51/6.85 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.51/6.85 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.51/6.85 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.51/6.85 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.51/6.85 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.51/6.85 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.51/6.85 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.51/6.85 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.51/6.85 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.51/6.85 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.51/6.85 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.51/6.85 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.51/6.85 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.51/6.85 (declare-fun tptp.deg () tptp.nat)
% 6.51/6.85 (declare-fun tptp.m () tptp.nat)
% 6.51/6.85 (declare-fun tptp.ma () tptp.nat)
% 6.51/6.85 (declare-fun tptp.maxy () tptp.nat)
% 6.51/6.85 (declare-fun tptp.mi () tptp.nat)
% 6.51/6.85 (declare-fun tptp.na () tptp.nat)
% 6.51/6.85 (declare-fun tptp.pr () tptp.nat)
% 6.51/6.85 (declare-fun tptp.res () tptp.nat)
% 6.51/6.85 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.51/6.85 (declare-fun tptp.xa () tptp.nat)
% 6.51/6.85 (declare-fun tptp.za () tptp.nat)
% 6.51/6.85 (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))))))
% 6.51/6.85 (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)))))))
% 6.51/6.85 (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)))))))
% 6.51/6.85 (assert (= (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.pr))
% 6.51/6.85 (assert (= (@ tptp.some_nat tptp.maxy) (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.pr))))
% 6.51/6.85 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.51/6.85 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_1))))
% 6.51/6.85 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 6.51/6.85 (assert (not (= tptp.za tptp.mi)))
% 6.51/6.85 (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)))
% 6.51/6.85 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) tptp.na))
% 6.51/6.85 (assert (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) tptp.pr))
% 6.51/6.85 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.51/6.85 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.51/6.85 (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))))
% 6.51/6.85 (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))))
% 6.51/6.85 (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))))
% 6.51/6.85 (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))))
% 6.51/6.85 (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))))
% 6.51/6.85 (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))))
% 6.51/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.51/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.51/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.51/6.85 (assert (not (@ (@ tptp.ord_less_nat tptp.pr) (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.51/6.85 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))))
% 6.51/6.85 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.51/6.85 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.51/6.85 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.51/6.86 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.51/6.86 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.51/6.86 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)))
% 6.51/6.86 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.51/6.86 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.51/6.86 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.51/6.86 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.51/6.86 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (not (forall ((Maxy tptp.nat)) (not (= (@ tptp.some_nat Maxy) (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.pr)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.51/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.51/6.86 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 6.51/6.86 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 6.51/6.86 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.51/6.86 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.51/6.86 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.51/6.86 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (exists ((Z tptp.real)) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Z) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (exists ((Z tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Z) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X3) (@ P Y5))) (@ P X3))) (@ P A))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y4) X)) (= (not (@ (@ tptp.ord_less_real X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y4) X)) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y4) X)) (= (not (@ (@ tptp.ord_less_num X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y4) X)) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y4) X)) (= (not (@ (@ tptp.ord_less_int X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_num Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.51/6.86 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.51/6.86 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A2))) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A2))) A2)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec3392354462482085612at_nat P) (@ tptp.collec3392354462482085612at_nat Q)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.51/6.86 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.51/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.51/6.86 (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 ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P3 M2)))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y4)) (or (@ (@ tptp.ord_less_real Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (or (@ (@ tptp.ord_less_rat Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y4)) (or (@ (@ tptp.ord_less_num Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (or (@ (@ tptp.ord_less_nat Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y4)) (or (@ (@ tptp.ord_less_int Y4) X) (= X Y4)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (@ (@ tptp.ord_less_num Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (@ (@ tptp.ord_less_num Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_rat X) Y4) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_num X) Y4) (@ (@ tptp.ord_less_num Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_nat X) Y4) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_int X) Y4) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_real Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_rat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_num Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_nat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_int Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.51/6.86 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.51/6.86 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (@ (@ tptp.ord_less_num Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) P))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y4) (=> (@ (@ tptp.ord_less_rat Y4) X) P))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y4) (=> (@ (@ tptp.ord_less_num Y4) X) P))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y4) (=> (@ (@ tptp.ord_less_nat Y4) X) P))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y4) (=> (@ (@ tptp.ord_less_int Y4) X) P))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y4) (= X Y4) (@ (@ tptp.ord_less_real Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y4) (= X Y4) (@ (@ tptp.ord_less_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X) Y4) (= X Y4) (@ (@ tptp.ord_less_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y4) (= X Y4) (@ (@ tptp.ord_less_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X) Y4) (= X Y4) (@ (@ tptp.ord_less_int Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (= Y4 X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (= Y4 X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (= Y4 X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (= Y4 X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (= Y4 X)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (@ (@ tptp.ord_less_num Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (or (@ (@ tptp.ord_less_real X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (or (@ (@ tptp.ord_less_set_nat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (or (@ (@ tptp.ord_less_rat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (or (@ (@ tptp.ord_less_num X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (or (@ (@ tptp.ord_less_nat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (or (@ (@ tptp.ord_less_int X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_real Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y4) (@ (@ tptp.ord_less_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y4) (@ (@ tptp.ord_less_int Y4) X))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_real Y4) Z2) (@ (@ tptp.ord_less_real X) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat) (Z2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (=> (@ (@ tptp.ord_less_set_nat Y4) Z2) (@ (@ tptp.ord_less_set_nat X) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ (@ tptp.ord_less_rat Y4) Z2) (@ (@ tptp.ord_less_rat X) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (=> (@ (@ tptp.ord_less_num Y4) Z2) (@ (@ tptp.ord_less_num X) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (=> (@ (@ tptp.ord_less_nat Y4) Z2) (@ (@ tptp.ord_less_nat X) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z2) (@ (@ tptp.ord_less_int X) Z2)))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (@ (@ tptp.ord_less_eq_num X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (@ (@ tptp.ord_less_eq_nat X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (@ (@ tptp.ord_less_eq_int X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y4)) (@ (@ tptp.ord_less_real Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y4)) (@ (@ tptp.ord_less_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y4)) (@ (@ tptp.ord_less_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y4)) (@ (@ tptp.ord_less_int Y4) X))))
% 6.51/6.86 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y) (not (= X2 Y))))))
% 6.51/6.86 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y) (not (= X2 Y))))))
% 6.51/6.86 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y) (not (= X2 Y))))))
% 6.51/6.86 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y) (not (= X2 Y))))))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y) (not (= X2 Y))))))
% 6.51/6.86 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y) (not (= X2 Y))))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y) (= X2 Y)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y) (= X2 Y)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y) (= X2 Y)))))
% 6.51/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.51/6.86 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.51/6.86 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.51/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A4) (not (@ (@ tptp.ord_less_eq_set_nat A4) B3))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B) (@ (@ tptp.ord_less_set_nat C) A)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A4) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A4) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A4) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B3) A4) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B3) A4) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A4) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A4) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A4) (= A4 B3)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X) W) (=> (@ (@ tptp.ord_less_real W) Y4) (@ (@ tptp.ord_less_eq_real W) Z2)))) (@ (@ tptp.ord_less_eq_real Y4) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W) (=> (@ (@ tptp.ord_less_rat W) Y4) (@ (@ tptp.ord_less_eq_rat W) Z2)))) (@ (@ tptp.ord_less_eq_rat Y4) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) W) (=> (@ (@ tptp.ord_less_real W) X) (@ (@ tptp.ord_less_eq_real Y4) W)))) (@ (@ tptp.ord_less_eq_real Y4) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) W) (=> (@ (@ tptp.ord_less_rat W) X) (@ (@ tptp.ord_less_eq_rat Y4) W)))) (@ (@ tptp.ord_less_eq_rat Y4) Z2)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B3) (not (@ (@ tptp.ord_less_eq_set_nat B3) A4))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat A) C)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B3) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B3) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (not (= A4 B3))))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B3) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A4) B3) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B3) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B3) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B3) (= A4 B3)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B3) (= A4 B3)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y4) X)) (@ (@ tptp.ord_less_real X) Y4))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y4) X)) (@ (@ tptp.ord_less_rat X) Y4))))
% 6.51/6.86 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y4) X)) (@ (@ tptp.ord_less_num X) Y4))))
% 6.51/6.86 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y4) X)) (@ (@ tptp.ord_less_nat X) Y4))))
% 6.51/6.86 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y4) X)) (@ (@ tptp.ord_less_int X) Y4))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y) (not (@ (@ tptp.ord_less_eq_set_nat Y) X2))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_eq_real X3) Z2))) (@ (@ tptp.ord_less_eq_real Y4) Z2))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat X3) Z2))) (@ (@ tptp.ord_less_eq_rat Y4) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (Y4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (@ (@ tptp.ord_less_eq_real Y4) X3))) (@ (@ tptp.ord_less_eq_real Y4) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (Y4 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (@ (@ tptp.ord_less_eq_rat Y4) X3))) (@ (@ tptp.ord_less_eq_rat Y4) Z2))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (= (not (@ (@ tptp.ord_less_real X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (= (not (@ (@ tptp.ord_less_set_nat X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (= (not (@ (@ tptp.ord_less_num X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (= (not (@ (@ tptp.ord_less_int X) Y4)) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (= (@ (@ tptp.ord_less_eq_real X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y4)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (= (@ (@ tptp.ord_less_eq_rat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (= (@ (@ tptp.ord_less_eq_num X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (= (@ (@ tptp.ord_less_eq_nat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (= (@ (@ tptp.ord_less_eq_int X) Y4) (= X Y4)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (= A B)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (not (@ (@ tptp.ord_less_real X) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X) (not (@ (@ tptp.ord_less_set_nat X) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (not (@ (@ tptp.ord_less_rat X) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (not (@ (@ tptp.ord_less_num X) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (not (@ (@ tptp.ord_less_nat X) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (not (@ (@ tptp.ord_less_int X) Y4)))))
% 6.51/6.86 (assert (forall ((B4 tptp.real) (A5 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A5)) (@ (@ tptp.ord_less_real A5) B4))))
% 6.51/6.86 (assert (forall ((B4 tptp.rat) (A5 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A5)) (@ (@ tptp.ord_less_rat A5) B4))))
% 6.51/6.86 (assert (forall ((B4 tptp.num) (A5 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A5)) (@ (@ tptp.ord_less_num A5) B4))))
% 6.51/6.86 (assert (forall ((B4 tptp.nat) (A5 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A5)) (@ (@ tptp.ord_less_nat A5) B4))))
% 6.51/6.86 (assert (forall ((B4 tptp.int) (A5 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A5)) (@ (@ tptp.ord_less_int A5) B4))))
% 6.51/6.86 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.51/6.86 (assert (forall ((Y4 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (= (@ (@ tptp.ord_less_eq_rat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (= (@ (@ tptp.ord_less_eq_num X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (= (@ (@ tptp.ord_less_eq_nat X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (= (@ (@ tptp.ord_less_eq_int X) Y4) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y4) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y4) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_set_nat X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_num X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_nat X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_int X) Y4))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A4)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (@ (@ tptp.ord_less_eq_rat B3) A4)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (@ (@ tptp.ord_less_eq_num B3) A4)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ tptp.ord_less_eq_nat B3) A4)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ tptp.ord_less_eq_int B3) A4)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.51/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A4) (@ (@ tptp.ord_less_eq_set_nat A4) B3)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (@ (@ tptp.ord_less_eq_rat A4) B3)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (@ (@ tptp.ord_less_eq_num A4) B3)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (@ (@ tptp.ord_less_eq_nat A4) B3)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (@ (@ tptp.ord_less_eq_int A4) B3)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z2) (@ _let_1 Z2))))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (= X Y4)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y) (@ (@ tptp.ord_less_eq_set_nat Y) X2)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((X2 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_rat Y) X2)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((X2 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y) (@ (@ tptp.ord_less_eq_num Y) X2)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_eq_nat Y) X2)))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((X2 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_int Y) X2)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y4))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _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)))))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_num Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y4))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _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)))))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y4))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _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)))))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_int Z2))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y4))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _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)))))))))))))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.51/6.86 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.51/6.86 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= (@ (@ tptp.vEBT_VEBT_high tptp.res) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.pr))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))) (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1) _let_2) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_1))))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.za) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.51/6.86 (assert (not (exists ((U tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))) U) (@ (@ tptp.ord_less_nat U) (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1)))))))
% 6.51/6.86 (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))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_vebt_member tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.51/6.86 (assert (not (= tptp.za tptp.ma)))
% 6.51/6.86 (assert (not (= tptp.mi tptp.ma)))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y4) Z2) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y4)) (@ tptp.some_nat Z2)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.res) tptp.xa))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_vebt_member tptp.summary) tptp.pr))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.res) tptp.ma))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.mi) tptp.res))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.51/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y4) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat Y4) X) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat Z4) X)) (@ (@ tptp.ord_less_eq_nat Z4) Y4)))))))
% 6.51/6.86 (assert (= (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.some_nat tptp.pr)))
% 6.51/6.86 (assert (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt tptp.summary)) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) tptp.pr))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y4 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 Y4) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y4) (or (@ (@ tptp.vEBT_vebt_member T) Y4) (= X Y4)))))))))
% 6.51/6.86 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1))) (or (= tptp.za tptp.mi) (= tptp.za tptp.ma) (and (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_1)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) _let_1))) (@ (@ tptp.power_power_nat _let_1) tptp.m))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (not (forall ((Pr tptp.nat)) (not (= (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.some_nat Pr))))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.pr) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.51/6.86 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.res) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.res) _let_1))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (not (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.pr)) tptp.bot_bot_set_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.51/6.86 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) tptp.pr))
% 6.51/6.86 (assert (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.pr)) X_1)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y4 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 Y4) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y4)) X))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))
% 6.51/6.86 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.51/6.86 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.51/6.86 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M3) N3) (@ P M3))) (@ P N3))) (@ P N))))
% 6.51/6.86 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.51/6.86 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.51/6.86 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.51/6.86 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.51/6.86 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)))
% 6.51/6.86 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.51/6.86 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 6.51/6.86 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.51/6.86 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 6.51/6.86 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.51/6.86 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.51/6.86 (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 ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat Z4) X2) (@ (@ tptp.ord_less_eq_nat Z4) Y))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) tptp.maxy))
% 6.51/6.86 (assert (= (@ tptp.some_nat tptp.maxy) (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) tptp.maxy))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) tptp.na))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.51/6.86 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y tptp.nat)) (= X (@ tptp.some_nat Y))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y tptp.num)) (= X (@ tptp.some_num Y))))))
% 6.51/6.86 (assert (forall ((X tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X (@ tptp.some_nat Y)))) (= X tptp.none_nat))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((X tptp.option_num)) (= (forall ((Y tptp.num)) (not (= X (@ tptp.some_num Y)))) (= X tptp.none_num))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y2)) (= X22 Y2))))
% 6.51/6.86 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y2)) (= X22 Y2))))
% 6.51/6.86 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y2)) (= X22 Y2))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W2)) Z2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W2)) Z2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W2)) Z2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2))) Z2))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.51/6.86 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.51/6.86 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.51/6.86 (assert (and (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.za) (@ (@ tptp.ord_less_nat tptp.za) tptp.xa)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 6.51/6.86 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 6.51/6.86 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))
% 6.51/6.86 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.51/6.86 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.51/6.86 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y4 tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y4 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y4 (@ tptp.some_nat B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y4 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y4 tptp.option_num)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y4 tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y4 (@ tptp.some_num B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y4 tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y4 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y4 (@ tptp.some_nat B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y4 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)) (=> (= Y4 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y4 tptp.option_num)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y4 tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y4 (@ tptp.some_num B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y4 tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y4 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y4 (@ tptp.some_nat B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y4 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y4 tptp.option_num)) (let ((_let_1 (@ (@ P X) Y4))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y4 tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y4 (@ tptp.some_num B2)) (@ (@ P X) Y4)))) _let_1))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.option_nat)) (=> (not (= Y4 tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y4 (@ tptp.some_nat X23))))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.option4927543243414619207at_nat)) (=> (not (= Y4 tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y4 (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.option_num)) (=> (not (= Y4 tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y4 (@ tptp.some_num X23))))))))
% 6.51/6.86 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 6.51/6.86 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.51/6.86 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.51/6.86 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 6.51/6.86 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.51/6.86 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.51/6.86 (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)))) (= tptp.res (@ tptp.the_nat (@ (@ 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))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= tptp.res (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat tptp.deg) _let_1))) tptp.pr)) tptp.maxy))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.res))
% 6.51/6.86 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.res))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.51/6.86 (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))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y4) Z2) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y4)) (@ tptp.some_nat Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y4) Z2) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y4)) (@ tptp.some_nat Z2)))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))
% 6.51/6.86 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) Z2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Z2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Z2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W2)) Z2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Z2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2))) Z2))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y4) _let_1)) X)) N) Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y4) _let_1)) X)) N) X)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ 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)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ 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)))))
% 6.51/6.86 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ 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))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ 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))))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.51/6.86 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.51/6.86 (assert (forall ((B tptp.real) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((B tptp.int) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X) Y4))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (assert (forall ((B tptp.real) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((B tptp.int) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))) (= (@ (@ 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) (@ (@ 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)))))))))
% 6.51/6.86 (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))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y4) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) N)) tptp.one_one_complex))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y4) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) N)) tptp.one_one_real))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y4) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y4) N)) tptp.one_one_rat))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y4) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y4) N)) tptp.one_one_nat))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y4) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) N)) tptp.one_one_int))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N))) (let ((_let_2 (@ tptp.times_times_complex Y4))) (=> (= (@ (@ tptp.times_times_complex X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N))) (let ((_let_2 (@ tptp.times_times_real Y4))) (=> (= (@ (@ tptp.times_times_real X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N))) (let ((_let_2 (@ tptp.times_times_rat Y4))) (=> (= (@ (@ tptp.times_times_rat X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y4))) (=> (= (@ (@ tptp.times_times_nat X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y4))) (=> (= (@ (@ tptp.times_times_int X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (U2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U2)) K))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex Z2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real Z2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat Z2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.nat)) (= (@ (@ tptp.times_times_nat Z2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int Z2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_complex Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_real Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_rat Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_nat Z2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_int Z2) Z2))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.51/6.86 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y4)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y4) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y4)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y4)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y4)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y4)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y4) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y4)))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ 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) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ 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)))))))))))))))
% 6.51/6.86 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ 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) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ 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)))))))))))))))
% 6.51/6.86 (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 ((M4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M4) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y4)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))))))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.51/6.86 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.51/6.86 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.51/6.86 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))))))))))
% 6.51/6.86 (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)))))))))))))))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y4) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y4)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y4) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y4)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y4) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.51/6.86 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U2 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) U2)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U2)) N))))))
% 6.51/6.86 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U2 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) U2)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U2)) M)) N)))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U2 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) U2)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U2)) N))))))
% 6.51/6.86 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U2 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) U2)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U2)) M)) N)))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U2)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U2)) N))))))
% 6.51/6.86 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U2)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U2)) M) N)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y4)) (= X Y4))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3)))))) (@ P N))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P M3))) (@ P N3))) (@ P N))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.51/6.86 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.51/6.86 (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 ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))))))
% 6.51/6.86 (assert (forall ((X tptp.list_VEBT_VEBT) (Y4 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y4))) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.list_o) (Y4 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y4))) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y4))) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.list_int) (Y4 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y4))) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y4))) (not (= X Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y4)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y4) X)) _let_1)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y4)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y4) X)) _let_1)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y4)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y4) X)) _let_1)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y4)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y4) X)) _let_1)))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U2 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) U2)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U2)) N))))))
% 6.51/6.86 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U2 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) U2)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U2)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U2)) M)) N)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I2))))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M5 tptp.nat)) (and (= M (@ tptp.suc M5)) (@ (@ tptp.ord_less_nat N) M5))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y4)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y4) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y4)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y4)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y4)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y4) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y4)))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M6) (exists ((M4 tptp.nat)) (= M6 (@ tptp.suc M4))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N3) (@ P M3))) (@ P N3))) (@ P N))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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) (Z tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M2) K3))))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.51/6.86 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K3)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.51/6.86 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.51/6.86 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 6.51/6.86 (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))))))))))))))))))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y4 tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb2) Y4) (=> (=> (= 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 (= Y4 (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B2)))))))))))))))
% 6.51/6.86 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb2 tptp.option_num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb2) Y4) (=> (=> (= 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 (= Y4 (@ tptp.some_num (@ (@ X A3) B2)))))))))))))))
% 6.51/6.86 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb2 tptp.option_nat) (Y4 tptp.option_nat)) (let ((_let_1 (not (= Y4 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb2) Y4) (=> (=> (= 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 (= Y4 (@ tptp.some_nat (@ (@ X A3) B2)))))))))))))))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_complex Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_real Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_Pr5648618587558075414at_nat (lambda ((Xs tptp.list_P6011104703257516679at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((Uu2 tptp.product_prod_nat_nat)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu2 tptp.list_nat)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_list_nat Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu2 tptp.vEBT_VEBT)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_VEBT_VEBT Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu2 Bool)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_o Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_nat Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)))))))))
% 6.51/6.86 (assert (= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_int Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.51/6.86 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.power_power_real X) N3))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.extended_enat) (Y4 tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z2) Y4) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y4) Z2)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y4)) Z2))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A4))))
% 6.51/6.86 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A4))))
% 6.51/6.86 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A4))))
% 6.51/6.86 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A4))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.51/6.86 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.51/6.86 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.51/6.86 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.51/6.86 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.51/6.86 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.51/6.86 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.51/6.86 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4))))
% 6.51/6.86 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A4))))
% 6.51/6.86 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A4))))
% 6.51/6.86 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A4))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_real) (B5 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B5) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B5)))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_complex) (B5 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B5) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B5)))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) B5) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ _let_1 B5)))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B5) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B5)))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_int) (B5 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B5) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B5)))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B5) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B5)))))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (exists ((C2 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A4) C2))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.51/6.86 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.51/6.86 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.51/6.86 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.51/6.86 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_real X) Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ (@ tptp.minus_minus_rat X) Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y4)) (@ (@ tptp.minus_minus_int X) Y4)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs2 Ys)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs2 Ys)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs2 Ys)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs2 Ys)))))
% 6.51/6.86 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X6 tptp.vEBT_VEBT)) (@ (@ P I4) X6)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))))
% 6.51/6.86 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X6 Bool)) (@ (@ P I4) X6)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs) I4)))))))))
% 6.51/6.86 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X6 tptp.nat)) (@ (@ P I4) X6)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs) I4)))))))))
% 6.51/6.86 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X6 tptp.int)) (@ (@ P I4) X6)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_int Xs) I4)))))))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.list_VEBT_VEBT) (Z3 tptp.list_VEBT_VEBT)) (= Y6 Z3)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys3) I4))))))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.list_o) (Z3 tptp.list_o)) (= Y6 Z3)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys3) I4))))))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.list_nat) (Z3 tptp.list_nat)) (= Y6 Z3)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 6.51/6.86 (assert (= (lambda ((Y6 tptp.list_int) (Z3 tptp.list_int)) (= Y6 Z3)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys3) I4))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) X))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I3)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I3)))) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I3)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I3)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I3)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))))
% 6.51/6.86 (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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))))))
% 6.51/6.86 (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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))))))
% 6.51/6.86 (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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I4)))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.51/6.86 (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)))))))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.51/6.86 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y4)) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))
% 6.51/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.51/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.51/6.86 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.51/6.86 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.51/6.86 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.51/6.86 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (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))))))))
% 6.51/6.86 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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))))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))
% 6.51/6.86 (assert (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (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))))))))
% 6.51/6.86 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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))))))))
% 6.51/6.86 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.51/6.86 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.51/6.86 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.51/6.86 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y4) _let_1)) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y4) _let_1)) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y4) _let_1)) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y4) _let_1)) (= X Y4))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.51/6.86 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.51/6.86 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.51/6.86 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.51/6.86 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.51/6.86 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y4 (@ tptp.suc Nat3))))))))
% 6.51/6.86 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.51/6.86 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.51/6.86 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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 ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3))))))) (@ P N)))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.complex) (Z2 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y4) (@ (@ tptp.divide1717551699836669952omplex W2) Z2)) (= (@ (@ tptp.times_times_complex X) Z2) (@ (@ tptp.times_times_complex W2) Y4)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y4) (@ (@ tptp.divide_divide_real W2) Z2)) (= (@ (@ tptp.times_times_real X) Z2) (@ (@ tptp.times_times_real W2) Y4)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y4) (@ (@ tptp.divide_divide_rat W2) Z2)) (= (@ (@ tptp.times_times_rat X) Z2) (@ (@ tptp.times_times_rat W2) Y4)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.51/6.86 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.51/6.86 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.51/6.86 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.51/6.86 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 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 Y4) E2)))) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 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 Y4) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real) (W2 tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z2)) (@ (@ tptp.divide_divide_real Y4) W2))))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z2)) (@ (@ tptp.divide_divide_rat Y4) W2))))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (W2 tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z2)) (@ (@ tptp.divide_divide_real Y4) W2))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (W2 tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z2)) (@ (@ tptp.divide_divide_rat Y4) W2))))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (W2 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_real W2) Z2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z2)) (@ (@ tptp.divide_divide_real Y4) W2)))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (W2 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_rat W2) Z2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z2)) (@ (@ tptp.divide_divide_rat Y4) W2)))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y4)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z2) Y4)) X) (@ (@ tptp.ord_less_real Z2) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z2) Y4)) X) (@ (@ tptp.ord_less_rat Z2) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z2) Y4)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z2) Y4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) Z2)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.complex) (Z2 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex W2) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z2)) (@ (@ tptp.times_times_complex W2) Y4))) (@ (@ tptp.times_times_complex Y4) Z2)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W2) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W2) Y4))) (@ (@ tptp.times_times_real Y4) Z2)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W2) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W2) Y4))) (@ (@ tptp.times_times_rat Y4) Z2)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.complex) (X tptp.complex) (Z2 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) Z2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z2) Y4))) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real) (Z2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y4)) Z2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z2) Y4))) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y4)) Z2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z2) Y4))) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.complex) (Z2 tptp.complex) (X tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z2) Y4))) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z2) (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z2) Y4))) Y4)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z2) (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z2) Y4))) Y4)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y4) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z2)) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y4) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z2)) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y4) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z2)) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z2)) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y4) Z2))) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z2)) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y4) Z2))) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z2)) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y4) Z2))) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.complex) (Z2 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex W2) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z2)) (@ (@ tptp.times_times_complex W2) Y4))) (@ (@ tptp.times_times_complex Y4) Z2)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W2) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W2) Y4))) (@ (@ tptp.times_times_real Y4) Z2)))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W2) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W2) Y4))) (@ (@ tptp.times_times_rat Y4) Z2)))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y4) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z2)) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y4) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y4) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z2)) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y4) Z2))) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z2)) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y4) Z2))) Z2)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z2)) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y4) Z2))) Z2)))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y4) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y4) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y4) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y4) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_real X) Y4) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_rat X) Y4) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat))))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_int X) Y4) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y4)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y4)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y4)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y4) tptp.zero_zero_int)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.51/6.86 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.51/6.86 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.51/6.86 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) X)) Y4)))) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (forall ((Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (=> (@ (@ tptp.ord_less_rat Z) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) X)) Y4)))) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z2) Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z2) Y4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) Z2)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) Y4)) X) (@ (@ tptp.ord_less_eq_real Z2) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) Y4)) X) (@ (@ tptp.ord_less_eq_rat Z2) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W2) Z2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W2) Y4))) (@ (@ tptp.times_times_real Y4) Z2))) tptp.zero_zero_real))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W2) Z2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W2) Y4))) (@ (@ tptp.times_times_rat Y4) Z2))) tptp.zero_zero_rat))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (Z2 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W2) Z2)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W2) Y4))) (@ (@ tptp.times_times_real Y4) Z2))) tptp.zero_zero_real))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W2) Z2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W2) Y4))) (@ (@ tptp.times_times_rat Y4) Z2))) tptp.zero_zero_rat))))))
% 6.51/6.86 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 6.51/6.86 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 6.51/6.86 (assert (forall ((X5 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X5))))
% 6.51/6.86 (assert (forall ((X5 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X5))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y4)) X)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y4)) X)))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y4)) X)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y4) X)) X)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y4) X)) X)))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y4) X)) X)))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))) (or (not (= X tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4))) (or (not (= X tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4))) (or (not (= X tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))) tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4))) tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4))) tptp.zero_zero_int))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((B tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (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))))))))
% 6.51/6.86 (assert (forall ((B tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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))))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (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))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.51/6.86 (assert (forall ((U2 tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U2) 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 U2) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U2))) S2))) V))))))
% 6.51/6.86 (assert (forall ((U2 tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U2) 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 U2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U2))) S2))) V))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (A tptp.real) (Y4 tptp.real) (U2 tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y4) A) (=> (@ _let_1 U2) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U2) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U2) X)) (@ (@ tptp.times_times_real V) Y4))) A)))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (A tptp.rat) (Y4 tptp.rat) (U2 tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y4) A) (=> (@ _let_1 U2) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U2) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U2) X)) (@ (@ tptp.times_times_rat V) Y4))) A)))))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (A tptp.int) (Y4 tptp.int) (U2 tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y4) A) (=> (@ _let_1 U2) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U2) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U2) X)) (@ (@ tptp.times_times_int V) Y4))) A)))))))))
% 6.51/6.86 (assert (forall ((B tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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)))))))))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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)))))))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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)))))))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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)))))))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ 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 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ 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 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ 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 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ 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 N4)) (@ _let_1 N))))))))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.51/6.86 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.86 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (= tptp.divide_divide_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M2) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.plus_plus_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) N2))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 6.51/6.86 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 6.51/6.86 (assert (forall ((C tptp.rat)) (= (lambda ((X2 tptp.rat)) (@ (@ tptp.times_times_rat X2) C)) (@ tptp.times_times_rat C))))
% 6.51/6.86 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 6.51/6.86 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 6.51/6.86 (assert (= tptp.times_times_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) N2))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf) tptp.none_nat)))
% 6.51/6.86 (assert (forall ((X tptp.real) (A tptp.real) (Y4 tptp.real) (U2 tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y4) A) (=> (@ _let_1 U2) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U2) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U2) X)) (@ (@ tptp.times_times_real V) Y4))) A)))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (A tptp.rat) (Y4 tptp.rat) (U2 tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y4) A) (=> (@ _let_1 U2) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U2) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U2) X)) (@ (@ tptp.times_times_rat V) Y4))) A)))))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (A tptp.int) (Y4 tptp.int) (U2 tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y4) A) (=> (@ _let_1 U2) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U2) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U2) X)) (@ (@ tptp.times_times_int V) Y4))) A)))))))))
% 6.51/6.86 (assert (forall ((B tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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))))))))))))
% 6.51/6.86 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (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)))))))))))))
% 6.51/6.86 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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)))))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X) _let_2) (@ (@ tptp.power_power_rat Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_eq_int X) Y4))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (= tptp.power_power_complex (lambda ((P4 tptp.complex) (M2 tptp.nat)) (@ (@ (@ tptp.if_complex (= M2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P4) (@ (@ tptp.power_power_complex P4) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.86 (assert (= tptp.power_power_real (lambda ((P4 tptp.real) (M2 tptp.nat)) (@ (@ (@ tptp.if_real (= M2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P4) (@ (@ tptp.power_power_real P4) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.86 (assert (= tptp.power_power_rat (lambda ((P4 tptp.rat) (M2 tptp.nat)) (@ (@ (@ tptp.if_rat (= M2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P4) (@ (@ tptp.power_power_rat P4) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.86 (assert (= tptp.power_power_nat (lambda ((P4 tptp.nat) (M2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P4) (@ (@ tptp.power_power_nat P4) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.86 (assert (= tptp.power_power_int (lambda ((P4 tptp.int) (M2 tptp.nat)) (@ (@ (@ tptp.if_int (= M2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P4) (@ (@ tptp.power_power_int P4) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj) tptp.none_nat)))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_real X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_rat X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4) (@ (@ tptp.ord_less_nat X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_int X) Y4))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) tptp.zero_zero_real)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) tptp.zero_zero_rat)))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) tptp.zero_zero_int)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real)))))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat)))))))
% 6.51/6.86 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (Z2 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex Z2) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z2)) (@ (@ tptp.times_times_complex Y4) W2)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real Z2) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real Y4) W2)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat Z2) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat Y4) W2)))))
% 6.51/6.86 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (Z2 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex Z2) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W2)) (@ (@ tptp.times_times_complex Y4) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real Z2) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W2)) (@ (@ tptp.times_times_real Y4) Z2)))))
% 6.51/6.86 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat Z2) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W2)) (@ (@ tptp.times_times_rat Y4) Z2)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((U2 tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U2) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y4)) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_real U2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.51/6.86 (assert (forall ((U2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U2) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X) Y4)) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_rat U2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.option_nat)) (let ((_let_1 (not (= Y4 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y4) (=> (=> (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 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y4 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 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y4 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) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _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 (= Y4 (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y4 (@ (@ (@ 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)))))))))))))))))))))))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A4 Bool) (B3 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B3))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) 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)) (= A22 (@ (@ 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 (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) 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)) (= A22 (@ (@ 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 (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) 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)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _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 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ 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 (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) 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)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _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 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.51/6.86 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 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) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_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) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 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) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_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) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 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) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (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))) M4)) (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) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 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) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (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))) M4)) (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)))))))))))))))))))))))))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((V tptp.num) (W2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 6.51/6.86 (assert (forall ((C tptp.complex)) (not (@ (@ tptp.member_complex C) tptp.bot_bot_set_complex))))
% 6.51/6.86 (assert (forall ((C tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat C) tptp.bot_bo2099793752762293965at_nat))))
% 6.51/6.86 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((C tptp.real)) (not (@ (@ tptp.member_real C) tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_complex)) (= (forall ((X2 tptp.complex)) (not (@ (@ tptp.member_complex X2) A2))) (= A2 tptp.bot_bot_set_complex))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X2) A2))) (= A2 tptp.bot_bo2099793752762293965at_nat))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (forall ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A2))) (= A2 tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (forall ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A2))) (= A2 tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (forall ((X2 tptp.real)) (not (@ (@ tptp.member_real X2) A2))) (= A2 tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((P (-> tptp.complex Bool))) (= (= (@ tptp.collect_complex P) tptp.bot_bot_set_complex) (forall ((X2 tptp.complex)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (forall ((X2 tptp.list_nat)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (forall ((X2 tptp.real)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.complex Bool))) (= (= tptp.bot_bot_set_complex (@ tptp.collect_complex P)) (forall ((X2 tptp.complex)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat P)) (forall ((X2 tptp.product_prod_nat_nat)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat P)) (forall ((X2 tptp.list_nat)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X2 tptp.int)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.real Bool))) (= (= tptp.bot_bot_set_real (@ tptp.collect_real P)) (forall ((X2 tptp.real)) (not (@ P X2))))))
% 6.51/6.86 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 6.51/6.86 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.51/6.86 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.51/6.86 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B5) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B5))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real) (B5 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B5) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B5))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B5) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B5))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Y4 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y4 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y4 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.51/6.86 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.51/6.86 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.51/6.86 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.51/6.86 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.51/6.86 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.51/6.86 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ P M2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.51/6.86 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ P M2))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.51/6.86 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.51/6.86 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A tptp.complex)) (not (@ (@ tptp.member_complex A) tptp.bot_bot_set_complex))))
% 6.51/6.86 (assert (forall ((A tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (not (@ (@ tptp.member_int A) tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (not (@ (@ tptp.member_real A) tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_complex) (A tptp.complex)) (=> (= A2 tptp.bot_bot_set_complex) (not (@ (@ tptp.member_complex A) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (= A2 tptp.bot_bo2099793752762293965at_nat) (not (@ (@ tptp.member8440522571783428010at_nat A) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (= A2 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (= A2 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (= A2 tptp.bot_bot_set_real) (not (@ (@ tptp.member_real A) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_complex)) (=> (forall ((Y3 tptp.complex)) (not (@ (@ tptp.member_complex Y3) A2))) (= A2 tptp.bot_bot_set_complex))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat Y3) A2))) (= A2 tptp.bot_bo2099793752762293965at_nat))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A2))) (= A2 tptp.bot_bot_set_nat))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (@ (@ tptp.member_int Y3) A2))) (= A2 tptp.bot_bot_set_int))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (=> (forall ((Y3 tptp.real)) (not (@ (@ tptp.member_real Y3) A2))) (= A2 tptp.bot_bot_set_real))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_complex)) (= (exists ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2)) (not (= A2 tptp.bot_bot_set_complex)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (exists ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A2)) (not (= A2 tptp.bot_bo2099793752762293965at_nat)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2)) (not (= A2 tptp.bot_bot_set_nat)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (= (exists ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2)) (not (= A2 tptp.bot_bot_set_int)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_real)) (= (exists ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2)) (not (= A2 tptp.bot_bot_set_real)))))
% 6.51/6.86 (assert (= tptp.bot_bot_set_complex (@ tptp.collect_complex tptp.bot_bot_complex_o)))
% 6.51/6.86 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat tptp.bot_bo482883023278783056_nat_o)))
% 6.51/6.86 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))
% 6.51/6.86 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 6.51/6.86 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 6.51/6.86 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real tptp.bot_bot_real_o)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N3)) Y4))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Y4 Bool)) (let ((_let_1 (not Y4))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y4) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y4) (=> (=> (exists ((Uu3 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) true))) Y4) (=> (=> (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))) Y4))))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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 ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5) (= (@ (@ tptp.power_power_real Y5) N) A)) (= Y5 X3)))))))))
% 6.51/6.86 (assert (= tptp.bot_bot_set_complex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) false))))
% 6.51/6.86 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) false))))
% 6.51/6.86 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) false))))
% 6.51/6.86 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) false))))
% 6.51/6.86 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) false))))
% 6.51/6.86 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) false))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y4) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> A3 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y4 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 (= Y4 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 (= Y4 (@ tptp.some_nat Mi2)))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y4) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> B2 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y4 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 (= Y4 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 (= Y4 (@ tptp.some_nat Ma2)))))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (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))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y4) (=> (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)) (= Y4 (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))) Y4) (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))) (= Y4 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.51/6.86 (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))))))))))))))))))))
% 6.51/6.86 (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))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y4) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) Y4) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y4) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((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))) (= Y4 (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))) (= Y4 (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))) (= Y4 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.51/6.86 (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))))))))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y4) (=> (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)) (= Y4 (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))) Y4) (=> (=> (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))) Y4) (=> (=> (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))) Y4) (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))) (= Y4 (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))))))))))))))))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B) D))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((I2 tptp.set_nat) (L2 tptp.set_nat) (U2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or4548717258645045905et_nat L2) U2)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I2) (@ (@ tptp.ord_less_eq_set_nat I2) U2)))))
% 6.51/6.86 (assert (forall ((I2 tptp.rat) (L2 tptp.rat) (U2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L2) U2)) (and (@ (@ tptp.ord_less_eq_rat L2) I2) (@ (@ tptp.ord_less_eq_rat I2) U2)))))
% 6.51/6.86 (assert (forall ((I2 tptp.num) (L2 tptp.num) (U2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L2) U2)) (and (@ (@ tptp.ord_less_eq_num L2) I2) (@ (@ tptp.ord_less_eq_num I2) U2)))))
% 6.51/6.86 (assert (forall ((I2 tptp.nat) (L2 tptp.nat) (U2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L2) U2)) (and (@ (@ tptp.ord_less_eq_nat L2) I2) (@ (@ tptp.ord_less_eq_nat I2) U2)))))
% 6.51/6.86 (assert (forall ((I2 tptp.int) (L2 tptp.int) (U2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L2) U2)) (and (@ (@ tptp.ord_less_eq_int L2) I2) (@ (@ tptp.ord_less_eq_int I2) U2)))))
% 6.51/6.86 (assert (forall ((I2 tptp.real) (L2 tptp.real) (U2 tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L2) U2)) (and (@ (@ tptp.ord_less_eq_real L2) I2) (@ (@ tptp.ord_less_eq_real I2) U2)))))
% 6.51/6.86 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L2) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.51/6.86 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int W2) (@ (@ tptp.minus_minus_int Z2) tptp.one_one_int)) (@ (@ tptp.ord_less_int W2) Z2))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int W2) (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W2) Z2))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z2) (@ (@ tptp.ord_less_int W2) Z2))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2)))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2)) Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((B4 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 B4) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q5)))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_int W2) Z2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z2))))
% 6.51/6.86 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 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 B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.51/6.86 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) 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) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2)) Z2) tptp.zero_zero_int))))
% 6.51/6.86 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.51/6.86 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.51/6.86 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.51/6.86 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 6.51/6.86 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.51/6.86 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.51/6.86 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.51/6.86 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.51/6.86 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 6.51/6.86 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)) (or (@ _let_1 Z2) (= W2 Z2))))))
% 6.51/6.86 (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 ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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 ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M4)))))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 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)) Ts2) 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)))))))))))
% 6.51/6.86 (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) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2)))) (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)))))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (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)))))))))))
% 6.51/6.86 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D)))) (@ _let_1 D))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P5 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) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P5 X3) (@ P5 (@ (@ 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)) (@ P5 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) B5) (@ P (@ (@ tptp.plus_plus_int Y) X2))))))))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 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)) (= (@ P5 X3) (@ P5 (@ (@ 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)) (@ P5 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))))))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B5) (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) B5) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (B5 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) B5) (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)))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y4) (=> (@ (@ 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) (=> (= Y4 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 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y4 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 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y4 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) (=> (= Y4 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) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X _let_1) (=> (= Y4 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) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X _let_1) (=> (= Y4 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 (= Y4 (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y4 (@ (@ (@ 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)))))))))))))))))))))))))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (not (@ (@ tptp.ord_less_real T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (not (@ (@ tptp.ord_less_rat T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (not (@ (@ tptp.ord_less_num T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (not (@ (@ tptp.ord_less_nat T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (not (@ (@ tptp.ord_less_int T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X5))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X5))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X5))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X5))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_real T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_rat T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (@ (@ tptp.ord_less_num T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (@ (@ tptp.ord_less_nat T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (@ (@ tptp.ord_less_int T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (not (@ (@ tptp.ord_less_real X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (not (@ (@ tptp.ord_less_rat X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (not (@ (@ tptp.ord_less_num X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (not (@ (@ tptp.ord_less_int X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (not (= X5 T)))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P5 X5) (@ Q6 X5))))))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.51/6.86 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.51/6.86 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (B5 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) B5) (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) B5) (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) B5) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (B5 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) B5) (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) B5) (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) B5) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.51/6.86 (assert (forall ((D tptp.int) (P5 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P5 X3) (@ P5 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((X_12 tptp.int)) (@ P5 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.51/6.86 (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 ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B5) (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) B5) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.minus_minus_int X5) D4) T))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B5) (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) B5) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.minus_minus_int X5) D4) T)))))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (B5 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) B5) (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)))))))
% 6.51/6.86 (assert (forall ((D4 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B5) (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) B5) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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))))))))))))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y4) (=> (@ (@ 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) (=> (= Y4 (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 Y4) (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 Y4) (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 Y4) (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) (=> (= Y4 (=> (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))))))))))))))))))))))
% 6.51/6.86 (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))))))))))))))))
% 6.51/6.86 (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))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y4) (=> (@ (@ 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) (=> (= Y4 (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 Y4) (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) (=> (= Y4 (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))))))))))))))))))
% 6.51/6.86 (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))))))))))))))))))))))))
% 6.51/6.86 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y4) (=> (@ (@ 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 Y4) (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 Y4) (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) (=> (= Y4 (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) (=> (= Y4 (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) (=> (= Y4 (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))))))))))))))))))))
% 6.51/6.86 (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))))))))))))))))))
% 6.51/6.86 (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)))))))))))))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_rat X) Y4))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_int X) Y4))))))
% 6.51/6.86 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real Y4) Z2)) (@ (@ tptp.ord_less_eq_real X) Y4)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat Y4) Z2)) (@ (@ tptp.ord_less_eq_rat X) Y4)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z2)) (@ (@ tptp.times_times_int Y4) Z2)) (@ (@ tptp.ord_less_eq_int X) Y4)))))
% 6.51/6.86 (assert (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))))
% 6.51/6.86 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((Z2 tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z2) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 6.51/6.86 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.51/6.86 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.51/6.86 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.51/6.86 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.51/6.86 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.51/6.86 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A5) B4)) C))))))
% 6.51/6.86 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A5) B4)) C))))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A5) B4)) C))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A5) B4)) C))))))
% 6.51/6.86 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A5) B4)) C))))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) B4)) C))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A5) B4)) C))))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B4)) C))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.51/6.86 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M2)))))))
% 6.51/6.86 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N4) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N4))))
% 6.51/6.86 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_eq_nat X2) M2)))))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.51/6.86 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (assert (forall ((F (-> tptp.nat tptp.nat)) (U2 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)) U2)))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P6 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P6) (=> (@ (@ tptp.ord_less_nat M) P6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P6) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P6))))) (@ P M)))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.modulo_modulo_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M2) N2)) M2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y4) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y4) (@ _let_1 Q22))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.51/6.86 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))
% 6.51/6.86 (assert (forall ((A2 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B5) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B5) N))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (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))))))))))
% 6.51/6.86 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y4) N)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y4) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (assert (= tptp.modulo_modulo_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2)))))
% 6.51/6.86 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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))))))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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)))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (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))))))
% 6.51/6.86 (assert (forall ((A2 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B5) (=> (@ (@ 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 B5) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B5) N))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.86 (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)))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real Y4) Z2)) (@ (@ tptp.ord_less_real X) Y4)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat Y4) Z2)) (@ (@ tptp.ord_less_rat X) Y4)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z2)) (@ (@ tptp.times_times_int Y4) Z2)) (@ (@ tptp.ord_less_int X) Y4)))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 6.51/6.87 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (exists ((Y tptp.complex)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.complex)) (=> (@ P Y) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ Q X2) Y))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (exists ((Y tptp.complex)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.complex)) (=> (@ P Y) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ Q X2) Y))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (exists ((Y tptp.complex)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.complex)) (=> (@ P Y) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ Q X2) Y))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.list_nat tptp.real Bool))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (= (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (exists ((Y tptp.real)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.real)) (=> (@ P Y) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ Q X2) Y))))))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real)))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y4 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y4 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y4 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y4 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y4 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_real (@ X I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y4 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_real (@ X I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y4 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y4 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_real (@ X I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (Y4 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X I4)) (@ Y4 I4)) tptp.one_one_rat))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y4 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X I4)) (@ Y4 I4)) tptp.one_one_rat))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y4 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y4 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y4 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y4 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y4 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y4 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y4 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y4 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (Y4 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y4 I4)) tptp.zero_zero_rat))))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y4 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y4 I4)) tptp.zero_zero_rat))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ 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 W2))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A2 tptp.int) (B5 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B5) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B5) N))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.int) (B5 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B5) (=> (@ (@ 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 B5) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B5) N))))))
% 6.51/6.87 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.51/6.87 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (@ tptp.finite3207457112153483333omplex tptp.bot_bot_set_complex))
% 6.51/6.87 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 6.51/6.87 (assert (@ tptp.finite_finite_int tptp.bot_bot_set_int))
% 6.51/6.87 (assert (@ tptp.finite_finite_real tptp.bot_bot_set_real))
% 6.51/6.87 (assert (forall ((S3 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex S3)) (not (= S3 tptp.bot_bot_set_complex)))))
% 6.51/6.87 (assert (forall ((S3 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S3)) (not (= S3 tptp.bot_bot_set_nat)))))
% 6.51/6.87 (assert (forall ((S3 tptp.set_int)) (=> (not (@ tptp.finite_finite_int S3)) (not (= S3 tptp.bot_bot_set_int)))))
% 6.51/6.87 (assert (forall ((S3 tptp.set_real)) (=> (not (@ tptp.finite_finite_real S3)) (not (= S3 tptp.bot_bot_set_real)))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.complex)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.complex)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (F (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((X2 tptp.complex)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (F (-> tptp.real tptp.list_nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Uu2 tptp.list_nat)) (exists ((X2 tptp.real)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.complex Bool)) (F (-> tptp.real tptp.complex tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.real) (Y tptp.complex)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.complex Bool)) (F (-> tptp.real tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.real) (Y tptp.complex)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.complex Bool)) (F (-> tptp.real tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((X2 tptp.real) (Y tptp.complex)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.real Bool)) (F (-> tptp.nat tptp.real tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (=> (@ tptp.finite_finite_real (@ tptp.collect_real Q)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.nat) (Y tptp.real)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.51/6.87 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))))))
% 6.51/6.87 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.51/6.87 (assert (forall ((X1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y2 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger X1) X22) (@ (@ tptp.produc6137756002093451184nteger Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.51/6.87 (assert (forall ((X1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y2 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger X1) X22) (@ (@ tptp.produc8603105652947943368nteger Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.51/6.87 (assert (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X22) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.51/6.87 (assert (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X22) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B4 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B4)) (and (= A A5) (= B B4)))))
% 6.51/6.87 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A5) B4)) (and (= A A5) (= B B4)))))
% 6.51/6.87 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A5) B4)) (and (= A A5) (= B B4)))))
% 6.51/6.87 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A5) B4)) (and (= A A5) (= B B4)))))
% 6.51/6.87 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A5) B4)) (and (= A A5) (= B B4)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (not (= Y4 (@ (@ tptp.product_Pair_int_int A3) B2)))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc8763457246119570046nteger)) (not (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (not (= Y4 (@ (@ tptp.produc6137756002093451184nteger A3) B2)))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc1908205239877642774nteger)) (not (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (not (= Y4 (@ (@ tptp.produc8603105652947943368nteger A3) B2)))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc2285326912895808259nt_int)) (not (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (not (= Y4 (@ (@ tptp.produc5700946648718959541nt_int A3) B2)))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc7773217078559923341nt_int)) (not (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (not (= Y4 (@ (@ tptp.produc4305682042979456191nt_int A3) B2)))))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y3 tptp.int)) (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc8763457246119570046nteger)) (exists ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (= P6 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc1908205239877642774nteger)) (exists ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (= P6 (@ (@ tptp.produc8603105652947943368nteger X3) Y3)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc2285326912895808259nt_int)) (exists ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P6 (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc7773217078559923341nt_int)) (exists ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P6 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)))))
% 6.51/6.87 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P6 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B2))) (@ P P6))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (P6 tptp.produc8763457246119570046nteger)) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc6137756002093451184nteger A3) B2))) (@ P P6))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (P6 tptp.produc1908205239877642774nteger)) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc8603105652947943368nteger A3) B2))) (@ P P6))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (P6 tptp.produc2285326912895808259nt_int)) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A3) B2))) (@ P P6))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (P6 tptp.produc7773217078559923341nt_int)) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A3) B2))) (@ P P6))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B4)) (not (=> (= A A5) (not (= B B4)))))))
% 6.51/6.87 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A5) B4)) (not (=> (= A A5) (not (= B B4)))))))
% 6.51/6.87 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A5) B4)) (not (=> (= A A5) (not (= B B4)))))))
% 6.51/6.87 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A5) B4)) (not (=> (= A A5) (not (= B B4)))))))
% 6.51/6.87 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A5) B4)) (not (=> (= A A5) (not (= B B4)))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc8763457246119570046nteger)) (not (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (not (= Y4 (@ (@ tptp.produc6137756002093451184nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3))))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc1908205239877642774nteger)) (not (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (not (= Y4 (@ (@ tptp.produc8603105652947943368nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3))))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc2285326912895808259nt_int)) (not (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (not (= Y4 (@ (@ tptp.produc5700946648718959541nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3))))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.produc7773217078559923341nt_int)) (not (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (not (= Y4 (@ (@ tptp.produc4305682042979456191nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (X tptp.produc8763457246119570046nteger)) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (@ P (@ (@ tptp.produc6137756002093451184nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3)))) (@ P X))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (X tptp.produc1908205239877642774nteger)) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (@ P (@ (@ tptp.produc8603105652947943368nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3)))) (@ P X))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X tptp.produc2285326912895808259nt_int)) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3)))) (@ P X))))
% 6.51/6.87 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X tptp.produc7773217078559923341nt_int)) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3)))) (@ P X))))
% 6.51/6.87 (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))))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M4) N3)) (@ (@ P M4) N3)))) (@ (@ P M) N)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.51/6.87 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.51/6.87 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.51/6.87 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.51/6.87 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 6.51/6.87 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 6.51/6.87 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)))
% 6.51/6.87 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 6.51/6.87 (assert (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X) X)))
% 6.51/6.87 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 6.51/6.87 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 6.51/6.87 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)))
% 6.51/6.87 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 6.51/6.87 (assert (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) tptp.bot_bo4199563552545308370d_enat) X)))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ (@ tptp.nth_nat Xs2) I2)) Xs2)))
% 6.51/6.87 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I2) (@ (@ tptp.nth_int Xs2) I2)) Xs2)))
% 6.51/6.87 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) Xs2)))
% 6.51/6.87 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.51/6.87 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.51/6.87 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.51/6.87 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.51/6.87 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.51/6.87 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B3)) B3) A4))))
% 6.51/6.87 (assert (forall ((Y4 tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y4) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4) X))))
% 6.51/6.87 (assert (forall ((Y4 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X) (= (@ (@ tptp.ord_max_set_nat X) Y4) X))))
% 6.51/6.87 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (= (@ (@ tptp.ord_max_rat X) Y4) X))))
% 6.51/6.87 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (= (@ (@ tptp.ord_max_num X) Y4) X))))
% 6.51/6.87 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (= (@ (@ tptp.ord_max_nat X) Y4) X))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (= (@ (@ tptp.ord_max_int X) Y4) X))))
% 6.51/6.87 (assert (forall ((X tptp.extended_enat) (Y4 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y4) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (= (@ (@ tptp.ord_max_set_nat X) Y4) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (= (@ (@ tptp.ord_max_rat X) Y4) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (= (@ (@ tptp.ord_max_num X) Y4) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (= (@ (@ tptp.ord_max_nat X) Y4) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (= (@ (@ tptp.ord_max_int X) Y4) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y4) Z2)) (@ (@ tptp.ord_max_real (@ _let_1 Y4)) (@ _let_1 Z2))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y4) Z2)) (@ (@ tptp.ord_max_rat (@ _let_1 Y4)) (@ _let_1 Z2))))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y4) Z2)) (@ (@ tptp.ord_max_nat (@ _let_1 Y4)) (@ _let_1 Z2))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y4) Z2)) (@ (@ tptp.ord_max_int (@ _let_1 Y4)) (@ _let_1 Z2))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y4)) Z2) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z2)) (@ (@ tptp.plus_plus_real Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y4)) Z2) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z2)) (@ (@ tptp.plus_plus_rat Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y4)) Z2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z2)) (@ (@ tptp.plus_plus_nat Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y4)) Z2) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z2)) (@ (@ tptp.plus_plus_int Y4) Z2)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B3)) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B3)) B3) A4))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.51/6.87 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 6.51/6.87 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (forall ((X tptp.product_prod_int_int)) (not (forall ((D3 tptp.int) (I3 tptp.int)) (not (= X (@ (@ tptp.product_Pair_int_int D3) I3)))))))
% 6.51/6.87 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F2 (-> tptp.int tptp.option6357759511663192854e_term)) (D3 tptp.int) (I3 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F2) (@ (@ tptp.product_Pair_int_int D3) I3))))))))
% 6.51/6.87 (assert (forall ((X tptp.produc2285326912895808259nt_int)) (not (forall ((F2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D3 tptp.int) (I3 tptp.int)) (not (= X (@ (@ tptp.produc5700946648718959541nt_int F2) (@ (@ tptp.product_Pair_int_int D3) I3))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y4) (=> (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 (= Y4 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_4) (and (=> _let_3 (= Y4 (@ _let_1 true))) (=> (not _let_3) (= Y4 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S))) (=> (= X _let_1) (not (= Y4 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S))) (=> (= X _let_1) (not (= Y4 _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 (= Y4 (@ (@ (@ (@ 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 (= Y4 (@ (@ (@ 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))))))))))))))))))))
% 6.51/6.87 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y4) (=> (@ (@ 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 (= Y4 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_4) (and (=> _let_3 (= Y4 (@ _let_1 true))) (=> (not _let_3) (= Y4 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S))) (=> (= X _let_1) (=> (= Y4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S))) (=> (= X _let_1) (=> (= Y4 _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) (=> (= Y4 (@ (@ (@ (@ 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) (=> (= Y4 (@ (@ (@ 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))))))))))))))))))))))
% 6.51/6.87 (assert (forall ((X tptp.extended_enat) (Y4 tptp.extended_enat) (Z2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4)) Z2) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z2) (@ (@ tptp.ord_le72135733267957522d_enat Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y4)) Z2) (and (@ (@ tptp.ord_less_real X) Z2) (@ (@ tptp.ord_less_real Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y4)) Z2) (and (@ (@ tptp.ord_less_rat X) Z2) (@ (@ tptp.ord_less_rat Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y4)) Z2) (and (@ (@ tptp.ord_less_num X) Z2) (@ (@ tptp.ord_less_num Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y4)) Z2) (and (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_nat Y4) Z2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y4)) Z2) (and (@ (@ tptp.ord_less_int X) Z2) (@ (@ tptp.ord_less_int Y4) Z2)))))
% 6.51/6.87 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.51/6.87 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.51/6.87 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.51/6.87 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.51/6.87 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M4 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M4)))))))
% 6.51/6.87 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.51/6.87 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.51/6.87 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.ord_max_rat A4) B3)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B3)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B3)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B3)))))
% 6.51/6.87 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.51/6.87 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.51/6.87 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.51/6.87 (assert (forall ((Z2 tptp.extended_enat) (X tptp.extended_enat) (Y4 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z2))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.num) (X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) A4))))
% 6.51/6.87 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) B3))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) B3))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) B3))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B3) B3))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) B3))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.extended_enat) (X tptp.extended_enat) (Y4 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z2))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.num) (X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z2))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y4)) (or (@ _let_1 X) (@ _let_1 Y4))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B3)) (not (= A4 B3))))))
% 6.51/6.87 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B3)) (not (= A4 B3))))))
% 6.51/6.87 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B3)) (not (= A4 B3))))))
% 6.51/6.87 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B3)) (not (= A4 B3))))))
% 6.51/6.87 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B3)) (not (= A4 B3))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X7 tptp.set_real)) (=> (not (= X7 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X7) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X7) (@ (@ tptp.ord_less_real X3) Xa))))) (not (@ tptp.finite_finite_real X7))))))
% 6.51/6.87 (assert (forall ((X7 tptp.set_rat)) (=> (not (= X7 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X7) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X7) (@ (@ tptp.ord_less_rat X3) Xa))))) (not (@ tptp.finite_finite_rat X7))))))
% 6.51/6.87 (assert (forall ((X7 tptp.set_num)) (=> (not (= X7 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X7) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X7) (@ (@ tptp.ord_less_num X3) Xa))))) (not (@ tptp.finite_finite_num X7))))))
% 6.51/6.87 (assert (forall ((X7 tptp.set_nat)) (=> (not (= X7 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X7) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X7) (@ (@ tptp.ord_less_nat X3) Xa))))) (not (@ tptp.finite_finite_nat X7))))))
% 6.51/6.87 (assert (forall ((X7 tptp.set_int)) (=> (not (= X7 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X7) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X7) (@ (@ tptp.ord_less_int X3) Xa))))) (not (@ tptp.finite_finite_int X7))))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B6 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B6) C4)) (@ (@ tptp.dvd_dvd_nat B6) B) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B6 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B6) C4)) (@ (@ tptp.dvd_dvd_int B6) B) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 6.51/6.87 (assert (forall ((P6 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P6) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.51/6.87 (assert (forall ((P6 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P6) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B3) K3))))))
% 6.51/6.87 (assert (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (exists ((K3 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B3) K3))))))
% 6.51/6.87 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K3))))))
% 6.51/6.87 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K3))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.51/6.87 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.51/6.87 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.51/6.87 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.51/6.87 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y4) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y4) N)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y4) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y4) N)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y4) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) N)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y4) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) N)))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y4) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) N)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.51/6.87 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.51/6.87 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.51/6.87 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z 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 Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z 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 Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z 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 Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z 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 Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z 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 Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z 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 Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2)))) (=> (@ (@ tptp.ord_less_real Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2)))) (=> (@ (@ tptp.ord_less_rat Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2)))) (=> (@ (@ tptp.ord_less_nat Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2)))) (=> (@ (@ tptp.ord_less_int Z) X5) (= _let_1 _let_1)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y4) M))))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y4) M))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) M))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) M))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) M))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D))) (exists ((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)))))))))))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.51/6.87 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.51/6.87 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.51/6.87 (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)))))))))))))))
% 6.51/6.87 (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)))))))))))))))
% 6.51/6.87 (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)))))))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.51/6.87 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.51/6.87 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (= (lambda ((Y6 tptp.code_integer) (Z3 tptp.code_integer)) (= Y6 Z3)) (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))))))))
% 6.51/6.87 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (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))))))))
% 6.51/6.87 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (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))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y4) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y4)) (= X Y4)))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (D4 tptp.int) (B5 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) B5) (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)))))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (D4 tptp.int) (B5 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) B5) (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y4 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((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 (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.set_real) (Y4 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y4) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y4))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 6.51/6.87 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 6.51/6.87 (assert (forall ((B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B)) B)))
% 6.51/6.87 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 6.51/6.87 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 6.51/6.87 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y4)) (@ (@ tptp.ord_less_eq_set_nat Y4) X))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.51/6.87 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.51/6.87 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.51/6.87 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.51/6.87 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.51/6.87 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)))
% 6.51/6.87 (assert (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)))
% 6.51/6.87 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)))
% 6.51/6.87 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.51/6.87 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.51/6.87 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.51/6.87 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real Z2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int Z2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex Z2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat Z2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z2) (@ tptp.uminus_uminus_real Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z2) (@ tptp.uminus_uminus_int Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z2) (@ tptp.uminus1482373934393186551omplex Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z2) (@ tptp.uminus_uminus_rat Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z2) (@ tptp.uminus1351360451143612070nteger Z2))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.51/6.87 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups2073611262835488442omplex G) tptp.bot_bot_set_nat) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups3049146728041665814omplex G) tptp.bot_bot_set_int) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups8778361861064173332t_real G) tptp.bot_bot_set_int) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) tptp.bot_bot_set_int) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 6.51/6.87 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G) tptp.bot_bot_set_real) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G) tptp.bot_bot_set_real) tptp.zero_zero_rat)))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.51/6.87 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.51/6.87 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((X tptp.product_prod_nat_nat) (N tptp.nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y4 tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.51/6.87 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U2))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U2)))) (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)))))))))
% 6.51/6.87 (assert (forall ((U2 tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U2)))) (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y4)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y4)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y4)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y4)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W2)))) Y4))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y4)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W2))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y4)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y4)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W2))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y4)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y4)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y4)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y4)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y4)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Y4)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Y4)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) Y4)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Y4)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W2)) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2)))) Y4))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ 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)))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ 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)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.51/6.87 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((P6 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P6))) P6)))
% 6.51/6.87 (assert (forall ((P6 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P6))) P6)))
% 6.51/6.87 (assert (forall ((P6 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P6))) P6)))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.51/6.87 (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)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.51/6.87 (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))
% 6.51/6.87 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.51/6.87 (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))
% 6.51/6.87 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y4)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y4))))
% 6.51/6.87 (assert (forall ((Y4 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y4)) (@ tptp.uminus5710092332889474511et_nat X)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.51/6.87 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.51/6.87 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.51/6.87 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.51/6.87 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.51/6.87 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.51/6.87 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B5 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B5)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I4)) (@ G J3)))) B5))) A2))))
% 6.51/6.87 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B5 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B5)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I4)) (@ G J3)))) B5))) A2))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I4)) (@ G J3)))) B5))) A2))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ G J3)))) B5))) A2))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I2) (@ G I2))))))))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.51/6.87 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P6)) (not (or (and P6 (not (@ P tptp.one_one_complex))) (and (not P6) (not (@ P tptp.zero_zero_complex))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P6)) (not (or (and P6 (not (@ P tptp.one_one_real))) (and (not P6) (not (@ P tptp.zero_zero_real))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.rat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P6)) (not (or (and P6 (not (@ P tptp.one_one_rat))) (and (not P6) (not (@ P tptp.zero_zero_rat))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.nat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P6)) (not (or (and P6 (not (@ P tptp.one_one_nat))) (and (not P6) (not (@ P tptp.zero_zero_nat))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.int Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P6)) (not (or (and P6 (not (@ P tptp.one_one_int))) (and (not P6) (not (@ P tptp.zero_zero_int))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.code_integer Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P6)) (not (or (and P6 (not (@ P tptp.one_one_Code_integer))) (and (not P6) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.complex Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P6)) (and (=> P6 (@ P tptp.one_one_complex)) (=> (not P6) (@ P tptp.zero_zero_complex))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.real Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P6)) (and (=> P6 (@ P tptp.one_one_real)) (=> (not P6) (@ P tptp.zero_zero_real))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.rat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P6)) (and (=> P6 (@ P tptp.one_one_rat)) (=> (not P6) (@ P tptp.zero_zero_rat))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.nat Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P6)) (and (=> P6 (@ P tptp.one_one_nat)) (=> (not P6) (@ P tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.int Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P6)) (and (=> P6 (@ P tptp.one_one_int)) (=> (not P6) (@ P tptp.zero_zero_int))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.code_integer Bool)) (P6 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P6)) (and (=> P6 (@ P tptp.one_one_Code_integer)) (=> (not P6) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.51/6.87 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P4 Bool)) (@ (@ (@ tptp.if_complex P4) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.51/6.87 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P4 Bool)) (@ (@ (@ tptp.if_real P4) tptp.one_one_real) tptp.zero_zero_real))))
% 6.51/6.87 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_rat P4) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.51/6.87 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_nat P4) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.51/6.87 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P4 Bool)) (@ (@ (@ tptp.if_int P4) tptp.one_one_int) tptp.zero_zero_int))))
% 6.51/6.87 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Code_integer P4) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.51/6.87 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.51/6.87 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.51/6.87 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.51/6.87 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.51/6.87 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.51/6.87 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.51/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.51/6.87 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W2))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((B5 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B5 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.51/6.87 (assert (forall ((B5 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B5 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.51/6.87 (assert (forall ((B5 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B5 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.51/6.87 (assert (forall ((B5 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B5 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.51/6.87 (assert (forall ((B5 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B5 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.51/6.87 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.51/6.87 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.51/6.87 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.51/6.87 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.51/6.87 (assert (forall ((U2 tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U2) U2))) (@ (@ tptp.times_times_real X) X))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex 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.complex)) (=> (@ (@ tptp.member_complex 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.groups5058264527183730370ex_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex 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.complex)) (=> (@ (@ tptp.member_complex 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.groups5058264527183730370ex_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ 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_nat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) S2)) (@ (@ tptp.groups5693394587270226106ex_nat G) T))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ 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_int (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) S2)) (@ (@ tptp.groups3539618377306564664at_int G) T))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ 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_int (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) S2)) (@ (@ tptp.groups5690904116761175830ex_int G) T))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) S2)) (@ (@ tptp.groups3539618377306564664at_int G) T))))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ 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_int (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) S2)) (@ (@ tptp.groups5690904116761175830ex_int G) T))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2)))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex 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.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5690904116761175830ex_int H2) S3)) (@ (@ tptp.groups5690904116761175830ex_int G) S3))))))))
% 6.51/6.87 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.int)) (G (-> tptp.int 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_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups4538972089207619220nt_int H2) S3)) (@ (@ tptp.groups4538972089207619220nt_int G) S3))))))))
% 6.51/6.87 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex 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.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups7754918857620584856omplex H2) S3)) (@ (@ tptp.groups7754918857620584856omplex G) S3))))))))
% 6.51/6.87 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat 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_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3542108847815614940at_nat H2) S3)) (@ (@ tptp.groups3542108847815614940at_nat G) S3))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.51/6.87 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.51/6.87 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.51/6.87 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.51/6.87 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.51/6.87 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.87 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.51/6.87 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (B5 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (B5 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B5 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B5 tptp.rat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (B5 tptp.rat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B5 tptp.rat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B5) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B5 tptp.rat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (B5 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (B5 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B5 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B5)))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y4) (@ tptp.uminus_uminus_real X)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.uminus_uminus_real X)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y4))))
% 6.51/6.87 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y4))))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((B tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((B tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z2))) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y4) Z2))) Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z2))) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y4) Z2))) Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z2))) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y4) Z2))) Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z2))) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y4) Z2))) Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z2))) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y4) Z2))) Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z2))) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y4) Z2))) Z2)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus_uminus_real Y4)))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus_uminus_int Y4)))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus1482373934393186551omplex Y4)))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus_uminus_rat Y4)))))))
% 6.51/6.87 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus1351360451143612070nteger Y4)))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.int) (B5 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B5) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.51/6.87 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B5) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B5) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B5) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B5) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B5) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B5) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B5))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((B tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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)))))))))))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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)))))))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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)))))))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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)))))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((U2 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 U2) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B5 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 B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B5))))))))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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)))))))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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)))))))))))))
% 6.51/6.87 (assert (forall ((B tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (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))))))))))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.51/6.87 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Y4 tptp.real) (X tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W2))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y4)) (@ _let_1 Z2)) (@ (@ tptp.plus_plus_real (@ _let_2 Z2)) (@ _let_1 Y4))) (or (= W2 X) (= Y4 Z2)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.rat) (Y4 tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W2))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y4)) (@ _let_1 Z2)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z2)) (@ _let_1 Y4))) (or (= W2 X) (= Y4 Z2)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.nat) (Y4 tptp.nat) (X tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) (@ _let_1 Z2)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z2)) (@ _let_1 Y4))) (or (= W2 X) (= Y4 Z2)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Y4 tptp.int) (X tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y4)) (@ _let_1 Z2)) (@ (@ tptp.plus_plus_int (@ _let_2 Z2)) (@ _let_1 Y4))) (or (= W2 X) (= Y4 Z2)))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))))))))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y4 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y4) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((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 (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.51/6.87 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.51/6.87 (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 ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W2)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) tptp.zero_zero_complex))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) tptp.zero_zero_rat))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) tptp.zero_zero_real))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (=> (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (=> (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (=> (@ (@ 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))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (=> (@ (@ 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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A2) tptp.zero_zero_complex))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A2) tptp.zero_zero_rat))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A2) tptp.zero_zero_real))))))
% 6.51/6.87 (assert (forall ((V tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ 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 W2)))) tptp.one_one_int))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.51/6.87 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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 ((M4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N3))))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N3))))) (not (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N3))))))))))))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.num)) (=> (not (= Y4 tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y4 (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y4 (@ tptp.bit1 X33)))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (U2 tptp.real) (V tptp.real)) (=> (= X Y4) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U2)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U2)) Y4))) V)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y4)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y4) X))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y4)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y4) X))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y4)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y4) X))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y4)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y4) X))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.51/6.87 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.51/6.87 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y4) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y4) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.51/6.87 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.51/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.51/6.87 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A2) (=> (not (= X2 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.51/6.87 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A2) (=> (not (= X2 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z2) _let_2)) _let_2))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z2) _let_2)) _let_2))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z2) _let_2)) _let_2))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z2) _let_2)) _let_2))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z2) _let_2)) _let_2))))))
% 6.51/6.87 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))) tptp.zero_zero_complex))))
% 6.51/6.87 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) (@ tptp.abs_abs_Code_integer Y4)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) (@ tptp.abs_abs_rat Y4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((Y4 tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y4) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y4))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y4))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y4))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y4))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I4 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I4 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_real (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_real (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ (@ tptp.times_times_real (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z2 tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y4) Z2)) (= Y4 (@ (@ tptp.plus_plus_real X) Z2)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z2)) tptp.one_one_int) (= Z2 tptp.zero_zero_int))))
% 6.51/6.87 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.51/6.87 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.51/6.87 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.51/6.87 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.51/6.87 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.87 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.51/6.87 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.51/6.87 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.51/6.87 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.51/6.87 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.51/6.87 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_nat I3) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K)))))))))
% 6.51/6.87 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.51/6.87 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.51/6.87 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.51/6.87 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((D tptp.int) (Z2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z2) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z2))) tptp.one_one_int)) D))))))
% 6.51/6.87 (assert (forall ((D tptp.int) (X tptp.int) (Z2 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 Z2))) tptp.one_one_int)) D))) Z2)))))
% 6.51/6.87 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 6.51/6.87 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y4)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y4)))))))))
% 6.51/6.87 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M2) (@ tptp.bit0 N2)))))))
% 6.51/6.87 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M2) (@ tptp.bit0 N2)))))))
% 6.51/6.87 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M2) (@ tptp.bit0 N2)))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.51/6.87 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.51/6.87 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int W2) Z2))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int W2) Z2))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z2)) (@ (@ tptp.ord_less_eq_int W2) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z2) (@ tptp.numera6690914467698888265omplex N)) (= Z2 (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z2) (@ tptp.numeral_numeral_real N)) (= Z2 (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z2) (@ tptp.numeral_numeral_rat N)) (= Z2 (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z2) _let_1) (= Z2 _let_1)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int W2) Z2))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int W2) Z2))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z2)) (@ (@ tptp.ord_less_int W2) Z2))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W2)) (= X (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (= X (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (= X (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (= X (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (= X (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W2) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2) (@ tptp.semiri681578069525770553at_rat X)) (= (@ (@ tptp.power_power_nat B) W2) X))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z2) tptp.one_one_complex) (= Z2 tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z2) tptp.one_one_int) (= Z2 tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z2) tptp.one_one_real) (= Z2 tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z2) tptp.one_one_rat) (= Z2 tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W2) Z2)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W2) Z2)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W2) Z2)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W2) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W2) Z2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W2) Z2)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (= X (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (= X (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (= X (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W2)) (= X (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2) (@ tptp.ring_1_of_int_rat X)) (= (@ (@ tptp.power_power_int B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W2) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W2) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W2) X))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z2)) N))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z2)) N))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z2)) N))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z2)) N))))
% 6.51/6.87 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.51/6.87 (assert (forall ((N tptp.nat) (W2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W2)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W2)) N))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.semiri8010041392384452111omplex Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) (@ tptp.semiri1314217659103216013at_int Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.semiri5074537144036343181t_real Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y4)) (= _let_1 Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.semiri681578069525770553at_rat Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.51/6.87 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y4) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y4) _let_1) (= Y4 _let_1)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) _let_1) (@ (@ tptp.ord_less_eq_int Z2) _let_1)))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.51/6.87 (assert (forall ((N tptp.num) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) _let_1) (@ (@ tptp.ord_less_int Z2) _let_1)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z2) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z2) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z2) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 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)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 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)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 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)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.ring_17405671764205052669omplex Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.ring_1_of_int_real Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.ring_1_of_int_rat Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y4) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= (@ tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.51/6.87 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N) (@ tptp.ring_1_of_int_real Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N) (@ tptp.ring_17405671764205052669omplex Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N) (@ tptp.ring_1_of_int_rat Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N) (@ tptp.ring_18347121197199848620nteger Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y4) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= (@ tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y4) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ (@ tptp.times_times_real Y4) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ (@ tptp.times_times_rat Y4) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ (@ tptp.times_times_int Y4) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ (@ tptp.times_times_int Y4) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ (@ tptp.times_times_real Y4) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y4) (@ (@ tptp.times_times_nat Y4) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ (@ tptp.times_times_rat Y4) _let_1)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)) (Z2 tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z2)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z2 tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z2)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z2 tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z2)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z2 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z2 tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z2)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z2 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z2 tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z2)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z2 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.51/6.87 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.51/6.87 (assert (forall ((P (-> tptp.int Bool)) (Z2 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 Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z2 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (N tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z2))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z4 tptp.int)) (exists ((N2 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y5 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y5) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X)))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.51/6.87 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z4 tptp.int)) (exists ((N2 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M2)) tptp.one_one_real)))))
% 6.51/6.87 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M2 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 M2)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M2)))))
% 6.51/6.87 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.51/6.87 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.51/6.87 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.51/6.87 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.51/6.87 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y4 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y4))) (and (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y4)))) (=> (@ (@ tptp.ord_less_nat X) Y4) (@ P tptp.zero_zero_int))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I4)) 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))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) 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))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) 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))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) 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))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I4)) 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))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) 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))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) 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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)))))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (exists ((Z tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)))))))
% 6.51/6.87 (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 ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 6.51/6.87 (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 ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((H2 tptp.real) (Z2 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 Z2))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z2) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z2)) 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)))))))))))))
% 6.51/6.87 (assert (forall ((H2 tptp.complex) (Z2 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 Z2))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z2) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) 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))))))))))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc8763457246119570046nteger) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc127349428274296955eger_o C) P6))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc1908205239877642774nteger) (C (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc8603105652947943368nteger A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc6253627499356882019eger_o C) P6))))
% 6.51/6.87 (assert (forall ((P6 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)) (=> (= P6 (@ (@ tptp.produc5700946648718959541nt_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc1573362020775583542_int_o C) P6))))
% 6.51/6.87 (assert (forall ((P6 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)) (=> (= P6 (@ (@ tptp.produc4305682042979456191nt_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc2558449545302689196_int_o C) P6))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc4947309494688390418_int_o C) P6))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int) (Z2 tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_nat Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z2) (@ (@ tptp.produc4251311855443802252et_nat C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int) (Z2 tptp.int) (C (-> tptp.int tptp.int tptp.set_int))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_int Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z2) (@ (@ tptp.produc73460835934605544et_int C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int) (Z2 tptp.real) (C (-> tptp.int tptp.int tptp.set_real))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_real Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z2) (@ (@ tptp.produc6452406959799940328t_real C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int) (Z2 tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_complex Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z2) (@ (@ tptp.produc8580519160106071146omplex C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.product_prod_int_int) (Z2 tptp.product_prod_nat_nat) (C (-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member8440522571783428010at_nat Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member8440522571783428010at_nat Z2) (@ (@ tptp.produc1656060378719767003at_nat C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc8763457246119570046nteger) (Z2 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)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_nat Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z2) (@ (@ tptp.produc3558942015123893603et_nat C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc8763457246119570046nteger) (Z2 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)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_int Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z2) (@ (@ tptp.produc8604463032469472703et_int C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc8763457246119570046nteger) (Z2 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)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_real Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z2) (@ (@ tptp.produc815715089573277247t_real C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc8763457246119570046nteger) (Z2 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)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_complex Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z2) (@ (@ tptp.produc2592262431452330817omplex C) P6)))))
% 6.51/6.87 (assert (forall ((P6 tptp.produc7773217078559923341nt_int) (Z2 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)) (=> (= P6 (@ (@ tptp.produc4305682042979456191nt_int A3) B2)) (@ (@ tptp.member_nat Z2) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z2) (@ (@ tptp.produc8289552606927098482et_nat C) P6)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_nat Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4251311855443802252et_nat C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (C (-> tptp.int tptp.int tptp.set_int)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc73460835934605544et_int C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_real Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6452406959799940328t_real C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_complex Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8580519160106071146omplex C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 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 Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1656060378719767003at_nat C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 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 Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc3558942015123893603et_nat C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 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 Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8604463032469472703et_int C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 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 Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc815715089573277247t_real C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 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 Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2592262431452330817omplex C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.51/6.87 (assert (forall ((Z2 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 Z2))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8289552606927098482et_nat C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.51/6.87 (assert (forall ((P6 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) P6) (@ (@ (@ C A3) B2) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P6) X))))
% 6.51/6.87 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A4) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.51/6.87 (assert (forall ((P Bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P) A) B)))) (and (=> P (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri1314217659103216013at_int B)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_nat Z2) (@ (@ tptp.produc4251311855443802252et_nat C) P6)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_nat Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (C (-> tptp.int tptp.int tptp.set_int)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_int Z2) (@ (@ tptp.produc73460835934605544et_int C) P6)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_int Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_real Z2) (@ (@ tptp.produc6452406959799940328t_real C) P6)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_real Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_complex Z2) (@ (@ tptp.produc8580519160106071146omplex C) P6)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_complex Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.product_prod_nat_nat) (C (-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.member8440522571783428010at_nat Z2) (@ (@ tptp.produc1656060378719767003at_nat C) P6)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member8440522571783428010at_nat Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat)) (P6 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_nat Z2) (@ (@ tptp.produc3558942015123893603et_nat C) P6)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_nat Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int)) (P6 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_int Z2) (@ (@ tptp.produc8604463032469472703et_int C) P6)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_int Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real)) (P6 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_real Z2) (@ (@ tptp.produc815715089573277247t_real C) P6)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_real Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex)) (P6 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_complex Z2) (@ (@ tptp.produc2592262431452330817omplex C) P6)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_complex Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat)) (P6 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_nat Z2) (@ (@ tptp.produc8289552606927098482et_nat C) P6)) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P6 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ tptp.member_nat Z2) (@ (@ C X3) Y3)))))))))
% 6.51/6.87 (assert (forall ((C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (P6 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.produc127349428274296955eger_o C) P6) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.51/6.87 (assert (forall ((C (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (P6 tptp.produc1908205239877642774nteger)) (=> (@ (@ tptp.produc6253627499356882019eger_o C) P6) (not (forall ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P6 (@ (@ tptp.produc8603105652947943368nteger X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.51/6.87 (assert (forall ((C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P6 tptp.produc2285326912895808259nt_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o C) P6) (not (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P6 (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.51/6.87 (assert (forall ((C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P6 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o C) P6) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P6 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.51/6.87 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P6 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P6) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P6 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P6 tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P6) Z2) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P6 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ (@ C X3) Y3) Z2))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))))
% 6.51/6.87 (assert (forall ((X tptp.rat)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X))))))
% 6.51/6.87 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (W2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W2))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.51/6.87 (assert (forall ((W2 tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.51/6.87 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.51/6.87 (assert (forall ((A tptp.complex) (W2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W2))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W2)))))
% 6.51/6.87 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.51/6.87 (assert (forall ((W2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) (@ tptp.numeral_numeral_real W2))))
% 6.51/6.87 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((W2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W2)) (@ tptp.numeral_numeral_real W2))))
% 6.51/6.87 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y4)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y4)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (N tptp.nat) (Z2 tptp.real)) (=> (= (@ (@ tptp.power_power_real W2) N) (@ (@ tptp.power_power_real Z2) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W2) (@ tptp.real_V7735802525324610683m_real Z2))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (N tptp.nat) (Z2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W2) N) (@ (@ tptp.power_power_complex Z2) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W2) (@ tptp.real_V1022390504157884413omplex Z2))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (R2 tptp.real) (Y4 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y4 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y4))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y4))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4))) E))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4))) E))))
% 6.51/6.87 (assert (forall ((X tptp.real) (R2 tptp.real) (Y4 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y4 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4))) E))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4))) E))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (E1 tptp.real) (Z2 tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y4) Z2))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z2))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E1 tptp.real) (Z2 tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y4) Z2))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z2))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y4))) E))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y4))) E))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real) (E1 tptp.real) (Z2 tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y4) Z2))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z2))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E1 tptp.real) (Z2 tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y4) Z2))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z2))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y4)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y4))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y4)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y4))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W2) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W2) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (W2 tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z2) M)) (@ (@ tptp.power_power_real W2) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z2) W2))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (W2 tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z2) M)) (@ (@ tptp.power_power_complex W2) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z2) W2))))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M2)))) (@ (@ (@ 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))))))))
% 6.51/6.87 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M2)))) (@ (@ (@ 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))))))))
% 6.51/6.87 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M2)))) (@ (@ (@ 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))))))))
% 6.51/6.87 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M2)))) (@ (@ (@ 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))))))))
% 6.51/6.87 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M2)))) (@ (@ (@ 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))))))))
% 6.51/6.87 (assert (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M2) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M2)) (@ (@ 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 M2) N2)) N2))))))
% 6.51/6.87 (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))))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y4))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y4)))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y4))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y4)))))))
% 6.51/6.87 (assert (forall ((H2 tptp.complex) (Z2 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 Z2))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z2) 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 ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z2) H2)) Q4)) (@ (@ tptp.power_power_complex Z2) (@ (@ 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))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.51/6.87 (assert (forall ((H2 tptp.rat) (Z2 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 Z2))) (=> (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 Z2) 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 ((P4 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z2) H2)) Q4)) (@ (@ tptp.power_power_rat Z2) (@ (@ 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))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.51/6.87 (assert (forall ((H2 tptp.real) (Z2 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 Z2))) (=> (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 Z2) 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 ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z2) H2)) Q4)) (@ (@ tptp.power_power_real Z2) (@ (@ 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))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.51/6.87 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I2) K))))
% 6.51/6.87 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.51/6.87 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.51/6.87 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.51/6.87 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X)) (@ tptp.set_ord_lessThan_rat Y4)) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y4)) (@ (@ tptp.ord_less_eq_num X) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y4)) (@ (@ tptp.ord_less_eq_int X) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.51/6.87 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.51/6.87 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.51/6.87 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X) tptp.bot_bot_set_real))))
% 6.51/6.87 (assert (= tptp.set_ord_lessThan_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U3))))))
% 6.51/6.87 (assert (= tptp.set_ord_lessThan_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U3))))))
% 6.51/6.87 (assert (= tptp.set_ord_lessThan_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U3))))))
% 6.51/6.87 (assert (= tptp.set_ord_lessThan_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U3))))))
% 6.51/6.87 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U3 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U3))))))
% 6.51/6.87 (assert (forall ((N tptp.extended_enat)) (= (= (@ tptp.set_or8419480210114673929d_enat N) tptp.bot_bo7653980558646680370d_enat) (= N tptp.bot_bo4199563552545308370d_enat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y4)))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) R2))) _let_1)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) R2))) _let_1)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) R2))) _let_1)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z2))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z2))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z2))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z2))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z2) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_complex Z2))) (@ (@ tptp.times_times_complex (@ _let_2 P4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z2) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z2))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z2) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_rat Z2))) (@ (@ tptp.times_times_rat (@ _let_2 P4)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z2) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z2) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_int Z2))) (@ (@ tptp.times_times_int (@ _let_2 P4)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z2) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z2))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z2) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_real Z2))) (@ (@ tptp.times_times_real (@ _let_2 P4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z2) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y4) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P4)) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (N tptp.nat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P4)) (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P4)) (@ (@ tptp.power_power_int Y4) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P4)) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.51/6.87 (assert (forall ((X tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_complex X) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (assert (forall ((X tptp.rat) (N tptp.nat) (Y4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y4) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_rat X) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_int X) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_real X) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M2) N2)) (@ (@ tptp.modulo_modulo_nat M2) N2)))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M2)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z2)) 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 Z2) N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z2)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z2) N2)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ tptp.summable_real F))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.51/6.87 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.51/6.87 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z2 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 Z2)) (@ 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 Z2) N2)))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z2 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 Z2)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2)))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F I3) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.51/6.87 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F I3) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z2) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z2) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z2) N2)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z2) N2)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z2 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_complex Z2) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z2 tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_real Z2) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4))))))))
% 6.51/6.87 (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 ((I4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I4))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (Z2 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 Z2) N2)))) (@ (@ tptp.power_power_complex Z2) M))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (Z2 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 Z2) N2)))) (@ (@ tptp.power_power_real Z2) M))))
% 6.51/6.87 (assert (forall ((M tptp.nat) (Z2 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 Z2) N2)))) (@ (@ tptp.power_power_int Z2) M))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S2))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (S3 tptp.real) (A2 tptp.set_nat) (S4 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S4 (@ (@ 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)))) S4))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z2 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 Z2)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z2 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 Z2)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) 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 Z2) N2))))) Z2))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) 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 Z2) N2))))) Z2))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z2) N2))))) Z2) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z2) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z2) N2))))) Z2) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z2) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.51/6.87 (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 ((N8 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M3) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M3) N9)))) E)))))))))))
% 6.51/6.87 (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 ((N8 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M3) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M3) N9)))) E)))))))))))
% 6.51/6.87 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N9)))))) R2))))))))
% 6.51/6.87 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N9)))))) R2))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ tptp.summable_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z2) I4))))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (assert (forall ((C tptp.real) (N4 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 N4) 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)))))
% 6.51/6.87 (assert (forall ((C tptp.real) (N4 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 N4) 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)))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M4)))) (=> (@ (@ 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))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M4)))) (=> (@ (@ 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))))))))
% 6.51/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M4)))) (=> (@ (@ 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))))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))
% 6.51/6.87 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.51/6.87 (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))
% 6.51/6.87 (assert (forall ((Y4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (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))
% 6.51/6.87 (assert (forall ((Y4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y4))))
% 6.51/6.87 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y4))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y4 tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y4) (@ (@ tptp.sums_real (lambda ((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) Y4))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.51/6.87 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X6 (-> tptp.nat tptp.real))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X6 N2)) (@ X6 M2))))))))
% 6.51/6.87 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X6 (-> tptp.nat tptp.set_nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X6 N2)) (@ X6 M2))))))))
% 6.51/6.87 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X6 (-> tptp.nat tptp.rat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ X6 M2))))))))
% 6.51/6.87 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X6 (-> tptp.nat tptp.num))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X6 N2)) (@ X6 M2))))))))
% 6.51/6.87 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X6 (-> tptp.nat tptp.nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 N2)) (@ X6 M2))))))))
% 6.51/6.87 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X6 (-> tptp.nat tptp.int))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X6 N2)) (@ X6 M2))))))))
% 6.51/6.87 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.51/6.87 (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)))
% 6.51/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.51/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.51/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))
% 6.51/6.87 (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)))
% 6.51/6.87 (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))
% 6.51/6.87 (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)))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y4))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y4))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 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))) (= Y4 (@ _let_1 (@ tptp.sin_real A3))))))))
% 6.51/6.87 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.51/6.87 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4))))) tptp.one_one_real)))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z2))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z2))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.cos_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z2))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.cos_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z2))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.sin_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z2))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.sin_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z2))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z2)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z2)) _let_1)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z2)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z2)) _let_1)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z2)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z2)) _let_1)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z2)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z2)) _let_1)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z2)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z2) W2)) _let_1)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z2)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z2) W2)) _let_1)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((W2 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 W2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.sin_complex W2)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.51/6.87 (assert (forall ((W2 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 W2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.sin_real W2)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.51/6.87 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) tptp.pi))))))
% 6.51/6.87 (assert (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))
% 6.51/6.87 (assert (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))
% 6.51/6.87 (assert (= tptp.diffs_rat (lambda ((C2 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C2 _let_1))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X (@ tptp.cos_real T3)) (= Y4 (@ tptp.sin_real T3)))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.51/6.87 (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 ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y5) tptp.zero_zero_real)) (= Y5 X3))))))
% 6.51/6.87 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.51/6.87 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (exists ((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) Y4) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.cos_real Y5) Y4)) (= Y5 X3)))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T3)) (= Y4 (@ tptp.sin_real T3)))))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T3)) (= Y4 (@ tptp.sin_real T3))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T3)) (not (= Y4 (@ tptp.sin_real T3))))))))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z2))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z2))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.87 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z2)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z2)) _let_1)))))))
% 6.51/6.87 (assert (forall ((W2 tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z2)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z2)) _let_1)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y4)) (@ tptp.sin_real X))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4)) (@ _let_1 Y4)))))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y4)) (= X Y4))))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((W2 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 W2)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W2)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 6.51/6.87 (assert (forall ((W2 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 W2)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W2)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y4)) (@ tptp.sin_real X))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4)) (@ (@ tptp.ord_less_real X) Y4))))))))))
% 6.51/6.87 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (exists ((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) Y4) (forall ((Y5 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)) Y5) (@ (@ tptp.ord_less_eq_real Y5) _let_1) (= (@ tptp.sin_real Y5) Y4)) (= Y5 X3)))))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (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)))))))))))
% 6.51/6.87 (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))))))))))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.51/6.87 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X6 (-> tptp.nat tptp.set_nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.51/6.87 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.51/6.87 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (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)))))))))))))
% 6.51/6.87 (assert (forall ((Z2 tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z2) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z2 (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))))
% 6.51/6.87 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.51/6.87 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.51/6.87 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.51/6.87 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.51/6.87 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.51/6.87 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.51/6.87 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.51/6.87 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.51/6.87 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.51/6.87 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.51/6.87 (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))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.51/6.87 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.51/6.87 (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))))))))
% 6.51/6.87 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 6.51/6.87 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.51/6.87 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (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)))))))
% 6.51/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 6.51/6.87 (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))))))
% 6.51/6.87 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.51/6.88 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_complex (= M2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_int (= M2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_rat (= M2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_real (= M2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (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 Y4) (@ tptp.tan_real X3)))))))
% 6.51/6.88 (assert (forall ((Y4 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) Y4) (forall ((Y5 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)) Y5) (@ (@ tptp.ord_less_real Y5) _let_1) (= (@ tptp.tan_real Y5) Y4)) (= Y5 X3)))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y4)) (@ tptp.tan_real X))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y4) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y4)) (@ tptp.tan_real X))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4)) (@ _let_1 Y4)))))))))))
% 6.51/6.88 (assert (forall ((Y4 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) Y4))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y4)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y4))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y4))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (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) Y4))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y4) (= (@ tptp.arctan Y4) X)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arctan Y4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y4))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.51/6.88 (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 ((B7 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M2)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B7) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y4))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y4))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y4))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y4))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y4))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y4))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y4))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y4))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y4))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y4))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y4))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z 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)) Z) (@ (@ tptp.ord_less_real Z) _let_1) (= (@ tptp.tan_real Z) X)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 6.51/6.88 (assert (forall ((Z2 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) Z2)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z2) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.51/6.88 (assert (forall ((Z2 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) Z2)) _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 Z2) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.51/6.88 (assert (forall ((Z2 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) Z2)) _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 Z2) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.51/6.88 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.plus_plus_complex I4) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))
% 6.51/6.88 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N2) tptp.zero_zero_int))))
% 6.51/6.88 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N2) tptp.zero_zero_real))))
% 6.51/6.88 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))
% 6.51/6.88 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.51/6.88 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.51/6.88 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.51/6.88 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 6.51/6.88 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.51/6.88 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 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 Y4) _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)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y4)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y4) (@ (@ tptp.times_times_complex Y4) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y4) (@ (@ tptp.times_times_real Y4) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.51/6.88 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.51/6.88 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.51/6.88 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.51/6.88 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4))))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y4) (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 Y4) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y4)) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z2) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z2) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z2) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z2) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z2) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z2) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y4) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y4)))))
% 6.51/6.88 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (Z2 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z2))) (=> (@ (@ 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 Z2) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (Z2 tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z2))) (=> (@ (@ 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 Z2) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z2))) (=> (@ (@ 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 Z2) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z2))) (=> (@ (@ 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 Z2) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y4)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ tptp.sqrt X) Y4)))))
% 6.51/6.88 (assert (forall ((U2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U2) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U2))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) X) (= Y4 tptp.zero_zero_real)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) Y4) (= X tptp.zero_zero_real)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z2)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z2)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z2)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y4)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))) (@ (@ tptp.plus_plus_real X) Y4))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y4))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z2))) _let_1)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z2))) _let_1)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 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 Y4) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((X tptp.real) (U2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U2) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y4)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))) U2))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z2))) (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 Z2))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z2))) (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 Z2))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (U2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U2) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y4) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y4) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))) U2)))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((Z2 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 Z2) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z2) (@ (@ 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))))))))
% 6.51/6.88 (assert (forall ((Z2 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 Z2) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ (@ 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 Z2) (@ (@ 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))))))))
% 6.51/6.88 (assert (forall ((Z2 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 Z2) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ (@ 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 Z2) (@ (@ 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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu2 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu2 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu2 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups225925009352817453ex_rat G) A2) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups861055069439313189ex_nat G) A2) tptp.one_one_nat))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups858564598930262913ex_int G) A2) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.51/6.88 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.51/6.88 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y4)) Y4)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y4)) Y4)))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.51/6.88 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A2) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_rat)))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.int tptp.rat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups1072433553688619179nt_rat G) A2) tptp.one_one_rat)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_rat)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.51/6.88 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.51/6.88 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups7440179247065528705omplex G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups7440179247065528705omplex (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups2316167850115554303t_real G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1681761925125756287l_real G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups1681761925125756287l_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups129246275422532515t_real (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups766887009212190081x_real G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups766887009212190081x_real (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups1072433553688619179nt_rat G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.one_one_rat))) A2)))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups4061424788464935467al_rat G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups4061424788464935467al_rat (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.one_one_rat))) A2)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex 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.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups861055069439313189ex_nat H2) S3)) (@ (@ tptp.groups861055069439313189ex_nat G) S3))))))))
% 6.51/6.88 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_int X15) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups858564598930262913ex_int H2) S3)) (@ (@ tptp.groups858564598930262913ex_int G) S3))))))))
% 6.51/6.88 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat 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_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups708209901874060359at_nat H2) S3)) (@ (@ tptp.groups708209901874060359at_nat G) S3))))))))
% 6.51/6.88 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_int X15) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups705719431365010083at_int H2) S3)) (@ (@ tptp.groups705719431365010083at_int G) S3))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T5 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S3 tptp.set_int) (I2 (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T5 tptp.set_real) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I2 (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T5 tptp.set_int) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T5 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_complex) (S3 tptp.set_int) (I2 (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T5 tptp.set_complex) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_complex) (S3 tptp.set_real) (I2 (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T5 tptp.set_complex) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_complex) (T4 tptp.set_int) (S3 tptp.set_complex) (I2 (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T5 tptp.set_int) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_complex (@ I2 B2)) (@ (@ tptp.minus_811609699411566653omplex S3) S4)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_complex) (T4 tptp.set_real) (S3 tptp.set_complex) (I2 (-> tptp.real tptp.complex)) (J (-> tptp.complex tptp.real)) (T5 tptp.set_real) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_complex (@ I2 B2)) (@ (@ tptp.minus_811609699411566653omplex S3) S4)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_complex) (T4 tptp.set_complex) (S3 tptp.set_complex) (I2 (-> tptp.complex tptp.complex)) (J (-> tptp.complex tptp.complex)) (T5 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S4)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_complex (@ I2 B2)) (@ (@ tptp.minus_811609699411566653omplex S3) S4)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S4) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.one_one_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T5 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.one_one_real))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups2316167850115554303t_real G) S3) (@ (@ tptp.groups2316167850115554303t_real H2) T5)))))))))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_int))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_int))))) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.51/6.88 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4694064378042380927al_int F) I5)))))))))
% 6.51/6.88 (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 ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups858564598930262913ex_int F) I5)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) (@ tptp.arccos X)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) I5)))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) I5)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y4)) (= X Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 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 B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 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 B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 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 B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5))) (@ _let_1 B5))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex H2))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B5 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 C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B5) C5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B5)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B5 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 C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B5)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B5 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 C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B5) C5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B5)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B5 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 C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B5)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat H2))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B5 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 C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B5) C5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B5)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B5 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 C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B5)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat H2))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B5)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex H2))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B5 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 C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B5) C5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B5)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B5 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 C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B5)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B5 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 C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B5) C5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B5)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B5 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 C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B5)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat H2))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B5 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 C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B5) C5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B5)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B5 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 C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B5)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat H2))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B5)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B5))))))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H2 X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) 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) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) 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) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2316167850115554303t_real G) S3) (@ (@ tptp.groups2316167850115554303t_real H2) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) 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) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) 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) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H2 X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) S3) (@ (@ tptp.groups1072433553688619179nt_rat H2) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) 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) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) 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) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S3) (@ (@ tptp.groups1707563613775114915nt_nat H2) T5))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7440179247065528705omplex G) T5) (@ (@ tptp.groups7440179247065528705omplex H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups713298508707869441omplex G) T5) (@ (@ tptp.groups713298508707869441omplex H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T5) (@ (@ tptp.groups3708469109370488835omplex H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2316167850115554303t_real G) T5) (@ (@ tptp.groups2316167850115554303t_real H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T5) (@ (@ tptp.groups1681761925125756287l_real H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups766887009212190081x_real G) T5) (@ (@ tptp.groups766887009212190081x_real H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) T5) (@ (@ tptp.groups1072433553688619179nt_rat H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) T5) (@ (@ tptp.groups4061424788464935467al_rat H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups225925009352817453ex_rat G) T5) (@ (@ tptp.groups225925009352817453ex_rat H2) S3))))))))
% 6.51/6.88 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) T5) (@ (@ tptp.groups1707563613775114915nt_nat H2) S3))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y4)) (= X Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.51/6.88 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.51/6.88 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.51/6.88 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y4)) (@ tptp.arccos X)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y4)) (@ (@ tptp.ord_less_real Y4) X))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) tptp.pi)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (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))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)) (@ (@ tptp.ord_less_real X) Y4))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y4)) Y4))))
% 6.51/6.88 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B3) A4)) Acc) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B3) (@ (@ F3 A4) Acc))))))
% 6.51/6.88 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb2 tptp.nat) (Xc tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb2) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb2) Xc) Y4) (and (=> _let_2 (= Y4 Xc)) (=> (not _let_2) (= Y4 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb2) (@ (@ X Xa2) Xc))))))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_int) (Z2 (-> tptp.int tptp.real)) (W2 (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups2316167850115554303t_real Z2) I5)) (@ (@ tptp.groups2316167850115554303t_real W2) I5)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_real) (Z2 (-> tptp.real tptp.real)) (W2 (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups1681761925125756287l_real Z2) I5)) (@ (@ tptp.groups1681761925125756287l_real W2) I5)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_complex) (Z2 (-> tptp.complex tptp.real)) (W2 (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups766887009212190081x_real Z2) I5)) (@ (@ tptp.groups766887009212190081x_real W2) I5)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_Pr1261947904930325089at_nat) (Z2 (-> tptp.product_prod_nat_nat tptp.real)) (W2 (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((I3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6036352826371341000t_real Z2) I5)) (@ (@ tptp.groups6036352826371341000t_real W2) I5)))) (@ (@ tptp.groups4567486121110086003t_real (lambda ((I4 tptp.product_prod_nat_nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_int) (Z2 (-> tptp.int tptp.complex)) (W2 (-> tptp.int tptp.complex))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7440179247065528705omplex Z2) I5)) (@ (@ tptp.groups7440179247065528705omplex W2) I5)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_real) (Z2 (-> tptp.real tptp.complex)) (W2 (-> tptp.real tptp.complex))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups713298508707869441omplex Z2) I5)) (@ (@ tptp.groups713298508707869441omplex W2) I5)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_complex) (Z2 (-> tptp.complex tptp.complex)) (W2 (-> tptp.complex tptp.complex))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups3708469109370488835omplex Z2) I5)) (@ (@ tptp.groups3708469109370488835omplex W2) I5)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_Pr1261947904930325089at_nat) (Z2 (-> tptp.product_prod_nat_nat tptp.complex)) (W2 (-> tptp.product_prod_nat_nat tptp.complex))) (=> (forall ((I3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups8110221916422527690omplex Z2) I5)) (@ (@ tptp.groups8110221916422527690omplex W2) I5)))) (@ (@ tptp.groups4567486121110086003t_real (lambda ((I4 tptp.product_prod_nat_nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_nat) (Z2 (-> tptp.nat tptp.real)) (W2 (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups129246275422532515t_real Z2) I5)) (@ (@ tptp.groups129246275422532515t_real W2) I5)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (assert (forall ((I5 tptp.set_nat) (Z2 (-> tptp.nat tptp.complex)) (W2 (-> tptp.nat tptp.complex))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W2 I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups6464643781859351333omplex Z2) I5)) (@ (@ tptp.groups6464643781859351333omplex W2) I5)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z2 I4)) (@ W2 I4))))) I5))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A2) B5) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A2) B5) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B5) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B5) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((B5 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B5) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B5) 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 B5)))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.51/6.88 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.51/6.88 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.51/6.88 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y4)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y4))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y4))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y4)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y4) (@ _let_1 (@ tptp.sin_real Y4)))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y4))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y4) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y4)) X))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (assert (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))))
% 6.51/6.88 (assert (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R2) _let_1))))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X) M2)))) (@ 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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex B)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)))))
% 6.51/6.88 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.51/6.88 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.51/6.88 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (= (@ tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X) tptp.one_one_rat) (= X tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_real B) A)))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ _let_1 A)))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ _let_1 A)))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.51/6.88 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.51/6.88 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.51/6.88 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real A) (@ tptp.inverse_inverse_real A)) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.inverse_inverse_rat A)) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y4))) (let ((_let_2 (@ tptp.times_times_real X))) (=> (= (@ (@ tptp.times_times_real Y4) X) (@ _let_2 Y4)) (= (@ (@ tptp.times_times_real _let_1) X) (@ _let_2 _let_1)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.complex) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y4))) (let ((_let_2 (@ tptp.times_times_complex X))) (=> (= (@ (@ tptp.times_times_complex Y4) X) (@ _let_2 Y4)) (= (@ (@ tptp.times_times_complex _let_1) X) (@ _let_2 _let_1)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y4))) (let ((_let_2 (@ tptp.times_times_rat X))) (=> (= (@ (@ tptp.times_times_rat Y4) X) (@ _let_2 Y4)) (= (@ (@ tptp.times_times_rat _let_1) X) (@ _let_2 _let_1)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.51/6.88 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N)))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat A)) N) (@ tptp.inverse_inverse_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.51/6.88 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.51/6.88 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ _let_1 tptp.zero_zero_real) (@ _let_1 A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (=> (not (= A tptp.zero_zero_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (=> (not (= A tptp.zero_zero_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.inverse_inverse_real A)) (=> (not (= A tptp.zero_zero_real)) (@ _let_1 A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ tptp.inverse_inverse_rat A)) (=> (not (= A tptp.zero_zero_rat)) (@ _let_1 A))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A)))))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B)) (@ tptp.invers8013647133539491842omplex A)))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 6.51/6.88 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))
% 6.51/6.88 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))
% 6.51/6.88 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))
% 6.51/6.88 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))
% 6.51/6.88 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))
% 6.51/6.88 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))
% 6.51/6.88 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B3)) A4))))
% 6.51/6.88 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B3)) A4))))
% 6.51/6.88 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B3)) A4))))
% 6.51/6.88 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.51/6.88 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.51/6.88 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((Xa2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.51/6.88 (assert (forall ((Xa2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.51/6.88 (assert (forall ((Xa2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X) (@ (@ tptp.times_times_rat X) _let_1)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Xa2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.51/6.88 (assert (forall ((Xa2 tptp.int) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.51/6.88 (assert (forall ((Xa2 tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X) (@ (@ tptp.times_times_rat X) _let_1)))))
% 6.51/6.88 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_2)) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_2)) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_2)) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.plus_plus_real A) B))) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.plus_plus_complex A) B))) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.plus_plus_rat A) B))) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real B) A))) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex B) A))) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat B) A))) _let_1))))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real A) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.51/6.88 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.51/6.88 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))))
% 6.51/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))))
% 6.51/6.88 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat A) B))) _let_1)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) X)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) X)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex (@ tptp.semiri5044797733671781792omplex N2))) (@ (@ tptp.power_power_complex X) N2))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W2))))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W2))))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W2))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))) X))))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N3))) X))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) M))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) M))))))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X)) M))))))))
% 6.51/6.88 (assert (= tptp.cot_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X2)) (@ tptp.sin_complex X2)))))
% 6.51/6.88 (assert (= tptp.cot_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 6.51/6.88 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 6.51/6.88 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.51/6.88 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.51/6.88 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) X2)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (A tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y4)) (@ _let_2 (@ _let_1 Y4)))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (A tptp.real) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y4)) (@ _let_2 (@ _let_1 Y4)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X) Y4))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_complex X) Y4))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I2) K))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.one_one_real) X) X)))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.one_one_real) X) X)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X)) (@ tptp.set_or4236626031148496127et_nat Y4)) (@ (@ tptp.ord_less_eq_set_nat X) Y4))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X)) (@ tptp.set_ord_atMost_rat Y4)) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X)) (@ tptp.set_ord_atMost_num Y4)) (@ (@ tptp.ord_less_eq_num X) Y4))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y4)) (@ (@ tptp.ord_less_eq_int X) Y4))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))
% 6.51/6.88 (assert (forall ((B tptp.real) (U2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real U2))) (= (= (@ (@ tptp.plus_plus_real B) (@ _let_1 A)) (@ (@ tptp.plus_plus_real A) (@ _let_1 B))) (or (= A B) (= U2 tptp.one_one_real))))))
% 6.51/6.88 (assert (forall ((B tptp.complex) (U2 tptp.real) (A tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex U2))) (= (= (@ (@ tptp.plus_plus_complex B) (@ _let_1 A)) (@ (@ tptp.plus_plus_complex A) (@ _let_1 B))) (or (= A B) (= U2 tptp.one_one_real))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X) Y4)) N) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) N)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X) Y4)) N) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_complex Y4) N)))))
% 6.51/6.88 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L2) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ tptp.uminus_uminus_real X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ tptp.uminus1482373934393186551omplex X))))
% 6.51/6.88 (assert (forall ((U2 tptp.real) (A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real tptp.one_one_real) U2)) A)) (@ (@ tptp.real_V1485227260804924795R_real U2) A)) A)))
% 6.51/6.88 (assert (forall ((U2 tptp.real) (A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.minus_minus_real tptp.one_one_real) U2)) A)) (@ (@ tptp.real_V2046097035970521341omplex U2) A)) A)))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((U2 tptp.num) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.numeral_numeral_real U2))) (= (@ (@ 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))))))
% 6.51/6.88 (assert (forall ((U2 tptp.num) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real U2))) (= (@ (@ tptp.real_V2046097035970521341omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real _let_1) (@ tptp.numeral_numeral_real W2))) A)))))
% 6.51/6.88 (assert (forall ((V tptp.num) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real W2))) (= (@ (@ 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))))))
% 6.51/6.88 (assert (forall ((V tptp.num) (W2 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 W2)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real W2)) _let_1)) A)))))
% 6.51/6.88 (assert (forall ((U2 tptp.num) (V tptp.num) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real W2))) (let ((_let_3 (@ tptp.numeral_numeral_real U2))) (= (@ (@ 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)))))))
% 6.51/6.88 (assert (forall ((U2 tptp.num) (V tptp.num) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real U2))) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real _let_2) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real _let_2) (@ tptp.numeral_numeral_real W2))) _let_1)) A))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.plus_plus_complex (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.51/6.88 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.51/6.88 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y)))))
% 6.51/6.88 (assert (forall ((H2 tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H2)))))
% 6.51/6.88 (assert (forall ((H2 tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H2)))))
% 6.51/6.88 (assert (forall ((H2 tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H2)))))
% 6.51/6.88 (assert (= tptp.set_ord_atMost_real (lambda ((U3 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U3))))))
% 6.51/6.88 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U3 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) U3))))))
% 6.51/6.88 (assert (= tptp.set_ord_atMost_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U3))))))
% 6.51/6.88 (assert (= tptp.set_ord_atMost_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U3))))))
% 6.51/6.88 (assert (= tptp.set_ord_atMost_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U3))))))
% 6.51/6.88 (assert (= tptp.set_ord_atMost_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U3))))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X) Y4)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y4) Xa2)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (Xa2 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real X) Y4)) Xa2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex X) Xa2)) (@ (@ tptp.real_V2046097035970521341omplex Y4) Xa2)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y4) (@ (@ tptp.times_times_real Y4) X)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y4)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) I4))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I4))) (@ (@ tptp.power_power_real X) I4))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real Y4) _let_1)))))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y4) (@ (@ tptp.times_times_complex Y4) X)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y4)) N)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) I4))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I4))) (@ (@ tptp.power_power_complex X) I4))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex Y4) _let_1)))))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ _let_1 B) (=> (@ _let_1 X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) Y4)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_real X) X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_complex X) X))))
% 6.51/6.88 (assert (forall ((M tptp.real) (X tptp.real) (C tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X)) C) Y4) (= X (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ _let_1 C))))))))
% 6.51/6.88 (assert (forall ((M tptp.real) (X tptp.complex) (C tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex M) X)) C) Y4) (= X (@ (@ tptp.minus_minus_complex (@ _let_1 Y4)) (@ _let_1 C))))))))
% 6.51/6.88 (assert (forall ((M tptp.real) (Y4 tptp.real) (X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y4 (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X)) C)) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ _let_1 C)) X))))))
% 6.51/6.88 (assert (forall ((M tptp.real) (Y4 tptp.complex) (X tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y4 (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex M) X)) C)) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y4)) (@ _let_1 C)) X))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (assert (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.51/6.88 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.51/6.88 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X2) I4)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I4)) (@ (@ tptp.power_power_complex X2) I4)))) _let_1)))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) (@ D I4)))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X2) I4)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ D I4)) (@ (@ tptp.power_power_real X2) I4)))) _let_1)))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) (@ D I4)))))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.int)) (B5 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))) B5)) (@ tptp.summable_int A)))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.nat)) (B5 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))) B5)) (@ tptp.summable_nat A)))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.real)) (B5 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))) B5)) (@ tptp.summable_real A)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X) N2))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.51/6.88 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) tptp.zero_zero_complex))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C I4) tptp.zero_zero_real))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex W) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_complex)))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real W) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_real)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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 ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))) (@ tptp.exp_real X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X) N2)))) (@ tptp.exp_complex X))))
% 6.51/6.88 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.51/6.88 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X) N2)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (not (= (@ C I4) tptp.zero_zero_complex)))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (not (= (@ C I4) tptp.zero_zero_real)))))))
% 6.51/6.88 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z4) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))))))
% 6.51/6.88 (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 ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z4) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B2 (-> tptp.nat tptp.complex))) (not (forall ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B2 (-> tptp.nat tptp.rat))) (not (forall ((Z5 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B2 (-> tptp.nat tptp.int))) (not (forall ((Z5 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real A) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B2 (-> tptp.nat tptp.real))) (not (forall ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B2 (-> tptp.nat tptp.complex))) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex A) I4)))) _let_1))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B2 (-> tptp.nat tptp.rat))) (forall ((Z5 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat A) I4)))) _let_1))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B2 (-> tptp.nat tptp.int))) (forall ((Z5 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C I4)) (@ (@ tptp.power_power_int A) I4)))) _let_1))))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B2 (-> tptp.nat tptp.real))) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real A) I4)))) _let_1))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K3) I4))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K3) I4))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K3) I4))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K3) I4))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N tptp.nat) (B (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ (@ tptp.power_power_complex X) I4)))) (@ 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))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N tptp.nat) (B (-> tptp.nat tptp.rat)) (X tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ (@ tptp.power_power_rat X) I4)))) (@ 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))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N tptp.nat) (B (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ (@ tptp.power_power_int X) I4)))) (@ 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))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N tptp.nat) (B (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ (@ tptp.power_power_real X) I4)))) (@ 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))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.complex)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex X2) I4)))) (@ 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)))))))
% 6.51/6.88 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.real)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real X2) I4)))) (@ 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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X) I4)))) (@ 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))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K3) I4))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ B (@ (@ tptp.minus_minus_nat K3) I4))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.one_one_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups6464643781859351333omplex (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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups129246275422532515t_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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.one_one_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups73079841787564623at_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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ 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 P6)) (@ (@ 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 P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.51/6.88 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.51/6.88 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Z2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_int Z2) N) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I4 N)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Z2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_complex Z2) N) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I4 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I4 N)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Z2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_rat Z2) N) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I4 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I4 N)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Z2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_8256067586552552935nteger Z2) N) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I4 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I4 N)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Z2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_real Z2) N) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I4 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I4 N)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I4)) (@ tptp.semiri8010041392384452111omplex I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I4)) (@ tptp.semiri4939895301339042750nteger I4))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I4)) (@ tptp.semiri1314217659103216013at_int I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I4)) (@ tptp.semiri681578069525770553at_rat I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ tptp.semiri5074537144036343181t_real I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) M))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) M))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) M))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K3)) A)) tptp.one_one_complex)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K3)) A)) tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ (@ tptp.power_power_complex X) I4)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ (@ tptp.power_power_complex Y4) I4)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ 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 Y4) K3))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ (@ tptp.power_power_rat X) I4)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ (@ tptp.power_power_rat Y4) I4)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y4)) (@ (@ 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 Y4) K3))) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ (@ tptp.power_power_int X) I4)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ (@ tptp.power_power_int Y4) I4)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y4)) (@ (@ 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 Y4) K3))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ (@ tptp.power_power_real X) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ (@ tptp.power_power_real Y4) I4)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ 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 Y4) K3))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X2) N2)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I4)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I4)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.51/6.88 (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 ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.51/6.88 (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 ((Z5 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ (@ tptp.power_power_complex X) I4)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ (@ tptp.power_power_complex Y4) I4)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I4)) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) 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))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ (@ tptp.power_power_rat X) I4)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ (@ tptp.power_power_rat Y4) I4)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) 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))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ (@ tptp.power_power_int X) I4)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ (@ tptp.power_power_int Y4) I4)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ (@ tptp.power_power_int Y4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) 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))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y4 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ (@ tptp.power_power_real X) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ (@ tptp.power_power_real Y4) I4)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A I4)) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) 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))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 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 P4) (@ _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 P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 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 P4) (@ _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 P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 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) P4)) (@ (@ 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 P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 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) P4)) (@ (@ 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 P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 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 P4) (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 P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 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 P4) (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 P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y4)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))) (@ tptp.sinh_real X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_complex) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X) N2))))) (@ tptp.sinh_complex X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))) tptp.zero_zero_real))) (@ tptp.cosh_real X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X) N2))) tptp.zero_zero_complex))) (@ tptp.cosh_complex X))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.51/6.88 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 6.51/6.88 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.51/6.88 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_real X) Y4)))))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z2) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z2))) _let_1)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.51/6.88 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X) Y4)))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.88 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex X2)))))
% 6.51/6.88 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)) (@ tptp.exp_complex X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)) (@ tptp.exp_real X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex X)) (@ tptp.exp_complex X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X)) (@ tptp.sinh_real X)) (@ tptp.exp_real X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y4))))))
% 6.51/6.88 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X))) (@ tptp.cosh_complex X))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X))) (@ tptp.cosh_real X))))))
% 6.51/6.88 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W2) Z2) (= W2 (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z2)))))))
% 6.51/6.88 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real))))
% 6.51/6.88 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (= (@ (@ tptp.complex2 X) Y4) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y4 tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_2)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_2)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y4)))))))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y4)))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y4))) (let ((_let_2 (@ tptp.tanh_complex X))) (=> (not (= (@ tptp.cosh_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y4) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y4))) (let ((_let_2 (@ tptp.tanh_real X))) (=> (not (= (@ tptp.cosh_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y4) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.cosh_real (lambda ((Z4 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z4)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.88 (assert (= tptp.cosh_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z4)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.51/6.88 (assert (= tptp.sinh_real (lambda ((Z4 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z4)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.51/6.88 (assert (= tptp.sinh_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z4)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (= (@ tptp.cosh_real X) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.complex)) (= (= (@ tptp.cosh_complex X) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.cosh_real (lambda ((X2 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))))))
% 6.51/6.88 (assert (= tptp.cosh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.sinh_real (lambda ((X2 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))))))
% 6.51/6.88 (assert (= tptp.sinh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.51/6.88 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.51/6.88 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.51/6.88 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.51/6.88 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z2))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) Z2))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z2))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.51/6.88 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.51/6.88 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.51/6.88 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.51/6.88 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.51/6.88 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.51/6.88 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y4)) (@ tptp.archim7802044766580827645g_real X)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y4)) (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 6.51/6.88 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.51/6.88 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.51/6.88 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 6.51/6.88 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.88 (assert (forall ((A tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y4)) Y4)))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ _let_1 (@ (@ tptp.powr_real X) Y4)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) B))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y4)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) A))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y4)) (@ (@ tptp.times_times_real Y4) (@ tptp.ln_ln_real X))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (B tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y4)) (@ (@ tptp.times_times_real Y4) (@ _let_1 X)))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y4)) X) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.log B) X)))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y4)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y4))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y4) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y4)))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y4)) X))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y4)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y4)))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y4)) X) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.log B) X)))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y4))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y4) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y4)))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y4)) X))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y4)))))))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y4) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y4)) X))))))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y4) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y4)) X))))))))))
% 6.51/6.88 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y4))))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 6.51/6.88 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.88 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.51/6.88 (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))
% 6.51/6.88 (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))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (exists ((A3 tptp.complex) (R3 tptp.real)) (= Z2 (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A3))))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y4)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y4)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R2)) (@ (@ tptp.times_times_real Y4) R2)))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y4)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R2)) Y4))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y4)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X)) Y4))))
% 6.51/6.88 (assert (= tptp.cis (lambda ((B3 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 6.51/6.88 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.51/6.88 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (exists ((R3 tptp.real) (A3 tptp.real)) (= Z2 (@ (@ 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)))))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (= (@ tptp.csqrt Z2) tptp.one_one_complex) (= Z2 tptp.one_one_complex))))
% 6.51/6.88 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z2)))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A32) (=> (=> (= A23 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R3)))))))))))))
% 6.51/6.88 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 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 (= A1 K3) (= A22 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 (= A1 K3) (= A22 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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))))))))))))
% 6.51/6.88 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4))))))
% 6.51/6.88 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_real X) Y4))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.51/6.88 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z2)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_int W2) Z2)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.51/6.88 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.51/6.88 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4)))))
% 6.51/6.88 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N))) Y4))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (W2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int W2) Z2)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z2))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 6.51/6.88 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W2) Z2))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W2))) (@ tptp.nat2 (@ tptp.abs_abs_int Z2))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.minus_minus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.modulo_modulo_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N) X)))))))
% 6.51/6.88 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y4) N))) (@ tptp.abs_abs_real Y4)))))
% 6.51/6.88 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int W2) Z2)))))
% 6.51/6.88 (assert (forall ((W2 tptp.int) (Z2 tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_eq_int W2) Z2)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z2) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z2)) (@ tptp.nat2 Z6))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z2) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z2)) (@ tptp.nat2 Z6))))))
% 6.51/6.88 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z2)) N)))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y4)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ 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 N4) X))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N) X)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (= (@ (@ tptp.power_power_real Y4) N) X) (= (@ (@ tptp.root N) X) Y4))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Y4 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y4) N) X) (= (@ (@ tptp.root N) X) Y4)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.suc (@ tptp.nat2 Z2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2))))))
% 6.51/6.88 (assert (forall ((W2 tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) M) (@ (@ tptp.ord_less_int W2) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z2) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z2))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ 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 N4) X))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 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) Y4) (and (=> _let_5 (= Y4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.51/6.88 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) tptp.zero_zero_nat)))
% 6.51/6.88 (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)))
% 6.51/6.88 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) tptp.one_one_nat)))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X)))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y4)) (@ tptp.inc (@ _let_1 Y4))))))
% 6.51/6.88 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.51/6.88 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.51/6.88 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.51/6.88 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y4)) (@ (@ tptp.plus_plus_num (@ _let_1 Y4)) X)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 6.51/6.88 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M2 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 M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.51/6.88 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M2 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 M2)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.51/6.88 (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))))))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y4 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) Y4) (=> _let_1 (not (=> (and (=> _let_6 (= Y4 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y4 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.51/6.88 (assert (forall ((W2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W2)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) N))))
% 6.51/6.88 (assert (forall ((W2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W2)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2)) N)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W2)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) (@ tptp.pred_numeral N)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W2)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2)) (@ tptp.pred_numeral N))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M3) (= (@ _let_1 M3) (@ _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)))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z2))) (=> (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)) Z2)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((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) A12)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J2) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)) (@ (@ P I3) J2)))) (@ (@ P A0) A12)))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4)))))
% 6.51/6.88 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y4)) (@ (@ tptp.plus_plus_int X) Y4))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M2 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 M2) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.51/6.88 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y4) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y4)) _let_1)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M2) _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 M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M2 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 M2)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.51/6.88 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y4 tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y4) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (not (= Y4 _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit0 N3))) (=> _let_1 (not (= Y4 (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y4 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))))))))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y4) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y4)) _let_1)))))))
% 6.51/6.88 (assert (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M2 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 M2)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M2) tptp.one_one_nat)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.sgn_sgn_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (= A4 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A4)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.51/6.88 (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 ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R2 (@ (@ tptp.plus_plus_rat S) T3)))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M2) tptp.one_one_nat)))))
% 6.51/6.88 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.51/6.88 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.times_times_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P6)) (@ (@ 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 P6)))))
% 6.51/6.88 (assert (forall ((Q2 tptp.int) (P6 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P6)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((P6 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.51/6.88 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.88 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))
% 6.51/6.88 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.51/6.88 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P6) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 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 C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P6)))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P6) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 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 C2) B3))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P6)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P6) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 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) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P6)))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P6) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 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) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P6)))))
% 6.51/6.88 (assert (forall ((R2 tptp.rat) (P6 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.51/6.88 (assert (= tptp.ord_less_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C2 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 C2) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))))
% 6.51/6.88 (assert (= tptp.ord_less_eq_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C2 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 C2) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P6)) (@ (@ 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 P6)))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P6)) (@ (@ 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 P6)))))
% 6.51/6.88 (assert (forall ((R2 tptp.product_prod_int_int) (P6 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.51/6.88 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P6 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P6) S2) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.51/6.88 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M2)) (@ X6 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.51/6.88 (assert (forall ((L2 tptp.nat) (U2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U2)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U2))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J2))))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((L2 tptp.int) (U2 tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U2) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U2))))
% 6.51/6.88 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.51/6.88 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.51/6.88 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.51/6.88 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.51/6.88 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.51/6.88 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z2)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.re Z2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.51/6.88 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.88 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 6.51/6.88 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.51/6.88 (assert (forall ((X tptp.produc1908205239877642774nteger)) (not (forall ((F2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I3 tptp.code_integer)) (not (= X (@ (@ tptp.produc8603105652947943368nteger F2) (@ (@ tptp.produc1086072967326762835nteger D3) I3))))))))
% 6.51/6.88 (assert (forall ((X tptp.produc8763457246119570046nteger)) (not (forall ((F2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I3 tptp.code_integer)) (not (= X (@ (@ tptp.produc6137756002093451184nteger F2) (@ (@ tptp.produc1086072967326762835nteger D3) I3))))))))
% 6.51/6.88 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 6.51/6.88 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.51/6.88 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.51/6.88 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y4)))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 6.51/6.88 (assert (= tptp.one_one_int tptp.one_one_int))
% 6.51/6.88 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_2 (@ tptp.re Z2))) (= (@ (@ 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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ 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)))))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.im Z2))) (= (@ tptp.im (@ tptp.csqrt Z2)) (@ (@ 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 Z2)) (@ tptp.re Z2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z2)) (@ tptp.re Z2))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z2)) (@ tptp.uminus_uminus_real (@ tptp.im Z2)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.51/6.88 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y4)))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y4))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y4))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y4))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z2))) (@ tptp.abs_abs_real (@ tptp.im Z2))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z2)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z2))) (@ tptp.cos_real (@ tptp.im Z2))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z2)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z2))) (@ tptp.sin_real (@ tptp.im Z2))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (assert (= tptp.exp_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z4)))) (@ tptp.cis (@ tptp.im Z4))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z2 tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)) tptp.zero_zero_real)))))
% 6.51/6.88 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z4 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 Z4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z4)) _let_1)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z2 tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((W2 tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.re W2))) (=> (= (@ (@ tptp.power_power_complex W2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z2) (=> (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 W2)))) (= (@ tptp.csqrt Z2) W2))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z2))) (@ tptp.abs_abs_real (@ tptp.im Z2)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z2)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z2))) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (assert (forall ((R2 tptp.complex) (Z2 tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.51/6.88 (assert (forall ((R2 tptp.complex) (Z2 tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y4) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y4)) (and (= X tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))))
% 6.51/6.88 (assert (forall ((Y4 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y4) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y4) X) (and (= X tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj Z2)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.times_times_complex (@ tptp.cnj X)) (@ tptp.cnj Y4)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (= (@ tptp.cnj Z2) tptp.one_one_complex) (= Z2 tptp.one_one_complex))))
% 6.51/6.88 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X)) (@ tptp.cnj Y4)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj Z2))) tptp.zero_zero_real)))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z4 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z4) (@ tptp.cnj Z4)))))))
% 6.51/6.88 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj Z2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj Z2)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z2) (@ tptp.cnj Z2)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z2))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z2) (@ tptp.cnj Z2)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z2)))) tptp.imaginary_unit))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((Z2 tptp.complex) (W2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj W2)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z2)) W2)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.51/6.88 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L)) (@ (@ tptp.modulo364778990260209775nteger K3) L)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.51/6.88 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.51/6.88 (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) (S5 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S5))) (= S5 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.51/6.88 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y4) (=> (@ (@ 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 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y4 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) (=> (= Y4 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) (=> (= Y4 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 6.51/6.88 (assert (forall ((U2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U2)) (@ tptp.suc U2))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 6.51/6.88 (assert (forall ((L2 tptp.nat) (U2 tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U2)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U2)) L2))))
% 6.51/6.88 (assert (forall ((L2 tptp.int) (U2 tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U2) L2)) tptp.one_one_int)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))) N)))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) N))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y4) (=> (@ (@ 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 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y4 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) (=> (= Y4 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) (=> (= Y4 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.51/6.88 (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) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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) S5)))))) _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) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.vEBT_VEBT) (Y4 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) Y4) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y4 (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y4) (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 Y4) (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) (=> Y4 (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 Y4) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M5)))) M)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M5) N)))) M)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y4 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) Y4) (and (=> _let_2 (= Y4 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y4 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.51/6.88 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M2) K3)) (@ (@ tptp.product_Pair_nat_nat M2) (@ (@ tptp.minus_minus_nat K3) M2))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M2) _let_1)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.51/6.88 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.divide_divide_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.51/6.88 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.51/6.88 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y4) (@ (@ tptp.modulo_modulo_nat X) Y4)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y4) (= (@ (@ tptp.bezw X) Y4) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y4)))))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y4 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) Y4) (and (=> _let_3 (= Y4 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y4 (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 6.51/6.88 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P6)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P6)))) tptp.one_one_int))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y4 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) Y4) (=> _let_1 (not (=> (and (=> _let_4 (= Y4 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y4 (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 6.51/6.88 (assert (= tptp.normalize (lambda ((P4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P4))) (let ((_let_2 (@ tptp.product_fst_int_int P4))) (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)))))))))))))
% 6.51/6.88 (assert (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (exists ((U4 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U4) X)) (@ (@ tptp.times_times_int V2) Y4)) (@ (@ tptp.gcd_gcd_int X) Y4)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y4) (=> _let_1 (not (=> (and (=> _let_3 (= Y4 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y4 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y4))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y4)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y4)))))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y4 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) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 X)) (=> (not _let_2) (= Y4 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))))
% 6.51/6.88 (assert (forall ((L2 tptp.int) (U2 tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U2)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U2) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))))
% 6.51/6.88 (assert (forall ((L2 tptp.int) (U2 tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U2) (@ (@ tptp.set_or5832277885323065728an_int L2) U2))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((L2 tptp.nat) (U2 tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U2)) (@ (@ tptp.minus_minus_nat U2) (@ tptp.suc L2)))))
% 6.51/6.88 (assert (forall ((L2 tptp.nat) (U2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U2) (@ (@ tptp.set_or5834768355832116004an_nat L2) U2))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N9) (@ (@ tptp.member_nat N9) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.51/6.88 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 6.51/6.88 (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 ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N9)) S3))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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 ((U3 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 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))) Xa2) X)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z2 (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.51/6.88 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.51/6.88 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0))) Xa2) X))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0))) Xa2) X))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U3)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))) Xa2) X)))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U3)))) __flatten_var_0))) Xa2) X)))))
% 6.51/6.88 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M7) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.51/6.88 (assert (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (=> (@ (@ tptp.member_nat B2) A2) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A3) B2)) A2)))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A2)) A2)))))
% 6.51/6.88 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U3) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.51/6.88 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U3) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.51/6.88 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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 ((U3 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 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U3)))) __flatten_var_0))))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U3)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y4)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y4))) X)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.51/6.88 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.51/6.88 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y4)) (@ tptp.sqr (@ _let_1 Y4))))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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)))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _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)))))))
% 6.51/6.88 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y4) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (= Y4 (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)) (= Y4 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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)))))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y4) (=> (@ (@ 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) (=> (= Y4 (= 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) (=> (= Y4 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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)))))))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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)))))))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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))))))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.51/6.88 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M2 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M2)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.51/6.88 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M2 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 ((P4 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) P4)))) (lambda ((P4 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P4))))) X2))) A4))) (@ (@ tptp.product_Pair_nat_num N2) M2)))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa2) Y4) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) (not (= Y4 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))))))))))))))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y4 tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa2) Y4) (=> (=> _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 ((M4 tptp.num)) (= X (@ tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (=> (=> (exists ((M4 tptp.num)) (= X (@ tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))))))))))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa2) Y4) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y4 tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))))))))))))))))))))
% 6.51/6.88 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.51/6.88 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.51/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((L2 tptp.nat) (U2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U2) (@ (@ tptp.set_or6659071591806873216st_nat L2) U2))))
% 6.51/6.88 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I4 tptp.int) (N2 tptp.nat)) (and (= Uu2 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((C tptp.nat) (Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y4))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y4))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y4))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y4) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.51/6.88 (assert (forall ((M7 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.51/6.88 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 6.51/6.88 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 6.51/6.88 (assert (forall ((A tptp.int) (B tptp.int) (P6 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A) B))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P6) Q2)) (= (@ (@ tptp.fract P6) Q2) _let_1)))))
% 6.51/6.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 6.51/6.88 (assert (forall ((A tptp.int) (B tptp.int) (P6 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ tptp.product_Pair_int_int P6) Q2)) (= (@ (@ tptp.fract P6) Q2) (@ (@ tptp.fract A) B)))))
% 6.51/6.88 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 6.51/6.88 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W2)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W2))))
% 6.51/6.88 (assert (forall ((L2 tptp.int) (U2 tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U2) (@ (@ tptp.set_or6656581121297822940st_int L2) U2))))
% 6.51/6.88 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A) B)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.51/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.51/6.88 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((W2 tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y4) (@ tptp.positive (@ (@ tptp.plus_plus_rat X) Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y4) (@ tptp.positive (@ (@ tptp.times_times_rat X) Y4))))))
% 6.51/6.88 (assert (forall ((L2 tptp.int) (U2 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 U2) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U2))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.51/6.88 (assert (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))))
% 6.51/6.88 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M2) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.51/6.88 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X8 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X8)) tptp.zero_zero_nat)))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (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)))))))))))))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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 ((Z tptp.real)) (and (@ (@ tptp.ord_less_real A) Z) (@ (@ tptp.ord_less_real Z) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z)))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((Z2 tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z4 tptp.real)) (@ (@ tptp.powr_real Z4) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z2) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.51/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.51/6.88 (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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.51/6.88 (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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.51/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 6.51/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real C) T3) (@ (@ tptp.ord_less_real T3) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real A) T3) (@ (@ tptp.ord_less_real T3) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B5 tptp.real)) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M3 tptp.nat) (T6 tptp.real)) (let ((_let_1 (@ tptp.suc M3))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M3))) (@ (@ tptp.minus_minus_real (@ (@ Diff M3) U3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M3) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real U3) P4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B5) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U3) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T6)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M3)) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real T6) P4)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B5) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T6) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.51/6.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.51/6.88 (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.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arccos)))))
% 6.51/6.88 (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.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.51/6.88 (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.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.51/6.88 (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 ((Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z) (=> (@ (@ tptp.ord_less_eq_real Z) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)) F)))) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z) (=> (@ (@ tptp.ord_less_eq_real Z) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)) G)))) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z) (=> (@ (@ tptp.ord_less_real Z) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z)) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real))))) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z) (=> (@ (@ tptp.ord_less_real Z) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z)) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C3))))))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y4 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) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y4 tptp.nil_int))) (not _let_1)))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J3)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.51/6.88 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J3)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y4) (and (=> _let_1 (= Y4 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y4 tptp.nil_int)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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 ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.51/6.88 (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 ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.51/6.88 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))
% 6.51/6.88 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N9)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N9))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_real R3) (@ X7 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X7 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.51/6.88 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))
% 6.51/6.88 (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)))
% 6.51/6.88 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N9)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 6.51/6.88 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 6.51/6.88 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 6.51/6.88 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 6.51/6.88 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C2)))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 6.51/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.51/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 6.51/6.88 (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)))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))
% 6.51/6.88 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.51/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.51/6.88 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.51/6.88 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M2 tptp.nat)) (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M2))))) M7)))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X6 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X6 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X6)))))
% 6.51/6.88 (assert (= tptp.divide_divide_nat (lambda ((M2 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)) M2))))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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) (Z tptp.real)) (and (@ (@ tptp.ord_less_real A) Z) (@ (@ tptp.ord_less_real Z) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.51/6.88 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.51/6.88 (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))))
% 6.51/6.88 (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.member_real (@ F X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.artanh_real (@ F X2)))))))))
% 6.51/6.88 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.51/6.88 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M2)) M2))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.51/6.88 (assert (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N4) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N4))))
% 6.51/6.88 (assert (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)))
% 6.51/6.88 (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))))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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 ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M5)))) M))))
% 6.51/6.88 (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 ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M5) N)))) M))))
% 6.51/6.88 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M2 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M2)))))))
% 6.51/6.88 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.51/6.88 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.51/6.88 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.51/6.88 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 6.51/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M2)))))
% 6.51/6.88 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M2))))))
% 6.51/6.88 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J3)))))
% 6.51/6.88 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M2))))))
% 6.51/6.88 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 6.51/6.88 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N4 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) N4))))) (@ (@ 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) N4)))))) (@ 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) N4))))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N4 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) N4))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 6.51/6.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M2) N2))) M2)))))
% 6.51/6.88 (assert (forall ((X tptp.list_nat) (Y4 tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y4) (=> (=> (= X tptp.nil_nat) (not (= Y4 tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y4 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (forall ((X tptp.list_nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y4) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y4 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs3))) (=> (= X _let_1) (=> (= Y4 (@ 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)))))))))))))
% 6.51/6.88 (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))))
% 6.51/6.88 (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))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A6 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A6) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N3))) A6)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N2)) (@ Y7 N2))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X7) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N2)) (@ Y7 N2))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (forall ((X7 (-> 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 (@ X7 N3))) R3)))))) (@ tptp.vanishes X7))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X7) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N9) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N9))) R2))))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 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) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 (@ 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) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 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) (=> (= Y4 (@ 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) (=> (= Y4 (@ 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 ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit1 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.51/6.88 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y4 _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) (=> (= Y4 (@ 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 ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 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 ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.rcis R2) A)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real tptp.one_one_real) R2)) (@ tptp.uminus_uminus_real A)))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.cos_real A)))))
% 6.51/6.88 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.sin_real A)))))
% 6.51/6.88 (assert (= tptp.cis (@ tptp.rcis tptp.one_one_real)))
% 6.51/6.88 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R1) R22)) (@ (@ tptp.plus_plus_real A) B)))))
% 6.51/6.88 (assert (= tptp.rcis (lambda ((R5 tptp.real) (A4 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A4)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.51/6.88 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.51/6.88 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M2)) (@ X6 N2)))) R5)))))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N2)) (@ Y7 N2))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N2)) (@ Y7 N2))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (not (@ tptp.vanishes X7)) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (exists ((K2 tptp.nat)) (or (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N9) (@ (@ tptp.ord_less_rat B2) (@ tptp.uminus_uminus_rat (@ X7 N9))))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N9) (@ (@ tptp.ord_less_rat B2) (@ X7 N9))))))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (not (@ tptp.vanishes X7)) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (exists ((K2 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N9) (@ (@ tptp.ord_less_rat B2) (@ tptp.abs_abs_rat (@ X7 N9))))))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X7) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M3) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N9) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M3)) (@ X7 N9)))) R2))))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M4) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M4)) (@ X7 N3)))) R3)))))))) (@ tptp.cauchy X7))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X7)) (@ tptp.real2 Y7)) (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 (@ X7 N2)) (@ (@ tptp.plus_plus_rat (@ Y7 N2)) R5))))))))))))
% 6.51/6.88 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.one_one_rat))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X7)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N2)) (@ Y7 N2)))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.times_times_real (@ tptp.real2 X7)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N2)) (@ Y7 N2)))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (= (not (@ tptp.positive2 (@ tptp.real2 X7))) (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 (@ X7 N2)) R5))))))))))
% 6.51/6.88 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (= (@ tptp.positive2 (@ tptp.real2 X7)) (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) (@ X7 N2)))))))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y4) (@ tptp.positive2 (@ (@ tptp.times_times_real X) Y4))))))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y4) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X) Y4))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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 ((M2 tptp.nat)) (@ P (@ tptp.suc M2))))))))))
% 6.51/6.88 (assert (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.code_integer_of_nat N2))) (let ((_let_2 (@ tptp.code_integer_of_nat M2))) (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))))))))))
% 6.51/6.88 (assert (forall ((N tptp.num)) (= (@ tptp.code_integer_of_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6620942414471956472nteger N))))
% 6.51/6.88 (assert (= (@ tptp.code_integer_of_nat tptp.one_one_nat) tptp.one_one_Code_integer))
% 6.51/6.88 (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 ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M2))))))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.last_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 6.51/6.88 (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)))))))))))
% 6.51/6.88 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.one_one_rat)) (lambda ((N2 tptp.nat)) tptp.one_one_rat)))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (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))))))))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y8 N2)))) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y8 N2)))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y8 N2)))) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y8 N2)))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)))) tptp.times_times_nat) tptp.times_times_nat))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)))) tptp.times_times_int) tptp.times_times_int))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) tptp.suc) tptp.suc))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)))) tptp.plus_plus_int) tptp.plus_plus_int))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)))) tptp.plus_plus_nat) tptp.plus_plus_nat))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (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))
% 6.51/6.88 (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))
% 6.51/6.88 (assert (@ (@ tptp.pcr_real (lambda ((N2 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y8 N2)))) tptp.plus_plus_real))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y8 N2)))) tptp.times_times_real))
% 6.51/6.88 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.51/6.88 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) 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))
% 6.51/6.88 (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))
% 6.51/6.88 (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))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (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))
% 6.51/6.88 (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))
% 6.51/6.88 (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 ((U3 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 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U3)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.51/6.88 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) tptp.pcr_int) (lambda ((N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.51/6.88 (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))
% 6.51/6.88 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U3)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.51/6.88 (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 ((U3 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 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __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 ((U3 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 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0)))))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (U2 tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y4)) (@ (@ tptp.product_Pair_nat_nat U2) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U2) Y4)))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.51/6.88 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X2) V4) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0)))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) 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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0)))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) 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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0)))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U3)) (@ (@ 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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U3)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))))
% 6.51/6.88 (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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U3)))) __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 ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U3)))) __flatten_var_0)))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.51/6.88 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) 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)))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (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))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (assert (= tptp.one_one_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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))))))
% 6.51/6.88 (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))))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (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)))))))
% 6.51/6.88 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real) tptp.id_o) (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)))))))))))
% 6.51/6.88 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.51/6.88 (assert (forall ((F5 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F5)) (@ tptp.finite_finite_nat F5))))
% 6.51/6.88 (assert (forall ((N tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A2)) (@ (@ tptp.insert_nat N) (@ _let_1 A2))))))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y4) Y4)))
% 6.51/6.88 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y4) X)))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y4) Y4)))
% 6.51/6.88 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y4) X)))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y4) Y4)))
% 6.51/6.88 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y4) X)))
% 6.51/6.88 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y4) Y4)))
% 6.51/6.88 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y4) X)))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y4) Y4)))
% 6.51/6.88 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y4) X)))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y4) Y4)))
% 6.51/6.88 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.extended_enat) (Y4 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.extended_enat) (Y4 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.list_int) (Y4 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.list_int) (Y4 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.option_nat) (Y4 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.option_nat) (Y4 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.option_num) (Y4 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.option_num) (Y4 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y4 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y4 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y4) X)))
% 47.50/47.83 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 47.50/47.83 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y4 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y4) Y4)))
% 47.50/47.83 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y4 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y4) X)))
% 47.50/47.83 (assert (not (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_VEBT_low tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) tptp.maxy)))
% 47.50/47.83 (set-info :filename cvc5---1.0.5_12079)
% 47.50/47.83 (check-sat-assuming ( true ))
% 47.50/47.83 ------- get file name : TPTP file name is ITP241^3
% 47.50/47.83 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12079.smt2...
% 47.50/47.83 --- Run --ho-elim --full-saturate-quant at 10...
% 47.50/47.83 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 47.50/47.83 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 47.50/47.83 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 47.50/47.83 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 47.50/47.83 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 116.77/117.01 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 116.77/117.01 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 116.77/117.01 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 116.77/117.01 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 116.77/117.01 % SZS status Theorem for ITP241^3
% 116.77/117.01 % SZS output start Proof for ITP241^3
% 116.77/117.01 (
% 116.77/117.01 (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.divide_divide_nat tptp.deg))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_4))) (let ((_let_6 (not (@ (@ tptp.ord_less_eq_nat _let_5) tptp.maxy)))) (let ((_let_7 (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat))) (let ((_let_8 (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) _let_7))) (let ((_let_9 (= tptp.times_times_rat (@ _let_8 (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_10 (= tptp.plus_plus_rat (@ _let_8 (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_11 (= tptp.uminus_uminus_rat (@ _let_7 (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_12 (= tptp.inverse_inverse_rat (@ _let_7 (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_13 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (let ((_let_14 (= 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_15 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_16 (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel))) (let ((_let_17 (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) _let_16))) (let ((_let_18 (= 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_19 (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel))) (let ((_let_20 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) _let_19))) (let ((_let_21 (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel))) (let ((_let_22 (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel))) (let ((_let_23 (= 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 ((U3 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X2) V4) (@ (@ tptp.plus_plus_nat U3) Y)))) __flatten_var_0)))))) (let ((_let_24 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_25 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_26 (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int))) (let ((_let_27 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) _let_26))) (let ((_let_28 (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int))) (let ((_let_29 (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int))) (let ((_let_30 (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat))) (let ((_let_31 (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) _let_30))) (let ((_let_32 (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)))) (let ((_let_33 (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)))) (let ((_let_34 (= 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_35 (= 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 ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M2)) (@ X6 N2)))) R5)))))))))))) (let ((_let_36 (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat)))) (let ((_let_37 (= tptp.bNF_Ca8459412986667044542atLess _let_36))) (let ((_let_38 (= tptp.rcis (lambda ((R5 tptp.real) (A4 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A4)))))) (let ((_let_39 (= 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_40 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M2) N2))) M2)))))) (let ((_let_41 (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M2))))))) (let ((_let_42 (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J3)))))) (let ((_let_43 (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M2))))))) (let ((_let_44 (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M2)))))) (let ((_let_45 (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))) (let ((_let_46 (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))) (let ((_let_47 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M2 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M2)))))))) (let ((_let_48 (@ tptp.bit0 _let_1))) (let ((_let_49 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_48))))))))) (let ((_let_50 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_49))) (let ((_let_51 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_52 (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real _let_51) tptp.one_one_real)))) (let ((_let_53 (= tptp.complete_Sup_Sup_nat (lambda ((X6 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X6 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X6)))))) (let ((_let_54 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_55 (@ tptp.topolo2177554685111907308n_real tptp.one_one_real))) (let ((_let_56 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_57 (@ tptp.filterlim_real_real tptp.tanh_real))) (let ((_let_58 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_59 (@ tptp.divide_divide_real tptp.pi))) (let ((_let_60 (@ _let_59 _let_58))) (let ((_let_61 (@ tptp.uminus_uminus_real _let_60))) (let ((_let_62 (@ tptp.filterlim_real_real tptp.tan_real))) (let ((_let_63 (@ tptp.filterlim_real_real tptp.artanh_real))) (let ((_let_64 (@ tptp.filterlim_real_real tptp.arctan))) (let ((_let_65 (@ tptp.topolo2177554685111907308n_real _let_60))) (let ((_let_66 (@ tptp.topolo2815343760600316023s_real tptp.one_one_real))) (let ((_let_67 (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C2)))))))) (let ((_let_68 (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))) (let ((_let_69 (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)))))) (let ((_let_70 (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))) (let ((_let_71 (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J3)))))) (let ((_let_72 (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_50)))) (let ((_let_73 (= 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_74 (@ tptp.insert_nat tptp.zero_zero_nat))) (let ((_let_75 (= 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_76 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_77 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_78 (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))) (let ((_let_79 (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I4 tptp.int) (N2 tptp.nat)) (and (= Uu2 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))) (let ((_let_80 (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M2 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M2)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))) (let ((_let_81 (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))) (let ((_let_82 (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))) (let ((_let_83 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_84 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_83))) (let ((_let_85 (@ _let_83 (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2)))))) (let ((_let_86 (= tptp.uminus_uminus_int _let_85))) (let ((_let_87 (= tptp.normalize (lambda ((P4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P4))) (let ((_let_2 (@ tptp.product_fst_int_int P4))) (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_88 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_89 (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.divide_divide_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_90 (= 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_91 (= 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_92 (= 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_93 (= 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_94 (@ tptp.numera6620942414471956472nteger _let_1))) (let ((_let_95 (= 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_96 (= tptp.real_V1022390504157884413omplex (lambda ((Z4 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 Z4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z4)) _let_1)))))))) (let ((_let_97 (= 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))))))))))) (let ((_let_98 (= 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_99 (= 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))))))) (let ((_let_100 (= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ 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_101 (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))) (let ((_let_102 (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))) (let ((_let_103 (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M2)) (@ X6 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))) (let ((_let_104 (= tptp.ord_less_eq_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C2 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 C2) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))))) (let ((_let_105 (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.times_times_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_106 (= 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_107 (= 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_108 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_109 (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))) (let ((_let_110 (= tptp.bit_se2161824704523386999it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M2) tptp.one_one_nat)))))) (let ((_let_111 (= tptp.sgn_sgn_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (= A4 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A4)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))) (let ((_let_112 (= 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_113 (= tptp.bit_se7882103937844011126it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M2) tptp.one_one_nat)))))) (let ((_let_114 (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))) (let ((_let_115 (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))) (let ((_let_116 (= tptp.bit_se1148574629649215175it_nat (lambda ((M2 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 M2) (@ (@ tptp.power_power_nat _let_1) N2))))))))) (let ((_let_117 (= 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_118 (= 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_119 (= 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_120 (= 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_121 (= 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_122 (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_123 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_124 (@ tptp.suc _let_123))) (let ((_let_125 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_126 (@ tptp.nat2 _let_125))) (let ((_let_127 (= 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_128 (= tptp.sqrt (@ tptp.root _let_2)))) (let ((_let_129 (= tptp.minus_minus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))) (let ((_let_130 (= 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_131 (= 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_132 (@ tptp.nat2 tptp.one_one_int))) (let ((_let_133 (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))) (let ((_let_134 (= 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_135 (= 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_136 (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 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 (= A1 K3) (= A22 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 (= A1 K3) (= A22 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_137 (= 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_138 (= 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_139 (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))) (let ((_let_140 (@ tptp.sqrt _let_58))) (let ((_let_141 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_142 (= tptp.cis (lambda ((B3 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))) (let ((_let_143 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_144 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_145 (@ tptp.times_times_complex _let_143))) (let ((_let_146 (@ tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_147 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_148 (@ tptp.power_power_nat _let_2))) (let ((_let_149 (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_148)))) (let ((_let_150 (@ tptp.times_times_real _let_58))) (let ((_let_151 (@ _let_150 tptp.pi))) (let ((_let_152 (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_153 (= 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_154 (= tptp.sinh_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z4)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (let ((_let_155 (= tptp.sinh_real (lambda ((Z4 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z4)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_156 (= tptp.cosh_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z4)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (let ((_let_157 (= tptp.cosh_real (lambda ((Z4 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z4)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_158 (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))) (let ((_let_159 (@ tptp.exp_real tptp.one_one_real))) (let ((_let_160 (= tptp.ln_ln_real (@ tptp.log _let_159)))) (let ((_let_161 (= 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_162 (= 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_163 (= 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_164 (= 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_165 (= 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_166 (= tptp.set_ord_atMost_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U3))))))) (let ((_let_167 (= tptp.set_ord_atMost_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U3))))))) (let ((_let_168 (= tptp.set_ord_atMost_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U3))))))) (let ((_let_169 (= tptp.set_ord_atMost_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U3))))))) (let ((_let_170 (= tptp.set_or4236626031148496127et_nat (lambda ((U3 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) U3))))))) (let ((_let_171 (= tptp.set_ord_atMost_real (lambda ((U3 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U3))))))) (let ((_let_172 (= tptp.real_V1485227260804924795R_real tptp.times_times_real))) (let ((_let_173 (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) X2)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))))) (let ((_let_174 (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))) (let ((_let_175 (= 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_176 (= 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_177 (= 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_178 (= tptp.cot_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))))) (let ((_let_179 (= tptp.cot_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X2)) (@ tptp.sin_complex X2)))))) (let ((_let_180 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_181 (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))) (let ((_let_182 (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))) (let ((_let_183 (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))) (let ((_let_184 (@ tptp.numeral_numeral_rat tptp.one))) (let ((_let_185 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_186 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_187 (@ tptp.arccos _let_51))) (let ((_let_188 (= _let_187 tptp.pi))) (let ((_let_189 (= 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_190 (= 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_191 (= 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_192 (= 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_193 (= 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_194 (= 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_195 (@ tptp.bit1 tptp.one))) (let ((_let_196 (@ tptp.numeral_numeral_real _let_195))) (let ((_let_197 (@ tptp.sqrt _let_196))) (let ((_let_198 (@ _let_59 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_195))))) (let ((_let_199 (@ (@ tptp.divide_divide_real _let_197) _let_58))) (let ((_let_200 (@ _let_59 _let_196))) (let ((_let_201 (@ (@ tptp.divide_divide_real _let_140) _let_58))) (let ((_let_202 (@ tptp.numeral_numeral_real _let_48))) (let ((_let_203 (@ _let_59 _let_202))) (let ((_let_204 (@ _let_180 _let_58))) (let ((_let_205 (= 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_206 (= 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_207 (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))) (let ((_let_208 (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))) (let ((_let_209 (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))) (let ((_let_210 (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))) (let ((_let_211 (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))) (let ((_let_212 (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))) (let ((_let_213 (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))) (let ((_let_214 (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N2) tptp.zero_zero_real))))) (let ((_let_215 (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N2) tptp.zero_zero_int))))) (let ((_let_216 (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.plus_plus_complex I4) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))) (let ((_let_217 (= 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_218 (= 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_219 (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))) (let ((_let_220 (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))) (let ((_let_221 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_222 (@ tptp.cos_real _let_58))) (let ((_let_223 (= tptp.diffs_rat (lambda ((C2 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C2 _let_1))))))) (let ((_let_224 (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))) (let ((_let_225 (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))) (let ((_let_226 (@ tptp.divide_divide_real _let_196))) (let ((_let_227 (@ (@ tptp.times_times_real (@ _let_226 _let_58)) tptp.pi))) (let ((_let_228 (= tptp.topolo4899668324122417113eq_int (lambda ((X6 (-> tptp.nat tptp.int))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X6 N2)) (@ X6 M2))))))))) (let ((_let_229 (= tptp.topolo4902158794631467389eq_nat (lambda ((X6 (-> tptp.nat tptp.nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 N2)) (@ X6 M2))))))))) (let ((_let_230 (= tptp.topolo1459490580787246023eq_num (lambda ((X6 (-> tptp.nat tptp.num))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X6 N2)) (@ X6 M2))))))))) (let ((_let_231 (= tptp.topolo4267028734544971653eq_rat (lambda ((X6 (-> tptp.nat tptp.rat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ X6 M2))))))))) (let ((_let_232 (= tptp.topolo7278393974255667507et_nat (lambda ((X6 (-> tptp.nat tptp.set_nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X6 N2)) (@ X6 M2))))))))) (let ((_let_233 (= tptp.topolo6980174941875973593q_real (lambda ((X6 (-> tptp.nat tptp.real))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X6 M2)) (@ X6 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X6 N2)) (@ X6 M2))))))))) (let ((_let_234 (@ tptp.bit1 _let_195))) (let ((_let_235 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1)))) (let ((_let_236 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_237 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_238 (@ tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_239 (@ tptp.power_power_int tptp.zero_zero_int))) (let ((_let_240 (@ tptp.power_power_real tptp.zero_zero_real))) (let ((_let_241 (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M2) N2)) (@ (@ tptp.modulo_modulo_nat M2) N2)))))) (let ((_let_242 (= tptp.set_or5984915006950818249n_real (lambda ((U3 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U3))))))) (let ((_let_243 (= tptp.set_ord_lessThan_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U3))))))) (let ((_let_244 (= tptp.set_ord_lessThan_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U3))))))) (let ((_let_245 (= tptp.set_ord_lessThan_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U3))))))) (let ((_let_246 (= tptp.set_ord_lessThan_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U3))))))) (let ((_let_247 (= 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_248 (= 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_249 (= 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_250 (= 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_251 (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))) (let ((_let_252 (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))) (let ((_let_253 (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))) (let ((_let_254 (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))) (let ((_let_255 (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z4 tptp.int)) (exists ((N2 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))) (let ((_let_256 (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_257 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_258 (@ tptp.numeral_numeral_int _let_195))) (let ((_let_259 (@ tptp.numeral_numeral_rat _let_195))) (let ((_let_260 (@ tptp.numera6690914467698888265omplex _let_195))) (let ((_let_261 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))) (let ((_let_262 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))) (let ((_let_263 (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))) (let ((_let_264 (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))) (let ((_let_265 (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_266 (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_267 (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_268 (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))) (let ((_let_269 (= 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_270 (= 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_271 (= 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_272 (= 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_273 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_274 (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_275 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_276 (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_277 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_278 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_279 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_280 (@ tptp.ord_le6747313008572928689nteger _let_257))) (let ((_let_281 (@ tptp.ord_less_rat _let_76))) (let ((_let_282 (@ tptp.ord_less_int _let_77))) (let ((_let_283 (@ tptp.ord_less_real _let_51))) (let ((_let_284 (@ tptp.ord_less_eq_int _let_77))) (let ((_let_285 (@ tptp.ord_less_eq_rat _let_76))) (let ((_let_286 (@ tptp.ord_le3102999989581377725nteger _let_257))) (let ((_let_287 (@ tptp.ord_less_eq_real _let_51))) (let ((_let_288 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_289 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_290 (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))) (let ((_let_291 (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))) (let ((_let_292 (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))) (let ((_let_293 (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))) (let ((_let_294 (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))) (let ((_let_295 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_296 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_297 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_298 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_299 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_300 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_301 (= tptp.zero_n2684676970156552555ol_int (lambda ((P4 Bool)) (@ (@ (@ tptp.if_int P4) tptp.one_one_int) tptp.zero_zero_int))))) (let ((_let_302 (= tptp.zero_n2687167440665602831ol_nat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_nat P4) tptp.one_one_nat) tptp.zero_zero_nat))))) (let ((_let_303 (= tptp.zero_n2052037380579107095ol_rat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_rat P4) tptp.one_one_rat) tptp.zero_zero_rat))))) (let ((_let_304 (= tptp.zero_n3304061248610475627l_real (lambda ((P4 Bool)) (@ (@ (@ tptp.if_real P4) tptp.one_one_real) tptp.zero_zero_real))))) (let ((_let_305 (= tptp.zero_n1201886186963655149omplex (lambda ((P4 Bool)) (@ (@ (@ tptp.if_complex P4) tptp.one_one_complex) tptp.zero_zero_complex))))) (let ((_let_306 (@ tptp.uminus1351360451143612070nteger _let_94))) (let ((_let_307 (@ tptp.uminus_uminus_rat _let_221))) (let ((_let_308 (@ tptp.uminus1482373934393186551omplex _let_144))) (let ((_let_309 (@ tptp.uminus_uminus_int _let_125))) (let ((_let_310 (@ tptp.uminus_uminus_real _let_58))) (let ((_let_311 (= (@ (@ tptp.modulo364778990260209775nteger _let_257) _let_94) tptp.one_one_Code_integer))) (let ((_let_312 (= (@ (@ tptp.modulo_modulo_int _let_77) _let_125) tptp.one_one_int))) (let ((_let_313 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_314 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_315 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_316 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_317 (@ tptp.minus_8373710615458151222nteger _let_257))) (let ((_let_318 (@ tptp.minus_minus_rat _let_76))) (let ((_let_319 (@ tptp.minus_minus_complex _let_147))) (let ((_let_320 (@ tptp.minus_minus_int _let_77))) (let ((_let_321 (@ tptp.minus_minus_real _let_51))) (let ((_let_322 (@ tptp.plus_p5714425477246183910nteger _let_257))) (let ((_let_323 (@ tptp.plus_plus_rat _let_76))) (let ((_let_324 (@ tptp.plus_plus_complex _let_147))) (let ((_let_325 (@ tptp.plus_plus_int _let_77))) (let ((_let_326 (@ tptp.plus_plus_real _let_51))) (let ((_let_327 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_328 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_329 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_330 (@ _let_322 tptp.one_one_Code_integer))) (let ((_let_331 (= _let_330 tptp.zero_z3403309356797280102nteger))) (let ((_let_332 (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))) (let ((_let_333 (= 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_334 (@ tptp.dvd_dvd_int _let_125))) (let ((_let_335 (@ tptp.dvd_dvd_nat _let_2))) (let ((_let_336 (@ tptp.dvd_dvd_Code_integer _let_94))) (let ((_let_337 (= 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_338 (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K3))))))) (let ((_let_339 (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K3))))))) (let ((_let_340 (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (exists ((K3 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B3) K3))))))) (let ((_let_341 (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B3) K3))))))) (let ((_let_342 (= 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_343 (= 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_344 (= 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_345 (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))) (let ((_let_346 (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))) (let ((_let_347 (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))) (let ((_let_348 (= tptp.ord_max_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B3)) B3) A4))))) (let ((_let_349 (= 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_350 (= tptp.ord_max_num (lambda ((A4 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B3)) B3) A4))))) (let ((_let_351 (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B3)) B3) A4))))) (let ((_let_352 (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B3)) B3) A4))))) (let ((_let_353 (= 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))))) (let ((_let_354 (= tptp.modulo_modulo_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2)))))) (let ((_let_355 (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M2)))))))) (let ((_let_356 (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) _let_94) tptp.one_one_Code_integer))) (let ((_let_357 (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) _let_125) tptp.one_one_int))) (let ((_let_358 (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) _let_2) tptp.one_one_nat))) (let ((_let_359 (= 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_360 (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_361 (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_362 (= tptp.bot_bot_set_real (@ tptp.collect_real tptp.bot_bot_real_o)))) (let ((_let_363 (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))) (let ((_let_364 (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))) (let ((_let_365 (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))) (let ((_let_366 (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat tptp.bot_bo482883023278783056_nat_o)))) (let ((_let_367 (= tptp.bot_bot_set_complex (@ tptp.collect_complex tptp.bot_bot_complex_o)))) (let ((_let_368 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_369 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_370 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_371 (@ _let_328 tptp.one_one_int))) (let ((_let_372 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_373 (@ _let_372 tptp.one_one_nat))) (let ((_let_374 (@ _let_327 tptp.one_one_rat))) (let ((_let_375 (@ _let_329 tptp.one_one_real))) (let ((_let_376 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_377 (@ _let_279 tptp.one_one_int))) (let ((_let_378 (@ _let_369 tptp.one_one_nat))) (let ((_let_379 (@ _let_278 tptp.one_one_rat))) (let ((_let_380 (@ _let_237 tptp.one_one_real))) (let ((_let_381 (@ _let_288 tptp.one_one_int))) (let ((_let_382 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_383 (@ _let_382 tptp.one_one_nat))) (let ((_let_384 (@ _let_289 tptp.one_one_rat))) (let ((_let_385 (@ _let_236 tptp.one_one_real))) (let ((_let_386 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_387 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_125) tptp.zero_zero_int))) (let ((_let_388 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_2))) (let ((_let_389 (= _let_388 tptp.zero_zero_nat))) (let ((_let_390 (@ _let_315 tptp.one_one_int))) (let ((_let_391 (= _let_390 tptp.zero_zero_int))) (let ((_let_392 (@ _let_313 tptp.one_one_rat))) (let ((_let_393 (= _let_392 tptp.zero_zero_rat))) (let ((_let_394 (@ _let_316 tptp.one_one_real))) (let ((_let_395 (= _let_394 tptp.zero_zero_real))) (let ((_let_396 (@ _let_314 tptp.one_one_complex))) (let ((_let_397 (= _let_396 tptp.zero_zero_complex))) (let ((_let_398 (= 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_399 (= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_int Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)))))))))) (let ((_let_400 (= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_nat Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)))))))))) (let ((_let_401 (= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu2 Bool)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_o Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)))))))))) (let ((_let_402 (= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu2 tptp.vEBT_VEBT)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_VEBT_VEBT Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))) (let ((_let_403 (= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu2 tptp.list_nat)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_list_nat Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))) (let ((_let_404 (= tptp.set_Pr5648618587558075414at_nat (lambda ((Xs tptp.list_P6011104703257516679at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((Uu2 tptp.product_prod_nat_nat)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)))))))))) (let ((_let_405 (= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_real Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)))))))))) (let ((_let_406 (= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((I4 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_complex Xs) I4)) (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)))))))))) (let ((_let_407 (= tptp.suc _let_372))) (let ((_let_408 (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))) (let ((_let_409 (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))) (let ((_let_410 (@ tptp.vEBT_VEBT_high tptp.xa))) (let ((_let_411 (@ _let_410 _let_4))) (let ((_let_412 (@ (@ tptp.vEBT_vebt_pred tptp.summary) _let_411))) (let ((_let_413 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_414 (@ _let_413 (@ tptp.the_nat _let_412)))) (let ((_let_415 (@ tptp.vEBT_vebt_maxt _let_414))) (let ((_let_416 (@ _let_148 _let_4))) (let ((_let_417 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat _let_416)))) (let ((_let_418 (@ (@ tptp.vEBT_VEBT_add (@ _let_417 _let_412)) _let_415))) (let ((_let_419 (@ tptp.some_nat tptp.mi))) (let ((_let_420 (@ tptp.ord_less_nat tptp.mi))) (let ((_let_421 (@ _let_420 tptp.xa))) (let ((_let_422 (= _let_412 tptp.none_nat))) (let ((_let_423 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary))) (let ((_let_424 (@ (@ tptp.vEBT_vebt_pred _let_423) tptp.xa))) (let ((_let_425 (@ _let_413 _let_411))) (let ((_let_426 (@ tptp.vEBT_vebt_mint _let_425))) (let ((_let_427 (@ tptp.vEBT_VEBT_low tptp.xa))) (let ((_let_428 (@ _let_427 _let_4))) (let ((_let_429 (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_428)) _let_426))) (let ((_let_430 (= _let_426 tptp.none_nat))) (let ((_let_431 (and (not _let_430) _let_429))) (let ((_let_432 (= _let_373 _let_2))) (let ((_let_433 (= _let_370 tptp.one_one_nat))) (let ((_let_434 (= _let_277 tptp.one_one_int))) (let ((_let_435 (= _let_184 tptp.one_one_rat))) (let ((_let_436 (= _let_186 tptp.one_one_real))) (let ((_let_437 (= _let_185 tptp.one_one_complex))) (let ((_let_438 (= _let_424 _let_418))) (let ((_let_439 (= 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_440 (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))) (let ((_let_441 (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))) (let ((_let_442 (@ tptp.vEBT_vebt_member _let_423))) (let ((_let_443 (= tptp.res (@ tptp.the_nat _let_418)))) (let ((_let_444 (@ tptp.ord_less_nat tptp.za))) (let ((_let_445 (= tptp.mi tptp.ma))) (let ((_let_446 (@ tptp.some_nat tptp.maxy))) (let ((_let_447 (= 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_448 (= 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 ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat Z4) X2) (@ (@ tptp.ord_less_eq_nat Z4) Y))))))))) (let ((_let_449 (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))) (let ((_let_450 (= tptp.m (@ tptp.suc tptp.na)))) (let ((_let_451 (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))) (let ((_let_452 (@ _let_148 tptp.m))) (let ((_let_453 (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_454 (= _let_453 _let_452))) (let ((_let_455 (@ _let_413 tptp.pr))) (let ((_let_456 (not _let_445))) (let ((_let_457 (@ (@ tptp.vEBT_VEBT_high tptp.res) _let_4))) (let ((_let_458 (@ tptp.ord_less_nat tptp.pr))) (let ((_let_459 (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_4))) (let ((_let_460 (@ tptp.ord_less_nat _let_459))) (let ((_let_461 (@ _let_413 _let_459))) (let ((_let_462 (@ (@ tptp.vEBT_vebt_member _let_461) _let_5))) (let ((_let_463 (= tptp.za tptp.ma))) (let ((_let_464 (= tptp.za tptp.mi))) (let ((_let_465 (= 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_466 (@ tptp.ord_less_nat tptp.res))) (let ((_let_467 (@ tptp.vEBT_vebt_member tptp.summary))) (let ((_let_468 (@ _let_148 tptp.deg))) (let ((_let_469 (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y) (not (= X2 Y))))))) (let ((_let_470 (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y) (not (= X2 Y))))))) (let ((_let_471 (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y) (not (= X2 Y))))))) (let ((_let_472 (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y) (not (= X2 Y))))))) (let ((_let_473 (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y) (not (= X2 Y))))))) (let ((_let_474 (= 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_475 (= 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_476 (@ (@ tptp.vEBT_invar_vebt _let_461) tptp.na))) (let ((_let_477 (= _let_4 tptp.na))) (let ((_let_478 (= _let_446 (@ tptp.vEBT_vebt_maxt _let_455)))) (let ((_let_479 (= _let_459 tptp.pr))) (let ((_let_480 (= 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_481 (= 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_482 (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))))))) (let ((_let_483 (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (let ((_let_1 (ho_7533 k_7532 Maxi))) (or (not (ho_7541 (ho_10447 k_14775 T) N)) (not (= _let_1 (ho_15528 k_15959 T))) (not (ho_7541 (ho_10447 k_15958 T) X)) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 X)) _let_1)))))) (let ((_let_484 (ho_7533 k_7532 tptp.maxy))) (let ((_let_485 (ho_7446 k_7445 tptp.one))) (let ((_let_486 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_487 (ho_7459 (ho_7461 k_7460 _let_485) (ho_7459 _let_486 _let_485)))) (let ((_let_488 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_489 (ho_7466 (ho_7465 k_7471 tptp.deg) _let_488))) (let ((_let_490 (ho_7466 (ho_7465 k_7464 _let_488) _let_489))) (let ((_let_491 (ho_7469 k_7468 k_7467))) (let ((_let_492 (ho_7466 (ho_7465 k_7471 tptp.za) _let_490))) (let ((_let_493 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_491 tptp.za) _let_487)) (ho_7459 _let_486 (ho_7459 (ho_7470 _let_491 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_491 _let_492) _let_487)) (ho_7459 (ho_7470 _let_491 _let_490) _let_487)))) _let_487)))))) (let ((_let_494 (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 _let_493)) _let_484))) (let ((_let_495 (ho_7822 (ho_7821 k_7820 tptp.treeList) _let_492))) (let ((_let_496 (ho_7541 (ho_10447 k_15958 _let_495) _let_493))) (let ((_let_497 (not _let_496))) (let ((_let_498 (= (ho_15528 k_15959 _let_495) _let_484))) (let ((_let_499 (not _let_498))) (let ((_let_500 (ho_7541 (ho_10447 k_14775 _let_495) _let_489))) (let ((_let_501 (not _let_500))) (let ((_let_502 (or _let_501 _let_499 _let_497 _let_494))) (let ((_let_503 (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_16405 x z) (ho_16405 y z)))) (= x y))))) (let ((_let_504 (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_16513 x z) (ho_16513 y z)))) (= x y))))) (let ((_let_505 (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_16399 x z) (ho_16399 y z)))) (= x y))))) (let ((_let_506 (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_16392 x z) (ho_16392 y z)))) (= x y))))) (let ((_let_507 (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_11110 x z) (ho_11110 y z)))) (= x y))))) (let ((_let_508 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_real)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_real)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_16395 x z) (ho_16395 y z)))) (= x y))))) (let ((_let_509 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_int)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_int)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16391 x z) (ho_16391 y z)))) (= x y))))) (let ((_let_510 (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_16389 x z) (ho_16389 y z)))) (= x y))))) (let ((_let_511 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16386 x z) (ho_16386 y z)))) (= x y))))) (let ((_let_512 (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_16374 x z) (ho_16374 y z)))) (= x y))))) (let ((_let_513 (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_16372 x z) (ho_16372 y z)))) (= x y))))) (let ((_let_514 (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_13807 x z) (ho_13807 y z)))) (= x y))))) (let ((_let_515 (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_16369 x z) (ho_16369 y z)))) (= x y))))) (let ((_let_516 (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_16370 x z) (ho_16370 y z)))) (= x y))))) (let ((_let_517 (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_12016 x z) (ho_12016 y z)))) (= x y))))) (let ((_let_518 (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_16361 x z) (ho_16361 y z)))) (= x y))))) (let ((_let_519 (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_16359 x z) (ho_16359 y z)))) (= x y))))) (let ((_let_520 (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_16358 x z) (ho_16358 y z)))) (= x y))))) (let ((_let_521 (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_7999 x z) (ho_7999 y z)))) (= x y))))) (let ((_let_522 (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_16356 x z) (ho_16356 y z)))) (= x y))))) (let ((_let_523 (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_16352 x z) (ho_16352 y z)))) (= x y))))) (let ((_let_524 (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_14520 x z) (ho_14520 y z)))) (= x y))))) (let ((_let_525 (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_16350 x z) (ho_16350 y z)))) (= x y))))) (let ((_let_526 (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_14524 x z) (ho_14524 y z)))) (= x y))))) (let ((_let_527 (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_16349 x z) (ho_16349 y z)))) (= x y))))) (let ((_let_528 (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_8100 x z) (ho_8100 y z)))) (= x y))))) (let ((_let_529 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_11990 x z) (ho_11990 y z)))) (= x y))))) (let ((_let_530 (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_16347 x z) (ho_16347 y z)))) (= x y))))) (let ((_let_531 (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_16346 x z) (ho_16346 y z)))) (= x y))))) (let ((_let_532 (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_16345 x z) (ho_16345 y z)))) (= x y))))) (let ((_let_533 (forall ((x |u_(-> tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16341 x z) (ho_16341 y z)))) (= x y))))) (let ((_let_534 (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_16337 x z) (ho_16337 y z)))) (= x y))))) (let ((_let_535 (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_16334 x z) (ho_16334 y z)))) (= x y))))) (let ((_let_536 (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_16329 x z) (ho_16329 y z)))) (= x y))))) (let ((_let_537 (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_16323 x z) (ho_16323 y z)))) (= x y))))) (let ((_let_538 (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_16199 x z) (ho_16199 y z)))) (= x y))))) (let ((_let_539 (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_13457 x z) (ho_13457 y z)))) (= x y))))) (let ((_let_540 (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_16317 x z) (ho_16317 y z)))) (= x y))))) (let ((_let_541 (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_16309 x z) (ho_16309 y z)))) (= x y))))) (let ((_let_542 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex Bool)_ tptp.complex tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex Bool)_ tptp.complex tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex Bool)|)) (= (ho_14570 x z) (ho_14570 y z)))) (= x y))))) (let ((_let_543 (forall ((x |u_(-> tptp.set_complex tptp.real)|) (y |u_(-> tptp.set_complex tptp.real)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_16310 x z) (ho_16310 y z)))) (= x y))))) (let ((_let_544 (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_16711 x z) (ho_16711 y z)))) (= x y))))) (let ((_let_545 (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_16306 x z) (ho_16306 y z)))) (= x y))))) (let ((_let_546 (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_16300 x z) (ho_16300 y z)))) (= x y))))) (let ((_let_547 (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_7644 x z) (ho_7644 y z)))) (= x y))))) (let ((_let_548 (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_16297 x z) (ho_16297 y z)))) (= x y))))) (let ((_let_549 (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_16292 x z) (ho_16292 y z)))) (= x y))))) (let ((_let_550 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_14565 x z) (ho_14565 y z)))) (= x y))))) (let ((_let_551 (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_16289 x z) (ho_16289 y z)))) (= x y))))) (let ((_let_552 (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_16286 x z) (ho_16286 y z)))) (= x y))))) (let ((_let_553 (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_16283 x z) (ho_16283 y z)))) (= x y))))) (let ((_let_554 (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_15335 x z) (ho_15335 y z)))) (= x y))))) (let ((_let_555 (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_16280 x z) (ho_16280 y z)))) (= x y))))) (let ((_let_556 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_complex)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_complex)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_16400 x z) (ho_16400 y z)))) (= x y))))) (let ((_let_557 (forall ((x |u_(-> tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_16047 x z) (ho_16047 y z)))) (= x y))))) (let ((_let_558 (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_16693 x z) (ho_16693 y z)))) (= x y))))) (let ((_let_559 (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_16275 x z) (ho_16275 y z)))) (= x y))))) (let ((_let_560 (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_8162 x z) (ho_8162 y z)))) (= x y))))) (let ((_let_561 (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_16264 x z) (ho_16264 y z)))) (= x y))))) (let ((_let_562 (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_16265 x z) (ho_16265 y z)))) (= x y))))) (let ((_let_563 (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_13806 x z) (ho_13806 y z)))) (= x y))))) (let ((_let_564 (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_16394 x z) (ho_16394 y z)))) (= x y))))) (let ((_let_565 (forall ((x |u_(-> tptp.produc8763457246119570046nteger Bool)|) (y |u_(-> tptp.produc8763457246119570046nteger Bool)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_16259 x z) (ho_16259 y z)))) (= x y))))) (let ((_let_566 (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_16258 x z) (ho_16258 y z)))) (= x y))))) (let ((_let_567 (forall ((x |u_(-> tptp.int tptp.option6357759511663192854e_term)|) (y |u_(-> tptp.int tptp.option6357759511663192854e_term)|)) (or (not (forall ((z tptp.int)) (= (ho_16255 x z) (ho_16255 y z)))) (= x y))))) (let ((_let_568 (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_13814 x z) (ho_13814 y z)))) (= x y))))) (let ((_let_569 (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_16253 x z) (ho_16253 y z)))) (= x y))))) (let ((_let_570 (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_16254 x z) (ho_16254 y z)))) (= x y))))) (let ((_let_571 (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_16249 x z) (ho_16249 y z)))) (= x y))))) (let ((_let_572 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16250 x z) (ho_16250 y z)))) (= x y))))) (let ((_let_573 (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_16247 x z) (ho_16247 y z)))) (= x y))))) (let ((_let_574 (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_7936 x z) (ho_7936 y z)))) (= x y))))) (let ((_let_575 (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_16245 x z) (ho_16245 y z)))) (= x y))))) (let ((_let_576 (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_16238 x z) (ho_16238 y z)))) (= x y))))) (let ((_let_577 (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_14485 x z) (ho_14485 y z)))) (= x y))))) (let ((_let_578 (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_16232 x z) (ho_16232 y z)))) (= x y))))) (let ((_let_579 (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_16230 x z) (ho_16230 y z)))) (= x y))))) (let ((_let_580 (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_15522 x z) (ho_15522 y z)))) (= x y))))) (let ((_let_581 (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_16228 x z) (ho_16228 y z)))) (= x y))))) (let ((_let_582 (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_16226 x z) (ho_16226 y z)))) (= x y))))) (let ((_let_583 (forall ((x |u_(-> tptp.int tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.int tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_16381 x z) (ho_16381 y z)))) (= x y))))) (let ((_let_584 (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_16222 x z) (ho_16222 y z)))) (= x y))))) (let ((_let_585 (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_16216 x z) (ho_16216 y z)))) (= x y))))) (let ((_let_586 (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_16213 x z) (ho_16213 y z)))) (= x y))))) (let ((_let_587 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_11974 x z) (ho_11974 y z)))) (= x y))))) (let ((_let_588 (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_16362 x z) (ho_16362 y z)))) (= x y))))) (let ((_let_589 (forall ((x |u_(-> tptp.set_real tptp.real)|) (y |u_(-> tptp.set_real tptp.real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_16293 x z) (ho_16293 y z)))) (= x y))))) (let ((_let_590 (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_14029 x z) (ho_14029 y z)))) (= x y))))) (let ((_let_591 (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_16754 x z) (ho_16754 y z)))) (= x y))))) (let ((_let_592 (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_16210 x z) (ho_16210 y z)))) (= x y))))) (let ((_let_593 (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_16211 x z) (ho_16211 y z)))) (= x y))))) (let ((_let_594 (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_16214 x z) (ho_16214 y z)))) (= x y))))) (let ((_let_595 (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_16207 x z) (ho_16207 y z)))) (= x y))))) (let ((_let_596 (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_8022 x z) (ho_8022 y z)))) (= x y))))) (let ((_let_597 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.num)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.num)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_10559 x z) (ho_10559 y z)))) (= x y))))) (let ((_let_598 (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_16204 x z) (ho_16204 y z)))) (= x y))))) (let ((_let_599 (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_16198 x z) (ho_16198 y z)))) (= x y))))) (let ((_let_600 (forall ((x |u_(-> tptp.int tptp.set_nat)|) (y |u_(-> tptp.int tptp.set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_16363 x z) (ho_16363 y z)))) (= x y))))) (let ((_let_601 (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_16192 x z) (ho_16192 y z)))) (= x y))))) (let ((_let_602 (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_16190 x z) (ho_16190 y z)))) (= x y))))) (let ((_let_603 (forall ((x |u_(-> tptp.real tptp.real tptp.complex)|) (y |u_(-> tptp.real tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_7732 x z) (ho_7732 y z)))) (= x y))))) (let ((_let_604 (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_16184 x z) (ho_16184 y z)))) (= x y))))) (let ((_let_605 (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_16185 x z) (ho_16185 y z)))) (= x y))))) (let ((_let_606 (forall ((x |u_(-> tptp.set_int tptp.complex)|) (y |u_(-> tptp.set_int tptp.complex)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16281 x z) (ho_16281 y z)))) (= x y))))) (let ((_let_607 (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_14320 x z) (ho_14320 y z)))) (= x y))))) (let ((_let_608 (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_8088 x z) (ho_8088 y z)))) (= x y))))) (let ((_let_609 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.int)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.int)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_10567 x z) (ho_10567 y z)))) (= x y))))) (let ((_let_610 (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_16178 x z) (ho_16178 y z)))) (= x y))))) (let ((_let_611 (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_16176 x z) (ho_16176 y z)))) (= x y))))) (let ((_let_612 (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_16179 x z) (ho_16179 y z)))) (= x y))))) (let ((_let_613 (forall ((x |u_(-> Bool tptp.product_prod_o_o)|) (y |u_(-> Bool tptp.product_prod_o_o)|)) (or (not (forall ((z Bool)) (= (ho_16173 x z) (ho_16173 y z)))) (= x y))))) (let ((_let_614 (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_16169 x z) (ho_16169 y z)))) (= x y))))) (let ((_let_615 (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_16166 x z) (ho_16166 y z)))) (= x y))))) (let ((_let_616 (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_16008 x z) (ho_16008 y z)))) (= x y))))) (let ((_let_617 (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_16163 x z) (ho_16163 y z)))) (= x y))))) (let ((_let_618 (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_13342 x z) (ho_13342 y z)))) (= x y))))) (let ((_let_619 (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_16793 x z) (ho_16793 y z)))) (= x y))))) (let ((_let_620 (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_16164 x z) (ho_16164 y z)))) (= x y))))) (let ((_let_621 (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_16792 x z) (ho_16792 y z)))) (= x y))))) (let ((_let_622 (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_16157 x z) (ho_16157 y z)))) (= x y))))) (let ((_let_623 (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_16154 x z) (ho_16154 y z)))) (= x y))))) (let ((_let_624 (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_16149 x z) (ho_16149 y z)))) (= x y))))) (let ((_let_625 (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_16150 x z) (ho_16150 y z)))) (= x y))))) (let ((_let_626 (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_13671 x z) (ho_13671 y z)))) (= x y))))) (let ((_let_627 (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_16710 x z) (ho_16710 y z)))) (= x y))))) (let ((_let_628 (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_16144 x z) (ho_16144 y z)))) (= x y))))) (let ((_let_629 (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_10000 x z) (ho_10000 y z)))) (= x y))))) (let ((_let_630 (forall ((x |u_(-> tptp.real tptp.nat tptp.nat)|) (y |u_(-> tptp.real tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_14414 x z) (ho_14414 y z)))) (= x y))))) (let ((_let_631 (forall ((x |u_(-> tptp.nat tptp.produc334124729049499915VEBT_o)|) (y |u_(-> tptp.nat tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_16147 x z) (ho_16147 y z)))) (= x y))))) (let ((_let_632 (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_16721 x z) (ho_16721 y z)))) (= x y))))) (let ((_let_633 (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_16134 x z) (ho_16134 y z)))) (= x y))))) (let ((_let_634 (forall ((x |u_(-> tptp.nat tptp.produc8243902056947475879T_VEBT)|) (y |u_(-> tptp.nat tptp.produc8243902056947475879T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_16138 x z) (ho_16138 y z)))) (= x y))))) (let ((_let_635 (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_10968 x z) (ho_10968 y z)))) (= x y))))) (let ((_let_636 (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_16131 x z) (ho_16131 y z)))) (= x y))))) (let ((_let_637 (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_16132 x z) (ho_16132 y z)))) (= x y))))) (let ((_let_638 (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_16123 x z) (ho_16123 y z)))) (= x y))))) (let ((_let_639 (forall ((x |u_(-> tptp.set_list_o Bool)|) (y |u_(-> tptp.set_list_o Bool)|)) (or (not (forall ((z tptp.set_list_o)) (= (ho_16120 x z) (ho_16120 y z)))) (= x y))))) (let ((_let_640 (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_16116 x z) (ho_16116 y z)))) (= x y))))) (let ((_let_641 (forall ((x |u_(-> tptp.set_list_complex Bool)|) (y |u_(-> tptp.set_list_complex Bool)|)) (or (not (forall ((z tptp.set_list_complex)) (= (ho_16112 x z) (ho_16112 y z)))) (= x y))))) (let ((_let_642 (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_16095 x z) (ho_16095 y z)))) (= x y))))) (let ((_let_643 (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_16086 x z) (ho_16086 y z)))) (= x y))))) (let ((_let_644 (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_16080 x z) (ho_16080 y z)))) (= x y))))) (let ((_let_645 (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_16081 x z) (ho_16081 y z)))) (= x y))))) (let ((_let_646 (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_16078 x z) (ho_16078 y z)))) (= x y))))) (let ((_let_647 (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_16075 x z) (ho_16075 y z)))) (= x y))))) (let ((_let_648 (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_16068 x z) (ho_16068 y z)))) (= x y))))) (let ((_let_649 (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_16065 x z) (ho_16065 y z)))) (= x y))))) (let ((_let_650 (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_16063 x z) (ho_16063 y z)))) (= x y))))) (let ((_let_651 (forall ((x |u_(-> tptp.rat tptp.set_rat Bool)|) (y |u_(-> tptp.rat tptp.set_rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_16057 x z) (ho_16057 y z)))) (= x y))))) (let ((_let_652 (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_16468 x z) (ho_16468 y z)))) (= x y))))) (let ((_let_653 (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_16052 x z) (ho_16052 y z)))) (= x y))))) (let ((_let_654 (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_16049 x z) (ho_16049 y z)))) (= x y))))) (let ((_let_655 (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_14374 x z) (ho_14374 y z)))) (= x y))))) (let ((_let_656 (forall ((x |u_(-> tptp.rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_16035 x z) (ho_16035 y z)))) (= x y))))) (let ((_let_657 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_16031 x z) (ho_16031 y z)))) (= x y))))) (let ((_let_658 (forall ((x |u_(-> tptp.option_num tptp.nat)|) (y |u_(-> tptp.option_num tptp.nat)|)) (or (not (forall ((z tptp.option_num)) (= (ho_16021 x z) (ho_16021 y z)))) (= x y))))) (let ((_let_659 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_16019 x z) (ho_16019 y z)))) (= x y))))) (let ((_let_660 (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_11905 x z) (ho_11905 y z)))) (= x y))))) (let ((_let_661 (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_16015 x z) (ho_16015 y z)))) (= x y))))) (let ((_let_662 (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_16005 x z) (ho_16005 y z)))) (= x y))))) (let ((_let_663 (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_16001 x z) (ho_16001 y z)))) (= x y))))) (let ((_let_664 (forall ((x |u_(-> tptp.set_real tptp.rat)|) (y |u_(-> tptp.set_real tptp.rat)|)) (or (not (forall ((z tptp.set_real)) (= (ho_11979 x z) (ho_11979 y z)))) (= x y))))) (let ((_let_665 (forall ((x |u_(-> tptp.nat tptp.produc2504756804600209347T_VEBT)|) (y |u_(-> tptp.nat tptp.produc2504756804600209347T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_16170 x z) (ho_16170 y z)))) (= x y))))) (let ((_let_666 (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_16000 x z) (ho_16000 y z)))) (= x y))))) (let ((_let_667 (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_16187 x z) (ho_16187 y z)))) (= x y))))) (let ((_let_668 (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_15999 x z) (ho_15999 y z)))) (= x y))))) (let ((_let_669 (forall ((x |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_7859 x z) (ho_7859 y z)))) (= x y))))) (let ((_let_670 (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_15995 x z) (ho_15995 y z)))) (= x y))))) (let ((_let_671 (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_7992 x z) (ho_7992 y z)))) (= x y))))) (let ((_let_672 (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_16719 x z) (ho_16719 y z)))) (= x y))))) (let ((_let_673 (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_15993 x z) (ho_15993 y z)))) (= x y))))) (let ((_let_674 (forall ((x |u_(-> Bool tptp.set_o Bool)|) (y |u_(-> Bool tptp.set_o Bool)|)) (or (not (forall ((z Bool)) (= (ho_15991 x z) (ho_15991 y z)))) (= x y))))) (let ((_let_675 (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_15985 x z) (ho_15985 y z)))) (= x y))))) (let ((_let_676 (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_15981 x z) (ho_15981 y z)))) (= x y))))) (let ((_let_677 (forall ((x |u_(-> tptp.num tptp.extended_enat)|) (y |u_(-> tptp.num tptp.extended_enat)|)) (or (not (forall ((z tptp.num)) (= (ho_15979 x z) (ho_15979 y z)))) (= x y))))) (let ((_let_678 (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_15976 x z) (ho_15976 y z)))) (= x y))))) (let ((_let_679 (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_8835 x z) (ho_8835 y z)))) (= x y))))) (let ((_let_680 (forall ((x |u_(-> tptp.option_nat tptp.nat)|) (y |u_(-> tptp.option_nat tptp.nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_15973 x z) (ho_15973 y z)))) (= x y))))) (let ((_let_681 (forall ((x |u_(-> tptp.int tptp.num)|) (y |u_(-> tptp.int tptp.num)|)) (or (not (forall ((z tptp.int)) (= (ho_15969 x z) (ho_15969 y z)))) (= x y))))) (let ((_let_682 (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_7641 x z) (ho_7641 y z)))) (= x y))))) (let ((_let_683 (forall ((x |u_(-> tptp.rat tptp.num)|) (y |u_(-> tptp.rat tptp.num)|)) (or (not (forall ((z tptp.rat)) (= (ho_15967 x z) (ho_15967 y z)))) (= x y))))) (let ((_let_684 (forall ((x |u_(-> tptp.num tptp.set_num Bool)|) (y |u_(-> tptp.num tptp.set_num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_16059 x z) (ho_16059 y z)))) (= x y))))) (let ((_let_685 (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_15961 x z) (ho_15961 y z)))) (= x y))))) (let ((_let_686 (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_15942 x z) (ho_15942 y z)))) (= x y))))) (let ((_let_687 (forall ((x |u_(-> tptp.real tptp.num)|) (y |u_(-> tptp.real tptp.num)|)) (or (not (forall ((z tptp.real)) (= (ho_15966 x z) (ho_15966 y z)))) (= x y))))) (let ((_let_688 (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_15934 x z) (ho_15934 y z)))) (= x y))))) (let ((_let_689 (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_15932 x z) (ho_15932 y z)))) (= x y))))) (let ((_let_690 (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_15929 x z) (ho_15929 y z)))) (= x y))))) (let ((_let_691 (forall ((x |u_(-> tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15930 x z) (ho_15930 y z)))) (= x y))))) (let ((_let_692 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15922 x z) (ho_15922 y z)))) (= x y))))) (let ((_let_693 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat)|)) (= (ho_15613 x z) (ho_15613 y z)))) (= x y))))) (let ((_let_694 (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_15525 x z) (ho_15525 y z)))) (= x y))))) (let ((_let_695 (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_7469 x z) (ho_7469 y z)))) (= x y))))) (let ((_let_696 (forall ((x |u_(-> _u_(-> tptp.num tptp.rat)_ tptp.num tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.num tptp.rat)_ tptp.num tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.rat)|)) (= (ho_15609 x z) (ho_15609 y z)))) (= x y))))) (let ((_let_697 (forall ((x |u_(-> tptp.num tptp.rat)|) (y |u_(-> tptp.num tptp.rat)|)) (or (not (forall ((z tptp.num)) (= (ho_15607 x z) (ho_15607 y z)))) (= x y))))) (let ((_let_698 (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_15528 x z) (ho_15528 y z)))) (= x y))))) (let ((_let_699 (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_16236 x z) (ho_16236 y z)))) (= x y))))) (let ((_let_700 (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_15518 x z) (ho_15518 y z)))) (= x y))))) (let ((_let_701 (forall ((x |u_(-> tptp.option_num Bool)|) (y |u_(-> tptp.option_num Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_15516 x z) (ho_15516 y z)))) (= x y))))) (let ((_let_702 (forall ((x |u_(-> Bool tptp.set_nat tptp.set_nat tptp.set_nat)|) (y |u_(-> Bool tptp.set_nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z Bool)) (= (ho_14357 x z) (ho_14357 y z)))) (= x y))))) (let ((_let_703 (forall ((x |u_(-> Bool Bool tptp.vEBT_VEBT)|) (y |u_(-> Bool Bool tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_14784 x z) (ho_14784 y z)))) (= x y))))) (let ((_let_704 (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_14782 x z) (ho_14782 y z)))) (= x y))))) (let ((_let_705 (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_14658 x z) (ho_14658 y z)))) (= x y))))) (let ((_let_706 (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_14646 x z) (ho_14646 y z)))) (= x y))))) (let ((_let_707 (forall ((x |u_(-> tptp.list_complex Bool)|) (y |u_(-> tptp.list_complex Bool)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_14648 x z) (ho_14648 y z)))) (= x y))))) (let ((_let_708 (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_8829 x z) (ho_8829 y z)))) (= x y))))) (let ((_let_709 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_12211 x z) (ho_12211 y z)))) (= x y))))) (let ((_let_710 (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_14638 x z) (ho_14638 y z)))) (= x y))))) (let ((_let_711 (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_14465 x z) (ho_14465 y z)))) (= x y))))) (let ((_let_712 (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_16243 x z) (ho_16243 y z)))) (= x y))))) (let ((_let_713 (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_14370 x z) (ho_14370 y z)))) (= x y))))) (let ((_let_714 (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_14639 x z) (ho_14639 y z)))) (= x y))))) (let ((_let_715 (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_14636 x z) (ho_14636 y z)))) (= x y))))) (let ((_let_716 (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_14632 x z) (ho_14632 y z)))) (= x y))))) (let ((_let_717 (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_16251 x z) (ho_16251 y z)))) (= x y))))) (let ((_let_718 (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_12199 x z) (ho_12199 y z)))) (= x y))))) (let ((_let_719 (forall ((x |u_(-> tptp.nat tptp.list_o Bool)|) (y |u_(-> tptp.nat tptp.list_o Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14633 x z) (ho_14633 y z)))) (= x y))))) (let ((_let_720 (forall ((x |u_(-> tptp.list_o Bool)|) (y |u_(-> tptp.list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_14634 x z) (ho_14634 y z)))) (= x y))))) (let ((_let_721 (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_14627 x z) (ho_14627 y z)))) (= x y))))) (let ((_let_722 (forall ((x |u_(-> tptp.set_o Bool)|) (y |u_(-> tptp.set_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_14630 x z) (ho_14630 y z)))) (= x y))))) (let ((_let_723 (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_16189 x z) (ho_16189 y z)))) (= x y))))) (let ((_let_724 (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_14623 x z) (ho_14623 y z)))) (= x y))))) (let ((_let_725 (forall ((x |u_(-> tptp.nat tptp.list_int Bool)|) (y |u_(-> tptp.nat tptp.list_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14624 x z) (ho_14624 y z)))) (= x y))))) (let ((_let_726 (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_14621 x z) (ho_14621 y z)))) (= x y))))) (let ((_let_727 (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_16322 x z) (ho_16322 y z)))) (= x y))))) (let ((_let_728 (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_14619 x z) (ho_14619 y z)))) (= x y))))) (let ((_let_729 (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_15996 x z) (ho_15996 y z)))) (= x y))))) (let ((_let_730 (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_8510 x z) (ho_8510 y z)))) (= x y))))) (let ((_let_731 (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_14612 x z) (ho_14612 y z)))) (= x y))))) (let ((_let_732 (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_14610 x z) (ho_14610 y z)))) (= x y))))) (let ((_let_733 (forall ((x |u_(-> tptp.num tptp.set_num)|) (y |u_(-> tptp.num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_16038 x z) (ho_16038 y z)))) (= x y))))) (let ((_let_734 (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_14606 x z) (ho_14606 y z)))) (= x y))))) (let ((_let_735 (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_14607 x z) (ho_14607 y z)))) (= x y))))) (let ((_let_736 (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_14602 x z) (ho_14602 y z)))) (= x y))))) (let ((_let_737 (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_7448 x z) (ho_7448 y z)))) (= x y))))) (let ((_let_738 (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_14599 x z) (ho_14599 y z)))) (= x y))))) (let ((_let_739 (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_11016 x z) (ho_11016 y z)))) (= x y))))) (let ((_let_740 (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_14594 x z) (ho_14594 y z)))) (= x y))))) (let ((_let_741 (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_7515 x z) (ho_7515 y z)))) (= x y))))) (let ((_let_742 (forall ((x |u_(-> tptp.real tptp.nat Bool)|) (y |u_(-> tptp.real tptp.nat Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_14592 x z) (ho_14592 y z)))) (= x y))))) (let ((_let_743 (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_14590 x z) (ho_14590 y z)))) (= x y))))) (let ((_let_744 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10532 x z) (ho_10532 y z)))) (= x y))))) (let ((_let_745 (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_14584 x z) (ho_14584 y z)))) (= x y))))) (let ((_let_746 (forall ((x |u_(-> tptp.complex tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_7993 x z) (ho_7993 y z)))) (= x y))))) (let ((_let_747 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex Bool)_ tptp.complex tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex Bool)_ tptp.complex tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex Bool)|)) (= (ho_14580 x z) (ho_14580 y z)))) (= x y))))) (let ((_let_748 (forall ((x |u_(-> tptp.complex tptp.real Bool)|) (y |u_(-> tptp.complex tptp.real Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_14581 x z) (ho_14581 y z)))) (= x y))))) (let ((_let_749 (forall ((x |u_(-> tptp.int tptp.nat tptp.real)|) (y |u_(-> tptp.int tptp.nat tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_12750 x z) (ho_12750 y z)))) (= x y))))) (let ((_let_750 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.real tptp.complex Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.real tptp.complex Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_14577 x z) (ho_14577 y z)))) (= x y))))) (let ((_let_751 (forall ((x |u_(-> tptp.real tptp.complex Bool)|) (y |u_(-> tptp.real tptp.complex Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_14575 x z) (ho_14575 y z)))) (= x y))))) (let ((_let_752 (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_16257 x z) (ho_16257 y z)))) (= x y))))) (let ((_let_753 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.complex)_ tptp.real tptp.complex)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.complex)_ tptp.real tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_12239 x z) (ho_12239 y z)))) (= x y))))) (let ((_let_754 (forall ((x |u_(-> tptp.complex tptp.nat Bool)|) (y |u_(-> tptp.complex tptp.nat Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_14571 x z) (ho_14571 y z)))) (= x y))))) (let ((_let_755 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.real Bool)_ tptp.real tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.real Bool)_ tptp.real tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.real Bool)|)) (= (ho_14562 x z) (ho_14562 y z)))) (= x y))))) (let ((_let_756 (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_16452 x z) (ho_16452 y z)))) (= x y))))) (let ((_let_757 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.list_nat tptp.real Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.list_nat tptp.real Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_14559 x z) (ho_14559 y z)))) (= x y))))) (let ((_let_758 (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_7855 x z) (ho_7855 y z)))) (= x y))))) (let ((_let_759 (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_16365 x z) (ho_16365 y z)))) (= x y))))) (let ((_let_760 (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_14517 x z) (ho_14517 y z)))) (= x y))))) (let ((_let_761 (forall ((x |u_(-> tptp.set_complex tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_complex tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_11971 x z) (ho_11971 y z)))) (= x y))))) (let ((_let_762 (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_14642 x z) (ho_14642 y z)))) (= x y))))) (let ((_let_763 (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_14506 x z) (ho_14506 y z)))) (= x y))))) (let ((_let_764 (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_16577 x z) (ho_16577 y z)))) (= x y))))) (let ((_let_765 (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_14507 x z) (ho_14507 y z)))) (= x y))))) (let ((_let_766 (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_14500 x z) (ho_14500 y z)))) (= x y))))) (let ((_let_767 (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_14089 x z) (ho_14089 y z)))) (= x y))))) (let ((_let_768 (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_16478 x z) (ho_16478 y z)))) (= x y))))) (let ((_let_769 (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_14498 x z) (ho_14498 y z)))) (= x y))))) (let ((_let_770 (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_8046 x z) (ho_8046 y z)))) (= x y))))) (let ((_let_771 (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_14493 x z) (ho_14493 y z)))) (= x y))))) (let ((_let_772 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex Bool)_ tptp.complex tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.complex Bool)_ tptp.complex tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex Bool)|)) (= (ho_14568 x z) (ho_14568 y z)))) (= x y))))) (let ((_let_773 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_14472 x z) (ho_14472 y z)))) (= x y))))) (let ((_let_774 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14467 x z) (ho_14467 y z)))) (= x y))))) (let ((_let_775 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_14468 x z) (ho_14468 y z)))) (= x y))))) (let ((_let_776 (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_14464 x z) (ho_14464 y z)))) (= x y))))) (let ((_let_777 (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_14461 x z) (ho_14461 y z)))) (= x y))))) (let ((_let_778 (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_14453 x z) (ho_14453 y z)))) (= x y))))) (let ((_let_779 (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_10249 x z) (ho_10249 y z)))) (= x y))))) (let ((_let_780 (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_14451 x z) (ho_14451 y z)))) (= x y))))) (let ((_let_781 (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_14449 x z) (ho_14449 y z)))) (= x y))))) (let ((_let_782 (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_16271 x z) (ho_16271 y z)))) (= x y))))) (let ((_let_783 (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_14445 x z) (ho_14445 y z)))) (= x y))))) (let ((_let_784 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real)|)) (= (ho_14443 x z) (ho_14443 y z)))) (= x y))))) (let ((_let_785 (forall ((x |u_(-> tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10195 x z) (ho_10195 y z)))) (= x y))))) (let ((_let_786 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat)_ _u_(-> tptp.complex Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.nat)_ _u_(-> tptp.complex Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat)|)) (= (ho_14441 x z) (ho_14441 y z)))) (= x y))))) (let ((_let_787 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_14439 x z) (ho_14439 y z)))) (= x y))))) (let ((_let_788 (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_16533 x z) (ho_16533 y z)))) (= x y))))) (let ((_let_789 (forall ((x |u_(-> _u_(-> tptp.real tptp.list_nat)_ _u_(-> tptp.real Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.real tptp.list_nat)_ _u_(-> tptp.real Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.list_nat)|)) (= (ho_14436 x z) (ho_14436 y z)))) (= x y))))) (let ((_let_790 (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_10360 x z) (ho_10360 y z)))) (= x y))))) (let ((_let_791 (forall ((x |u_(-> tptp.real tptp.list_nat)|) (y |u_(-> tptp.real tptp.list_nat)|)) (or (not (forall ((z tptp.real)) (= (ho_14434 x z) (ho_14434 y z)))) (= x y))))) (let ((_let_792 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_14437 x z) (ho_14437 y z)))) (= x y))))) (let ((_let_793 (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_14432 x z) (ho_14432 y z)))) (= x y))))) (let ((_let_794 (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_16071 x z) (ho_16071 y z)))) (= x y))))) (let ((_let_795 (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_14433 x z) (ho_14433 y z)))) (= x y))))) (let ((_let_796 (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_14428 x z) (ho_14428 y z)))) (= x y))))) (let ((_let_797 (forall ((x |u_(-> tptp.real tptp.real tptp.nat)|) (y |u_(-> tptp.real tptp.real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_14426 x z) (ho_14426 y z)))) (= x y))))) (let ((_let_798 (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_16089 x z) (ho_16089 y z)))) (= x y))))) (let ((_let_799 (forall ((x |u_(-> tptp.set_nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11960 x z) (ho_11960 y z)))) (= x y))))) (let ((_let_800 (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_12645 x z) (ho_12645 y z)))) (= x y))))) (let ((_let_801 (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_14429 x z) (ho_14429 y z)))) (= x y))))) (let ((_let_802 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_10147 x z) (ho_10147 y z)))) (= x y))))) (let ((_let_803 (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_14430 x z) (ho_14430 y z)))) (= x y))))) (let ((_let_804 (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_16382 x z) (ho_16382 y z)))) (= x y))))) (let ((_let_805 (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_14423 x z) (ho_14423 y z)))) (= x y))))) (let ((_let_806 (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_16402 x z) (ho_16402 y z)))) (= x y))))) (let ((_let_807 (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_13097 x z) (ho_13097 y z)))) (= x y))))) (let ((_let_808 (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_16315 x z) (ho_16315 y z)))) (= x y))))) (let ((_let_809 (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_14424 x z) (ho_14424 y z)))) (= x y))))) (let ((_let_810 (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_14425 x z) (ho_14425 y z)))) (= x y))))) (let ((_let_811 (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_14413 x z) (ho_14413 y z)))) (= x y))))) (let ((_let_812 (forall ((x |u_(-> tptp.real tptp.complex tptp.real)|) (y |u_(-> tptp.real tptp.complex tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_14405 x z) (ho_14405 y z)))) (= x y))))) (let ((_let_813 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_7927 x z) (ho_7927 y z)))) (= x y))))) (let ((_let_814 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_14408 x z) (ho_14408 y z)))) (= x y))))) (let ((_let_815 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_14409 x z) (ho_14409 y z)))) (= x y))))) (let ((_let_816 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex tptp.nat)|)) (= (ho_14402 x z) (ho_14402 y z)))) (= x y))))) (let ((_let_817 (forall ((x |u_(-> tptp.real tptp.complex tptp.nat)|) (y |u_(-> tptp.real tptp.complex tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_14400 x z) (ho_14400 y z)))) (= x y))))) (let ((_let_818 (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_16778 x z) (ho_16778 y z)))) (= x y))))) (let ((_let_819 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_14403 x z) (ho_14403 y z)))) (= x y))))) (let ((_let_820 (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_15329 x z) (ho_15329 y z)))) (= x y))))) (let ((_let_821 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_14404 x z) (ho_14404 y z)))) (= x y))))) (let ((_let_822 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex tptp.complex)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex tptp.complex)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex tptp.complex)|)) (= (ho_14398 x z) (ho_14398 y z)))) (= x y))))) (let ((_let_823 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_14395 x z) (ho_14395 y z)))) (= x y))))) (let ((_let_824 (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_14382 x z) (ho_14382 y z)))) (= x y))))) (let ((_let_825 (forall ((x |u_(-> Bool tptp.vEBT_VEBT)|) (y |u_(-> Bool tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_14785 x z) (ho_14785 y z)))) (= x y))))) (let ((_let_826 (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_14383 x z) (ho_14383 y z)))) (= x y))))) (let ((_let_827 (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_16779 x z) (ho_16779 y z)))) (= x y))))) (let ((_let_828 (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_14378 x z) (ho_14378 y z)))) (= x y))))) (let ((_let_829 (forall ((x |u_(-> tptp.nat Bool Bool)|) (y |u_(-> tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14379 x z) (ho_14379 y z)))) (= x y))))) (let ((_let_830 (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_12212 x z) (ho_12212 y z)))) (= x y))))) (let ((_let_831 (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_16627 x z) (ho_16627 y z)))) (= x y))))) (let ((_let_832 (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_14355 x z) (ho_14355 y z)))) (= x y))))) (let ((_let_833 (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_8537 x z) (ho_8537 y z)))) (= x y))))) (let ((_let_834 (forall ((x |u_(-> tptp.produc9072475918466114483BT_nat Bool)|) (y |u_(-> tptp.produc9072475918466114483BT_nat Bool)|)) (or (not (forall ((z tptp.produc9072475918466114483BT_nat)) (= (ho_16098 x z) (ho_16098 y z)))) (= x y))))) (let ((_let_835 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_15935 x z) (ho_15935 y z)))) (= x y))))) (let ((_let_836 (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_14330 x z) (ho_14330 y z)))) (= x y))))) (let ((_let_837 (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_14326 x z) (ho_14326 y z)))) (= x y))))) (let ((_let_838 (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_14324 x z) (ho_14324 y z)))) (= x y))))) (let ((_let_839 (forall ((x |u_(-> tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_7853 x z) (ho_7853 y z)))) (= x y))))) (let ((_let_840 (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_15937 x z) (ho_15937 y z)))) (= x y))))) (let ((_let_841 (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_16380 x z) (ho_16380 y z)))) (= x y))))) (let ((_let_842 (forall ((x |u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_10770 x z) (ho_10770 y z)))) (= x y))))) (let ((_let_843 (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_14314 x z) (ho_14314 y z)))) (= x y))))) (let ((_let_844 (forall ((x |u_(-> tptp.nat Bool tptp.list_o)|) (y |u_(-> tptp.nat Bool tptp.list_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_14315 x z) (ho_14315 y z)))) (= x y))))) (let ((_let_845 (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_16328 x z) (ho_16328 y z)))) (= x y))))) (let ((_let_846 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14471 x z) (ho_14471 y z)))) (= x y))))) (let ((_let_847 (forall ((x |u_(-> Bool tptp.list_o)|) (y |u_(-> Bool tptp.list_o)|)) (or (not (forall ((z Bool)) (= (ho_14316 x z) (ho_14316 y z)))) (= x y))))) (let ((_let_848 (forall ((x |u_(-> tptp.nat tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9997 x z) (ho_9997 y z)))) (= x y))))) (let ((_let_849 (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_16234 x z) (ho_16234 y z)))) (= x y))))) (let ((_let_850 (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_14311 x z) (ho_14311 y z)))) (= x y))))) (let ((_let_851 (forall ((x |u_(-> tptp.nat tptp.real tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.real tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_10166 x z) (ho_10166 y z)))) (= x y))))) (let ((_let_852 (forall ((x |u_(-> tptp.nat Bool Bool Bool)|) (y |u_(-> tptp.nat Bool Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14312 x z) (ho_14312 y z)))) (= x y))))) (let ((_let_853 (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_14309 x z) (ho_14309 y z)))) (= x y))))) (let ((_let_854 (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_14307 x z) (ho_14307 y z)))) (= x y))))) (let ((_let_855 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_7495 x z) (ho_7495 y z)))) (= x y))))) (let ((_let_856 (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_10801 x z) (ho_10801 y z)))) (= x y))))) (let ((_let_857 (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_14305 x z) (ho_14305 y z)))) (= x y))))) (let ((_let_858 (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_14262 x z) (ho_14262 y z)))) (= x y))))) (let ((_let_859 (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_14263 x z) (ho_14263 y z)))) (= x y))))) (let ((_let_860 (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_14264 x z) (ho_14264 y z)))) (= x y))))) (let ((_let_861 (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_14258 x z) (ho_14258 y z)))) (= x y))))) (let ((_let_862 (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_15963 x z) (ho_15963 y z)))) (= x y))))) (let ((_let_863 (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_14199 x z) (ho_14199 y z)))) (= x y))))) (let ((_let_864 (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_16366 x z) (ho_16366 y z)))) (= x y))))) (let ((_let_865 (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_14176 x z) (ho_14176 y z)))) (= x y))))) (let ((_let_866 (forall ((x |u_(-> tptp.real tptp.list_real)|) (y |u_(-> tptp.real tptp.list_real)|)) (or (not (forall ((z tptp.real)) (= (ho_14177 x z) (ho_14177 y z)))) (= x y))))) (let ((_let_867 (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_16681 x z) (ho_16681 y z)))) (= x y))))) (let ((_let_868 (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_14171 x z) (ho_14171 y z)))) (= x y))))) (let ((_let_869 (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_7479 x z) (ho_7479 y z)))) (= x y))))) (let ((_let_870 (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_16758 x z) (ho_16758 y z)))) (= x y))))) (let ((_let_871 (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_14168 x z) (ho_14168 y z)))) (= x y))))) (let ((_let_872 (forall ((x |u_(-> tptp.set_real tptp.nat)|) (y |u_(-> tptp.set_real tptp.nat)|)) (or (not (forall ((z tptp.set_real)) (= (ho_16298 x z) (ho_16298 y z)))) (= x y))))) (let ((_let_873 (forall ((x |u_(-> tptp.complex tptp.complex Bool)|) (y |u_(-> tptp.complex tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_14169 x z) (ho_14169 y z)))) (= x y))))) (let ((_let_874 (forall ((x |u_(-> Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_16569 x z) (ho_16569 y z)))) (= x y))))) (let ((_let_875 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14163 x z) (ho_14163 y z)))) (= x y))))) (let ((_let_876 (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_7635 x z) (ho_7635 y z)))) (= x y))))) (let ((_let_877 (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_14155 x z) (ho_14155 y z)))) (= x y))))) (let ((_let_878 (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_14149 x z) (ho_14149 y z)))) (= x y))))) (let ((_let_879 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_16759 x z) (ho_16759 y z)))) (= x y))))) (let ((_let_880 (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_14150 x z) (ho_14150 y z)))) (= x y))))) (let ((_let_881 (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_14146 x z) (ho_14146 y z)))) (= x y))))) (let ((_let_882 (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_16841 x z) (ho_16841 y z)))) (= x y))))) (let ((_let_883 (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_14147 x z) (ho_14147 y z)))) (= x y))))) (let ((_let_884 (forall ((x |u_(-> tptp.rat tptp.num tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.num tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_14129 x z) (ho_14129 y z)))) (= x y))))) (let ((_let_885 (forall ((x |u_(-> tptp.list_VEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_14640 x z) (ho_14640 y z)))) (= x y))))) (let ((_let_886 (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_14103 x z) (ho_14103 y z)))) (= x y))))) (let ((_let_887 (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_14104 x z) (ho_14104 y z)))) (= x y))))) (let ((_let_888 (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_14100 x z) (ho_14100 y z)))) (= x y))))) (let ((_let_889 (forall ((x |u_(-> tptp.set_int tptp.int)|) (y |u_(-> tptp.set_int tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14101 x z) (ho_14101 y z)))) (= x y))))) (let ((_let_890 (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_14093 x z) (ho_14093 y z)))) (= x y))))) (let ((_let_891 (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_15338 x z) (ho_15338 y z)))) (= x y))))) (let ((_let_892 (forall ((x |u_(-> tptp.set_int tptp.nat)|) (y |u_(-> tptp.set_int tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16287 x z) (ho_16287 y z)))) (= x y))))) (let ((_let_893 (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_7911 x z) (ho_7911 y z)))) (= x y))))) (let ((_let_894 (forall ((x |u_(-> tptp.set_complex tptp.complex)|) (y |u_(-> tptp.set_complex tptp.complex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_14094 x z) (ho_14094 y z)))) (= x y))))) (let ((_let_895 (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_14090 x z) (ho_14090 y z)))) (= x y))))) (let ((_let_896 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.real Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.real Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.real Bool)|)) (= (ho_14560 x z) (ho_14560 y z)))) (= x y))))) (let ((_let_897 (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_14091 x z) (ho_14091 y z)))) (= x y))))) (let ((_let_898 (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_14086 x z) (ho_14086 y z)))) (= x y))))) (let ((_let_899 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_16044 x z) (ho_16044 y z)))) (= x y))))) (let ((_let_900 (forall ((x |u_(-> tptp.int tptp.list_int)|) (y |u_(-> tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_7922 x z) (ho_7922 y z)))) (= x y))))) (let ((_let_901 (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_14087 x z) (ho_14087 y z)))) (= x y))))) (let ((_let_902 (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_14074 x z) (ho_14074 y z)))) (= x y))))) (let ((_let_903 (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_14070 x z) (ho_14070 y z)))) (= x y))))) (let ((_let_904 (forall ((x |u_(-> tptp.list_real tptp.nat)|) (y |u_(-> tptp.list_real tptp.nat)|)) (or (not (forall ((z tptp.list_real)) (= (ho_14027 x z) (ho_14027 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_14025 x z) (ho_14025 y z)))) (= x y))))) (let ((_let_906 (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_15927 x z) (ho_15927 y z)))) (= x y))))) (let ((_let_907 (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_14022 x z) (ho_14022 y z)))) (= x y))))) (let ((_let_908 (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_14020 x z) (ho_14020 y z)))) (= x y))))) (let ((_let_909 (forall ((x |u_(-> tptp.int tptp.set_real)|) (y |u_(-> tptp.int tptp.set_real)|)) (or (not (forall ((z tptp.int)) (= (ho_16371 x z) (ho_16371 y z)))) (= x y))))) (let ((_let_910 (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_16182 x z) (ho_16182 y z)))) (= x y))))) (let ((_let_911 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_14018 x z) (ho_14018 y z)))) (= x y))))) (let ((_let_912 (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_13414 x z) (ho_13414 y z)))) (= x y))))) (let ((_let_913 (forall ((x |u_(-> tptp.num tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.num tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_13873 x z) (ho_13873 y z)))) (= x y))))) (let ((_let_914 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_nat)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_nat)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_16385 x z) (ho_16385 y z)))) (= x y))))) (let ((_let_915 (forall ((x |u_(-> tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_10771 x z) (ho_10771 y z)))) (= x y))))) (let ((_let_916 (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_13809 x z) (ho_13809 y z)))) (= x y))))) (let ((_let_917 (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_16072 x z) (ho_16072 y z)))) (= x y))))) (let ((_let_918 (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_14494 x z) (ho_14494 y z)))) (= x y))))) (let ((_let_919 (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_7538 x z) (ho_7538 y z)))) (= x y))))) (let ((_let_920 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.rat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_13765 x z) (ho_13765 y z)))) (= x y))))) (let ((_let_921 (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_13748 x z) (ho_13748 y z)))) (= x y))))) (let ((_let_922 (forall ((x |u_(-> tptp.real tptp.set_real)|) (y |u_(-> tptp.real tptp.set_real)|)) (or (not (forall ((z tptp.real)) (= (ho_16041 x z) (ho_16041 y z)))) (= x y))))) (let ((_let_923 (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_13674 x z) (ho_13674 y z)))) (= x y))))) (let ((_let_924 (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_15998 x z) (ho_15998 y z)))) (= x y))))) (let ((_let_925 (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_13670 x z) (ho_13670 y z)))) (= x y))))) (let ((_let_926 (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_16723 x z) (ho_16723 y z)))) (= x y))))) (let ((_let_927 (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_13668 x z) (ho_13668 y z)))) (= x y))))) (let ((_let_928 (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_16158 x z) (ho_16158 y z)))) (= x y))))) (let ((_let_929 (forall ((x |u_(-> tptp.real tptp.real tptp.real tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_11046 x z) (ho_11046 y z)))) (= x y))))) (let ((_let_930 (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_16815 x z) (ho_16815 y z)))) (= x y))))) (let ((_let_931 (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_16087 x z) (ho_16087 y z)))) (= x y))))) (let ((_let_932 (forall ((x |u_(-> tptp.complex tptp.code_integer)|) (y |u_(-> tptp.complex tptp.code_integer)|)) (or (not (forall ((z tptp.complex)) (= (ho_13661 x z) (ho_13661 y z)))) (= x y))))) (let ((_let_933 (forall ((x |u_(-> tptp.num tptp.nat tptp.real)|) (y |u_(-> tptp.num tptp.nat tptp.real)|)) (or (not (forall ((z tptp.num)) (= (ho_12760 x z) (ho_12760 y z)))) (= x y))))) (let ((_let_934 (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_14478 x z) (ho_14478 y z)))) (= x y))))) (let ((_let_935 (forall ((x |u_(-> tptp.complex tptp.list_complex)|) (y |u_(-> tptp.complex tptp.list_complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_14172 x z) (ho_14172 y z)))) (= x y))))) (let ((_let_936 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_7781 x z) (ho_7781 y z)))) (= x y))))) (let ((_let_937 (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_13654 x z) (ho_13654 y z)))) (= x y))))) (let ((_let_938 (forall ((x |u_(-> tptp.set_complex tptp.nat)|) (y |u_(-> tptp.set_complex tptp.nat)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_16301 x z) (ho_16301 y z)))) (= x y))))) (let ((_let_939 (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_13576 x z) (ho_13576 y z)))) (= x y))))) (let ((_let_940 (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_13573 x z) (ho_13573 y z)))) (= x y))))) (let ((_let_941 (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_8075 x z) (ho_8075 y z)))) (= x y))))) (let ((_let_942 (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_13650 x z) (ho_13650 y z)))) (= x y))))) (let ((_let_943 (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_7714 x z) (ho_7714 y z)))) (= x y))))) (let ((_let_944 (forall ((x |u_(-> tptp.num tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.num tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_13512 x z) (ho_13512 y z)))) (= x y))))) (let ((_let_945 (forall ((x |u_(-> tptp.set_real tptp.complex)|) (y |u_(-> tptp.set_real tptp.complex)|)) (or (not (forall ((z tptp.set_real)) (= (ho_16290 x z) (ho_16290 y z)))) (= x y))))) (let ((_let_946 (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_13503 x z) (ho_13503 y z)))) (= x y))))) (let ((_let_947 (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_16143 x z) (ho_16143 y z)))) (= x y))))) (let ((_let_948 (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_16009 x z) (ho_16009 y z)))) (= x y))))) (let ((_let_949 (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_13501 x z) (ho_13501 y z)))) (= x y))))) (let ((_let_950 (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_10566 x z) (ho_10566 y z)))) (= x y))))) (let ((_let_951 (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_13467 x z) (ho_13467 y z)))) (= x y))))) (let ((_let_952 (forall ((x |u_(-> tptp.real _u_(-> tptp.real tptp.complex)_ tptp.real tptp.complex)|) (y |u_(-> tptp.real _u_(-> tptp.real tptp.complex)_ tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_12341 x z) (ho_12341 y z)))) (= x y))))) (let ((_let_953 (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_14497 x z) (ho_14497 y z)))) (= x y))))) (let ((_let_954 (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_13667 x z) (ho_13667 y z)))) (= x y))))) (let ((_let_955 (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_16840 x z) (ho_16840 y z)))) (= x y))))) (let ((_let_956 (forall ((x |u_(-> tptp.list_nat tptp.real Bool)|) (y |u_(-> tptp.list_nat tptp.real Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_14557 x z) (ho_14557 y z)))) (= x y))))) (let ((_let_957 (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_13420 x z) (ho_13420 y z)))) (= x y))))) (let ((_let_958 (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_13410 x z) (ho_13410 y z)))) (= x y))))) (let ((_let_959 (forall ((x |u_(-> tptp.nat tptp.produc9072475918466114483BT_nat)|) (y |u_(-> tptp.nat tptp.produc9072475918466114483BT_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16090 x z) (ho_16090 y z)))) (= x y))))) (let ((_let_960 (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_13411 x z) (ho_13411 y z)))) (= x y))))) (let ((_let_961 (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_16220 x z) (ho_16220 y z)))) (= x y))))) (let ((_let_962 (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_13343 x z) (ho_13343 y z)))) (= x y))))) (let ((_let_963 (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_10431 x z) (ho_10431 y z)))) (= x y))))) (let ((_let_964 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_12236 x z) (ho_12236 y z)))) (= x y))))) (let ((_let_965 (forall ((x |u_(-> Bool tptp.product_prod_nat_o)|) (y |u_(-> Bool tptp.product_prod_nat_o)|)) (or (not (forall ((z Bool)) (= (ho_16208 x z) (ho_16208 y z)))) (= x y))))) (let ((_let_966 (forall ((x |u_(-> tptp.rat tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_13291 x z) (ho_13291 y z)))) (= x y))))) (let ((_let_967 (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_13181 x z) (ho_13181 y z)))) (= x y))))) (let ((_let_968 (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_13178 x z) (ho_13178 y z)))) (= x y))))) (let ((_let_969 (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_16152 x z) (ho_16152 y z)))) (= x y))))) (let ((_let_970 (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_13176 x z) (ho_13176 y z)))) (= x y))))) (let ((_let_971 (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_10452 x z) (ho_10452 y z)))) (= x y))))) (let ((_let_972 (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_13153 x z) (ho_13153 y z)))) (= x y))))) (let ((_let_973 (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_13129 x z) (ho_13129 y z)))) (= x y))))) (let ((_let_974 (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_16599 x z) (ho_16599 y z)))) (= x y))))) (let ((_let_975 (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_13664 x z) (ho_13664 y z)))) (= x y))))) (let ((_let_976 (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_16766 x z) (ho_16766 y z)))) (= x y))))) (let ((_let_977 (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_12809 x z) (ho_12809 y z)))) (= x y))))) (let ((_let_978 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.set_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_nat)|)) (= (ho_12806 x z) (ho_12806 y z)))) (= x y))))) (let ((_let_979 (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_13460 x z) (ho_13460 y z)))) (= x y))))) (let ((_let_980 (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_12801 x z) (ho_12801 y z)))) (= x y))))) (let ((_let_981 (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_12798 x z) (ho_12798 y z)))) (= x y))))) (let ((_let_982 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex tptp.real)|)) (= (ho_14407 x z) (ho_14407 y z)))) (= x y))))) (let ((_let_983 (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_12749 x z) (ho_12749 y z)))) (= x y))))) (let ((_let_984 (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_10354 x z) (ho_10354 y z)))) (= x y))))) (let ((_let_985 (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_12659 x z) (ho_12659 y z)))) (= x y))))) (let ((_let_986 (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_11911 x z) (ho_11911 y z)))) (= x y))))) (let ((_let_987 (forall ((x |u_(-> tptp.extended_enat Bool)|) (y |u_(-> tptp.extended_enat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_14259 x z) (ho_14259 y z)))) (= x y))))) (let ((_let_988 (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_11058 x z) (ho_11058 y z)))) (= x y))))) (let ((_let_989 (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_12655 x z) (ho_12655 y z)))) (= x y))))) (let ((_let_990 (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_10122 x z) (ho_10122 y z)))) (= x y))))) (let ((_let_991 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_7496 x z) (ho_7496 y z)))) (= x y))))) (let ((_let_992 (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_8092 x z) (ho_8092 y z)))) (= x y))))) (let ((_let_993 (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_10474 x z) (ho_10474 y z)))) (= x y))))) (let ((_let_994 (forall ((x |u_(-> tptp.int tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_10059 x z) (ho_10059 y z)))) (= x y))))) (let ((_let_995 (forall ((x |u_(-> tptp.real tptp.nat tptp.complex)|) (y |u_(-> tptp.real tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_7738 x z) (ho_7738 y z)))) (= x y))))) (let ((_let_996 (forall ((x |u_(-> tptp.set_nat tptp.real)|) (y |u_(-> tptp.set_nat tptp.real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10258 x z) (ho_10258 y z)))) (= x y))))) (let ((_let_997 (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_16375 x z) (ho_16375 y z)))) (= x y))))) (let ((_let_998 (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_16196 x z) (ho_16196 y z)))) (= x y))))) (let ((_let_999 (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_12200 x z) (ho_12200 y z)))) (= x y))))) (let ((_let_1000 (forall ((x |u_(-> tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_10060 x z) (ho_10060 y z)))) (= x y))))) (let ((_let_1001 (forall ((x |u_(-> tptp.int tptp.set_complex)|) (y |u_(-> tptp.int tptp.set_complex)|)) (or (not (forall ((z tptp.int)) (= (ho_16376 x z) (ho_16376 y z)))) (= x y))))) (let ((_let_1002 (forall ((x |u_(-> tptp.code_integer tptp.num)|) (y |u_(-> tptp.code_integer tptp.num)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_7882 x z) (ho_7882 y z)))) (= x y))))) (let ((_let_1003 (forall ((x |u_(-> tptp.list_complex tptp.nat)|) (y |u_(-> tptp.list_complex tptp.nat)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_8996 x z) (ho_8996 y z)))) (= x y))))) (let ((_let_1004 (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_10326 x z) (ho_10326 y z)))) (= x y))))) (let ((_let_1005 (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_8826 x z) (ho_8826 y z)))) (= x y))))) (let ((_let_1006 (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_10204 x z) (ho_10204 y z)))) (= x y))))) (let ((_let_1007 (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_8397 x z) (ho_8397 y z)))) (= x y))))) (let ((_let_1008 (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_7834 x z) (ho_7834 y z)))) (= x y))))) (let ((_let_1009 (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_16011 x z) (ho_16011 y z)))) (= x y))))) (let ((_let_1010 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_8986 x z) (ho_8986 y z)))) (= x y))))) (let ((_let_1011 (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_10983 x z) (ho_10983 y z)))) (= x y))))) (let ((_let_1012 (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_16273 x z) (ho_16273 y z)))) (= x y))))) (let ((_let_1013 (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_8132 x z) (ho_8132 y z)))) (= x y))))) (let ((_let_1014 (forall ((x |u_(-> _u_(-> tptp.real tptp.int)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int)|)) (= (ho_12150 x z) (ho_12150 y z)))) (= x y))))) (let ((_let_1015 (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_12215 x z) (ho_12215 y z)))) (= x y))))) (let ((_let_1016 (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_11358 x z) (ho_11358 y z)))) (= x y))))) (let ((_let_1017 (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_16172 x z) (ho_16172 y z)))) (= x y))))) (let ((_let_1018 (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_8126 x z) (ho_8126 y z)))) (= x y))))) (let ((_let_1019 (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_8113 x z) (ho_8113 y z)))) (= x y))))) (let ((_let_1020 (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_10279 x z) (ho_10279 y z)))) (= x y))))) (let ((_let_1021 (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_7632 x z) (ho_7632 y z)))) (= x y))))) (let ((_let_1022 (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_16240 x z) (ho_16240 y z)))) (= x y))))) (let ((_let_1023 (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_16202 x z) (ho_16202 y z)))) (= x y))))) (let ((_let_1024 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_12323 x z) (ho_12323 y z)))) (= x y))))) (let ((_let_1025 (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_12017 x z) (ho_12017 y z)))) (= x y))))) (let ((_let_1026 (forall ((x |u_(-> tptp.set_set_nat tptp.set_nat)|) (y |u_(-> tptp.set_set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_16619 x z) (ho_16619 y z)))) (= x y))))) (let ((_let_1027 (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_8108 x z) (ho_8108 y z)))) (= x y))))) (let ((_let_1028 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14384 x z) (ho_14384 y z)))) (= x y))))) (let ((_let_1029 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_complex)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_complex)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16401 x z) (ho_16401 y z)))) (= x y))))) (let ((_let_1030 (forall ((x |u_(-> tptp.set_num Bool)|) (y |u_(-> tptp.set_num Bool)|)) (or (not (forall ((z tptp.set_num)) (= (ho_16053 x z) (ho_16053 y z)))) (= x y))))) (let ((_let_1031 (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_8109 x z) (ho_8109 y z)))) (= x y))))) (let ((_let_1032 (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_8089 x z) (ho_8089 y z)))) (= x y))))) (let ((_let_1033 (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_8072 x z) (ho_8072 y z)))) (= x y))))) (let ((_let_1034 (forall ((x |u_(-> tptp.set_real tptp.int)|) (y |u_(-> tptp.set_real tptp.int)|)) (or (not (forall ((z tptp.set_real)) (= (ho_16304 x z) (ho_16304 y z)))) (= x y))))) (let ((_let_1035 (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_7907 x z) (ho_7907 y z)))) (= x y))))) (let ((_let_1036 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_8069 x z) (ho_8069 y z)))) (= x y))))) (let ((_let_1037 (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_14303 x z) (ho_14303 y z)))) (= x y))))) (let ((_let_1038 (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_8066 x z) (ho_8066 y z)))) (= x y))))) (let ((_let_1039 (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_16025 x z) (ho_16025 y z)))) (= x y))))) (let ((_let_1040 (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_14474 x z) (ho_14474 y z)))) (= x y))))) (let ((_let_1041 (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_10523 x z) (ho_10523 y z)))) (= x y))))) (let ((_let_1042 (forall ((x |u_(-> tptp.int tptp.nat tptp.int Bool)|) (y |u_(-> tptp.int tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_14195 x z) (ho_14195 y z)))) (= x y))))) (let ((_let_1043 (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_8062 x z) (ho_8062 y z)))) (= x y))))) (let ((_let_1044 (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_8085 x z) (ho_8085 y z)))) (= x y))))) (let ((_let_1045 (forall ((x |u_(-> tptp.set_int tptp.real)|) (y |u_(-> tptp.set_int tptp.real)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16284 x z) (ho_16284 y z)))) (= x y))))) (let ((_let_1046 (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_10121 x z) (ho_10121 y z)))) (= x y))))) (let ((_let_1047 (forall ((x |u_(-> tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_8055 x z) (ho_8055 y z)))) (= x y))))) (let ((_let_1048 (forall ((x |u_(-> tptp.produc2285326912895808259nt_int Bool)|) (y |u_(-> tptp.produc2285326912895808259nt_int Bool)|)) (or (not (forall ((z tptp.produc2285326912895808259nt_int)) (= (ho_16261 x z) (ho_16261 y z)))) (= x y))))) (let ((_let_1049 (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_10125 x z) (ho_10125 y z)))) (= x y))))) (let ((_let_1050 (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_13417 x z) (ho_13417 y z)))) (= x y))))) (let ((_let_1051 (forall ((x |u_(-> tptp.nat tptp.produc8025551001238799321T_VEBT)|) (y |u_(-> tptp.nat tptp.produc8025551001238799321T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_16205 x z) (ho_16205 y z)))) (= x y))))) (let ((_let_1052 (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_8993 x z) (ho_8993 y z)))) (= x y))))) (let ((_let_1053 (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_7873 x z) (ho_7873 y z)))) (= x y))))) (let ((_let_1054 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_11959 x z) (ho_11959 y z)))) (= x y))))) (let ((_let_1055 (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_14644 x z) (ho_14644 y z)))) (= x y))))) (let ((_let_1056 (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_8043 x z) (ho_8043 y z)))) (= x y))))) (let ((_let_1057 (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_8533 x z) (ho_8533 y z)))) (= x y))))) (let ((_let_1058 (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_12160 x z) (ho_12160 y z)))) (= x y))))) (let ((_let_1059 (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_8021 x z) (ho_8021 y z)))) (= x y))))) (let ((_let_1060 (forall ((x |u_(-> tptp.nat tptp.num)|) (y |u_(-> tptp.nat tptp.num)|)) (or (not (forall ((z tptp.nat)) (= (ho_7474 x z) (ho_7474 y z)))) (= x y))))) (let ((_let_1061 (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_12183 x z) (ho_12183 y z)))) (= x y))))) (let ((_let_1062 (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_11114 x z) (ho_11114 y z)))) (= x y))))) (let ((_let_1063 (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_16110 x z) (ho_16110 y z)))) (= x y))))) (let ((_let_1064 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_8018 x z) (ho_8018 y z)))) (= x y))))) (let ((_let_1065 (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_14629 x z) (ho_14629 y z)))) (= x y))))) (let ((_let_1066 (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_8014 x z) (ho_8014 y z)))) (= x y))))) (let ((_let_1067 (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_16344 x z) (ho_16344 y z)))) (= x y))))) (let ((_let_1068 (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_10063 x z) (ho_10063 y z)))) (= x y))))) (let ((_let_1069 (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_10501 x z) (ho_10501 y z)))) (= x y))))) (let ((_let_1070 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_16055 x z) (ho_16055 y z)))) (= x y))))) (let ((_let_1071 (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_10698 x z) (ho_10698 y z)))) (= x y))))) (let ((_let_1072 (forall ((x |u_(-> tptp.complex tptp.set_complex Bool)|) (y |u_(-> tptp.complex tptp.set_complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_12217 x z) (ho_12217 y z)))) (= x y))))) (let ((_let_1073 (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_10497 x z) (ho_10497 y z)))) (= x y))))) (let ((_let_1074 (forall ((x |u_(-> tptp.int tptp.nat Bool)|) (y |u_(-> tptp.int tptp.nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_10662 x z) (ho_10662 y z)))) (= x y))))) (let ((_let_1075 (forall ((x |u_(-> tptp.complex Bool)|) (y |u_(-> tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_8994 x z) (ho_8994 y z)))) (= x y))))) (let ((_let_1076 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_8074 x z) (ho_8074 y z)))) (= x y))))) (let ((_let_1077 (forall ((x |u_(-> tptp.nat tptp.complex tptp.real)|) (y |u_(-> tptp.nat tptp.complex tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_12657 x z) (ho_12657 y z)))) (= x y))))) (let ((_let_1078 (forall ((x |u_(-> tptp.int tptp.real)|) (y |u_(-> tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_7990 x z) (ho_7990 y z)))) (= x y))))) (let ((_let_1079 (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_7871 x z) (ho_7871 y z)))) (= x y))))) (let ((_let_1080 (forall ((x |u_(-> tptp.num tptp.complex)|) (y |u_(-> tptp.num tptp.complex)|)) (or (not (forall ((z tptp.num)) (= (ho_7985 x z) (ho_7985 y z)))) (= x y))))) (let ((_let_1081 (forall ((x |u_(-> tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_7958 x z) (ho_7958 y z)))) (= x y))))) (let ((_let_1082 (forall ((x |u_(-> Bool tptp.produc334124729049499915VEBT_o)|) (y |u_(-> Bool tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z Bool)) (= (ho_16141 x z) (ho_16141 y z)))) (= x y))))) (let ((_let_1083 (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_10194 x z) (ho_10194 y z)))) (= x y))))) (let ((_let_1084 (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_14609 x z) (ho_14609 y z)))) (= x y))))) (let ((_let_1085 (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_11635 x z) (ho_11635 y z)))) (= x y))))) (let ((_let_1086 (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_16814 x z) (ho_16814 y z)))) (= x y))))) (let ((_let_1087 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_7939 x z) (ho_7939 y z)))) (= x y))))) (let ((_let_1088 (forall ((x |u_(-> tptp.list_int tptp.nat)|) (y |u_(-> tptp.list_int tptp.nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_7924 x z) (ho_7924 y z)))) (= x y))))) (let ((_let_1089 (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_14516 x z) (ho_14516 y z)))) (= x y))))) (let ((_let_1090 (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_13406 x z) (ho_13406 y z)))) (= x y))))) (let ((_let_1091 (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_11975 x z) (ho_11975 y z)))) (= x y))))) (let ((_let_1092 (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_7921 x z) (ho_7921 y z)))) (= x y))))) (let ((_let_1093 (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_8998 x z) (ho_8998 y z)))) (= x y))))) (let ((_let_1094 (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_7912 x z) (ho_7912 y z)))) (= x y))))) (let ((_let_1095 (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_7754 x z) (ho_7754 y z)))) (= x y))))) (let ((_let_1096 (forall ((x |u_(-> tptp.rat tptp.nat)|) (y |u_(-> tptp.rat tptp.nat)|)) (or (not (forall ((z tptp.rat)) (= (ho_15968 x z) (ho_15968 y z)))) (= x y))))) (let ((_let_1097 (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_12181 x z) (ho_12181 y z)))) (= x y))))) (let ((_let_1098 (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_7892 x z) (ho_7892 y z)))) (= x y))))) (let ((_let_1099 (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_10509 x z) (ho_10509 y z)))) (= x y))))) (let ((_let_1100 (forall ((x |u_(-> tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7750 x z) (ho_7750 y z)))) (= x y))))) (let ((_let_1101 (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_15997 x z) (ho_15997 y z)))) (= x y))))) (let ((_let_1102 (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_14098 x z) (ho_14098 y z)))) (= x y))))) (let ((_let_1103 (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_16458 x z) (ho_16458 y z)))) (= x y))))) (let ((_let_1104 (forall ((x |u_(-> tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_7890 x z) (ho_7890 y z)))) (= x y))))) (let ((_let_1105 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_16043 x z) (ho_16043 y z)))) (= x y))))) (let ((_let_1106 (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_10023 x z) (ho_10023 y z)))) (= x y))))) (let ((_let_1107 (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_16332 x z) (ho_16332 y z)))) (= x y))))) (let ((_let_1108 (forall ((x |u_(-> Bool tptp.produc6271795597528267376eger_o)|) (y |u_(-> Bool tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z Bool)) (= (ho_7874 x z) (ho_7874 y z)))) (= x y))))) (let ((_let_1109 (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_13810 x z) (ho_13810 y z)))) (= x y))))) (let ((_let_1110 (forall ((x |u_(-> tptp.set_complex tptp.int)|) (y |u_(-> tptp.set_complex tptp.int)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_16307 x z) (ho_16307 y z)))) (= x y))))) (let ((_let_1111 (forall ((x |u_(-> tptp.int tptp.code_integer)|) (y |u_(-> tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.int)) (= (ho_10580 x z) (ho_10580 y z)))) (= x y))))) (let ((_let_1112 (forall ((x |u_(-> tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7636 x z) (ho_7636 y z)))) (= x y))))) (let ((_let_1113 (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_10546 x z) (ho_10546 y z)))) (= x y))))) (let ((_let_1114 (forall ((x |u_(-> tptp.real tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.real tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_7665 x z) (ho_7665 y z)))) (= x y))))) (let ((_let_1115 (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_11000 x z) (ho_11000 y z)))) (= x y))))) (let ((_let_1116 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_7540 x z) (ho_7540 y z)))) (= x y))))) (let ((_let_1117 (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_10013 x z) (ho_10013 y z)))) (= x y))))) (let ((_let_1118 (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_7861 x z) (ho_7861 y z)))) (= x y))))) (let ((_let_1119 (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_16114 x z) (ho_16114 y z)))) (= x y))))) (let ((_let_1120 (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_16338 x z) (ho_16338 y z)))) (= x y))))) (let ((_let_1121 (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_7777 x z) (ho_7777 y z)))) (= x y))))) (let ((_let_1122 (forall ((x |u_(-> tptp.num tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_7884 x z) (ho_7884 y z)))) (= x y))))) (let ((_let_1123 (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_11088 x z) (ho_11088 y z)))) (= x y))))) (let ((_let_1124 (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_8058 x z) (ho_8058 y z)))) (= x y))))) (let ((_let_1125 (forall ((x |u_(-> tptp.nat tptp.option_num)|) (y |u_(-> tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_7531 x z) (ho_7531 y z)))) (= x y))))) (let ((_let_1126 (forall ((x |u_(-> tptp.real tptp.complex)|) (y |u_(-> tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_7728 x z) (ho_7728 y z)))) (= x y))))) (let ((_let_1127 (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_11192 x z) (ho_11192 y z)))) (= x y))))) (let ((_let_1128 (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_7526 x z) (ho_7526 y z)))) (= x y))))) (let ((_let_1129 (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_14328 x z) (ho_14328 y z)))) (= x y))))) (let ((_let_1130 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_7638 x z) (ho_7638 y z)))) (= x y))))) (let ((_let_1131 (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_8834 x z) (ho_8834 y z)))) (= x y))))) (let ((_let_1132 (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_11126 x z) (ho_11126 y z)))) (= x y))))) (let ((_let_1133 (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_8288 x z) (ho_8288 y z)))) (= x y))))) (let ((_let_1134 (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_16384 x z) (ho_16384 y z)))) (= x y))))) (let ((_let_1135 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_12233 x z) (ho_12233 y z)))) (= x y))))) (let ((_let_1136 (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_14523 x z) (ho_14523 y z)))) (= x y))))) (let ((_let_1137 (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_16062 x z) (ho_16062 y z)))) (= x y))))) (let ((_let_1138 (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_7528 x z) (ho_7528 y z)))) (= x y))))) (let ((_let_1139 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_7463 x z) (ho_7463 y z)))) (= x y))))) (let ((_let_1140 (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_7630 x z) (ho_7630 y z)))) (= x y))))) (let ((_let_1141 (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_8827 x z) (ho_8827 y z)))) (= x y))))) (let ((_let_1142 (forall ((x |u_(-> tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_7937 x z) (ho_7937 y z)))) (= x y))))) (let ((_let_1143 (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_12164 x z) (ho_12164 y z)))) (= x y))))) (let ((_let_1144 (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_7527 x z) (ho_7527 y z)))) (= x y))))) (let ((_let_1145 (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_7869 x z) (ho_7869 y z)))) (= x y))))) (let ((_let_1146 (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_11136 x z) (ho_11136 y z)))) (= x y))))) (let ((_let_1147 (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_7643 x z) (ho_7643 y z)))) (= x y))))) (let ((_let_1148 (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_8013 x z) (ho_8013 y z)))) (= x y))))) (let ((_let_1149 (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_16544 x z) (ho_16544 y z)))) (= x y))))) (let ((_let_1150 (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_14085 x z) (ho_14085 y z)))) (= x y))))) (let ((_let_1151 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_10588 x z) (ho_10588 y z)))) (= x y))))) (let ((_let_1152 (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_12014 x z) (ho_12014 y z)))) (= x y))))) (let ((_let_1153 (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_7888 x z) (ho_7888 y z)))) (= x y))))) (let ((_let_1154 (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_16137 x z) (ho_16137 y z)))) (= x y))))) (let ((_let_1155 (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_10506 x z) (ho_10506 y z)))) (= x y))))) (let ((_let_1156 (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_7518 x z) (ho_7518 y z)))) (= x y))))) (let ((_let_1157 (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_7539 x z) (ho_7539 y z)))) (= x y))))) (let ((_let_1158 (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_7926 x z) (ho_7926 y z)))) (= x y))))) (let ((_let_1159 (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_10172 x z) (ho_10172 y z)))) (= x y))))) (let ((_let_1160 (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_16303 x z) (ho_16303 y z)))) (= x y))))) (let ((_let_1161 (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_16326 x z) (ho_16326 y z)))) (= x y))))) (let ((_let_1162 (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_14588 x z) (ho_14588 y z)))) (= x y))))) (let ((_let_1163 (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_7848 x z) (ho_7848 y z)))) (= x y))))) (let ((_let_1164 (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_14591 x z) (ho_14591 y z)))) (= x y))))) (let ((_let_1165 (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_7710 x z) (ho_7710 y z)))) (= x y))))) (let ((_let_1166 (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_14586 x z) (ho_14586 y z)))) (= x y))))) (let ((_let_1167 (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_14600 x z) (ho_14600 y z)))) (= x y))))) (let ((_let_1168 (forall ((x |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.int tptp.complex)|) (y |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.int tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.int tptp.complex)|)) (= (ho_12244 x z) (ho_12244 y z)))) (= x y))))) (let ((_let_1169 (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_14510 x z) (ho_14510 y z)))) (= x y))))) (let ((_let_1170 (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_16566 x z) (ho_16566 y z)))) (= x y))))) (let ((_let_1171 (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_10062 x z) (ho_10062 y z)))) (= x y))))) (let ((_let_1172 (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_7833 x z) (ho_7833 y z)))) (= x y))))) (let ((_let_1173 (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_14513 x z) (ho_14513 y z)))) (= x y))))) (let ((_let_1174 (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_12139 x z) (ho_12139 y z)))) (= x y))))) (let ((_let_1175 (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_12759 x z) (ho_12759 y z)))) (= x y))))) (let ((_let_1176 (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_8026 x z) (ho_8026 y z)))) (= x y))))) (let ((_let_1177 (forall ((x |u_(-> tptp.set_list_int Bool)|) (y |u_(-> tptp.set_list_int Bool)|)) (or (not (forall ((z tptp.set_list_int)) (= (ho_16125 x z) (ho_16125 y z)))) (= x y))))) (let ((_let_1178 (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_7791 x z) (ho_7791 y z)))) (= x y))))) (let ((_let_1179 (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_7530 x z) (ho_7530 y z)))) (= x y))))) (let ((_let_1180 (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_16353 x z) (ho_16353 y z)))) (= x y))))) (let ((_let_1181 (forall ((x |u_(-> tptp.set_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11991 x z) (ho_11991 y z)))) (= x y))))) (let ((_let_1182 (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_7880 x z) (ho_7880 y z)))) (= x y))))) (let ((_let_1183 (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_10550 x z) (ho_10550 y z)))) (= x y))))) (let ((_let_1184 (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_16379 x z) (ho_16379 y z)))) (= x y))))) (let ((_let_1185 (forall ((x |u_(-> tptp.set_real tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_real tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_11982 x z) (ho_11982 y z)))) (= x y))))) (let ((_let_1186 (forall ((x |u_(-> tptp.real tptp.int)|) (y |u_(-> tptp.real tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_12148 x z) (ho_12148 y z)))) (= x y))))) (let ((_let_1187 (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_7778 x z) (ho_7778 y z)))) (= x y))))) (let ((_let_1188 (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_7452 x z) (ho_7452 y z)))) (= x y))))) (let ((_let_1189 (forall ((x |u_(-> tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_7446 x z) (ho_7446 y z)))) (= x y))))) (let ((_let_1190 (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_14504 x z) (ho_14504 y z)))) (= x y))))) (let ((_let_1191 (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_16040 x z) (ho_16040 y z)))) (= x y))))) (let ((_let_1192 (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_7812 x z) (ho_7812 y z)))) (= x y))))) (let ((_let_1193 (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_14417 x z) (ho_14417 y z)))) (= x y))))) (let ((_let_1194 (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_8990 x z) (ho_8990 y z)))) (= x y))))) (let ((_let_1195 (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_14105 x z) (ho_14105 y z)))) (= x y))))) (let ((_let_1196 (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_16417 x z) (ho_16417 y z)))) (= x y))))) (let ((_let_1197 (forall ((x |u_(-> tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_7470 x z) (ho_7470 y z)))) (= x y))))) (let ((_let_1198 (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_8825 x z) (ho_8825 y z)))) (= x y))))) (let ((_let_1199 (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_7886 x z) (ho_7886 y z)))) (= x y))))) (let ((_let_1200 (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_14165 x z) (ho_14165 y z)))) (= x y))))) (let ((_let_1201 (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_16002 x z) (ho_16002 y z)))) (= x y))))) (let ((_let_1202 (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_7480 x z) (ho_7480 y z)))) (= x y))))) (let ((_let_1203 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_7862 x z) (ho_7862 y z)))) (= x y))))) (let ((_let_1204 (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_10112 x z) (ho_10112 y z)))) (= x y))))) (let ((_let_1205 (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_12795 x z) (ho_12795 y z)))) (= x y))))) (let ((_let_1206 (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_8534 x z) (ho_8534 y z)))) (= x y))))) (let ((_let_1207 (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_7483 x z) (ho_7483 y z)))) (= x y))))) (let ((_let_1208 (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_10371 x z) (ho_10371 y z)))) (= x y))))) (let ((_let_1209 (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_14511 x z) (ho_14511 y z)))) (= x y))))) (let ((_let_1210 (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_10688 x z) (ho_10688 y z)))) (= x y))))) (let ((_let_1211 (forall ((x |u_(-> tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_7817 x z) (ho_7817 y z)))) (= x y))))) (let ((_let_1212 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_7863 x z) (ho_7863 y z)))) (= x y))))) (let ((_let_1213 (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_10315 x z) (ho_10315 y z)))) (= x y))))) (let ((_let_1214 (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_7457 x z) (ho_7457 y z)))) (= x y))))) (let ((_let_1215 (forall ((x |u_(-> tptp.num tptp.real)|) (y |u_(-> tptp.num tptp.real)|)) (or (not (forall ((z tptp.num)) (= (ho_7510 x z) (ho_7510 y z)))) (= x y))))) (let ((_let_1216 (forall ((x |u_(-> tptp.set_nat tptp.complex)|) (y |u_(-> tptp.set_nat tptp.complex)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10946 x z) (ho_10946 y z)))) (= x y))))) (let ((_let_1217 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_8071 x z) (ho_8071 y z)))) (= x y))))) (let ((_let_1218 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_7459 x z) (ho_7459 y z)))) (= x y))))) (let ((_let_1219 (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_7836 x z) (ho_7836 y z)))) (= x y))))) (let ((_let_1220 (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_10697 x z) (ho_10697 y z)))) (= x y))))) (let ((_let_1221 (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_16397 x z) (ho_16397 y z)))) (= x y))))) (let ((_let_1222 (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_12006 x z) (ho_12006 y z)))) (= x y))))) (let ((_let_1223 (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_16471 x z) (ho_16471 y z)))) (= x y))))) (let ((_let_1224 (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_7633 x z) (ho_7633 y z)))) (= x y))))) (let ((_let_1225 (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_7715 x z) (ho_7715 y z)))) (= x y))))) (let ((_let_1226 (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_14455 x z) (ho_14455 y z)))) (= x y))))) (let ((_let_1227 (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_12206 x z) (ho_12206 y z)))) (= x y))))) (let ((_let_1228 (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_7454 x z) (ho_7454 y z)))) (= x y))))) (let ((_let_1229 (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_10475 x z) (ho_10475 y z)))) (= x y))))) (let ((_let_1230 (forall ((x |u_(-> tptp.real tptp.real tptp.nat tptp.complex)|) (y |u_(-> tptp.real tptp.real tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_10170 x z) (ho_10170 y z)))) (= x y))))) (let ((_let_1231 (forall ((x |u_(-> tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_7711 x z) (ho_7711 y z)))) (= x y))))) (let ((_let_1232 (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_16175 x z) (ho_16175 y z)))) (= x y))))) (let ((_let_1233 (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_7493 x z) (ho_7493 y z)))) (= x y))))) (let ((_let_1234 (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_16024 x z) (ho_16024 y z)))) (= x y))))) (let ((_let_1235 (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_14781 x z) (ho_14781 y z)))) (= x y))))) (let ((_let_1236 (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_14174 x z) (ho_14174 y z)))) (= x y))))) (let ((_let_1237 (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_12222 x z) (ho_12222 y z)))) (= x y))))) (let ((_let_1238 (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_16160 x z) (ho_16160 y z)))) (= x y))))) (let ((_let_1239 (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_13505 x z) (ho_13505 y z)))) (= x y))))) (let ((_let_1240 (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_11182 x z) (ho_11182 y z)))) (= x y))))) (let ((_let_1241 (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_16387 x z) (ho_16387 y z)))) (= x y))))) (let ((_let_1242 (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_7639 x z) (ho_7639 y z)))) (= x y))))) (let ((_let_1243 (forall ((x |u_(-> Bool tptp.code_integer)|) (y |u_(-> Bool tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_7846 x z) (ho_7846 y z)))) (= x y))))) (let ((_let_1244 (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_16801 x z) (ho_16801 y z)))) (= x y))))) (let ((_let_1245 (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_15977 x z) (ho_15977 y z)))) (= x y))))) (let ((_let_1246 (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_7489 x z) (ho_7489 y z)))) (= x y))))) (let ((_let_1247 (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_16118 x z) (ho_16118 y z)))) (= x y))))) (let ((_let_1248 (forall ((x |u_(-> tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_7988 x z) (ho_7988 y z)))) (= x y))))) (let ((_let_1249 (forall ((x |u_(-> tptp.filter1242075044329608583at_nat Bool)|) (y |u_(-> tptp.filter1242075044329608583at_nat Bool)|)) (or (not (forall ((z tptp.filter1242075044329608583at_nat)) (= (ho_16675 x z) (ho_16675 y z)))) (= x y))))) (let ((_let_1250 (forall ((x |u_(-> tptp.rat Bool)|) (y |u_(-> tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_10052 x z) (ho_10052 y z)))) (= x y))))) (let ((_let_1251 (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_10022 x z) (ho_10022 y z)))) (= x y))))) (let ((_let_1252 (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_16083 x z) (ho_16083 y z)))) (= x y))))) (let ((_let_1253 (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_10990 x z) (ho_10990 y z)))) (= x y))))) (let ((_let_1254 (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_8833 x z) (ho_8833 y z)))) (= x y))))) (let ((_let_1255 (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_8129 x z) (ho_8129 y z)))) (= x y))))) (let ((_let_1256 (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_12188 x z) (ho_12188 y z)))) (= x y))))) (let ((_let_1257 (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_16493 x z) (ho_16493 y z)))) (= x y))))) (let ((_let_1258 (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_7761 x z) (ho_7761 y z)))) (= x y))))) (let ((_let_1259 (forall ((x |u_(-> tptp.set_int Bool)|) (y |u_(-> tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_10704 x z) (ho_10704 y z)))) (= x y))))) (let ((_let_1260 (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_14484 x z) (ho_14484 y z)))) (= x y))))) (let ((_let_1261 (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_7456 x z) (ho_7456 y z)))) (= x y))))) (let ((_let_1262 (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_15971 x z) (ho_15971 y z)))) (= x y))))) (let ((_let_1263 (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_11123 x z) (ho_11123 y z)))) (= x y))))) (let ((_let_1264 (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_8830 x z) (ho_8830 y z)))) (= x y))))) (let ((_let_1265 (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_8035 x z) (ho_8035 y z)))) (= x y))))) (let ((_let_1266 (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_7482 x z) (ho_7482 y z)))) (= x y))))) (let ((_let_1267 (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_16224 x z) (ho_16224 y z)))) (= x y))))) (let ((_let_1268 (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_7800 x z) (ho_7800 y z)))) (= x y))))) (let ((_let_1269 (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_7788 x z) (ho_7788 y z)))) (= x y))))) (let ((_let_1270 (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_14487 x z) (ho_14487 y z)))) (= x y))))) (let ((_let_1271 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_7822 x z) (ho_7822 y z)))) (= x y))))) (let ((_let_1272 (forall ((x |u_(-> Bool Bool Bool)|) (y |u_(-> Bool Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_10005 x z) (ho_10005 y z)))) (= x y))))) (let ((_let_1273 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_8015 x z) (ho_8015 y z)))) (= x y))))) (let ((_let_1274 (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_10280 x z) (ho_10280 y z)))) (= x y))))) (let ((_let_1275 (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_14420 x z) (ho_14420 y z)))) (= x y))))) (let ((_let_1276 (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_10621 x z) (ho_10621 y z)))) (= x y))))) (let ((_let_1277 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_12230 x z) (ho_12230 y z)))) (= x y))))) (let ((_let_1278 (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_11127 x z) (ho_11127 y z)))) (= x y))))) (let ((_let_1279 (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_16659 x z) (ho_16659 y z)))) (= x y))))) (let ((_let_1280 (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_7704 x z) (ho_7704 y z)))) (= x y))))) (let ((_let_1281 (forall ((x |u_(-> tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_10196 x z) (ho_10196 y z)))) (= x y))))) (let ((_let_1282 (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_16195 x z) (ho_16195 y z)))) (= x y))))) (let ((_let_1283 (forall ((x |u_(-> tptp.set_int tptp.rat)|) (y |u_(-> tptp.set_int tptp.rat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11988 x z) (ho_11988 y z)))) (= x y))))) (let ((_let_1284 (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_8050 x z) (ho_8050 y z)))) (= x y))))) (let ((_let_1285 (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_10998 x z) (ho_10998 y z)))) (= x y))))) (let ((_let_1286 (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_8981 x z) (ho_8981 y z)))) (= x y))))) (let ((_let_1287 (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_16806 x z) (ho_16806 y z)))) (= x y))))) (let ((_let_1288 (forall ((x |u_(-> tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_7512 x z) (ho_7512 y z)))) (= x y))))) (let ((_let_1289 (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_13407 x z) (ho_13407 y z)))) (= x y))))) (let ((_let_1290 (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_8010 x z) (ho_8010 y z)))) (= x y))))) (let ((_let_1291 (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_11178 x z) (ho_11178 y z)))) (= x y))))) (let ((_let_1292 (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_7478 x z) (ho_7478 y z)))) (= x y))))) (let ((_let_1293 (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_11199 x z) (ho_11199 y z)))) (= x y))))) (let ((_let_1294 (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_10120 x z) (ho_10120 y z)))) (= x y))))) (let ((_let_1295 (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_7819 x z) (ho_7819 y z)))) (= x y))))) (let ((_let_1296 (forall ((x |u_(-> _u_(-> tptp.complex tptp.int)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.int)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.int)|)) (= (ho_12147 x z) (ho_12147 y z)))) (= x y))))) (let ((_let_1297 (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_15332 x z) (ho_15332 y z)))) (= x y))))) (let ((_let_1298 (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_13581 x z) (ho_13581 y z)))) (= x y))))) (let ((_let_1299 (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_8831 x z) (ho_8831 y z)))) (= x y))))) (let ((_let_1300 (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_15939 x z) (ho_15939 y z)))) (= x y))))) (let ((_let_1301 (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_8158 x z) (ho_8158 y z)))) (= x y))))) (let ((_let_1302 (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_8057 x z) (ho_8057 y z)))) (= x y))))) (let ((_let_1303 (forall ((x |u_(-> tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_7443 x z) (ho_7443 y z)))) (= x y))))) (let ((_let_1304 (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_11914 x z) (ho_11914 y z)))) (= x y))))) (let ((_let_1305 (forall ((x |u_(-> tptp.produc1908205239877642774nteger Bool)|) (y |u_(-> tptp.produc1908205239877642774nteger Bool)|)) (or (not (forall ((z tptp.produc1908205239877642774nteger)) (= (ho_16260 x z) (ho_16260 y z)))) (= x y))))) (let ((_let_1306 (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_7894 x z) (ho_7894 y z)))) (= x y))))) (let ((_let_1307 (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_14318 x z) (ho_14318 y z)))) (= x y))))) (let ((_let_1308 (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_7700 x z) (ho_7700 y z)))) (= x y))))) (let ((_let_1309 (forall ((x |u_(-> tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_8063 x z) (ho_8063 y z)))) (= x y))))) (let ((_let_1310 (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_7485 x z) (ho_7485 y z)))) (= x y))))) (let ((_let_1311 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.complex)_ tptp.int tptp.complex)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.complex)_ tptp.int tptp.complex)|)) (or (not (forall ((z tptp.int)) (= (ho_12344 x z) (ho_12344 y z)))) (= x y))))) (let ((_let_1312 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7465 x z) (ho_7465 y z)))) (= x y))))) (let ((_let_1313 (forall ((x |u_(-> tptp.real tptp.code_integer)|) (y |u_(-> tptp.real tptp.code_integer)|)) (or (not (forall ((z tptp.real)) (= (ho_13665 x z) (ho_13665 y z)))) (= x y))))) (let ((_let_1314 (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_8049 x z) (ho_8049 y z)))) (= x y))))) (let ((_let_1315 (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_10455 x z) (ho_10455 y z)))) (= x y))))) (let ((_let_1316 (forall ((x |u_(-> tptp.option_num tptp.num)|) (y |u_(-> tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_7490 x z) (ho_7490 y z)))) (= x y))))) (let ((_let_1317 (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_7850 x z) (ho_7850 y z)))) (= x y))))) (let ((_let_1318 (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_16335 x z) (ho_16335 y z)))) (= x y))))) (let ((_let_1319 (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_10992 x z) (ho_10992 y z)))) (= x y))))) (let ((_let_1320 (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_8535 x z) (ho_8535 y z)))) (= x y))))) (let ((_let_1321 (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_7698 x z) (ho_7698 y z)))) (= x y))))) (let ((_let_1322 (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_7878 x z) (ho_7878 y z)))) (= x y))))) (let ((_let_1323 (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_10207 x z) (ho_10207 y z)))) (= x y))))) (let ((_let_1324 (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_16724 x z) (ho_16724 y z)))) (= x y))))) (let ((_let_1325 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_12220 x z) (ho_12220 y z)))) (= x y))))) (let ((_let_1326 (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_14411 x z) (ho_14411 y z)))) (= x y))))) (let ((_let_1327 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.nat)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat)|)) (= (ho_12153 x z) (ho_12153 y z)))) (= x y))))) (let ((_let_1328 (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_7697 x z) (ho_7697 y z)))) (= x y))))) (let ((_let_1329 (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_7702 x z) (ho_7702 y z)))) (= x y))))) (let ((_let_1330 (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_7701 x z) (ho_7701 y z)))) (= x y))))) (let ((_let_1331 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_12334 x z) (ho_12334 y z)))) (= x y))))) (let ((_let_1332 (forall ((x |u_(-> tptp.list_int Bool)|) (y |u_(-> tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_14625 x z) (ho_14625 y z)))) (= x y))))) (let ((_let_1333 (forall ((x |u_(-> tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_7507 x z) (ho_7507 y z)))) (= x y))))) (let ((_let_1334 (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_10979 x z) (ho_10979 y z)))) (= x y))))) (let ((_let_1335 (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_7709 x z) (ho_7709 y z)))) (= x y))))) (let ((_let_1336 (forall ((x |u_(-> tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_7775 x z) (ho_7775 y z)))) (= x y))))) (let ((_let_1337 (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_10376 x z) (ho_10376 y z)))) (= x y))))) (let ((_let_1338 (forall ((x |u_(-> tptp.int tptp.set_int Bool)|) (y |u_(-> tptp.int tptp.set_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_10703 x z) (ho_10703 y z)))) (= x y))))) (let ((_let_1339 (forall ((x |u_(-> tptp.rat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_11776 x z) (ho_11776 y z)))) (= x y))))) (let ((_let_1340 (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_7708 x z) (ho_7708 y z)))) (= x y))))) (let ((_let_1341 (forall ((x |u_(-> tptp.num tptp.option_num)|) (y |u_(-> tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_7441 x z) (ho_7441 y z)))) (= x y))))) (let ((_let_1342 (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_8983 x z) (ho_8983 y z)))) (= x y))))) (let ((_let_1343 (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_15965 x z) (ho_15965 y z)))) (= x y))))) (let ((_let_1344 (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_16034 x z) (ho_16034 y z)))) (= x y))))) (let ((_let_1345 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_13766 x z) (ho_13766 y z)))) (= x y))))) (let ((_let_1346 (forall ((x |u_(-> tptp.num tptp.code_integer)|) (y |u_(-> tptp.num tptp.code_integer)|)) (or (not (forall ((z tptp.num)) (= (ho_7901 x z) (ho_7901 y z)))) (= x y))))) (let ((_let_1347 (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_11355 x z) (ho_11355 y z)))) (= x y))))) (let ((_let_1348 (forall ((x |u_(-> tptp.complex _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|) (y |u_(-> tptp.complex _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|)) (or (not (forall ((z tptp.complex)) (= (ho_12326 x z) (ho_12326 y z)))) (= x y))))) (let ((_let_1349 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11742 x z) (ho_11742 y z)))) (= x y))))) (let ((_let_1350 (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_16074 x z) (ho_16074 y z)))) (= x y))))) (let ((_let_1351 (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_13509 x z) (ho_13509 y z)))) (= x y))))) (let ((_let_1352 (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_7716 x z) (ho_7716 y z)))) (= x y))))) (let ((_let_1353 (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_16037 x z) (ho_16037 y z)))) (= x y))))) (let ((_let_1354 (forall ((x |u_(-> tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_10116 x z) (ho_10116 y z)))) (= x y))))) (let ((_let_1355 (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_8042 x z) (ho_8042 y z)))) (= x y))))) (let ((_let_1356 (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_14477 x z) (ho_14477 y z)))) (= x y))))) (let ((_let_1357 (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_8822 x z) (ho_8822 y z)))) (= x y))))) (let ((_let_1358 (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_16355 x z) (ho_16355 y z)))) (= x y))))) (let ((_let_1359 (forall ((x |u_(-> tptp.num tptp.int Bool)|) (y |u_(-> tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_10806 x z) (ho_10806 y z)))) (= x y))))) (let ((_let_1360 (forall ((x |u_(-> tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_7736 x z) (ho_7736 y z)))) (= x y))))) (let ((_let_1361 (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_10505 x z) (ho_10505 y z)))) (= x y))))) (let ((_let_1362 (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_11141 x z) (ho_11141 y z)))) (= x y))))) (let ((_let_1363 (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_16069 x z) (ho_16069 y z)))) (= x y))))) (let ((_let_1364 (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_16377 x z) (ho_16377 y z)))) (= x y))))) (let ((_let_1365 (forall ((x |u_(-> tptp.complex tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_7735 x z) (ho_7735 y z)))) (= x y))))) (let ((_let_1366 (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_7865 x z) (ho_7865 y z)))) (= x y))))) (let ((_let_1367 (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_7535 x z) (ho_7535 y z)))) (= x y))))) (let ((_let_1368 (forall ((x |u_(-> tptp.int tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_10395 x z) (ho_10395 y z)))) (= x y))))) (let ((_let_1369 (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_7749 x z) (ho_7749 y z)))) (= x y))))) (let ((_let_1370 (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_7795 x z) (ho_7795 y z)))) (= x y))))) (let ((_let_1371 (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_7450 x z) (ho_7450 y z)))) (= x y))))) (let ((_let_1372 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_7516 x z) (ho_7516 y z)))) (= x y))))) (let ((_let_1373 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_7752 x z) (ho_7752 y z)))) (= x y))))) (let ((_let_1374 (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_7774 x z) (ho_7774 y z)))) (= x y))))) (let ((_let_1375 (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_14097 x z) (ho_14097 y z)))) (= x y))))) (let ((_let_1376 (forall ((x |u_(-> tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_16604 x z) (ho_16604 y z)))) (= x y))))) (let ((_let_1377 (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_8065 x z) (ho_8065 y z)))) (= x y))))) (let ((_let_1378 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10531 x z) (ho_10531 y z)))) (= x y))))) (let ((_let_1379 (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_7514 x z) (ho_7514 y z)))) (= x y))))) (let ((_let_1380 (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_7494 x z) (ho_7494 y z)))) (= x y))))) (let ((_let_1381 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.int)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.int)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_16462 x z) (ho_16462 y z)))) (= x y))))) (let ((_let_1382 (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_8039 x z) (ho_8039 y z)))) (= x y))))) (let ((_let_1383 (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_13452 x z) (ho_13452 y z)))) (= x y))))) (let ((_let_1384 (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_8139 x z) (ho_8139 y z)))) (= x y))))) (let ((_let_1385 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_7780 x z) (ho_7780 y z)))) (= x y))))) (let ((_let_1386 (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_12021 x z) (ho_12021 y z)))) (= x y))))) (let ((_let_1387 (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_7821 x z) (ho_7821 y z)))) (= x y))))) (let ((_let_1388 (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_8093 x z) (ho_8093 y z)))) (= x y))))) (let ((_let_1389 (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_13813 x z) (ho_13813 y z)))) (= x y))))) (let ((_let_1390 (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_7811 x z) (ho_7811 y z)))) (= x y))))) (let ((_let_1391 (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_16764 x z) (ho_16764 y z)))) (= x y))))) (let ((_let_1392 (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_7816 x z) (ho_7816 y z)))) (= x y))))) (let ((_let_1393 (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_8396 x z) (ho_8396 y z)))) (= x y))))) (let ((_let_1394 (forall ((x |u_(-> tptp.real tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_7519 x z) (ho_7519 y z)))) (= x y))))) (let ((_let_1395 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_8023 x z) (ho_8023 y z)))) (= x y))))) (let ((_let_1396 (forall ((x |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.complex tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.complex tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.rat)|)) (= (ho_11963 x z) (ho_11963 y z)))) (= x y))))) (let ((_let_1397 (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_13507 x z) (ho_13507 y z)))) (= x y))))) (let ((_let_1398 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_16832 x z) (ho_16832 y z)))) (= x y))))) (let ((_let_1399 (forall ((x |u_(-> tptp.complex tptp.nat tptp.real)|) (y |u_(-> tptp.complex tptp.nat tptp.real)|)) (or (not (forall ((z tptp.complex)) (= (ho_7896 x z) (ho_7896 y z)))) (= x y))))) (let ((_let_1400 (forall ((x |u_(-> tptp.option_nat Bool)|) (y |u_(-> tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_7536 x z) (ho_7536 y z)))) (= x y))))) (let ((_let_1401 (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_7488 x z) (ho_7488 y z)))) (= x y))))) (let ((_let_1402 (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_16167 x z) (ho_16167 y z)))) (= x y))))) (let ((_let_1403 (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_16775 x z) (ho_16775 y z)))) (= x y))))) (let ((_let_1404 (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_12276 x z) (ho_12276 y z)))) (= x y))))) (let ((_let_1405 (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_14377 x z) (ho_14377 y z)))) (= x y))))) (let ((_let_1406 (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_7837 x z) (ho_7837 y z)))) (= x y))))) (let ((_let_1407 (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_16560 x z) (ho_16560 y z)))) (= x y))))) (let ((_let_1408 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_7717 x z) (ho_7717 y z)))) (= x y))))) (let ((_let_1409 (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_10450 x z) (ho_10450 y z)))) (= x y))))) (let ((_let_1410 (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_14503 x z) (ho_14503 y z)))) (= x y))))) (let ((_let_1411 (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_10337 x z) (ho_10337 y z)))) (= x y))))) (let ((_let_1412 (forall ((x |u_(-> tptp.real tptp.int Bool)|) (y |u_(-> tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_10717 x z) (ho_10717 y z)))) (= x y))))) (let ((_let_1413 (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_16811 x z) (ho_16811 y z)))) (= x y))))) (let ((_let_1414 (forall ((x |u_(-> tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_7508 x z) (ho_7508 y z)))) (= x y))))) (let ((_let_1415 (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_8038 x z) (ho_8038 y z)))) (= x y))))) (let ((_let_1416 (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_7852 x z) (ho_7852 y z)))) (= x y))))) (let ((_let_1417 (forall ((x |u_(-> tptp.real tptp.complex tptp.complex)|) (y |u_(-> tptp.real tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_14396 x z) (ho_14396 y z)))) (= x y))))) (let ((_let_1418 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7466 x z) (ho_7466 y z)))) (= x y))))) (let ((_let_1419 (forall ((x |u_(-> tptp.real tptp.real tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.real tptp.real tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_10127 x z) (ho_10127 y z)))) (= x y))))) (let ((_let_1420 (forall ((x |u_(-> tptp.int tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.int tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.int)) (= (ho_16155 x z) (ho_16155 y z)))) (= x y))))) (let ((_let_1421 (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_13663 x z) (ho_13663 y z)))) (= x y))))) (let ((_let_1422 (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_16753 x z) (ho_16753 y z)))) (= x y))))) (let ((_let_1423 (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_16066 x z) (ho_16066 y z)))) (= x y))))) (let ((_let_1424 (forall ((x |u_(-> tptp.nat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10148 x z) (ho_10148 y z)))) (= x y))))) (let ((_let_1425 (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_12180 x z) (ho_12180 y z)))) (= x y))))) (let ((_let_1426 (forall ((x |u_(-> tptp.nat tptp.real Bool)|) (y |u_(-> tptp.nat tptp.real Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11356 x z) (ho_11356 y z)))) (= x y))))) (let ((_let_1427 (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_16140 x z) (ho_16140 y z)))) (= x y))))) (let ((_let_1428 (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_7998 x z) (ho_7998 y z)))) (= x y))))) (let ((_let_1429 (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_11967 x z) (ho_11967 y z)))) (= x y))))) (let ((_let_1430 (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_10205 x z) (ho_10205 y z)))) (= x y))))) (let ((_let_1431 (forall ((x |u_(-> tptp.set_nat tptp.rat)|) (y |u_(-> tptp.set_nat tptp.rat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10988 x z) (ho_10988 y z)))) (= x y))))) (let ((_let_1432 (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_10208 x z) (ho_10208 y z)))) (= x y))))) (let ((_let_1433 (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_13574 x z) (ho_13574 y z)))) (= x y))))) (let ((_let_1434 (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_10240 x z) (ho_10240 y z)))) (= x y))))) (let ((_let_1435 (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_16084 x z) (ho_16084 y z)))) (= x y))))) (let ((_let_1436 (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_11253 x z) (ho_11253 y z)))) (= x y))))) (let ((_let_1437 (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_15975 x z) (ho_15975 y z)))) (= x y))))) (let ((_let_1438 (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_14491 x z) (ho_14491 y z)))) (= x y))))) (let ((_let_1439 (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_12209 x z) (ho_12209 y z)))) (= x y))))) (let ((_let_1440 (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_10593 x z) (ho_10593 y z)))) (= x y))))) (let ((_let_1441 (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_14777 x z) (ho_14777 y z)))) (= x y))))) (let ((_let_1442 (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_16007 x z) (ho_16007 y z)))) (= x y))))) (let ((_let_1443 (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_12190 x z) (ho_12190 y z)))) (= x y))))) (let ((_let_1444 (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_10369 x z) (ho_10369 y z)))) (= x y))))) (let ((_let_1445 (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_11115 x z) (ho_11115 y z)))) (= x y))))) (let ((_let_1446 (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_12162 x z) (ho_12162 y z)))) (= x y))))) (let ((_let_1447 (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_10257 x z) (ho_10257 y z)))) (= x y))))) (let ((_let_1448 (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_14332 x z) (ho_14332 y z)))) (= x y))))) (let ((_let_1449 (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_10330 x z) (ho_10330 y z)))) (= x y))))) (let ((_let_1450 (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_16839 x z) (ho_16839 y z)))) (= x y))))) (let ((_let_1451 (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_14419 x z) (ho_14419 y z)))) (= x y))))) (let ((_let_1452 (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_7870 x z) (ho_7870 y z)))) (= x y))))) (let ((_let_1453 (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_10314 x z) (ho_10314 y z)))) (= x y))))) (let ((_let_1454 (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_10318 x z) (ho_10318 y z)))) (= x y))))) (let ((_let_1455 (forall ((x |u_(-> tptp.nat tptp.rat tptp.real)|) (y |u_(-> tptp.nat tptp.rat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_12649 x z) (ho_12649 y z)))) (= x y))))) (let ((_let_1456 (forall ((x |u_(-> tptp.produc7773217078559923341nt_int Bool)|) (y |u_(-> tptp.produc7773217078559923341nt_int Bool)|)) (or (not (forall ((z tptp.produc7773217078559923341nt_int)) (= (ho_16262 x z) (ho_16262 y z)))) (= x y))))) (let ((_let_1457 (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_13577 x z) (ho_13577 y z)))) (= x y))))) (let ((_let_1458 (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_10291 x z) (ho_10291 y z)))) (= x y))))) (let ((_let_1459 (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_16838 x z) (ho_16838 y z)))) (= x y))))) (let ((_let_1460 (forall ((x |u_(-> tptp.rat tptp.int)|) (y |u_(-> tptp.rat tptp.int)|)) (or (not (forall ((z tptp.rat)) (= (ho_10818 x z) (ho_10818 y z)))) (= x y))))) (let ((_let_1461 (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_10434 x z) (ho_10434 y z)))) (= x y))))) (let ((_let_1462 (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_10489 x z) (ho_10489 y z)))) (= x y))))) (let ((_let_1463 (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_16146 x z) (ho_16146 y z)))) (= x y))))) (let ((_let_1464 (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_8054 x z) (ho_8054 y z)))) (= x y))))) (let ((_let_1465 (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_14519 x z) (ho_14519 y z)))) (= x y))))) (let ((_let_1466 (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_10432 x z) (ho_10432 y z)))) (= x y))))) (let ((_let_1467 (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_10435 x z) (ho_10435 y z)))) (= x y))))) (let ((_let_1468 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex Bool)|)) (= (ho_14578 x z) (ho_14578 y z)))) (= x y))))) (let ((_let_1469 (forall ((x |u_(-> tptp.complex tptp.nat)|) (y |u_(-> tptp.complex tptp.nat)|)) (or (not (forall ((z tptp.complex)) (= (ho_12151 x z) (ho_12151 y z)))) (= x y))))) (let ((_let_1470 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_int)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_int)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_16390 x z) (ho_16390 y z)))) (= x y))))) (let ((_let_1471 (forall ((x |u_(-> tptp.num tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_10444 x z) (ho_10444 y z)))) (= x y))))) (let ((_let_1472 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.real tptp.complex)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.real tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_12240 x z) (ho_12240 y z)))) (= x y))))) (let ((_let_1473 (forall ((x |u_(-> tptp.set_VEBT_VEBT Bool)|) (y |u_(-> tptp.set_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.set_VEBT_VEBT)) (= (ho_10453 x z) (ho_10453 y z)))) (= x y))))) (let ((_let_1474 (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_14780 x z) (ho_14780 y z)))) (= x y))))) (let ((_let_1475 (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_14354 x z) (ho_14354 y z)))) (= x y))))) (let ((_let_1476 (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_16703 x z) (ho_16703 y z)))) (= x y))))) (let ((_let_1477 (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_10456 x z) (ho_10456 y z)))) (= x y))))) (let ((_let_1478 (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_14416 x z) (ho_14416 y z)))) (= x y))))) (let ((_let_1479 (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_11987 x z) (ho_11987 y z)))) (= x y))))) (let ((_let_1480 (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_10498 x z) (ho_10498 y z)))) (= x y))))) (let ((_let_1481 (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_10503 x z) (ho_10503 y z)))) (= x y))))) (let ((_let_1482 (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_16694 x z) (ho_16694 y z)))) (= x y))))) (let ((_let_1483 (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_10374 x z) (ho_10374 y z)))) (= x y))))) (let ((_let_1484 (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_12208 x z) (ho_12208 y z)))) (= x y))))) (let ((_let_1485 (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_10510 x z) (ho_10510 y z)))) (= x y))))) (let ((_let_1486 (forall ((x |u_(-> tptp.list_o tptp.nat)|) (y |u_(-> tptp.list_o tptp.nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_8988 x z) (ho_8988 y z)))) (= x y))))) (let ((_let_1487 (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_10599 x z) (ho_10599 y z)))) (= x y))))) (let ((_let_1488 (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_16757 x z) (ho_16757 y z)))) (= x y))))) (let ((_let_1489 (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_10508 x z) (ho_10508 y z)))) (= x y))))) (let ((_let_1490 (forall ((x |u_(-> tptp.nat tptp.complex Bool)|) (y |u_(-> tptp.nat tptp.complex Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10521 x z) (ho_10521 y z)))) (= x y))))) (let ((_let_1491 (forall ((x |u_(-> tptp.nat tptp.option_nat)|) (y |u_(-> tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7533 x z) (ho_7533 y z)))) (= x y))))) (let ((_let_1492 (forall ((x |u_(-> tptp.num tptp.nat Bool)|) (y |u_(-> tptp.num tptp.nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_10600 x z) (ho_10600 y z)))) (= x y))))) (let ((_let_1493 (forall ((x |u_(-> tptp.int tptp.int tptp.list_int tptp.list_int)|) (y |u_(-> tptp.int tptp.int tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_10321 x z) (ho_10321 y z)))) (= x y))))) (let ((_let_1494 (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_10529 x z) (ho_10529 y z)))) (= x y))))) (let ((_let_1495 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_11984 x z) (ho_11984 y z)))) (= x y))))) (let ((_let_1496 (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_16193 x z) (ho_16193 y z)))) (= x y))))) (let ((_let_1497 (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_7458 x z) (ho_7458 y z)))) (= x y))))) (let ((_let_1498 (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_12007 x z) (ho_12007 y z)))) (= x y))))) (let ((_let_1499 (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_10534 x z) (ho_10534 y z)))) (= x y))))) (let ((_let_1500 (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_12191 x z) (ho_12191 y z)))) (= x y))))) (let ((_let_1501 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_10547 x z) (ho_10547 y z)))) (= x y))))) (let ((_let_1502 (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_10690 x z) (ho_10690 y z)))) (= x y))))) (let ((_let_1503 (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_10549 x z) (ho_10549 y z)))) (= x y))))) (let ((_let_1504 (forall ((x |u_(-> tptp.set_set_nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_16046 x z) (ho_16046 y z)))) (= x y))))) (let ((_let_1505 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_10555 x z) (ho_10555 y z)))) (= x y))))) (let ((_let_1506 (forall ((x |u_(-> tptp.nat tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.nat tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_16161 x z) (ho_16161 y z)))) (= x y))))) (let ((_let_1507 (forall ((x |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_10585 x z) (ho_10585 y z)))) (= x y))))) (let ((_let_1508 (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_8530 x z) (ho_8530 y z)))) (= x y))))) (let ((_let_1509 (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_10554 x z) (ho_10554 y z)))) (= x y))))) (let ((_let_1510 (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_16077 x z) (ho_16077 y z)))) (= x y))))) (let ((_let_1511 (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_12010 x z) (ho_12010 y z)))) (= x y))))) (let ((_let_1512 (forall ((x |u_(-> tptp.real _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|) (y |u_(-> tptp.real _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_12320 x z) (ho_12320 y z)))) (= x y))))) (let ((_let_1513 (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_16517 x z) (ho_16517 y z)))) (= x y))))) (let ((_let_1514 (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_16674 x z) (ho_16674 y z)))) (= x y))))) (let ((_let_1515 (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_13749 x z) (ho_13749 y z)))) (= x y))))) (let ((_let_1516 (forall ((x |u_(-> tptp.list_o Bool Bool)|) (y |u_(-> tptp.list_o Bool Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_8985 x z) (ho_8985 y z)))) (= x y))))) (let ((_let_1517 (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_10558 x z) (ho_10558 y z)))) (= x y))))) (let ((_let_1518 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.set_real tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.set_real tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_11981 x z) (ho_11981 y z)))) (= x y))))) (let ((_let_1519 (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_10551 x z) (ho_10551 y z)))) (= x y))))) (let ((_let_1520 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.nat tptp.complex Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.nat tptp.complex Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_14573 x z) (ho_14573 y z)))) (= x y))))) (let ((_let_1521 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_14322 x z) (ho_14322 y z)))) (= x y))))) (let ((_let_1522 (forall ((x |u_(-> tptp.rat tptp.real)|) (y |u_(-> tptp.rat tptp.real)|)) (or (not (forall ((z tptp.rat)) (= (ho_12650 x z) (ho_12650 y z)))) (= x y))))) (let ((_let_1523 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex Bool)|)) (= (ho_14566 x z) (ho_14566 y z)))) (= x y))))) (let ((_let_1524 (forall ((x |u_(-> tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_10619 x z) (ho_10619 y z)))) (= x y))))) (let ((_let_1525 (forall ((x |u_(-> Bool tptp.int)|) (y |u_(-> Bool tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_10649 x z) (ho_10649 y z)))) (= x y))))) (let ((_let_1526 (forall ((x |u_(-> tptp.complex tptp.real)|) (y |u_(-> tptp.complex tptp.real)|)) (or (not (forall ((z tptp.complex)) (= (ho_7730 x z) (ho_7730 y z)))) (= x y))))) (let ((_let_1527 (forall ((x |u_(-> tptp.int tptp.set_int)|) (y |u_(-> tptp.int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_10691 x z) (ho_10691 y z)))) (= x y))))) (let ((_let_1528 (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_10694 x z) (ho_10694 y z)))) (= x y))))) (let ((_let_1529 (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_11999 x z) (ho_11999 y z)))) (= x y))))) (let ((_let_1530 (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_14480 x z) (ho_14480 y z)))) (= x y))))) (let ((_let_1531 (forall ((x |u_(-> tptp.num tptp.int tptp.int Bool)|) (y |u_(-> tptp.num tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_10823 x z) (ho_10823 y z)))) (= x y))))) (let ((_let_1532 (forall ((x |u_(-> tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10788 x z) (ho_10788 y z)))) (= x y))))) (let ((_let_1533 (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_16201 x z) (ho_16201 y z)))) (= x y))))) (let ((_let_1534 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_15602 x z) (ho_15602 y z)))) (= x y))))) (let ((_let_1535 (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_10814 x z) (ho_10814 y z)))) (= x y))))) (let ((_let_1536 (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_10859 x z) (ho_10859 y z)))) (= x y))))) (let ((_let_1537 (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_8823 x z) (ho_8823 y z)))) (= x y))))) (let ((_let_1538 (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_10945 x z) (ho_10945 y z)))) (= x y))))) (let ((_let_1539 (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_10967 x z) (ho_10967 y z)))) (= x y))))) (let ((_let_1540 (forall ((x |u_(-> tptp.set_nat tptp.nat)|) (y |u_(-> tptp.set_nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10234 x z) (ho_10234 y z)))) (= x y))))) (let ((_let_1541 (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_7476 x z) (ho_7476 y z)))) (= x y))))) (let ((_let_1542 (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_11995 x z) (ho_11995 y z)))) (= x y))))) (let ((_let_1543 (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_10971 x z) (ho_10971 y z)))) (= x y))))) (let ((_let_1544 (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_16787 x z) (ho_16787 y z)))) (= x y))))) (let ((_let_1545 (forall ((x |u_(-> tptp.set_nat tptp.int)|) (y |u_(-> tptp.set_nat tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10976 x z) (ho_10976 y z)))) (= x y))))) (let ((_let_1546 (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_14166 x z) (ho_14166 y z)))) (= x y))))) (let ((_let_1547 (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_10975 x z) (ho_10975 y z)))) (= x y))))) (let ((_let_1548 (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_10980 x z) (ho_10980 y z)))) (= x y))))) (let ((_let_1549 (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_10987 x z) (ho_10987 y z)))) (= x y))))) (let ((_let_1550 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_7461 x z) (ho_7461 y z)))) (= x y))))) (let ((_let_1551 (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_7899 x z) (ho_7899 y z)))) (= x y))))) (let ((_let_1552 (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_10999 x z) (ho_10999 y z)))) (= x y))))) (let ((_let_1553 (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_14595 x z) (ho_14595 y z)))) (= x y))))) (let ((_let_1554 (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_12011 x z) (ho_12011 y z)))) (= x y))))) (let ((_let_1555 (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_14369 x z) (ho_14369 y z)))) (= x y))))) (let ((_let_1556 (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_11013 x z) (ho_11013 y z)))) (= x y))))) (let ((_let_1557 (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_13673 x z) (ho_13673 y z)))) (= x y))))) (let ((_let_1558 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat)|)) (= (ho_12156 x z) (ho_12156 y z)))) (= x y))))) (let ((_let_1559 (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_7858 x z) (ho_7858 y z)))) (= x y))))) (let ((_let_1560 (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_11051 x z) (ho_11051 y z)))) (= x y))))) (let ((_let_1561 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_real)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_real)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16396 x z) (ho_16396 y z)))) (= x y))))) (let ((_let_1562 (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_14447 x z) (ho_14447 y z)))) (= x y))))) (let ((_let_1563 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_11053 x z) (ho_11053 y z)))) (= x y))))) (let ((_let_1564 (forall ((x |u_(-> tptp.complex tptp.complex tptp.complex tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.complex tptp.complex tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_11060 x z) (ho_11060 y z)))) (= x y))))) (let ((_let_1565 (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_12135 x z) (ho_12135 y z)))) (= x y))))) (let ((_let_1566 (forall ((x |u_(-> Bool tptp.int tptp.int Bool)|) (y |u_(-> Bool tptp.int tptp.int Bool)|)) (or (not (forall ((z Bool)) (= (ho_14050 x z) (ho_14050 y z)))) (= x y))))) (let ((_let_1567 (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_11111 x z) (ho_11111 y z)))) (= x y))))) (let ((_let_1568 (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_16135 x z) (ho_16135 y z)))) (= x y))))) (let ((_let_1569 (forall ((x |u_(-> tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_15520 x z) (ho_15520 y z)))) (= x y))))) (let ((_let_1570 (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_10317 x z) (ho_10317 y z)))) (= x y))))) (let ((_let_1571 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_14399 x z) (ho_14399 y z)))) (= x y))))) (let ((_let_1572 (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_9995 x z) (ho_9995 y z)))) (= x y))))) (let ((_let_1573 (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_12003 x z) (ho_12003 y z)))) (= x y))))) (let ((_let_1574 (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_14412 x z) (ho_14412 y z)))) (= x y))))) (let ((_let_1575 (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_11109 x z) (ho_11109 y z)))) (= x y))))) (let ((_let_1576 (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_11118 x z) (ho_11118 y z)))) (= x y))))) (let ((_let_1577 (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_14096 x z) (ho_14096 y z)))) (= x y))))) (let ((_let_1578 (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_11168 x z) (ho_11168 y z)))) (= x y))))) (let ((_let_1579 (forall ((x |u_(-> tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_7876 x z) (ho_7876 y z)))) (= x y))))) (let ((_let_1580 (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_11130 x z) (ho_11130 y z)))) (= x y))))) (let ((_let_1581 (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_14373 x z) (ho_14373 y z)))) (= x y))))) (let ((_let_1582 (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_11137 x z) (ho_11137 y z)))) (= x y))))) (let ((_let_1583 (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_16181 x z) (ho_16181 y z)))) (= x y))))) (let ((_let_1584 (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_16796 x z) (ho_16796 y z)))) (= x y))))) (let ((_let_1585 (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_11135 x z) (ho_11135 y z)))) (= x y))))) (let ((_let_1586 (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_11140 x z) (ho_11140 y z)))) (= x y))))) (let ((_let_1587 (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_16583 x z) (ho_16583 y z)))) (= x y))))) (let ((_let_1588 (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_11239 x z) (ho_11239 y z)))) (= x y))))) (let ((_let_1589 (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_11186 x z) (ho_11186 y z)))) (= x y))))) (let ((_let_1590 (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_16367 x z) (ho_16367 y z)))) (= x y))))) (let ((_let_1591 (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_10978 x z) (ho_10978 y z)))) (= x y))))) (let ((_let_1592 (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_11190 x z) (ho_11190 y z)))) (= x y))))) (let ((_let_1593 (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_16538 x z) (ho_16538 y z)))) (= x y))))) (let ((_let_1594 (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_11193 x z) (ho_11193 y z)))) (= x y))))) (let ((_let_1595 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex Bool)|)) (= (ho_14574 x z) (ho_14574 y z)))) (= x y))))) (let ((_let_1596 (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_11246 x z) (ho_11246 y z)))) (= x y))))) (let ((_let_1597 (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_11260 x z) (ho_11260 y z)))) (= x y))))) (let ((_let_1598 (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_11292 x z) (ho_11292 y z)))) (= x y))))) (let ((_let_1599 (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_14421 x z) (ho_14421 y z)))) (= x y))))) (let ((_let_1600 (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_7995 x z) (ho_7995 y z)))) (= x y))))) (let ((_let_1601 (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_11297 x z) (ho_11297 y z)))) (= x y))))) (let ((_let_1602 (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_10991 x z) (ho_10991 y z)))) (= x y))))) (let ((_let_1603 (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_10623 x z) (ho_10623 y z)))) (= x y))))) (let ((_let_1604 (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_12000 x z) (ho_12000 y z)))) (= x y))))) (let ((_let_1605 (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_10693 x z) (ho_10693 y z)))) (= x y))))) (let ((_let_1606 (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_16813 x z) (ho_16813 y z)))) (= x y))))) (let ((_let_1607 (forall ((x |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.rat)|)) (= (ho_12158 x z) (ho_12158 y z)))) (= x y))))) (let ((_let_1608 (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_16218 x z) (ho_16218 y z)))) (= x y))))) (let ((_let_1609 (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_11301 x z) (ho_11301 y z)))) (= x y))))) (let ((_let_1610 (forall ((x |u_(-> tptp.num Bool)|) (y |u_(-> tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_11541 x z) (ho_11541 y z)))) (= x y))))) (let ((_let_1611 (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_16331 x z) (ho_16331 y z)))) (= x y))))) (let ((_let_1612 (forall ((x |u_(-> tptp.num tptp.num Bool)|) (y |u_(-> tptp.num tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_11540 x z) (ho_11540 y z)))) (= x y))))) (let ((_let_1613 (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_11579 x z) (ho_11579 y z)))) (= x y))))) (let ((_let_1614 (forall ((x |u_(-> tptp.rat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_11754 x z) (ho_11754 y z)))) (= x y))))) (let ((_let_1615 (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_12136 x z) (ho_12136 y z)))) (= x y))))) (let ((_let_1616 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_14394 x z) (ho_14394 y z)))) (= x y))))) (let ((_let_1617 (forall ((x |u_(-> tptp.complex tptp.int tptp.int Bool)|) (y |u_(-> tptp.complex tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_11964 x z) (ho_11964 y z)))) (= x y))))) (let ((_let_1618 (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_11917 x z) (ho_11917 y z)))) (= x y))))) (let ((_let_1619 (forall ((x |u_(-> tptp.complex tptp.rat)|) (y |u_(-> tptp.complex tptp.rat)|)) (or (not (forall ((z tptp.complex)) (= (ho_11961 x z) (ho_11961 y z)))) (= x y))))) (let ((_let_1620 (forall ((x |u_(-> tptp.set_complex tptp.rat)|) (y |u_(-> tptp.set_complex tptp.rat)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_11968 x z) (ho_11968 y z)))) (= x y))))) (let ((_let_1621 (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_8112 x z) (ho_8112 y z)))) (= x y))))) (let ((_let_1622 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_10586 x z) (ho_10586 y z)))) (= x y))))) (let ((_let_1623 (forall ((x |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.set_complex tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.set_complex tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.rat)|)) (= (ho_11970 x z) (ho_11970 y z)))) (= x y))))) (let ((_let_1624 (forall ((x |u_(-> tptp.real tptp.rat)|) (y |u_(-> tptp.real tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_11972 x z) (ho_11972 y z)))) (= x y))))) (let ((_let_1625 (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_11978 x z) (ho_11978 y z)))) (= x y))))) (let ((_let_1626 (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_10298 x z) (ho_10298 y z)))) (= x y))))) (let ((_let_1627 (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_11997 x z) (ho_11997 y z)))) (= x y))))) (let ((_let_1628 (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_12001 x z) (ho_12001 y z)))) (= x y))))) (let ((_let_1629 (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_16325 x z) (ho_16325 y z)))) (= x y))))) (let ((_let_1630 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_12227 x z) (ho_12227 y z)))) (= x y))))) (let ((_let_1631 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_7541 x z) (ho_7541 y z)))) (= x y))))) (let ((_let_1632 (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_12004 x z) (ho_12004 y z)))) (= x y))))) (let ((_let_1633 (forall ((x |u_(-> tptp.int tptp.complex)|) (y |u_(-> tptp.int tptp.complex)|)) (or (not (forall ((z tptp.int)) (= (ho_12008 x z) (ho_12008 y z)))) (= x y))))) (let ((_let_1634 (forall ((x |u_(-> tptp.nat tptp.list_complex Bool)|) (y |u_(-> tptp.nat tptp.list_complex Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14647 x z) (ho_14647 y z)))) (= x y))))) (let ((_let_1635 (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_12013 x z) (ho_12013 y z)))) (= x y))))) (let ((_let_1636 (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_12214 x z) (ho_12214 y z)))) (= x y))))) (let ((_let_1637 (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_12411 x z) (ho_12411 y z)))) (= x y))))) (let ((_let_1638 (forall ((x |u_(-> tptp.real tptp.nat)|) (y |u_(-> tptp.real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_12154 x z) (ho_12154 y z)))) (= x y))))) (let ((_let_1639 (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_14604 x z) (ho_14604 y z)))) (= x y))))) (let ((_let_1640 (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_12166 x z) (ho_12166 y z)))) (= x y))))) (let ((_let_1641 (forall ((x |u_(-> tptp.filter_real Bool)|) (y |u_(-> tptp.filter_real Bool)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_16588 x z) (ho_16588 y z)))) (= x y))))) (let ((_let_1642 (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_11089 x z) (ho_11089 y z)))) (= x y))))) (let ((_let_1643 (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_12168 x z) (ho_12168 y z)))) (= x y))))) (let ((_let_1644 (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_12184 x z) (ho_12184 y z)))) (= x y))))) (let ((_let_1645 (forall ((x |u_(-> tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9998 x z) (ho_9998 y z)))) (= x y))))) (let ((_let_1646 (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_12187 x z) (ho_12187 y z)))) (= x y))))) (let ((_let_1647 (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_16476 x z) (ho_16476 y z)))) (= x y))))) (let ((_let_1648 (forall ((x |u_(-> tptp.num tptp.nat)|) (y |u_(-> tptp.num tptp.nat)|)) (or (not (forall ((z tptp.num)) (= (ho_13587 x z) (ho_13587 y z)))) (= x y))))) (let ((_let_1649 (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_8160 x z) (ho_8160 y z)))) (= x y))))) (let ((_let_1650 (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_16097 x z) (ho_16097 y z)))) (= x y))))) (let ((_let_1651 (forall ((x |u_(-> tptp.real tptp.nat tptp.rat)|) (y |u_(-> tptp.real tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_7663 x z) (ho_7663 y z)))) (= x y))))) (let ((_let_1652 (forall ((x |u_(-> tptp.set_real Bool)|) (y |u_(-> tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_12203 x z) (ho_12203 y z)))) (= x y))))) (let ((_let_1653 (forall ((x |u_(-> tptp.set_rat Bool)|) (y |u_(-> tptp.set_rat Bool)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_16050 x z) (ho_16050 y z)))) (= x y))))) (let ((_let_1654 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.complex)_ tptp.int tptp.complex)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.complex)_ tptp.int tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_12243 x z) (ho_12243 y z)))) (= x y))))) (let ((_let_1655 (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_16314 x z) (ho_16314 y z)))) (= x y))))) (let ((_let_1656 (forall ((x |u_(-> tptp.real tptp.set_real Bool)|) (y |u_(-> tptp.real tptp.set_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_12202 x z) (ho_12202 y z)))) (= x y))))) (let ((_let_1657 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_12205 x z) (ho_12205 y z)))) (= x y))))) (let ((_let_1658 (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_14490 x z) (ho_14490 y z)))) (= x y))))) (let ((_let_1659 (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_10447 x z) (ho_10447 y z)))) (= x y))))) (let ((_let_1660 (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_12020 x z) (ho_12020 y z)))) (= x y))))) (let ((_let_1661 (forall ((x |u_(-> tptp.real _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|) (y |u_(-> tptp.real _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_12331 x z) (ho_12331 y z)))) (= x y))))) (let ((_let_1662 (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_16786 x z) (ho_16786 y z)))) (= x y))))) (let ((_let_1663 (forall ((x |u_(-> tptp.set_complex Bool)|) (y |u_(-> tptp.set_complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_12218 x z) (ho_12218 y z)))) (= x y))))) (let ((_let_1664 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_12224 x z) (ho_12224 y z)))) (= x y))))) (let ((_let_1665 (forall ((x |u_(-> tptp.complex tptp.int)|) (y |u_(-> tptp.complex tptp.int)|)) (or (not (forall ((z tptp.complex)) (= (ho_12145 x z) (ho_12145 y z)))) (= x y))))) (let ((_let_1666 (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_12289 x z) (ho_12289 y z)))) (= x y))))) (let ((_let_1667 (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_14583 x z) (ho_14583 y z)))) (= x y))))) (let ((_let_1668 (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_14481 x z) (ho_14481 y z)))) (= x y))))) (let ((_let_1669 (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_14779 x z) (ho_14779 y z)))) (= x y))))) (let ((_let_1670 (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_14597 x z) (ho_14597 y z)))) (= x y))))) (let ((_let_1671 (forall ((x |u_(-> tptp.real tptp.list_nat Bool)|) (y |u_(-> tptp.real tptp.list_nat Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_14563 x z) (ho_14563 y z)))) (= x y))))) (let ((_let_1672 (forall ((x |u_(-> tptp.nat tptp.int tptp.real)|) (y |u_(-> tptp.nat tptp.int tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_12643 x z) (ho_12643 y z)))) (= x y))))) (let ((_let_1673 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_16246 x z) (ho_16246 y z)))) (= x y))))) (let ((_let_1674 (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_12652 x z) (ho_12652 y z)))) (= x y))))) (let ((_let_1675 (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_16404 x z) (ho_16404 y z)))) (= x y))))) (let ((_let_1676 (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_16408 x z) (ho_16408 y z)))) (= x y))))) (let ((_let_1677 (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_16410 x z) (ho_16410 y z)))) (= x y))))) (let ((_let_1678 (forall ((x |u_(-> tptp.extended_enat tptp.set_Extended_enat)|) (y |u_(-> tptp.extended_enat tptp.set_Extended_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_16412 x z) (ho_16412 y z)))) (= x y))))) (let ((_let_1679 (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_16816 x z) (ho_16816 y z)))) (= x y))))) (let ((_let_1680 (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_16415 x z) (ho_16415 y z)))) (= x y))))) (let ((_let_1681 (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_16419 x z) (ho_16419 y z)))) (= x y))))) (let ((_let_1682 (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_16421 x z) (ho_16421 y z)))) (= x y))))) (let ((_let_1683 (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_16423 x z) (ho_16423 y z)))) (= x y))))) (let ((_let_1684 (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_16427 x z) (ho_16427 y z)))) (= x y))))) (let ((_let_1685 (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_16429 x z) (ho_16429 y z)))) (= x y))))) (let ((_let_1686 (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_16449 x z) (ho_16449 y z)))) (= x y))))) (let ((_let_1687 (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_16448 x z) (ho_16448 y z)))) (= x y))))) (let ((_let_1688 (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_16453 x z) (ho_16453 y z)))) (= x y))))) (let ((_let_1689 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ tptp.set_Pr1261947904930325089at_nat tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ tptp.set_Pr1261947904930325089at_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (= (ho_16461 x z) (ho_16461 y z)))) (= x y))))) (let ((_let_1690 (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_16465 x z) (ho_16465 y z)))) (= x y))))) (let ((_let_1691 (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_16467 x z) (ho_16467 y z)))) (= x y))))) (let ((_let_1692 (forall ((x |u_(-> tptp.list_o tptp.int)|) (y |u_(-> tptp.list_o tptp.int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_16484 x z) (ho_16484 y z)))) (= x y))))) (let ((_let_1693 (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_16483 x z) (ho_16483 y z)))) (= x y))))) (let ((_let_1694 (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_16482 x z) (ho_16482 y z)))) (= x y))))) (let ((_let_1695 (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_16487 x z) (ho_16487 y z)))) (= x y))))) (let ((_let_1696 (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_16499 x z) (ho_16499 y z)))) (= x y))))) (let ((_let_1697 (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_16506 x z) (ho_16506 y z)))) (= x y))))) (let ((_let_1698 (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_16519 x z) (ho_16519 y z)))) (= x y))))) (let ((_let_1699 (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_16677 x z) (ho_16677 y z)))) (= x y))))) (let ((_let_1700 (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_16518 x z) (ho_16518 y z)))) (= x y))))) (let ((_let_1701 (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_16613 x z) (ho_16613 y z)))) (= x y))))) (let ((_let_1702 (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_16516 x z) (ho_16516 y z)))) (= x y))))) (let ((_let_1703 (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_16524 x z) (ho_16524 y z)))) (= x y))))) (let ((_let_1704 (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_16523 x z) (ho_16523 y z)))) (= x y))))) (let ((_let_1705 (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_16522 x z) (ho_16522 y z)))) (= x y))))) (let ((_let_1706 (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_16526 x z) (ho_16526 y z)))) (= x y))))) (let ((_let_1707 (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_16529 x z) (ho_16529 y z)))) (= x y))))) (let ((_let_1708 (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_16781 x z) (ho_16781 y z)))) (= x y))))) (let ((_let_1709 (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_16528 x z) (ho_16528 y z)))) (= x y))))) (let ((_let_1710 (forall ((x |u_(-> tptp.option_num tptp.int)|) (y |u_(-> tptp.option_num tptp.int)|)) (or (not (forall ((z tptp.option_num)) (= (ho_16534 x z) (ho_16534 y z)))) (= x y))))) (let ((_let_1711 (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_16532 x z) (ho_16532 y z)))) (= x y))))) (let ((_let_1712 (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_16536 x z) (ho_16536 y z)))) (= x y))))) (let ((_let_1713 (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_16542 x z) (ho_16542 y z)))) (= x y))))) (let ((_let_1714 (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_16812 x z) (ho_16812 y z)))) (= x y))))) (let ((_let_1715 (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_16546 x z) (ho_16546 y z)))) (= x y))))) (let ((_let_1716 (forall ((x |u_(-> tptp.set_Product_unit tptp.nat)|) (y |u_(-> tptp.set_Product_unit tptp.nat)|)) (or (not (forall ((z tptp.set_Product_unit)) (= (ho_16549 x z) (ho_16549 y z)))) (= x y))))) (let ((_let_1717 (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_16686 x z) (ho_16686 y z)))) (= x y))))) (let ((_let_1718 (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_16551 x z) (ho_16551 y z)))) (= x y))))) (let ((_let_1719 (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_16553 x z) (ho_16553 y z)))) (= x y))))) (let ((_let_1720 (forall ((x |u_(-> tptp.set_o tptp.nat)|) (y |u_(-> tptp.set_o tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_16555 x z) (ho_16555 y z)))) (= x y))))) (let ((_let_1721 (forall ((x |u_(-> tptp.nat tptp.char)|) (y |u_(-> tptp.nat tptp.char)|)) (or (not (forall ((z tptp.nat)) (= (ho_16557 x z) (ho_16557 y z)))) (= x y))))) (let ((_let_1722 (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_16559 x z) (ho_16559 y z)))) (= x y))))) (let ((_let_1723 (forall ((x |u_(-> tptp.set_char tptp.nat)|) (y |u_(-> tptp.set_char tptp.nat)|)) (or (not (forall ((z tptp.set_char)) (= (ho_16562 x z) (ho_16562 y z)))) (= x y))))) (let ((_let_1724 (forall ((x |u_(-> Bool tptp.char)|) (y |u_(-> Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_16571 x z) (ho_16571 y z)))) (= x y))))) (let ((_let_1725 (forall ((x |u_(-> Bool Bool tptp.char)|) (y |u_(-> Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_16570 x z) (ho_16570 y z)))) (= x y))))) (let ((_let_1726 (forall ((x |u_(-> Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_16568 x z) (ho_16568 y z)))) (= x y))))) (let ((_let_1727 (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_16567 x z) (ho_16567 y z)))) (= x y))))) (let ((_let_1728 (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_16565 x z) (ho_16565 y z)))) (= x y))))) (let ((_let_1729 (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_16564 x z) (ho_16564 y z)))) (= x y))))) (let ((_let_1730 (forall ((x |u_(-> tptp.char tptp.nat)|) (y |u_(-> tptp.char tptp.nat)|)) (or (not (forall ((z tptp.char)) (= (ho_16573 x z) (ho_16573 y z)))) (= x y))))) (let ((_let_1731 (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_16576 x z) (ho_16576 y z)))) (= x y))))) (let ((_let_1732 (forall ((x |u_(-> tptp.char tptp.code_integer)|) (y |u_(-> tptp.char tptp.code_integer)|)) (or (not (forall ((z tptp.char)) (= (ho_16579 x z) (ho_16579 y z)))) (= x y))))) (let ((_let_1733 (forall ((x |u_(-> tptp.char tptp.char)|) (y |u_(-> tptp.char tptp.char)|)) (or (not (forall ((z tptp.char)) (= (ho_16581 x z) (ho_16581 y z)))) (= x y))))) (let ((_let_1734 (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_16584 x z) (ho_16584 y z)))) (= x y))))) (let ((_let_1735 (forall ((x |u_(-> tptp.real tptp.filter_real Bool)|) (y |u_(-> tptp.real tptp.filter_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_16587 x z) (ho_16587 y z)))) (= x y))))) (let ((_let_1736 (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_16586 x z) (ho_16586 y z)))) (= x y))))) (let ((_let_1737 (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_16592 x z) (ho_16592 y z)))) (= x y))))) (let ((_let_1738 (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_16591 x z) (ho_16591 y z)))) (= x y))))) (let ((_let_1739 (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_16595 x z) (ho_16595 y z)))) (= x y))))) (let ((_let_1740 (forall ((x |u_(-> tptp.real tptp.filter_real)|) (y |u_(-> tptp.real tptp.filter_real)|)) (or (not (forall ((z tptp.real)) (= (ho_16597 x z) (ho_16597 y z)))) (= x y))))) (let ((_let_1741 (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_16600 x z) (ho_16600 y z)))) (= x y))))) (let ((_let_1742 (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_16603 x z) (ho_16603 y z)))) (= x y))))) (let ((_let_1743 (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_16602 x z) (ho_16602 y z)))) (= x y))))) (let ((_let_1744 (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_16607 x z) (ho_16607 y z)))) (= x y))))) (let ((_let_1745 (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_16606 x z) (ho_16606 y z)))) (= x y))))) (let ((_let_1746 (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_16609 x z) (ho_16609 y z)))) (= x y))))) (let ((_let_1747 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_nat tptp.set_set_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_nat)|)) (= (ho_16617 x z) (ho_16617 y z)))) (= x y))))) (let ((_let_1748 (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_16621 x z) (ho_16621 y z)))) (= x y))))) (let ((_let_1749 (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_16625 x z) (ho_16625 y z)))) (= x y))))) (let ((_let_1750 (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_16630 x z) (ho_16630 y z)))) (= x y))))) (let ((_let_1751 (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_16634 x z) (ho_16634 y z)))) (= x y))))) (let ((_let_1752 (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_16641 x z) (ho_16641 y z)))) (= x y))))) (let ((_let_1753 (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_16643 x z) (ho_16643 y z)))) (= x y))))) (let ((_let_1754 (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_16645 x z) (ho_16645 y z)))) (= x y))))) (let ((_let_1755 (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_16649 x z) (ho_16649 y z)))) (= x y))))) (let ((_let_1756 (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_16653 x z) (ho_16653 y z)))) (= x y))))) (let ((_let_1757 (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_16652 x z) (ho_16652 y z)))) (= x y))))) (let ((_let_1758 (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_16655 x z) (ho_16655 y z)))) (= x y))))) (let ((_let_1759 (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_16736 x z) (ho_16736 y z)))) (= x y))))) (let ((_let_1760 (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_16660 x z) (ho_16660 y z)))) (= x y))))) (let ((_let_1761 (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_16657 x z) (ho_16657 y z)))) (= x y))))) (let ((_let_1762 (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_16665 x z) (ho_16665 y z)))) (= x y))))) (let ((_let_1763 (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_16672 x z) (ho_16672 y z)))) (= x y))))) (let ((_let_1764 (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_16671 x z) (ho_16671 y z)))) (= x y))))) (let ((_let_1765 (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_16678 x z) (ho_16678 y z)))) (= x y))))) (let ((_let_1766 (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_16685 x z) (ho_16685 y z)))) (= x y))))) (let ((_let_1767 (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_16684 x z) (ho_16684 y z)))) (= x y))))) (let ((_let_1768 (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_16683 x z) (ho_16683 y z)))) (= x y))))) (let ((_let_1769 (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_16689 x z) (ho_16689 y z)))) (= x y))))) (let ((_let_1770 (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_16688 x z) (ho_16688 y z)))) (= x y))))) (let ((_let_1771 (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_16692 x z) (ho_16692 y z)))) (= x y))))) (let ((_let_1772 (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_16691 x z) (ho_16691 y z)))) (= x y))))) (let ((_let_1773 (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_16697 x z) (ho_16697 y z)))) (= x y))))) (let ((_let_1774 (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_16696 x z) (ho_16696 y z)))) (= x y))))) (let ((_let_1775 (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_16700 x z) (ho_16700 y z)))) (= x y))))) (let ((_let_1776 (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_16699 x z) (ho_16699 y z)))) (= x y))))) (let ((_let_1777 (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_16708 x z) (ho_16708 y z)))) (= x y))))) (let ((_let_1778 (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_16707 x z) (ho_16707 y z)))) (= x y))))) (let ((_let_1779 (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_16717 x z) (ho_16717 y z)))) (= x y))))) (let ((_let_1780 (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_16702 x z) (ho_16702 y z)))) (= x y))))) (let ((_let_1781 (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_16706 x z) (ho_16706 y z)))) (= x y))))) (let ((_let_1782 (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_16705 x z) (ho_16705 y z)))) (= x y))))) (let ((_let_1783 (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_16716 x z) (ho_16716 y z)))) (= x y))))) (let ((_let_1784 (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_16715 x z) (ho_16715 y z)))) (= x y))))) (let ((_let_1785 (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_16718 x z) (ho_16718 y z)))) (= x y))))) (let ((_let_1786 (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_16714 x z) (ho_16714 y z)))) (= x y))))) (let ((_let_1787 (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_16713 x z) (ho_16713 y z)))) (= x y))))) (let ((_let_1788 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_16726 x z) (ho_16726 y z)))) (= x y))))) (let ((_let_1789 (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_16725 x z) (ho_16725 y z)))) (= x y))))) (let ((_let_1790 (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_16735 x z) (ho_16735 y z)))) (= x y))))) (let ((_let_1791 (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_16728 x z) (ho_16728 y z)))) (= x y))))) (let ((_let_1792 (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_16731 x z) (ho_16731 y z)))) (= x y))))) (let ((_let_1793 (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_16730 x z) (ho_16730 y z)))) (= x y))))) (let ((_let_1794 (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_16734 x z) (ho_16734 y z)))) (= x y))))) (let ((_let_1795 (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_16733 x z) (ho_16733 y z)))) (= x y))))) (let ((_let_1796 (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_16744 x z) (ho_16744 y z)))) (= x y))))) (let ((_let_1797 (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_16743 x z) (ho_16743 y z)))) (= x y))))) (let ((_let_1798 (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_16837 x z) (ho_16837 y z)))) (= x y))))) (let ((_let_1799 (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_16739 x z) (ho_16739 y z)))) (= x y))))) (let ((_let_1800 (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_16738 x z) (ho_16738 y z)))) (= x y))))) (let ((_let_1801 (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_16742 x z) (ho_16742 y z)))) (= x y))))) (let ((_let_1802 (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_16741 x z) (ho_16741 y z)))) (= x y))))) (let ((_let_1803 (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_16752 x z) (ho_16752 y z)))) (= x y))))) (let ((_let_1804 (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_16751 x z) (ho_16751 y z)))) (= x y))))) (let ((_let_1805 (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_16747 x z) (ho_16747 y z)))) (= x y))))) (let ((_let_1806 (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_16746 x z) (ho_16746 y z)))) (= x y))))) (let ((_let_1807 (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_16750 x z) (ho_16750 y z)))) (= x y))))) (let ((_let_1808 (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_16749 x z) (ho_16749 y z)))) (= x y))))) (let ((_let_1809 (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_16756 x z) (ho_16756 y z)))) (= x y))))) (let ((_let_1810 (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_16768 x z) (ho_16768 y z)))) (= x y))))) (let ((_let_1811 (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_16773 x z) (ho_16773 y z)))) (= x y))))) (let ((_let_1812 (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_16761 x z) (ho_16761 y z)))) (= x y))))) (let ((_let_1813 (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_16763 x z) (ho_16763 y z)))) (= x y))))) (let ((_let_1814 (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_16767 x z) (ho_16767 y z)))) (= x y))))) (let ((_let_1815 (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_16772 x z) (ho_16772 y z)))) (= x y))))) (let ((_let_1816 (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_16771 x z) (ho_16771 y z)))) (= x y))))) (let ((_let_1817 (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_16770 x z) (ho_16770 y z)))) (= x y))))) (let ((_let_1818 (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_16780 x z) (ho_16780 y z)))) (= x y))))) (let ((_let_1819 (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_16776 x z) (ho_16776 y z)))) (= x y))))) (let ((_let_1820 (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_16789 x z) (ho_16789 y z)))) (= x y))))) (let ((_let_1821 (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_16788 x z) (ho_16788 y z)))) (= x y))))) (let ((_let_1822 (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_16790 x z) (ho_16790 y z)))) (= x y))))) (let ((_let_1823 (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_16784 x z) (ho_16784 y z)))) (= x y))))) (let ((_let_1824 (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_16783 x z) (ho_16783 y z)))) (= x y))))) (let ((_let_1825 (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_16798 x z) (ho_16798 y z)))) (= x y))))) (let ((_let_1826 (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_16797 x z) (ho_16797 y z)))) (= x y))))) (let ((_let_1827 (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_16836 x z) (ho_16836 y z)))) (= x y))))) (let ((_let_1828 (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_16795 x z) (ho_16795 y z)))) (= x y))))) (let ((_let_1829 (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_16805 x z) (ho_16805 y z)))) (= x y))))) (let ((_let_1830 (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_16800 x z) (ho_16800 y z)))) (= x y))))) (let ((_let_1831 (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_16804 x z) (ho_16804 y z)))) (= x y))))) (let ((_let_1832 (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_16803 x z) (ho_16803 y z)))) (= x y))))) (let ((_let_1833 (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_16835 x z) (ho_16835 y z)))) (= x y))))) (let ((_let_1834 (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_16809 x z) (ho_16809 y z)))) (= x y))))) (let ((_let_1835 (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_16808 x z) (ho_16808 y z)))) (= x y))))) (let ((_let_1836 (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_16821 x z) (ho_16821 y z)))) (= x y))))) (let ((_let_1837 (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_16820 x z) (ho_16820 y z)))) (= x y))))) (let ((_let_1838 (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_16819 x z) (ho_16819 y z)))) (= x y))))) (let ((_let_1839 (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_16818 x z) (ho_16818 y z)))) (= x y))))) (let ((_let_1840 (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_16826 x z) (ho_16826 y z)))) (= x y))))) (let ((_let_1841 (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_16825 x z) (ho_16825 y z)))) (= x y))))) (let ((_let_1842 (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_16824 x z) (ho_16824 y z)))) (= x y))))) (let ((_let_1843 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_16830 x z) (ho_16830 y z)))) (= x y))))) (let ((_let_1844 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_16829 x z) (ho_16829 y z)))) (= x y))))) (let ((_let_1845 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.rat)|)) (= (ho_16828 x z) (ho_16828 y z)))) (= x y))))) (let ((_let_1846 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_nat)|)) (= (ho_16833 x z) (ho_16833 y z)))) (= x y))))) (let ((_let_1847 (forall ((BOUND_VARIABLE_1495931 tptp.num)) (= (ho_7441 k_7440 BOUND_VARIABLE_1495931) (ho_7441 k_7444 (ho_7443 k_7442 BOUND_VARIABLE_1495931)))))) (let ((_let_1848 (forall ((BOUND_VARIABLE_1495872 tptp.nat) (BOUND_VARIABLE_1495873 tptp.num)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7466 (ho_7465 k_7464 _let_4) BOUND_VARIABLE_1495872))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7463 k_7462 (ho_7446 k_7445 BOUND_VARIABLE_1495873)))) (let ((_let_8 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 _let_7) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_6 (ho_7466 (ho_7465 k_7471 _let_7) _let_5)) _let_3)) (ho_7459 (ho_7470 _let_6 _let_5) _let_3)))) _let_3)))))) (let ((_let_9 (ho_7441 (ho_7476 k_7475 tptp.one) tptp.one))) (= (ho_7441 (ho_7485 k_7484 BOUND_VARIABLE_1495872) BOUND_VARIABLE_1495873) (ho_7480 (ho_7483 (ho_7482 k_7481 _let_9) k_7440) (ho_7480 (ho_7479 (ho_7478 k_7477 (= _let_8 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 _let_1)) _let_4))) _let_9) (ho_7441 k_7444 (ho_7474 k_7473 _let_8))))))))))))))))) (let ((_let_1849 (forall ((BOUND_VARIABLE_1495813 tptp.nat) (BOUND_VARIABLE_1495814 tptp.num)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7466 (ho_7465 k_7464 _let_4) BOUND_VARIABLE_1495813))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7463 k_7462 (ho_7446 k_7445 BOUND_VARIABLE_1495814)))) (let ((_let_8 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 _let_7) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_6 (ho_7466 (ho_7465 k_7471 _let_7) _let_5)) _let_3)) (ho_7459 (ho_7470 _let_6 _let_5) _let_3)))) _let_3)))))) (= (ho_7441 k_7444 (ho_7490 (ho_7489 (ho_7488 k_7487 tptp.one) k_7486) (ho_7480 (ho_7479 (ho_7478 k_7477 (= (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 _let_1)) _let_4) _let_8)) (ho_7441 (ho_7476 k_7475 tptp.one) tptp.one)) (ho_7441 k_7444 (ho_7474 k_7473 _let_8))))) (ho_7441 (ho_7485 k_7491 BOUND_VARIABLE_1495813) BOUND_VARIABLE_1495814))))))))))))) (let ((_let_1850 (forall ((BOUND_VARIABLE_1495788 tptp.int) (BOUND_VARIABLE_1495789 tptp.int) (BOUND_VARIABLE_1495790 tptp.int) (BOUND_VARIABLE_1495791 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7492 BOUND_VARIABLE_1495788) BOUND_VARIABLE_1495789) BOUND_VARIABLE_1495790) BOUND_VARIABLE_1495791) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495789) BOUND_VARIABLE_1495791)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495788) BOUND_VARIABLE_1495790)))))))))) (let ((_let_1851 (forall ((BOUND_VARIABLE_1495763 tptp.int) (BOUND_VARIABLE_1495764 tptp.int) (BOUND_VARIABLE_1495765 tptp.int) (BOUND_VARIABLE_1495766 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7497 BOUND_VARIABLE_1495763) BOUND_VARIABLE_1495764) BOUND_VARIABLE_1495765) BOUND_VARIABLE_1495766) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495764) BOUND_VARIABLE_1495766)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495763) BOUND_VARIABLE_1495765)))))))))) (let ((_let_1852 (forall ((BOUND_VARIABLE_1495738 tptp.int) (BOUND_VARIABLE_1495739 tptp.int) (BOUND_VARIABLE_1495740 tptp.int) (BOUND_VARIABLE_1495741 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7498 BOUND_VARIABLE_1495738) BOUND_VARIABLE_1495739) BOUND_VARIABLE_1495740) BOUND_VARIABLE_1495741) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495739) BOUND_VARIABLE_1495741)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495738) BOUND_VARIABLE_1495740)))))))))) (let ((_let_1853 (forall ((BOUND_VARIABLE_1495713 tptp.int) (BOUND_VARIABLE_1495714 tptp.int) (BOUND_VARIABLE_1495715 tptp.int) (BOUND_VARIABLE_1495716 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7499 BOUND_VARIABLE_1495713) BOUND_VARIABLE_1495714) BOUND_VARIABLE_1495715) BOUND_VARIABLE_1495716) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495714) BOUND_VARIABLE_1495716)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495713) BOUND_VARIABLE_1495715)))))))))) (let ((_let_1854 (forall ((BOUND_VARIABLE_1495688 tptp.int) (BOUND_VARIABLE_1495689 tptp.int) (BOUND_VARIABLE_1495690 tptp.int) (BOUND_VARIABLE_1495691 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7500 BOUND_VARIABLE_1495688) BOUND_VARIABLE_1495689) BOUND_VARIABLE_1495690) BOUND_VARIABLE_1495691) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495689) BOUND_VARIABLE_1495691)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495688) BOUND_VARIABLE_1495690)))))))))) (let ((_let_1855 (forall ((BOUND_VARIABLE_1495663 tptp.int) (BOUND_VARIABLE_1495664 tptp.int) (BOUND_VARIABLE_1495665 tptp.int) (BOUND_VARIABLE_1495666 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7501 BOUND_VARIABLE_1495663) BOUND_VARIABLE_1495664) BOUND_VARIABLE_1495665) BOUND_VARIABLE_1495666) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495664) BOUND_VARIABLE_1495666)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495663) BOUND_VARIABLE_1495665)))))))))) (let ((_let_1856 (forall ((BOUND_VARIABLE_1495638 tptp.int) (BOUND_VARIABLE_1495639 tptp.int) (BOUND_VARIABLE_1495640 tptp.int) (BOUND_VARIABLE_1495641 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7502 BOUND_VARIABLE_1495638) BOUND_VARIABLE_1495639) BOUND_VARIABLE_1495640) BOUND_VARIABLE_1495641) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495639) BOUND_VARIABLE_1495641)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495638) BOUND_VARIABLE_1495640)))))))))) (let ((_let_1857 (forall ((BOUND_VARIABLE_1495613 tptp.int) (BOUND_VARIABLE_1495614 tptp.int) (BOUND_VARIABLE_1495615 tptp.int) (BOUND_VARIABLE_1495616 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7503 BOUND_VARIABLE_1495613) BOUND_VARIABLE_1495614) BOUND_VARIABLE_1495615) BOUND_VARIABLE_1495616) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495614) BOUND_VARIABLE_1495616)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495613) BOUND_VARIABLE_1495615)))))))))) (let ((_let_1858 (forall ((BOUND_VARIABLE_1495588 tptp.int) (BOUND_VARIABLE_1495589 tptp.int) (BOUND_VARIABLE_1495590 tptp.int) (BOUND_VARIABLE_1495591 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7504 BOUND_VARIABLE_1495588) BOUND_VARIABLE_1495589) BOUND_VARIABLE_1495590) BOUND_VARIABLE_1495591) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495589) BOUND_VARIABLE_1495591)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495588) BOUND_VARIABLE_1495590)))))))))) (let ((_let_1859 (forall ((BOUND_VARIABLE_1495563 tptp.int) (BOUND_VARIABLE_1495564 tptp.int) (BOUND_VARIABLE_1495565 tptp.int) (BOUND_VARIABLE_1495566 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7505 BOUND_VARIABLE_1495563) BOUND_VARIABLE_1495564) BOUND_VARIABLE_1495565) BOUND_VARIABLE_1495566) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495564) BOUND_VARIABLE_1495566)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495563) BOUND_VARIABLE_1495565)))))))))) (let ((_let_1860 (forall ((BOUND_VARIABLE_1495500 tptp.real) (BOUND_VARIABLE_1495501 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1495501) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7524 BOUND_VARIABLE_1495500) BOUND_VARIABLE_1495501) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1495501 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1495501 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1495500) BOUND_VARIABLE_1495501))))))))))))))))) (let ((_let_1861 (forall ((BOUND_VARIABLE_1495391 tptp.num) (BOUND_VARIABLE_1495392 tptp.nat)) (= (ho_7441 (ho_7528 (ho_7527 (ho_7526 k_7525 (ho_7441 k_7444 tptp.one)) (ho_7485 k_7484 BOUND_VARIABLE_1495392)) (ho_7485 k_7491 BOUND_VARIABLE_1495392)) BOUND_VARIABLE_1495391) (ho_7531 (ho_7530 k_7529 BOUND_VARIABLE_1495391) BOUND_VARIABLE_1495392))))) (let ((_let_1862 (forall ((BOUND_VARIABLE_1495345 tptp.nat) (BOUND_VARIABLE_1495346 tptp.nat) (BOUND_VARIABLE_1495347 tptp.nat) (BOUND_VARIABLE_1495348 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495345) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495348) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495347) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495346) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7537 BOUND_VARIABLE_1495345) BOUND_VARIABLE_1495346) BOUND_VARIABLE_1495347) BOUND_VARIABLE_1495348)))))))) (let ((_let_1863 (forall ((BOUND_VARIABLE_1495299 tptp.nat) (BOUND_VARIABLE_1495300 tptp.nat) (BOUND_VARIABLE_1495301 tptp.nat) (BOUND_VARIABLE_1495302 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495299) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495302) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495301) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1495300) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7543 BOUND_VARIABLE_1495299) BOUND_VARIABLE_1495300) BOUND_VARIABLE_1495301) BOUND_VARIABLE_1495302)))))))) (let ((_let_1864 (forall ((BOUND_VARIABLE_1495270 tptp.int) (BOUND_VARIABLE_1495271 tptp.int) (BOUND_VARIABLE_1495272 tptp.int) (BOUND_VARIABLE_1495273 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7544 BOUND_VARIABLE_1495270) BOUND_VARIABLE_1495271) BOUND_VARIABLE_1495272) BOUND_VARIABLE_1495273) (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495271) BOUND_VARIABLE_1495272) (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495270) BOUND_VARIABLE_1495273)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1))))))))) (not (= (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495270) BOUND_VARIABLE_1495273) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495271) BOUND_VARIABLE_1495272)))))))) (let ((_let_1865 (forall ((BOUND_VARIABLE_1495245 tptp.int) (BOUND_VARIABLE_1495246 tptp.int) (BOUND_VARIABLE_1495247 tptp.int) (BOUND_VARIABLE_1495248 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7545 BOUND_VARIABLE_1495245) BOUND_VARIABLE_1495246) BOUND_VARIABLE_1495247) BOUND_VARIABLE_1495248) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495246) BOUND_VARIABLE_1495248)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495245) BOUND_VARIABLE_1495247)))))))))) (let ((_let_1866 (forall ((BOUND_VARIABLE_1495220 tptp.int) (BOUND_VARIABLE_1495221 tptp.int) (BOUND_VARIABLE_1495222 tptp.int) (BOUND_VARIABLE_1495223 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7546 BOUND_VARIABLE_1495220) BOUND_VARIABLE_1495221) BOUND_VARIABLE_1495222) BOUND_VARIABLE_1495223) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495221) BOUND_VARIABLE_1495223)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495220) BOUND_VARIABLE_1495222)))))))))) (let ((_let_1867 (forall ((BOUND_VARIABLE_1495195 tptp.int) (BOUND_VARIABLE_1495196 tptp.int) (BOUND_VARIABLE_1495197 tptp.int) (BOUND_VARIABLE_1495198 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7547 BOUND_VARIABLE_1495195) BOUND_VARIABLE_1495196) BOUND_VARIABLE_1495197) BOUND_VARIABLE_1495198) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495196) BOUND_VARIABLE_1495198)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495195) BOUND_VARIABLE_1495197)))))))))) (let ((_let_1868 (forall ((BOUND_VARIABLE_1495170 tptp.int) (BOUND_VARIABLE_1495171 tptp.int) (BOUND_VARIABLE_1495172 tptp.int) (BOUND_VARIABLE_1495173 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7548 BOUND_VARIABLE_1495170) BOUND_VARIABLE_1495171) BOUND_VARIABLE_1495172) BOUND_VARIABLE_1495173) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495171) BOUND_VARIABLE_1495173)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495170) BOUND_VARIABLE_1495172)))))))))) (let ((_let_1869 (forall ((BOUND_VARIABLE_1495145 tptp.int) (BOUND_VARIABLE_1495146 tptp.int) (BOUND_VARIABLE_1495147 tptp.int) (BOUND_VARIABLE_1495148 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7549 BOUND_VARIABLE_1495145) BOUND_VARIABLE_1495146) BOUND_VARIABLE_1495147) BOUND_VARIABLE_1495148) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495146) BOUND_VARIABLE_1495148)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495145) BOUND_VARIABLE_1495147)))))))))) (let ((_let_1870 (forall ((BOUND_VARIABLE_1495120 tptp.int) (BOUND_VARIABLE_1495121 tptp.int) (BOUND_VARIABLE_1495122 tptp.int) (BOUND_VARIABLE_1495123 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7550 BOUND_VARIABLE_1495120) BOUND_VARIABLE_1495121) BOUND_VARIABLE_1495122) BOUND_VARIABLE_1495123) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495121) BOUND_VARIABLE_1495123)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1495120) BOUND_VARIABLE_1495122)))))))))) (let ((_let_1871 (forall ((BOUND_VARIABLE_1495057 tptp.real) (BOUND_VARIABLE_1495058 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1495058) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7551 BOUND_VARIABLE_1495057) BOUND_VARIABLE_1495058) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1495058 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1495058 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1495057) BOUND_VARIABLE_1495058))))))))))))))))) (let ((_let_1872 (forall ((BOUND_VARIABLE_1494994 tptp.real) (BOUND_VARIABLE_1494995 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494995) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7552 BOUND_VARIABLE_1494994) BOUND_VARIABLE_1494995) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494995 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494995 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494994) BOUND_VARIABLE_1494995))))))))))))))))) (let ((_let_1873 (forall ((BOUND_VARIABLE_1494931 tptp.real) (BOUND_VARIABLE_1494932 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494932) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7553 BOUND_VARIABLE_1494931) BOUND_VARIABLE_1494932) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494932 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494932 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494931) BOUND_VARIABLE_1494932))))))))))))))))) (let ((_let_1874 (forall ((BOUND_VARIABLE_1494868 tptp.real) (BOUND_VARIABLE_1494869 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494869) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7554 BOUND_VARIABLE_1494868) BOUND_VARIABLE_1494869) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494869 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494869 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494868) BOUND_VARIABLE_1494869))))))))))))))))) (let ((_let_1875 (forall ((BOUND_VARIABLE_1494805 tptp.real) (BOUND_VARIABLE_1494806 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494806) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7555 BOUND_VARIABLE_1494805) BOUND_VARIABLE_1494806) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494806 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494806 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494805) BOUND_VARIABLE_1494806))))))))))))))))) (let ((_let_1876 (forall ((BOUND_VARIABLE_1494742 tptp.real) (BOUND_VARIABLE_1494743 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494743) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7556 BOUND_VARIABLE_1494742) BOUND_VARIABLE_1494743) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494743 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494743 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494742) BOUND_VARIABLE_1494743))))))))))))))))) (let ((_let_1877 (forall ((BOUND_VARIABLE_1494687 tptp.real) (BOUND_VARIABLE_1494688 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7557 BOUND_VARIABLE_1494687) BOUND_VARIABLE_1494688) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494688 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1494688) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494688 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1494688) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494687) BOUND_VARIABLE_1494688))))))))))))))) (let ((_let_1878 (forall ((BOUND_VARIABLE_1494624 tptp.real) (BOUND_VARIABLE_1494625 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494625) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7558 BOUND_VARIABLE_1494624) BOUND_VARIABLE_1494625) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494625 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494625 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494624) BOUND_VARIABLE_1494625))))))))))))))))) (let ((_let_1879 (forall ((BOUND_VARIABLE_1494569 tptp.real) (BOUND_VARIABLE_1494570 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7559 BOUND_VARIABLE_1494569) BOUND_VARIABLE_1494570) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494570 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1494570) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494570 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1494570) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494569) BOUND_VARIABLE_1494570))))))))))))))) (let ((_let_1880 (forall ((BOUND_VARIABLE_1494506 tptp.real) (BOUND_VARIABLE_1494507 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494507) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7560 BOUND_VARIABLE_1494506) BOUND_VARIABLE_1494507) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494507 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494507 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494506) BOUND_VARIABLE_1494507))))))))))))))))) (let ((_let_1881 (forall ((BOUND_VARIABLE_1494451 tptp.real) (BOUND_VARIABLE_1494452 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7561 BOUND_VARIABLE_1494451) BOUND_VARIABLE_1494452) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494452 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1494452) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494452 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1494452) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494451) BOUND_VARIABLE_1494452))))))))))))))) (let ((_let_1882 (forall ((BOUND_VARIABLE_1494388 tptp.real) (BOUND_VARIABLE_1494389 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494389) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7562 BOUND_VARIABLE_1494388) BOUND_VARIABLE_1494389) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494389 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494389 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494388) BOUND_VARIABLE_1494389))))))))))))))))) (let ((_let_1883 (forall ((BOUND_VARIABLE_1494333 tptp.real) (BOUND_VARIABLE_1494334 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7563 BOUND_VARIABLE_1494333) BOUND_VARIABLE_1494334) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494334 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1494334) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494334 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1494334) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494333) BOUND_VARIABLE_1494334))))))))))))))) (let ((_let_1884 (forall ((BOUND_VARIABLE_1494270 tptp.real) (BOUND_VARIABLE_1494271 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494271) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7564 BOUND_VARIABLE_1494270) BOUND_VARIABLE_1494271) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494271 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494271 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494270) BOUND_VARIABLE_1494271))))))))))))))))) (let ((_let_1885 (forall ((BOUND_VARIABLE_1494215 tptp.real) (BOUND_VARIABLE_1494216 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7565 BOUND_VARIABLE_1494215) BOUND_VARIABLE_1494216) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494216 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1494216) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494216 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1494216) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494215) BOUND_VARIABLE_1494216))))))))))))))) (let ((_let_1886 (forall ((BOUND_VARIABLE_1494152 tptp.real) (BOUND_VARIABLE_1494153 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1494153) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7566 BOUND_VARIABLE_1494152) BOUND_VARIABLE_1494153) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494153 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494153 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494152) BOUND_VARIABLE_1494153))))))))))))))))) (let ((_let_1887 (forall ((BOUND_VARIABLE_1494097 tptp.real) (BOUND_VARIABLE_1494098 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7567 BOUND_VARIABLE_1494097) BOUND_VARIABLE_1494098) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1494098 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1494098) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1494098 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1494098) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1494097) BOUND_VARIABLE_1494098))))))))))))))) (let ((_let_1888 (forall ((BOUND_VARIABLE_1494072 tptp.int) (BOUND_VARIABLE_1494073 tptp.int) (BOUND_VARIABLE_1494074 tptp.int) (BOUND_VARIABLE_1494075 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7568 BOUND_VARIABLE_1494072) BOUND_VARIABLE_1494073) BOUND_VARIABLE_1494074) BOUND_VARIABLE_1494075) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1494073) BOUND_VARIABLE_1494075)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1494072) BOUND_VARIABLE_1494074)))))))))) (let ((_let_1889 (forall ((BOUND_VARIABLE_1494047 tptp.int) (BOUND_VARIABLE_1494048 tptp.int) (BOUND_VARIABLE_1494049 tptp.int) (BOUND_VARIABLE_1494050 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7569 BOUND_VARIABLE_1494047) BOUND_VARIABLE_1494048) BOUND_VARIABLE_1494049) BOUND_VARIABLE_1494050) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1494048) BOUND_VARIABLE_1494050)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1494047) BOUND_VARIABLE_1494049)))))))))) (let ((_let_1890 (forall ((BOUND_VARIABLE_1494022 tptp.int) (BOUND_VARIABLE_1494023 tptp.int) (BOUND_VARIABLE_1494024 tptp.int) (BOUND_VARIABLE_1494025 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7570 BOUND_VARIABLE_1494022) BOUND_VARIABLE_1494023) BOUND_VARIABLE_1494024) BOUND_VARIABLE_1494025) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1494023) BOUND_VARIABLE_1494025)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1494022) BOUND_VARIABLE_1494024)))))))))) (let ((_let_1891 (forall ((BOUND_VARIABLE_1493997 tptp.int) (BOUND_VARIABLE_1493998 tptp.int) (BOUND_VARIABLE_1493999 tptp.int) (BOUND_VARIABLE_1494000 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7571 BOUND_VARIABLE_1493997) BOUND_VARIABLE_1493998) BOUND_VARIABLE_1493999) BOUND_VARIABLE_1494000) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493998) BOUND_VARIABLE_1494000)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493997) BOUND_VARIABLE_1493999)))))))))) (let ((_let_1892 (forall ((BOUND_VARIABLE_1493972 tptp.int) (BOUND_VARIABLE_1493973 tptp.int) (BOUND_VARIABLE_1493974 tptp.int) (BOUND_VARIABLE_1493975 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7572 BOUND_VARIABLE_1493972) BOUND_VARIABLE_1493973) BOUND_VARIABLE_1493974) BOUND_VARIABLE_1493975) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493973) BOUND_VARIABLE_1493975)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493972) BOUND_VARIABLE_1493974)))))))))) (let ((_let_1893 (forall ((BOUND_VARIABLE_1493947 tptp.int) (BOUND_VARIABLE_1493948 tptp.int) (BOUND_VARIABLE_1493949 tptp.int) (BOUND_VARIABLE_1493950 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7573 BOUND_VARIABLE_1493947) BOUND_VARIABLE_1493948) BOUND_VARIABLE_1493949) BOUND_VARIABLE_1493950) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493948) BOUND_VARIABLE_1493950)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493947) BOUND_VARIABLE_1493949)))))))))) (let ((_let_1894 (forall ((BOUND_VARIABLE_1493922 tptp.int) (BOUND_VARIABLE_1493923 tptp.int) (BOUND_VARIABLE_1493924 tptp.int) (BOUND_VARIABLE_1493925 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7574 BOUND_VARIABLE_1493922) BOUND_VARIABLE_1493923) BOUND_VARIABLE_1493924) BOUND_VARIABLE_1493925) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493923) BOUND_VARIABLE_1493925)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493922) BOUND_VARIABLE_1493924)))))))))) (let ((_let_1895 (forall ((BOUND_VARIABLE_1493897 tptp.int) (BOUND_VARIABLE_1493898 tptp.int) (BOUND_VARIABLE_1493899 tptp.int) (BOUND_VARIABLE_1493900 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7575 BOUND_VARIABLE_1493897) BOUND_VARIABLE_1493898) BOUND_VARIABLE_1493899) BOUND_VARIABLE_1493900) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493898) BOUND_VARIABLE_1493900)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493897) BOUND_VARIABLE_1493899)))))))))) (let ((_let_1896 (forall ((BOUND_VARIABLE_1493872 tptp.int) (BOUND_VARIABLE_1493873 tptp.int) (BOUND_VARIABLE_1493874 tptp.int) (BOUND_VARIABLE_1493875 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7576 BOUND_VARIABLE_1493872) BOUND_VARIABLE_1493873) BOUND_VARIABLE_1493874) BOUND_VARIABLE_1493875) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493873) BOUND_VARIABLE_1493875)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493872) BOUND_VARIABLE_1493874)))))))))) (let ((_let_1897 (forall ((BOUND_VARIABLE_1493847 tptp.int) (BOUND_VARIABLE_1493848 tptp.int) (BOUND_VARIABLE_1493849 tptp.int) (BOUND_VARIABLE_1493850 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7577 BOUND_VARIABLE_1493847) BOUND_VARIABLE_1493848) BOUND_VARIABLE_1493849) BOUND_VARIABLE_1493850) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493848) BOUND_VARIABLE_1493850)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493847) BOUND_VARIABLE_1493849)))))))))) (let ((_let_1898 (forall ((BOUND_VARIABLE_1493822 tptp.int) (BOUND_VARIABLE_1493823 tptp.int) (BOUND_VARIABLE_1493824 tptp.int) (BOUND_VARIABLE_1493825 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7578 BOUND_VARIABLE_1493822) BOUND_VARIABLE_1493823) BOUND_VARIABLE_1493824) BOUND_VARIABLE_1493825) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493823) BOUND_VARIABLE_1493825)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493822) BOUND_VARIABLE_1493824)))))))))) (let ((_let_1899 (forall ((BOUND_VARIABLE_1493797 tptp.int) (BOUND_VARIABLE_1493798 tptp.int) (BOUND_VARIABLE_1493799 tptp.int) (BOUND_VARIABLE_1493800 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7579 BOUND_VARIABLE_1493797) BOUND_VARIABLE_1493798) BOUND_VARIABLE_1493799) BOUND_VARIABLE_1493800) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493798) BOUND_VARIABLE_1493800)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493797) BOUND_VARIABLE_1493799)))))))))) (let ((_let_1900 (forall ((BOUND_VARIABLE_1493772 tptp.int) (BOUND_VARIABLE_1493773 tptp.int) (BOUND_VARIABLE_1493774 tptp.int) (BOUND_VARIABLE_1493775 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7580 BOUND_VARIABLE_1493772) BOUND_VARIABLE_1493773) BOUND_VARIABLE_1493774) BOUND_VARIABLE_1493775) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493773) BOUND_VARIABLE_1493775)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493772) BOUND_VARIABLE_1493774)))))))))) (let ((_let_1901 (forall ((BOUND_VARIABLE_1493747 tptp.int) (BOUND_VARIABLE_1493748 tptp.int) (BOUND_VARIABLE_1493749 tptp.int) (BOUND_VARIABLE_1493750 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7581 BOUND_VARIABLE_1493747) BOUND_VARIABLE_1493748) BOUND_VARIABLE_1493749) BOUND_VARIABLE_1493750) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493748) BOUND_VARIABLE_1493750)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493747) BOUND_VARIABLE_1493749)))))))))) (let ((_let_1902 (forall ((BOUND_VARIABLE_1493722 tptp.int) (BOUND_VARIABLE_1493723 tptp.int) (BOUND_VARIABLE_1493724 tptp.int) (BOUND_VARIABLE_1493725 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7582 BOUND_VARIABLE_1493722) BOUND_VARIABLE_1493723) BOUND_VARIABLE_1493724) BOUND_VARIABLE_1493725) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493723) BOUND_VARIABLE_1493725)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493722) BOUND_VARIABLE_1493724)))))))))) (let ((_let_1903 (forall ((BOUND_VARIABLE_1493697 tptp.int) (BOUND_VARIABLE_1493698 tptp.int) (BOUND_VARIABLE_1493699 tptp.int) (BOUND_VARIABLE_1493700 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7583 BOUND_VARIABLE_1493697) BOUND_VARIABLE_1493698) BOUND_VARIABLE_1493699) BOUND_VARIABLE_1493700) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493698) BOUND_VARIABLE_1493700)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493697) BOUND_VARIABLE_1493699)))))))))) (let ((_let_1904 (forall ((BOUND_VARIABLE_1493672 tptp.int) (BOUND_VARIABLE_1493673 tptp.int) (BOUND_VARIABLE_1493674 tptp.int) (BOUND_VARIABLE_1493675 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7584 BOUND_VARIABLE_1493672) BOUND_VARIABLE_1493673) BOUND_VARIABLE_1493674) BOUND_VARIABLE_1493675) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493673) BOUND_VARIABLE_1493675)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493672) BOUND_VARIABLE_1493674)))))))))) (let ((_let_1905 (forall ((BOUND_VARIABLE_1493647 tptp.int) (BOUND_VARIABLE_1493648 tptp.int) (BOUND_VARIABLE_1493649 tptp.int) (BOUND_VARIABLE_1493650 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7585 BOUND_VARIABLE_1493647) BOUND_VARIABLE_1493648) BOUND_VARIABLE_1493649) BOUND_VARIABLE_1493650) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493648) BOUND_VARIABLE_1493650)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493647) BOUND_VARIABLE_1493649)))))))))) (let ((_let_1906 (forall ((BOUND_VARIABLE_1493622 tptp.int) (BOUND_VARIABLE_1493623 tptp.int) (BOUND_VARIABLE_1493624 tptp.int) (BOUND_VARIABLE_1493625 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7586 BOUND_VARIABLE_1493622) BOUND_VARIABLE_1493623) BOUND_VARIABLE_1493624) BOUND_VARIABLE_1493625) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493623) BOUND_VARIABLE_1493625)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493622) BOUND_VARIABLE_1493624)))))))))) (let ((_let_1907 (forall ((BOUND_VARIABLE_1493597 tptp.int) (BOUND_VARIABLE_1493598 tptp.int) (BOUND_VARIABLE_1493599 tptp.int) (BOUND_VARIABLE_1493600 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7587 BOUND_VARIABLE_1493597) BOUND_VARIABLE_1493598) BOUND_VARIABLE_1493599) BOUND_VARIABLE_1493600) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493598) BOUND_VARIABLE_1493600)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493597) BOUND_VARIABLE_1493599)))))))))) (let ((_let_1908 (forall ((BOUND_VARIABLE_1493572 tptp.int) (BOUND_VARIABLE_1493573 tptp.int) (BOUND_VARIABLE_1493574 tptp.int) (BOUND_VARIABLE_1493575 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7588 BOUND_VARIABLE_1493572) BOUND_VARIABLE_1493573) BOUND_VARIABLE_1493574) BOUND_VARIABLE_1493575) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493573) BOUND_VARIABLE_1493575)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493572) BOUND_VARIABLE_1493574)))))))))) (let ((_let_1909 (forall ((BOUND_VARIABLE_1493547 tptp.int) (BOUND_VARIABLE_1493548 tptp.int) (BOUND_VARIABLE_1493549 tptp.int) (BOUND_VARIABLE_1493550 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7589 BOUND_VARIABLE_1493547) BOUND_VARIABLE_1493548) BOUND_VARIABLE_1493549) BOUND_VARIABLE_1493550) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493548) BOUND_VARIABLE_1493550)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493547) BOUND_VARIABLE_1493549)))))))))) (let ((_let_1910 (forall ((BOUND_VARIABLE_1493522 tptp.int) (BOUND_VARIABLE_1493523 tptp.int) (BOUND_VARIABLE_1493524 tptp.int) (BOUND_VARIABLE_1493525 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7590 BOUND_VARIABLE_1493522) BOUND_VARIABLE_1493523) BOUND_VARIABLE_1493524) BOUND_VARIABLE_1493525) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493523) BOUND_VARIABLE_1493525)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493522) BOUND_VARIABLE_1493524)))))))))) (let ((_let_1911 (forall ((BOUND_VARIABLE_1493497 tptp.int) (BOUND_VARIABLE_1493498 tptp.int) (BOUND_VARIABLE_1493499 tptp.int) (BOUND_VARIABLE_1493500 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7591 BOUND_VARIABLE_1493497) BOUND_VARIABLE_1493498) BOUND_VARIABLE_1493499) BOUND_VARIABLE_1493500) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493498) BOUND_VARIABLE_1493500)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493497) BOUND_VARIABLE_1493499)))))))))) (let ((_let_1912 (forall ((BOUND_VARIABLE_1493472 tptp.int) (BOUND_VARIABLE_1493473 tptp.int) (BOUND_VARIABLE_1493474 tptp.int) (BOUND_VARIABLE_1493475 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7592 BOUND_VARIABLE_1493472) BOUND_VARIABLE_1493473) BOUND_VARIABLE_1493474) BOUND_VARIABLE_1493475) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493473) BOUND_VARIABLE_1493475)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493472) BOUND_VARIABLE_1493474)))))))))) (let ((_let_1913 (forall ((BOUND_VARIABLE_1493447 tptp.int) (BOUND_VARIABLE_1493448 tptp.int) (BOUND_VARIABLE_1493449 tptp.int) (BOUND_VARIABLE_1493450 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7593 BOUND_VARIABLE_1493447) BOUND_VARIABLE_1493448) BOUND_VARIABLE_1493449) BOUND_VARIABLE_1493450) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493448) BOUND_VARIABLE_1493450)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493447) BOUND_VARIABLE_1493449)))))))))) (let ((_let_1914 (forall ((BOUND_VARIABLE_1493422 tptp.int) (BOUND_VARIABLE_1493423 tptp.int) (BOUND_VARIABLE_1493424 tptp.int) (BOUND_VARIABLE_1493425 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7594 BOUND_VARIABLE_1493422) BOUND_VARIABLE_1493423) BOUND_VARIABLE_1493424) BOUND_VARIABLE_1493425) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493423) BOUND_VARIABLE_1493425)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493422) BOUND_VARIABLE_1493424)))))))))) (let ((_let_1915 (forall ((BOUND_VARIABLE_1493397 tptp.int) (BOUND_VARIABLE_1493398 tptp.int) (BOUND_VARIABLE_1493399 tptp.int) (BOUND_VARIABLE_1493400 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7595 BOUND_VARIABLE_1493397) BOUND_VARIABLE_1493398) BOUND_VARIABLE_1493399) BOUND_VARIABLE_1493400) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493398) BOUND_VARIABLE_1493400)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493397) BOUND_VARIABLE_1493399)))))))))) (let ((_let_1916 (forall ((BOUND_VARIABLE_1493372 tptp.int) (BOUND_VARIABLE_1493373 tptp.int) (BOUND_VARIABLE_1493374 tptp.int) (BOUND_VARIABLE_1493375 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7596 BOUND_VARIABLE_1493372) BOUND_VARIABLE_1493373) BOUND_VARIABLE_1493374) BOUND_VARIABLE_1493375) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493373) BOUND_VARIABLE_1493375)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493372) BOUND_VARIABLE_1493374)))))))))) (let ((_let_1917 (forall ((BOUND_VARIABLE_1493347 tptp.int) (BOUND_VARIABLE_1493348 tptp.int) (BOUND_VARIABLE_1493349 tptp.int) (BOUND_VARIABLE_1493350 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7597 BOUND_VARIABLE_1493347) BOUND_VARIABLE_1493348) BOUND_VARIABLE_1493349) BOUND_VARIABLE_1493350) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493348) BOUND_VARIABLE_1493350)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493347) BOUND_VARIABLE_1493349)))))))))) (let ((_let_1918 (forall ((BOUND_VARIABLE_1493322 tptp.int) (BOUND_VARIABLE_1493323 tptp.int) (BOUND_VARIABLE_1493324 tptp.int) (BOUND_VARIABLE_1493325 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7598 BOUND_VARIABLE_1493322) BOUND_VARIABLE_1493323) BOUND_VARIABLE_1493324) BOUND_VARIABLE_1493325) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493323) BOUND_VARIABLE_1493325)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493322) BOUND_VARIABLE_1493324)))))))))) (let ((_let_1919 (forall ((BOUND_VARIABLE_1493297 tptp.int) (BOUND_VARIABLE_1493298 tptp.int) (BOUND_VARIABLE_1493299 tptp.int) (BOUND_VARIABLE_1493300 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7599 BOUND_VARIABLE_1493297) BOUND_VARIABLE_1493298) BOUND_VARIABLE_1493299) BOUND_VARIABLE_1493300) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493298) BOUND_VARIABLE_1493300)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493297) BOUND_VARIABLE_1493299)))))))))) (let ((_let_1920 (forall ((BOUND_VARIABLE_1493272 tptp.int) (BOUND_VARIABLE_1493273 tptp.int) (BOUND_VARIABLE_1493274 tptp.int) (BOUND_VARIABLE_1493275 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7600 BOUND_VARIABLE_1493272) BOUND_VARIABLE_1493273) BOUND_VARIABLE_1493274) BOUND_VARIABLE_1493275) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493273) BOUND_VARIABLE_1493275)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493272) BOUND_VARIABLE_1493274)))))))))) (let ((_let_1921 (forall ((BOUND_VARIABLE_1493247 tptp.int) (BOUND_VARIABLE_1493248 tptp.int) (BOUND_VARIABLE_1493249 tptp.int) (BOUND_VARIABLE_1493250 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7601 BOUND_VARIABLE_1493247) BOUND_VARIABLE_1493248) BOUND_VARIABLE_1493249) BOUND_VARIABLE_1493250) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493248) BOUND_VARIABLE_1493250)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493247) BOUND_VARIABLE_1493249)))))))))) (let ((_let_1922 (forall ((BOUND_VARIABLE_1493222 tptp.int) (BOUND_VARIABLE_1493223 tptp.int) (BOUND_VARIABLE_1493224 tptp.int) (BOUND_VARIABLE_1493225 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7602 BOUND_VARIABLE_1493222) BOUND_VARIABLE_1493223) BOUND_VARIABLE_1493224) BOUND_VARIABLE_1493225) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493223) BOUND_VARIABLE_1493225)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493222) BOUND_VARIABLE_1493224)))))))))) (let ((_let_1923 (forall ((BOUND_VARIABLE_1493197 tptp.int) (BOUND_VARIABLE_1493198 tptp.int) (BOUND_VARIABLE_1493199 tptp.int) (BOUND_VARIABLE_1493200 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7603 BOUND_VARIABLE_1493197) BOUND_VARIABLE_1493198) BOUND_VARIABLE_1493199) BOUND_VARIABLE_1493200) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493198) BOUND_VARIABLE_1493200)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493197) BOUND_VARIABLE_1493199)))))))))) (let ((_let_1924 (forall ((BOUND_VARIABLE_1493172 tptp.int) (BOUND_VARIABLE_1493173 tptp.int) (BOUND_VARIABLE_1493174 tptp.int) (BOUND_VARIABLE_1493175 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7604 BOUND_VARIABLE_1493172) BOUND_VARIABLE_1493173) BOUND_VARIABLE_1493174) BOUND_VARIABLE_1493175) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493173) BOUND_VARIABLE_1493175)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493172) BOUND_VARIABLE_1493174)))))))))) (let ((_let_1925 (forall ((BOUND_VARIABLE_1493147 tptp.int) (BOUND_VARIABLE_1493148 tptp.int) (BOUND_VARIABLE_1493149 tptp.int) (BOUND_VARIABLE_1493150 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7605 BOUND_VARIABLE_1493147) BOUND_VARIABLE_1493148) BOUND_VARIABLE_1493149) BOUND_VARIABLE_1493150) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493148) BOUND_VARIABLE_1493150)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493147) BOUND_VARIABLE_1493149)))))))))) (let ((_let_1926 (forall ((BOUND_VARIABLE_1493122 tptp.int) (BOUND_VARIABLE_1493123 tptp.int) (BOUND_VARIABLE_1493124 tptp.int) (BOUND_VARIABLE_1493125 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7606 BOUND_VARIABLE_1493122) BOUND_VARIABLE_1493123) BOUND_VARIABLE_1493124) BOUND_VARIABLE_1493125) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493123) BOUND_VARIABLE_1493125)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493122) BOUND_VARIABLE_1493124)))))))))) (let ((_let_1927 (forall ((BOUND_VARIABLE_1493097 tptp.int) (BOUND_VARIABLE_1493098 tptp.int) (BOUND_VARIABLE_1493099 tptp.int) (BOUND_VARIABLE_1493100 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7607 BOUND_VARIABLE_1493097) BOUND_VARIABLE_1493098) BOUND_VARIABLE_1493099) BOUND_VARIABLE_1493100) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493098) BOUND_VARIABLE_1493100)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493097) BOUND_VARIABLE_1493099)))))))))) (let ((_let_1928 (forall ((BOUND_VARIABLE_1493072 tptp.int) (BOUND_VARIABLE_1493073 tptp.int) (BOUND_VARIABLE_1493074 tptp.int) (BOUND_VARIABLE_1493075 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7608 BOUND_VARIABLE_1493072) BOUND_VARIABLE_1493073) BOUND_VARIABLE_1493074) BOUND_VARIABLE_1493075) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493073) BOUND_VARIABLE_1493075)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493072) BOUND_VARIABLE_1493074)))))))))) (let ((_let_1929 (forall ((BOUND_VARIABLE_1493047 tptp.int) (BOUND_VARIABLE_1493048 tptp.int) (BOUND_VARIABLE_1493049 tptp.int) (BOUND_VARIABLE_1493050 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7609 BOUND_VARIABLE_1493047) BOUND_VARIABLE_1493048) BOUND_VARIABLE_1493049) BOUND_VARIABLE_1493050) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493048) BOUND_VARIABLE_1493050)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493047) BOUND_VARIABLE_1493049)))))))))) (let ((_let_1930 (forall ((BOUND_VARIABLE_1493022 tptp.int) (BOUND_VARIABLE_1493023 tptp.int) (BOUND_VARIABLE_1493024 tptp.int) (BOUND_VARIABLE_1493025 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7610 BOUND_VARIABLE_1493022) BOUND_VARIABLE_1493023) BOUND_VARIABLE_1493024) BOUND_VARIABLE_1493025) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493023) BOUND_VARIABLE_1493025)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1493022) BOUND_VARIABLE_1493024)))))))))) (let ((_let_1931 (forall ((BOUND_VARIABLE_1492997 tptp.int) (BOUND_VARIABLE_1492998 tptp.int) (BOUND_VARIABLE_1492999 tptp.int) (BOUND_VARIABLE_1493000 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7611 BOUND_VARIABLE_1492997) BOUND_VARIABLE_1492998) BOUND_VARIABLE_1492999) BOUND_VARIABLE_1493000) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492998) BOUND_VARIABLE_1493000)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492997) BOUND_VARIABLE_1492999)))))))))) (let ((_let_1932 (forall ((BOUND_VARIABLE_1492972 tptp.int) (BOUND_VARIABLE_1492973 tptp.int) (BOUND_VARIABLE_1492974 tptp.int) (BOUND_VARIABLE_1492975 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7612 BOUND_VARIABLE_1492972) BOUND_VARIABLE_1492973) BOUND_VARIABLE_1492974) BOUND_VARIABLE_1492975) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492973) BOUND_VARIABLE_1492975)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492972) BOUND_VARIABLE_1492974)))))))))) (let ((_let_1933 (forall ((BOUND_VARIABLE_1492947 tptp.int) (BOUND_VARIABLE_1492948 tptp.int) (BOUND_VARIABLE_1492949 tptp.int) (BOUND_VARIABLE_1492950 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7613 BOUND_VARIABLE_1492947) BOUND_VARIABLE_1492948) BOUND_VARIABLE_1492949) BOUND_VARIABLE_1492950) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492948) BOUND_VARIABLE_1492950)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492947) BOUND_VARIABLE_1492949)))))))))) (let ((_let_1934 (forall ((BOUND_VARIABLE_1492922 tptp.int) (BOUND_VARIABLE_1492923 tptp.int) (BOUND_VARIABLE_1492924 tptp.int) (BOUND_VARIABLE_1492925 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7614 BOUND_VARIABLE_1492922) BOUND_VARIABLE_1492923) BOUND_VARIABLE_1492924) BOUND_VARIABLE_1492925) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492923) BOUND_VARIABLE_1492925)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492922) BOUND_VARIABLE_1492924)))))))))) (let ((_let_1935 (forall ((BOUND_VARIABLE_1492897 tptp.int) (BOUND_VARIABLE_1492898 tptp.int) (BOUND_VARIABLE_1492899 tptp.int) (BOUND_VARIABLE_1492900 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7615 BOUND_VARIABLE_1492897) BOUND_VARIABLE_1492898) BOUND_VARIABLE_1492899) BOUND_VARIABLE_1492900) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492898) BOUND_VARIABLE_1492900)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492897) BOUND_VARIABLE_1492899)))))))))) (let ((_let_1936 (forall ((BOUND_VARIABLE_1492872 tptp.int) (BOUND_VARIABLE_1492873 tptp.int) (BOUND_VARIABLE_1492874 tptp.int) (BOUND_VARIABLE_1492875 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7616 BOUND_VARIABLE_1492872) BOUND_VARIABLE_1492873) BOUND_VARIABLE_1492874) BOUND_VARIABLE_1492875) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492873) BOUND_VARIABLE_1492875)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492872) BOUND_VARIABLE_1492874)))))))))) (let ((_let_1937 (forall ((BOUND_VARIABLE_1492847 tptp.int) (BOUND_VARIABLE_1492848 tptp.int) (BOUND_VARIABLE_1492849 tptp.int) (BOUND_VARIABLE_1492850 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7617 BOUND_VARIABLE_1492847) BOUND_VARIABLE_1492848) BOUND_VARIABLE_1492849) BOUND_VARIABLE_1492850) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492848) BOUND_VARIABLE_1492850)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492847) BOUND_VARIABLE_1492849)))))))))) (let ((_let_1938 (forall ((BOUND_VARIABLE_1492822 tptp.int) (BOUND_VARIABLE_1492823 tptp.int) (BOUND_VARIABLE_1492824 tptp.int) (BOUND_VARIABLE_1492825 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7618 BOUND_VARIABLE_1492822) BOUND_VARIABLE_1492823) BOUND_VARIABLE_1492824) BOUND_VARIABLE_1492825) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492823) BOUND_VARIABLE_1492825)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492822) BOUND_VARIABLE_1492824)))))))))) (let ((_let_1939 (forall ((BOUND_VARIABLE_1492797 tptp.int) (BOUND_VARIABLE_1492798 tptp.int) (BOUND_VARIABLE_1492799 tptp.int) (BOUND_VARIABLE_1492800 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7619 BOUND_VARIABLE_1492797) BOUND_VARIABLE_1492798) BOUND_VARIABLE_1492799) BOUND_VARIABLE_1492800) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492798) BOUND_VARIABLE_1492800)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492797) BOUND_VARIABLE_1492799)))))))))) (let ((_let_1940 (forall ((BOUND_VARIABLE_1492772 tptp.int) (BOUND_VARIABLE_1492773 tptp.int) (BOUND_VARIABLE_1492774 tptp.int) (BOUND_VARIABLE_1492775 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7620 BOUND_VARIABLE_1492772) BOUND_VARIABLE_1492773) BOUND_VARIABLE_1492774) BOUND_VARIABLE_1492775) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492773) BOUND_VARIABLE_1492775)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492772) BOUND_VARIABLE_1492774)))))))))) (let ((_let_1941 (forall ((BOUND_VARIABLE_1492747 tptp.int) (BOUND_VARIABLE_1492748 tptp.int) (BOUND_VARIABLE_1492749 tptp.int) (BOUND_VARIABLE_1492750 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7621 BOUND_VARIABLE_1492747) BOUND_VARIABLE_1492748) BOUND_VARIABLE_1492749) BOUND_VARIABLE_1492750) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492748) BOUND_VARIABLE_1492750)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492747) BOUND_VARIABLE_1492749)))))))))) (let ((_let_1942 (forall ((BOUND_VARIABLE_1492722 tptp.int) (BOUND_VARIABLE_1492723 tptp.int) (BOUND_VARIABLE_1492724 tptp.int) (BOUND_VARIABLE_1492725 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7622 BOUND_VARIABLE_1492722) BOUND_VARIABLE_1492723) BOUND_VARIABLE_1492724) BOUND_VARIABLE_1492725) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492723) BOUND_VARIABLE_1492725)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492722) BOUND_VARIABLE_1492724)))))))))) (let ((_let_1943 (forall ((BOUND_VARIABLE_1492697 tptp.int) (BOUND_VARIABLE_1492698 tptp.int) (BOUND_VARIABLE_1492699 tptp.int) (BOUND_VARIABLE_1492700 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7623 BOUND_VARIABLE_1492697) BOUND_VARIABLE_1492698) BOUND_VARIABLE_1492699) BOUND_VARIABLE_1492700) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492698) BOUND_VARIABLE_1492700)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492697) BOUND_VARIABLE_1492699)))))))))) (let ((_let_1944 (forall ((BOUND_VARIABLE_1492672 tptp.int) (BOUND_VARIABLE_1492673 tptp.int) (BOUND_VARIABLE_1492674 tptp.int) (BOUND_VARIABLE_1492675 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7624 BOUND_VARIABLE_1492672) BOUND_VARIABLE_1492673) BOUND_VARIABLE_1492674) BOUND_VARIABLE_1492675) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492673) BOUND_VARIABLE_1492675)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492672) BOUND_VARIABLE_1492674)))))))))) (let ((_let_1945 (forall ((BOUND_VARIABLE_1492647 tptp.int) (BOUND_VARIABLE_1492648 tptp.int) (BOUND_VARIABLE_1492649 tptp.int) (BOUND_VARIABLE_1492650 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7625 BOUND_VARIABLE_1492647) BOUND_VARIABLE_1492648) BOUND_VARIABLE_1492649) BOUND_VARIABLE_1492650) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492648) BOUND_VARIABLE_1492650)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492647) BOUND_VARIABLE_1492649)))))))))) (let ((_let_1946 (forall ((BOUND_VARIABLE_1492622 tptp.int) (BOUND_VARIABLE_1492623 tptp.int) (BOUND_VARIABLE_1492624 tptp.int) (BOUND_VARIABLE_1492625 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7626 BOUND_VARIABLE_1492622) BOUND_VARIABLE_1492623) BOUND_VARIABLE_1492624) BOUND_VARIABLE_1492625) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492623) BOUND_VARIABLE_1492625)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492622) BOUND_VARIABLE_1492624)))))))))) (let ((_let_1947 (forall ((BOUND_VARIABLE_1492597 tptp.int) (BOUND_VARIABLE_1492598 tptp.int) (BOUND_VARIABLE_1492599 tptp.int) (BOUND_VARIABLE_1492600 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7627 BOUND_VARIABLE_1492597) BOUND_VARIABLE_1492598) BOUND_VARIABLE_1492599) BOUND_VARIABLE_1492600) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492598) BOUND_VARIABLE_1492600)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1492597) BOUND_VARIABLE_1492599)))))))))) (let ((_let_1948 (forall ((BOUND_VARIABLE_1492566 tptp.nat) (BOUND_VARIABLE_1492567 tptp.nat) (BOUND_VARIABLE_1492568 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1492568)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1492566) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1492567) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_7628 BOUND_VARIABLE_1492566) BOUND_VARIABLE_1492567) BOUND_VARIABLE_1492568))))))))) (let ((_let_1949 (forall ((BOUND_VARIABLE_1492524 tptp.rat) (BOUND_VARIABLE_1492525 tptp.int) (BOUND_VARIABLE_1492526 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7492 BOUND_VARIABLE_1492526) BOUND_VARIABLE_1492525)) (ho_7630 k_7629 BOUND_VARIABLE_1492524)) (ho_7496 (ho_7495 (ho_7635 k_7634 BOUND_VARIABLE_1492524) BOUND_VARIABLE_1492525) BOUND_VARIABLE_1492526))))) (let ((_let_1950 (forall ((BOUND_VARIABLE_1520142 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1492481 tptp.nat) (BOUND_VARIABLE_1492482 tptp.int) (BOUND_VARIABLE_1492483 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7497 BOUND_VARIABLE_1492483) BOUND_VARIABLE_1492482)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1520142 BOUND_VARIABLE_1492481))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_7637 BOUND_VARIABLE_1520142) BOUND_VARIABLE_1492481) BOUND_VARIABLE_1492482) BOUND_VARIABLE_1492483))))) (let ((_let_1951 (forall ((BOUND_VARIABLE_1492438 tptp.nat) (BOUND_VARIABLE_1492439 tptp.nat) (BOUND_VARIABLE_1492440 tptp.nat) (BOUND_VARIABLE_1492441 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492438) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492441) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492439) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492440) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7642 BOUND_VARIABLE_1492438) BOUND_VARIABLE_1492439) BOUND_VARIABLE_1492440) BOUND_VARIABLE_1492441)))))))) (let ((_let_1952 (forall ((BOUND_VARIABLE_1492396 tptp.nat) (BOUND_VARIABLE_1492397 tptp.nat) (BOUND_VARIABLE_1492398 tptp.nat) (BOUND_VARIABLE_1492399 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492396) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492399) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492397) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492398) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7645 BOUND_VARIABLE_1492396) BOUND_VARIABLE_1492397) BOUND_VARIABLE_1492398) BOUND_VARIABLE_1492399)))))))) (let ((_let_1953 (forall ((BOUND_VARIABLE_1492354 tptp.nat) (BOUND_VARIABLE_1492355 tptp.nat) (BOUND_VARIABLE_1492356 tptp.nat) (BOUND_VARIABLE_1492357 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492354) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492356) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492355) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492357) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7646 BOUND_VARIABLE_1492354) BOUND_VARIABLE_1492355) BOUND_VARIABLE_1492356) BOUND_VARIABLE_1492357)))))))) (let ((_let_1954 (forall ((BOUND_VARIABLE_1492312 tptp.nat) (BOUND_VARIABLE_1492313 tptp.nat) (BOUND_VARIABLE_1492314 tptp.nat) (BOUND_VARIABLE_1492315 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492312) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492314) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492313) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492315) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7647 BOUND_VARIABLE_1492312) BOUND_VARIABLE_1492313) BOUND_VARIABLE_1492314) BOUND_VARIABLE_1492315)))))))) (let ((_let_1955 (forall ((BOUND_VARIABLE_1492266 tptp.nat) (BOUND_VARIABLE_1492267 tptp.nat) (BOUND_VARIABLE_1492268 tptp.nat) (BOUND_VARIABLE_1492269 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492266) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492269) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492268) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492267) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7648 BOUND_VARIABLE_1492266) BOUND_VARIABLE_1492267) BOUND_VARIABLE_1492268) BOUND_VARIABLE_1492269)))))))) (let ((_let_1956 (forall ((BOUND_VARIABLE_1492220 tptp.nat) (BOUND_VARIABLE_1492221 tptp.nat) (BOUND_VARIABLE_1492222 tptp.nat) (BOUND_VARIABLE_1492223 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492220) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492223) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492222) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492221) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7649 BOUND_VARIABLE_1492220) BOUND_VARIABLE_1492221) BOUND_VARIABLE_1492222) BOUND_VARIABLE_1492223)))))))) (let ((_let_1957 (forall ((BOUND_VARIABLE_1492174 tptp.nat) (BOUND_VARIABLE_1492175 tptp.nat) (BOUND_VARIABLE_1492176 tptp.nat) (BOUND_VARIABLE_1492177 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492174) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492177) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492176) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492175) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7650 BOUND_VARIABLE_1492174) BOUND_VARIABLE_1492175) BOUND_VARIABLE_1492176) BOUND_VARIABLE_1492177)))))))) (let ((_let_1958 (forall ((BOUND_VARIABLE_1492128 tptp.nat) (BOUND_VARIABLE_1492129 tptp.nat) (BOUND_VARIABLE_1492130 tptp.nat) (BOUND_VARIABLE_1492131 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492128) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492131) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492130) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492129) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7651 BOUND_VARIABLE_1492128) BOUND_VARIABLE_1492129) BOUND_VARIABLE_1492130) BOUND_VARIABLE_1492131)))))))) (let ((_let_1959 (forall ((BOUND_VARIABLE_1492088 tptp.nat) (BOUND_VARIABLE_1492089 tptp.nat) (BOUND_VARIABLE_1492090 tptp.nat) (BOUND_VARIABLE_1492091 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7652 BOUND_VARIABLE_1492088) BOUND_VARIABLE_1492089) BOUND_VARIABLE_1492090) BOUND_VARIABLE_1492091) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492088) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492091) _let_2))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492090) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492089) _let_2))))))))))) (let ((_let_1960 (forall ((BOUND_VARIABLE_1492010 tptp.nat) (BOUND_VARIABLE_1492011 tptp.nat) (BOUND_VARIABLE_1492012 tptp.nat) (BOUND_VARIABLE_1492013 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492012) _let_2))) (let ((_let_5 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492011) _let_2)))) (let ((_let_6 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492013) _let_2))) (let ((_let_7 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1492010) _let_2)))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_4))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_6))) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_6))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_4))) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7653 BOUND_VARIABLE_1492010) BOUND_VARIABLE_1492011) BOUND_VARIABLE_1492012) BOUND_VARIABLE_1492013)))))))))))) (let ((_let_1961 (forall ((BOUND_VARIABLE_1491932 tptp.nat) (BOUND_VARIABLE_1491933 tptp.nat) (BOUND_VARIABLE_1491934 tptp.nat) (BOUND_VARIABLE_1491935 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491934) _let_2))) (let ((_let_5 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491933) _let_2)))) (let ((_let_6 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491935) _let_2))) (let ((_let_7 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491932) _let_2)))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_4))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_6))) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_6))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_4))) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7654 BOUND_VARIABLE_1491932) BOUND_VARIABLE_1491933) BOUND_VARIABLE_1491934) BOUND_VARIABLE_1491935)))))))))))) (let ((_let_1962 (forall ((BOUND_VARIABLE_1491890 tptp.nat) (BOUND_VARIABLE_1491891 tptp.nat) (BOUND_VARIABLE_1491892 tptp.nat) (BOUND_VARIABLE_1491893 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491890) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491892) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491891) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491893) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7655 BOUND_VARIABLE_1491890) BOUND_VARIABLE_1491891) BOUND_VARIABLE_1491892) BOUND_VARIABLE_1491893)))))))) (let ((_let_1963 (forall ((BOUND_VARIABLE_1491844 tptp.nat) (BOUND_VARIABLE_1491845 tptp.nat) (BOUND_VARIABLE_1491846 tptp.nat) (BOUND_VARIABLE_1491847 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491844) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491847) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491846) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491845) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7656 BOUND_VARIABLE_1491844) BOUND_VARIABLE_1491845) BOUND_VARIABLE_1491846) BOUND_VARIABLE_1491847)))))))) (let ((_let_1964 (forall ((BOUND_VARIABLE_1491798 tptp.nat) (BOUND_VARIABLE_1491799 tptp.nat) (BOUND_VARIABLE_1491800 tptp.nat) (BOUND_VARIABLE_1491801 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491798) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491801) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491800) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491799) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7657 BOUND_VARIABLE_1491798) BOUND_VARIABLE_1491799) BOUND_VARIABLE_1491800) BOUND_VARIABLE_1491801)))))))) (let ((_let_1965 (forall ((BOUND_VARIABLE_1491756 tptp.nat) (BOUND_VARIABLE_1491757 tptp.nat) (BOUND_VARIABLE_1491758 tptp.nat) (BOUND_VARIABLE_1491759 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491756) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491759) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491757) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491758) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7658 BOUND_VARIABLE_1491756) BOUND_VARIABLE_1491757) BOUND_VARIABLE_1491758) BOUND_VARIABLE_1491759)))))))) (let ((_let_1966 (forall ((BOUND_VARIABLE_1491678 tptp.nat) (BOUND_VARIABLE_1491679 tptp.nat) (BOUND_VARIABLE_1491680 tptp.nat) (BOUND_VARIABLE_1491681 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491680) _let_2))) (let ((_let_5 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491679) _let_2)))) (let ((_let_6 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491681) _let_2))) (let ((_let_7 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1491678) _let_2)))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_4))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_6))) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_6))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_4))) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7659 BOUND_VARIABLE_1491678) BOUND_VARIABLE_1491679) BOUND_VARIABLE_1491680) BOUND_VARIABLE_1491681)))))))))))) (let ((_let_1967 (forall ((BOUND_VARIABLE_1491636 tptp.rat) (BOUND_VARIABLE_1491637 tptp.int) (BOUND_VARIABLE_1491638 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7498 BOUND_VARIABLE_1491638) BOUND_VARIABLE_1491637)) (ho_7630 k_7629 BOUND_VARIABLE_1491636)) (ho_7496 (ho_7495 (ho_7635 k_7660 BOUND_VARIABLE_1491636) BOUND_VARIABLE_1491637) BOUND_VARIABLE_1491638))))) (let ((_let_1968 (forall ((BOUND_VARIABLE_1520690 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1491593 tptp.nat) (BOUND_VARIABLE_1491594 tptp.int) (BOUND_VARIABLE_1491595 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7499 BOUND_VARIABLE_1491595) BOUND_VARIABLE_1491594)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1520690 BOUND_VARIABLE_1491593))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_7661 BOUND_VARIABLE_1520690) BOUND_VARIABLE_1491593) BOUND_VARIABLE_1491594) BOUND_VARIABLE_1491595))))) (let ((_let_1969 (forall ((BOUND_VARIABLE_1491547 tptp.real) (BOUND_VARIABLE_1491548 tptp.nat) (BOUND_VARIABLE_1491549 tptp.int) (BOUND_VARIABLE_1491550 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7500 BOUND_VARIABLE_1491550) BOUND_VARIABLE_1491549)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 BOUND_VARIABLE_1491547) BOUND_VARIABLE_1491548))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 k_7664 BOUND_VARIABLE_1491547) BOUND_VARIABLE_1491548) BOUND_VARIABLE_1491549) BOUND_VARIABLE_1491550))))) (let ((_let_1970 (forall ((BOUND_VARIABLE_1491505 tptp.rat) (BOUND_VARIABLE_1491506 tptp.int) (BOUND_VARIABLE_1491507 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7501 BOUND_VARIABLE_1491507) BOUND_VARIABLE_1491506)) (ho_7630 k_7629 BOUND_VARIABLE_1491505)) (ho_7496 (ho_7495 (ho_7635 k_7666 BOUND_VARIABLE_1491505) BOUND_VARIABLE_1491506) BOUND_VARIABLE_1491507))))) (let ((_let_1971 (forall ((BOUND_VARIABLE_1520748 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1491462 tptp.nat) (BOUND_VARIABLE_1491463 tptp.int) (BOUND_VARIABLE_1491464 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7502 BOUND_VARIABLE_1491464) BOUND_VARIABLE_1491463)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1520748 BOUND_VARIABLE_1491462))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_7667 BOUND_VARIABLE_1520748) BOUND_VARIABLE_1491462) BOUND_VARIABLE_1491463) BOUND_VARIABLE_1491464))))) (let ((_let_1972 (forall ((BOUND_VARIABLE_1491419 tptp.rat) (BOUND_VARIABLE_1491420 tptp.int) (BOUND_VARIABLE_1491421 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7503 BOUND_VARIABLE_1491421) BOUND_VARIABLE_1491420)) (ho_7630 k_7629 BOUND_VARIABLE_1491419)) (ho_7496 (ho_7495 (ho_7635 k_7668 BOUND_VARIABLE_1491419) BOUND_VARIABLE_1491420) BOUND_VARIABLE_1491421))))) (let ((_let_1973 (forall ((BOUND_VARIABLE_1520781 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1491376 tptp.nat) (BOUND_VARIABLE_1491377 tptp.int) (BOUND_VARIABLE_1491378 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7504 BOUND_VARIABLE_1491378) BOUND_VARIABLE_1491377)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1520781 BOUND_VARIABLE_1491376))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_7669 BOUND_VARIABLE_1520781) BOUND_VARIABLE_1491376) BOUND_VARIABLE_1491377) BOUND_VARIABLE_1491378))))) (let ((_let_1974 (forall ((BOUND_VARIABLE_1491350 tptp.int) (BOUND_VARIABLE_1491351 tptp.int) (BOUND_VARIABLE_1491352 tptp.int) (BOUND_VARIABLE_1491353 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7670 BOUND_VARIABLE_1491350) BOUND_VARIABLE_1491351) BOUND_VARIABLE_1491352) BOUND_VARIABLE_1491353) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491351) BOUND_VARIABLE_1491353)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491350) BOUND_VARIABLE_1491352)))))))))) (let ((_let_1975 (forall ((BOUND_VARIABLE_1491325 tptp.int) (BOUND_VARIABLE_1491326 tptp.int) (BOUND_VARIABLE_1491327 tptp.int) (BOUND_VARIABLE_1491328 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7671 BOUND_VARIABLE_1491325) BOUND_VARIABLE_1491326) BOUND_VARIABLE_1491327) BOUND_VARIABLE_1491328) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491326) BOUND_VARIABLE_1491328)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491325) BOUND_VARIABLE_1491327)))))))))) (let ((_let_1976 (forall ((BOUND_VARIABLE_1491300 tptp.int) (BOUND_VARIABLE_1491301 tptp.int) (BOUND_VARIABLE_1491302 tptp.int) (BOUND_VARIABLE_1491303 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7672 BOUND_VARIABLE_1491300) BOUND_VARIABLE_1491301) BOUND_VARIABLE_1491302) BOUND_VARIABLE_1491303) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491301) BOUND_VARIABLE_1491303)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491300) BOUND_VARIABLE_1491302)))))))))) (let ((_let_1977 (forall ((BOUND_VARIABLE_1491275 tptp.int) (BOUND_VARIABLE_1491276 tptp.int) (BOUND_VARIABLE_1491277 tptp.int) (BOUND_VARIABLE_1491278 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7673 BOUND_VARIABLE_1491275) BOUND_VARIABLE_1491276) BOUND_VARIABLE_1491277) BOUND_VARIABLE_1491278) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491276) BOUND_VARIABLE_1491278)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491275) BOUND_VARIABLE_1491277)))))))))) (let ((_let_1978 (forall ((BOUND_VARIABLE_1491250 tptp.int) (BOUND_VARIABLE_1491251 tptp.int) (BOUND_VARIABLE_1491252 tptp.int) (BOUND_VARIABLE_1491253 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7674 BOUND_VARIABLE_1491250) BOUND_VARIABLE_1491251) BOUND_VARIABLE_1491252) BOUND_VARIABLE_1491253) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491251) BOUND_VARIABLE_1491253)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491250) BOUND_VARIABLE_1491252)))))))))) (let ((_let_1979 (forall ((BOUND_VARIABLE_1491225 tptp.int) (BOUND_VARIABLE_1491226 tptp.int) (BOUND_VARIABLE_1491227 tptp.int) (BOUND_VARIABLE_1491228 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7675 BOUND_VARIABLE_1491225) BOUND_VARIABLE_1491226) BOUND_VARIABLE_1491227) BOUND_VARIABLE_1491228) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491226) BOUND_VARIABLE_1491228)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491225) BOUND_VARIABLE_1491227)))))))))) (let ((_let_1980 (forall ((BOUND_VARIABLE_1491200 tptp.int) (BOUND_VARIABLE_1491201 tptp.int) (BOUND_VARIABLE_1491202 tptp.int) (BOUND_VARIABLE_1491203 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7676 BOUND_VARIABLE_1491200) BOUND_VARIABLE_1491201) BOUND_VARIABLE_1491202) BOUND_VARIABLE_1491203) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491201) BOUND_VARIABLE_1491203)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491200) BOUND_VARIABLE_1491202)))))))))) (let ((_let_1981 (forall ((BOUND_VARIABLE_1491175 tptp.int) (BOUND_VARIABLE_1491176 tptp.int) (BOUND_VARIABLE_1491177 tptp.int) (BOUND_VARIABLE_1491178 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7677 BOUND_VARIABLE_1491175) BOUND_VARIABLE_1491176) BOUND_VARIABLE_1491177) BOUND_VARIABLE_1491178) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491176) BOUND_VARIABLE_1491178)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491175) BOUND_VARIABLE_1491177)))))))))) (let ((_let_1982 (forall ((BOUND_VARIABLE_1491150 tptp.int) (BOUND_VARIABLE_1491151 tptp.int) (BOUND_VARIABLE_1491152 tptp.int) (BOUND_VARIABLE_1491153 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7678 BOUND_VARIABLE_1491150) BOUND_VARIABLE_1491151) BOUND_VARIABLE_1491152) BOUND_VARIABLE_1491153) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491151) BOUND_VARIABLE_1491153)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491150) BOUND_VARIABLE_1491152)))))))))) (let ((_let_1983 (forall ((BOUND_VARIABLE_1491125 tptp.int) (BOUND_VARIABLE_1491126 tptp.int) (BOUND_VARIABLE_1491127 tptp.int) (BOUND_VARIABLE_1491128 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7679 BOUND_VARIABLE_1491125) BOUND_VARIABLE_1491126) BOUND_VARIABLE_1491127) BOUND_VARIABLE_1491128) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491126) BOUND_VARIABLE_1491128)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491125) BOUND_VARIABLE_1491127)))))))))) (let ((_let_1984 (forall ((BOUND_VARIABLE_1491100 tptp.int) (BOUND_VARIABLE_1491101 tptp.int) (BOUND_VARIABLE_1491102 tptp.int) (BOUND_VARIABLE_1491103 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7680 BOUND_VARIABLE_1491100) BOUND_VARIABLE_1491101) BOUND_VARIABLE_1491102) BOUND_VARIABLE_1491103) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491101) BOUND_VARIABLE_1491103)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491100) BOUND_VARIABLE_1491102)))))))))) (let ((_let_1985 (forall ((BOUND_VARIABLE_1491075 tptp.int) (BOUND_VARIABLE_1491076 tptp.int) (BOUND_VARIABLE_1491077 tptp.int) (BOUND_VARIABLE_1491078 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7681 BOUND_VARIABLE_1491075) BOUND_VARIABLE_1491076) BOUND_VARIABLE_1491077) BOUND_VARIABLE_1491078) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491076) BOUND_VARIABLE_1491078)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491075) BOUND_VARIABLE_1491077)))))))))) (let ((_let_1986 (forall ((BOUND_VARIABLE_1491050 tptp.int) (BOUND_VARIABLE_1491051 tptp.int) (BOUND_VARIABLE_1491052 tptp.int) (BOUND_VARIABLE_1491053 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7682 BOUND_VARIABLE_1491050) BOUND_VARIABLE_1491051) BOUND_VARIABLE_1491052) BOUND_VARIABLE_1491053) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491051) BOUND_VARIABLE_1491053)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491050) BOUND_VARIABLE_1491052)))))))))) (let ((_let_1987 (forall ((BOUND_VARIABLE_1491025 tptp.int) (BOUND_VARIABLE_1491026 tptp.int) (BOUND_VARIABLE_1491027 tptp.int) (BOUND_VARIABLE_1491028 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7683 BOUND_VARIABLE_1491025) BOUND_VARIABLE_1491026) BOUND_VARIABLE_1491027) BOUND_VARIABLE_1491028) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491026) BOUND_VARIABLE_1491028)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491025) BOUND_VARIABLE_1491027)))))))))) (let ((_let_1988 (forall ((BOUND_VARIABLE_1491000 tptp.int) (BOUND_VARIABLE_1491001 tptp.int) (BOUND_VARIABLE_1491002 tptp.int) (BOUND_VARIABLE_1491003 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7684 BOUND_VARIABLE_1491000) BOUND_VARIABLE_1491001) BOUND_VARIABLE_1491002) BOUND_VARIABLE_1491003) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491001) BOUND_VARIABLE_1491003)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1491000) BOUND_VARIABLE_1491002)))))))))) (let ((_let_1989 (forall ((BOUND_VARIABLE_1490975 tptp.int) (BOUND_VARIABLE_1490976 tptp.int) (BOUND_VARIABLE_1490977 tptp.int) (BOUND_VARIABLE_1490978 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7685 BOUND_VARIABLE_1490975) BOUND_VARIABLE_1490976) BOUND_VARIABLE_1490977) BOUND_VARIABLE_1490978) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490976) BOUND_VARIABLE_1490978)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490975) BOUND_VARIABLE_1490977)))))))))) (let ((_let_1990 (forall ((BOUND_VARIABLE_1490950 tptp.int) (BOUND_VARIABLE_1490951 tptp.int) (BOUND_VARIABLE_1490952 tptp.int) (BOUND_VARIABLE_1490953 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7686 BOUND_VARIABLE_1490950) BOUND_VARIABLE_1490951) BOUND_VARIABLE_1490952) BOUND_VARIABLE_1490953) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490951) BOUND_VARIABLE_1490953)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490950) BOUND_VARIABLE_1490952)))))))))) (let ((_let_1991 (forall ((BOUND_VARIABLE_1490925 tptp.int) (BOUND_VARIABLE_1490926 tptp.int) (BOUND_VARIABLE_1490927 tptp.int) (BOUND_VARIABLE_1490928 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7687 BOUND_VARIABLE_1490925) BOUND_VARIABLE_1490926) BOUND_VARIABLE_1490927) BOUND_VARIABLE_1490928) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490926) BOUND_VARIABLE_1490928)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490925) BOUND_VARIABLE_1490927)))))))))) (let ((_let_1992 (forall ((BOUND_VARIABLE_1490900 tptp.int) (BOUND_VARIABLE_1490901 tptp.int) (BOUND_VARIABLE_1490902 tptp.int) (BOUND_VARIABLE_1490903 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7688 BOUND_VARIABLE_1490900) BOUND_VARIABLE_1490901) BOUND_VARIABLE_1490902) BOUND_VARIABLE_1490903) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490901) BOUND_VARIABLE_1490903)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490900) BOUND_VARIABLE_1490902)))))))))) (let ((_let_1993 (forall ((BOUND_VARIABLE_1490875 tptp.int) (BOUND_VARIABLE_1490876 tptp.int) (BOUND_VARIABLE_1490877 tptp.int) (BOUND_VARIABLE_1490878 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7689 BOUND_VARIABLE_1490875) BOUND_VARIABLE_1490876) BOUND_VARIABLE_1490877) BOUND_VARIABLE_1490878) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490876) BOUND_VARIABLE_1490878)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490875) BOUND_VARIABLE_1490877)))))))))) (let ((_let_1994 (forall ((BOUND_VARIABLE_1490850 tptp.int) (BOUND_VARIABLE_1490851 tptp.int) (BOUND_VARIABLE_1490852 tptp.int) (BOUND_VARIABLE_1490853 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7690 BOUND_VARIABLE_1490850) BOUND_VARIABLE_1490851) BOUND_VARIABLE_1490852) BOUND_VARIABLE_1490853) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490851) BOUND_VARIABLE_1490853)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490850) BOUND_VARIABLE_1490852)))))))))) (let ((_let_1995 (forall ((BOUND_VARIABLE_1490825 tptp.int) (BOUND_VARIABLE_1490826 tptp.int) (BOUND_VARIABLE_1490827 tptp.int) (BOUND_VARIABLE_1490828 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7691 BOUND_VARIABLE_1490825) BOUND_VARIABLE_1490826) BOUND_VARIABLE_1490827) BOUND_VARIABLE_1490828) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490826) BOUND_VARIABLE_1490828)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490825) BOUND_VARIABLE_1490827)))))))))) (let ((_let_1996 (forall ((BOUND_VARIABLE_1490800 tptp.int) (BOUND_VARIABLE_1490801 tptp.int) (BOUND_VARIABLE_1490802 tptp.int) (BOUND_VARIABLE_1490803 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7692 BOUND_VARIABLE_1490800) BOUND_VARIABLE_1490801) BOUND_VARIABLE_1490802) BOUND_VARIABLE_1490803) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490801) BOUND_VARIABLE_1490803)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490800) BOUND_VARIABLE_1490802)))))))))) (let ((_let_1997 (forall ((BOUND_VARIABLE_1490775 tptp.int) (BOUND_VARIABLE_1490776 tptp.int) (BOUND_VARIABLE_1490777 tptp.int) (BOUND_VARIABLE_1490778 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7693 BOUND_VARIABLE_1490775) BOUND_VARIABLE_1490776) BOUND_VARIABLE_1490777) BOUND_VARIABLE_1490778) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490776) BOUND_VARIABLE_1490778)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490775) BOUND_VARIABLE_1490777)))))))))) (let ((_let_1998 (forall ((BOUND_VARIABLE_1490750 tptp.int) (BOUND_VARIABLE_1490751 tptp.int) (BOUND_VARIABLE_1490752 tptp.int) (BOUND_VARIABLE_1490753 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7694 BOUND_VARIABLE_1490750) BOUND_VARIABLE_1490751) BOUND_VARIABLE_1490752) BOUND_VARIABLE_1490753) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490751) BOUND_VARIABLE_1490753)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490750) BOUND_VARIABLE_1490752)))))))))) (let ((_let_1999 (forall ((BOUND_VARIABLE_1490725 tptp.int) (BOUND_VARIABLE_1490726 tptp.int) (BOUND_VARIABLE_1490727 tptp.int) (BOUND_VARIABLE_1490728 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7695 BOUND_VARIABLE_1490725) BOUND_VARIABLE_1490726) BOUND_VARIABLE_1490727) BOUND_VARIABLE_1490728) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490726) BOUND_VARIABLE_1490728)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490725) BOUND_VARIABLE_1490727)))))))))) (let ((_let_2000 (forall ((BOUND_VARIABLE_1490685 tptp.int) (BOUND_VARIABLE_1490686 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7505 BOUND_VARIABLE_1490686) BOUND_VARIABLE_1490685)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_7718 BOUND_VARIABLE_1490685) BOUND_VARIABLE_1490686))))))))) (let ((_let_2001 (forall ((BOUND_VARIABLE_1490660 tptp.int) (BOUND_VARIABLE_1490661 tptp.int) (BOUND_VARIABLE_1490662 tptp.int) (BOUND_VARIABLE_1490663 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7719 BOUND_VARIABLE_1490660) BOUND_VARIABLE_1490661) BOUND_VARIABLE_1490662) BOUND_VARIABLE_1490663) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490661) BOUND_VARIABLE_1490663)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490660) BOUND_VARIABLE_1490662)))))))))) (let ((_let_2002 (forall ((BOUND_VARIABLE_1490635 tptp.int) (BOUND_VARIABLE_1490636 tptp.int) (BOUND_VARIABLE_1490637 tptp.int) (BOUND_VARIABLE_1490638 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7720 BOUND_VARIABLE_1490635) BOUND_VARIABLE_1490636) BOUND_VARIABLE_1490637) BOUND_VARIABLE_1490638) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490636) BOUND_VARIABLE_1490638)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490635) BOUND_VARIABLE_1490637)))))))))) (let ((_let_2003 (forall ((BOUND_VARIABLE_1490610 tptp.int) (BOUND_VARIABLE_1490611 tptp.int) (BOUND_VARIABLE_1490612 tptp.int) (BOUND_VARIABLE_1490613 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7721 BOUND_VARIABLE_1490610) BOUND_VARIABLE_1490611) BOUND_VARIABLE_1490612) BOUND_VARIABLE_1490613) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490611) BOUND_VARIABLE_1490613)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490610) BOUND_VARIABLE_1490612)))))))))) (let ((_let_2004 (forall ((BOUND_VARIABLE_1490585 tptp.int) (BOUND_VARIABLE_1490586 tptp.int) (BOUND_VARIABLE_1490587 tptp.int) (BOUND_VARIABLE_1490588 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7722 BOUND_VARIABLE_1490585) BOUND_VARIABLE_1490586) BOUND_VARIABLE_1490587) BOUND_VARIABLE_1490588) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490586) BOUND_VARIABLE_1490588)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490585) BOUND_VARIABLE_1490587)))))))))) (let ((_let_2005 (forall ((BOUND_VARIABLE_1490560 tptp.int) (BOUND_VARIABLE_1490561 tptp.int) (BOUND_VARIABLE_1490562 tptp.int) (BOUND_VARIABLE_1490563 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7723 BOUND_VARIABLE_1490560) BOUND_VARIABLE_1490561) BOUND_VARIABLE_1490562) BOUND_VARIABLE_1490563) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490561) BOUND_VARIABLE_1490563)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490560) BOUND_VARIABLE_1490562)))))))))) (let ((_let_2006 (forall ((BOUND_VARIABLE_1490535 tptp.int) (BOUND_VARIABLE_1490536 tptp.int) (BOUND_VARIABLE_1490537 tptp.int) (BOUND_VARIABLE_1490538 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7724 BOUND_VARIABLE_1490535) BOUND_VARIABLE_1490536) BOUND_VARIABLE_1490537) BOUND_VARIABLE_1490538) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490536) BOUND_VARIABLE_1490538)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490535) BOUND_VARIABLE_1490537)))))))))) (let ((_let_2007 (forall ((BOUND_VARIABLE_1490510 tptp.int) (BOUND_VARIABLE_1490511 tptp.int) (BOUND_VARIABLE_1490512 tptp.int) (BOUND_VARIABLE_1490513 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7725 BOUND_VARIABLE_1490510) BOUND_VARIABLE_1490511) BOUND_VARIABLE_1490512) BOUND_VARIABLE_1490513) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490511) BOUND_VARIABLE_1490513)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490510) BOUND_VARIABLE_1490512)))))))))) (let ((_let_2008 (forall ((BOUND_VARIABLE_1490485 tptp.int) (BOUND_VARIABLE_1490486 tptp.int) (BOUND_VARIABLE_1490487 tptp.int) (BOUND_VARIABLE_1490488 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7726 BOUND_VARIABLE_1490485) BOUND_VARIABLE_1490486) BOUND_VARIABLE_1490487) BOUND_VARIABLE_1490488) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490486) BOUND_VARIABLE_1490488)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490485) BOUND_VARIABLE_1490487)))))))))) (let ((_let_2009 (forall ((BOUND_VARIABLE_1490412 tptp.real) (BOUND_VARIABLE_1490413 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1490413) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 BOUND_VARIABLE_1490412))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_7737 BOUND_VARIABLE_1490412) BOUND_VARIABLE_1490413)))))))))))))))))))))) (let ((_let_2010 (forall ((BOUND_VARIABLE_1490339 tptp.real) (BOUND_VARIABLE_1490340 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1490340) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 BOUND_VARIABLE_1490339))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_7739 BOUND_VARIABLE_1490339) BOUND_VARIABLE_1490340)))))))))))))))))))))) (let ((_let_2011 (forall ((BOUND_VARIABLE_1490314 tptp.int) (BOUND_VARIABLE_1490315 tptp.int) (BOUND_VARIABLE_1490316 tptp.int) (BOUND_VARIABLE_1490317 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7740 BOUND_VARIABLE_1490314) BOUND_VARIABLE_1490315) BOUND_VARIABLE_1490316) BOUND_VARIABLE_1490317) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490315) BOUND_VARIABLE_1490317)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490314) BOUND_VARIABLE_1490316)))))))))) (let ((_let_2012 (forall ((BOUND_VARIABLE_1490289 tptp.int) (BOUND_VARIABLE_1490290 tptp.int) (BOUND_VARIABLE_1490291 tptp.int) (BOUND_VARIABLE_1490292 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7741 BOUND_VARIABLE_1490289) BOUND_VARIABLE_1490290) BOUND_VARIABLE_1490291) BOUND_VARIABLE_1490292) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490290) BOUND_VARIABLE_1490292)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490289) BOUND_VARIABLE_1490291)))))))))) (let ((_let_2013 (forall ((BOUND_VARIABLE_1490264 tptp.int) (BOUND_VARIABLE_1490265 tptp.int) (BOUND_VARIABLE_1490266 tptp.int) (BOUND_VARIABLE_1490267 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7742 BOUND_VARIABLE_1490264) BOUND_VARIABLE_1490265) BOUND_VARIABLE_1490266) BOUND_VARIABLE_1490267) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490265) BOUND_VARIABLE_1490267)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490264) BOUND_VARIABLE_1490266)))))))))) (let ((_let_2014 (forall ((BOUND_VARIABLE_1490239 tptp.int) (BOUND_VARIABLE_1490240 tptp.int) (BOUND_VARIABLE_1490241 tptp.int) (BOUND_VARIABLE_1490242 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7743 BOUND_VARIABLE_1490239) BOUND_VARIABLE_1490240) BOUND_VARIABLE_1490241) BOUND_VARIABLE_1490242) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490240) BOUND_VARIABLE_1490242)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490239) BOUND_VARIABLE_1490241)))))))))) (let ((_let_2015 (forall ((BOUND_VARIABLE_1490214 tptp.int) (BOUND_VARIABLE_1490215 tptp.int) (BOUND_VARIABLE_1490216 tptp.int) (BOUND_VARIABLE_1490217 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7744 BOUND_VARIABLE_1490214) BOUND_VARIABLE_1490215) BOUND_VARIABLE_1490216) BOUND_VARIABLE_1490217) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490215) BOUND_VARIABLE_1490217)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490214) BOUND_VARIABLE_1490216)))))))))) (let ((_let_2016 (forall ((BOUND_VARIABLE_1490189 tptp.int) (BOUND_VARIABLE_1490190 tptp.int) (BOUND_VARIABLE_1490191 tptp.int) (BOUND_VARIABLE_1490192 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7745 BOUND_VARIABLE_1490189) BOUND_VARIABLE_1490190) BOUND_VARIABLE_1490191) BOUND_VARIABLE_1490192) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490190) BOUND_VARIABLE_1490192)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490189) BOUND_VARIABLE_1490191)))))))))) (let ((_let_2017 (forall ((BOUND_VARIABLE_1490164 tptp.int) (BOUND_VARIABLE_1490165 tptp.int) (BOUND_VARIABLE_1490166 tptp.int) (BOUND_VARIABLE_1490167 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7746 BOUND_VARIABLE_1490164) BOUND_VARIABLE_1490165) BOUND_VARIABLE_1490166) BOUND_VARIABLE_1490167) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490165) BOUND_VARIABLE_1490167)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1490164) BOUND_VARIABLE_1490166)))))))))) (let ((_let_2018 (forall ((BOUND_VARIABLE_1490154 tptp.nat) (BOUND_VARIABLE_1490155 tptp.nat)) (= (ho_7541 (ho_7540 k_7747 BOUND_VARIABLE_1490154) BOUND_VARIABLE_1490155) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1490155)) (ho_7533 k_7532 BOUND_VARIABLE_1490154)))))) (let ((_let_2019 (forall ((BOUND_VARIABLE_1490114 tptp.nat) (BOUND_VARIABLE_1490115 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7466 (ho_7465 k_7471 _let_4) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1490114) _let_2)))))) (or (not (= BOUND_VARIABLE_1490115 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_7755 BOUND_VARIABLE_1490114) BOUND_VARIABLE_1490115))))) (let ((_let_2020 (forall ((BOUND_VARIABLE_1490104 tptp.nat) (BOUND_VARIABLE_1490105 tptp.nat)) (= (ho_7541 (ho_7540 k_7756 BOUND_VARIABLE_1490104) BOUND_VARIABLE_1490105) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1490105)) (ho_7533 k_7532 BOUND_VARIABLE_1490104)))))) (let ((_let_2021 (forall ((BOUND_VARIABLE_1490086 tptp.nat) (BOUND_VARIABLE_1490087 tptp.nat)) (= (ho_7541 (ho_7540 k_7757 BOUND_VARIABLE_1490086) BOUND_VARIABLE_1490087) (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7750 (ho_7749 k_7748 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) BOUND_VARIABLE_1490086))) (or (not (= BOUND_VARIABLE_1490087 (ho_7466 (ho_7754 k_7753 _let_1) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_1)))))))))))) (let ((_let_2022 (forall ((BOUND_VARIABLE_1490056 tptp.nat) (BOUND_VARIABLE_1490057 tptp.nat) (BOUND_VARIABLE_1490058 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1490058) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1490056) _let_2))))) (ho_7533 k_7532 BOUND_VARIABLE_1490057)) (ho_7541 (ho_7540 (ho_7539 k_7758 BOUND_VARIABLE_1490056) BOUND_VARIABLE_1490057) BOUND_VARIABLE_1490058)))))))) (let ((_let_2023 (forall ((BOUND_VARIABLE_1490030 tptp.nat) (BOUND_VARIABLE_1490031 tptp.nat)) (= (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1490030 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1490031) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))) (ho_7541 (ho_7540 k_7759 BOUND_VARIABLE_1490030) BOUND_VARIABLE_1490031))))) (let ((_let_2024 (forall ((BOUND_VARIABLE_1521990 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1490021 tptp.nat)) (= (ho_7508 (ho_7761 k_7760 BOUND_VARIABLE_1521990) BOUND_VARIABLE_1490021) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1490021)) (ho_7508 BOUND_VARIABLE_1521990 BOUND_VARIABLE_1490021)))))) (let ((_let_2025 (forall ((BOUND_VARIABLE_1489988 tptp.nat) (BOUND_VARIABLE_1489989 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489989)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489988) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_7762 BOUND_VARIABLE_1489988) BOUND_VARIABLE_1489989)))))))) (let ((_let_2026 (forall ((BOUND_VARIABLE_1522026 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489979 tptp.nat)) (= (ho_7508 (ho_7761 k_7763 BOUND_VARIABLE_1522026) BOUND_VARIABLE_1489979) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1489979)) (ho_7508 BOUND_VARIABLE_1522026 BOUND_VARIABLE_1489979)))))) (let ((_let_2027 (forall ((BOUND_VARIABLE_1489946 tptp.nat) (BOUND_VARIABLE_1489947 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489947)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489946) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_7764 BOUND_VARIABLE_1489946) BOUND_VARIABLE_1489947)))))))) (let ((_let_2028 (forall ((BOUND_VARIABLE_1522059 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489937 tptp.nat)) (= (ho_7508 (ho_7761 k_7765 BOUND_VARIABLE_1522059) BOUND_VARIABLE_1489937) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1489937)) (ho_7508 BOUND_VARIABLE_1522059 BOUND_VARIABLE_1489937)))))) (let ((_let_2029 (forall ((BOUND_VARIABLE_1489914 tptp.nat) (BOUND_VARIABLE_1489915 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489915)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489914) _let_2))))) (ho_7541 (ho_7540 k_7766 BOUND_VARIABLE_1489914) BOUND_VARIABLE_1489915)))))))) (let ((_let_2030 (forall ((BOUND_VARIABLE_1522087 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489905 tptp.nat)) (= (ho_7508 (ho_7761 k_7767 BOUND_VARIABLE_1522087) BOUND_VARIABLE_1489905) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1489905)) (ho_7508 BOUND_VARIABLE_1522087 BOUND_VARIABLE_1489905)))))) (let ((_let_2031 (forall ((BOUND_VARIABLE_1489872 tptp.nat) (BOUND_VARIABLE_1489873 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489873)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489872) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_7768 BOUND_VARIABLE_1489872) BOUND_VARIABLE_1489873)))))))) (let ((_let_2032 (forall ((BOUND_VARIABLE_1522120 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489863 tptp.nat)) (= (ho_7508 (ho_7761 k_7769 BOUND_VARIABLE_1522120) BOUND_VARIABLE_1489863) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1489863)) (ho_7508 BOUND_VARIABLE_1522120 BOUND_VARIABLE_1489863)))))) (let ((_let_2033 (forall ((BOUND_VARIABLE_1489840 tptp.nat) (BOUND_VARIABLE_1489841 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489841)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489840) _let_2))))) (ho_7541 (ho_7540 k_7770 BOUND_VARIABLE_1489840) BOUND_VARIABLE_1489841)))))))) (let ((_let_2034 (forall ((BOUND_VARIABLE_1522148 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489831 tptp.nat)) (= (ho_7508 (ho_7761 k_7771 BOUND_VARIABLE_1522148) BOUND_VARIABLE_1489831) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1489831)) (ho_7508 BOUND_VARIABLE_1522148 BOUND_VARIABLE_1489831)))))) (let ((_let_2035 (forall ((BOUND_VARIABLE_1489808 tptp.nat) (BOUND_VARIABLE_1489809 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489809)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489808) _let_2))))) (ho_7541 (ho_7540 k_7772 BOUND_VARIABLE_1489808) BOUND_VARIABLE_1489809)))))))) (let ((_let_2036 (forall ((BOUND_VARIABLE_1522174 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489752 tptp.nat) (BOUND_VARIABLE_1489753 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7775 (ho_7774 k_7773 BOUND_VARIABLE_1522174) BOUND_VARIABLE_1489752) BOUND_VARIABLE_1489753) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1489753 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1489753) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1489753 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1489753) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7508 BOUND_VARIABLE_1522174 BOUND_VARIABLE_1489752)) BOUND_VARIABLE_1489753))))))))))))))) (let ((_let_2037 (forall ((BOUND_VARIABLE_1522222 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489691 tptp.nat) (BOUND_VARIABLE_1489692 tptp.real) (BOUND_VARIABLE_1489693 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 (ho_7778 (ho_7777 k_7776 BOUND_VARIABLE_1522222) BOUND_VARIABLE_1489691) BOUND_VARIABLE_1489692) BOUND_VARIABLE_1489693) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1489693 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1489693) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1489693 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1489693) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7523 (ho_7508 BOUND_VARIABLE_1522222 BOUND_VARIABLE_1489691)) (ho_7516 k_7521 BOUND_VARIABLE_1489692))) BOUND_VARIABLE_1489693))))))))))))))) (let ((_let_2038 (forall ((BOUND_VARIABLE_1489663 tptp.nat) (BOUND_VARIABLE_1489664 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1489664 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_7782 BOUND_VARIABLE_1489663) BOUND_VARIABLE_1489664) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1489664) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489664) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1489664)) BOUND_VARIABLE_1489664)) BOUND_VARIABLE_1489663))))))))))) (let ((_let_2039 (forall ((BOUND_VARIABLE_1489636 tptp.nat) (BOUND_VARIABLE_1489637 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1489637 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_7783 BOUND_VARIABLE_1489636) BOUND_VARIABLE_1489637) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1489637) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489637) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1489637)) BOUND_VARIABLE_1489637)) BOUND_VARIABLE_1489636))))))))))) (let ((_let_2040 (forall ((BOUND_VARIABLE_1489581 tptp.real) (BOUND_VARIABLE_1489582 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7784 BOUND_VARIABLE_1489581) BOUND_VARIABLE_1489582) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1489582 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1489582) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1489582 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1489582) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1489581) BOUND_VARIABLE_1489582))))))))))))))) (let ((_let_2041 (forall ((BOUND_VARIABLE_1489518 tptp.real) (BOUND_VARIABLE_1489519 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1489519) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7785 BOUND_VARIABLE_1489518) BOUND_VARIABLE_1489519) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1489519 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1489519 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1489518) BOUND_VARIABLE_1489519))))))))))))))))) (let ((_let_2042 (forall ((BOUND_VARIABLE_1489471 tptp.real) (BOUND_VARIABLE_1489472 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489472) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (let ((_let_5 (ho_7510 k_7509 tptp.one))) (let ((_let_6 (ho_7516 k_7521 _let_5))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_6) BOUND_VARIABLE_1489472)) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 _let_5) (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) _let_4) (ho_7516 (ho_7519 k_7523 _let_5) _let_6))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1489471) _let_4))) (ho_7508 (ho_7507 k_7789 BOUND_VARIABLE_1489471) BOUND_VARIABLE_1489472))))))))))) (let ((_let_2043 (forall ((BOUND_VARIABLE_1522464 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1489417 tptp.nat) (BOUND_VARIABLE_1489418 tptp.real) (BOUND_VARIABLE_1489419 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1489419) _let_4))) (let ((_let_8 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_7778 (ho_7791 k_7790 BOUND_VARIABLE_1522464) BOUND_VARIABLE_1489417) BOUND_VARIABLE_1489418) BOUND_VARIABLE_1489419) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1522464 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1489417) _let_4)) _let_7))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1489419 _let_8)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_8) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1489418) BOUND_VARIABLE_1489419)))))))))))))) (let ((_let_2044 (forall ((BOUND_VARIABLE_1489377 tptp.nat) (BOUND_VARIABLE_1489378 tptp.nat) (BOUND_VARIABLE_1489379 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1489379)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1489377) _let_3)))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1489378) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_7792 BOUND_VARIABLE_1489377) BOUND_VARIABLE_1489378) BOUND_VARIABLE_1489379))))))))) (let ((_let_2045 (forall ((BOUND_VARIABLE_1489350 tptp.nat) (BOUND_VARIABLE_1489351 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1489351 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_7793 BOUND_VARIABLE_1489350) BOUND_VARIABLE_1489351) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1489351) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489351) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1489351)) BOUND_VARIABLE_1489351)) BOUND_VARIABLE_1489350))))))))))) (let ((_let_2046 (forall ((BOUND_VARIABLE_1489321 tptp.real) (BOUND_VARIABLE_1489322 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (and (ho_7781 (ho_7780 k_7779 (ho_7516 k_7521 _let_1)) BOUND_VARIABLE_1489322) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489322) _let_1) (= BOUND_VARIABLE_1489321 (ho_7795 k_7794 (ho_7507 k_7524 BOUND_VARIABLE_1489322)))) (ho_7781 (ho_7780 k_7797 BOUND_VARIABLE_1489321) BOUND_VARIABLE_1489322)))))) (let ((_let_2047 (forall ((BOUND_VARIABLE_1489294 tptp.nat) (BOUND_VARIABLE_1489295 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1489295 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_7798 BOUND_VARIABLE_1489294) BOUND_VARIABLE_1489295) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1489295) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489295) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1489295)) BOUND_VARIABLE_1489295)) BOUND_VARIABLE_1489294))))))))))) (let ((_let_2048 (forall ((BOUND_VARIABLE_1522601 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1489271 tptp.real) (BOUND_VARIABLE_1489272 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1522601 BOUND_VARIABLE_1489272)) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1489271) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489272) _let_2))))) (ho_7508 (ho_7507 (ho_7800 k_7799 BOUND_VARIABLE_1522601) BOUND_VARIABLE_1489271) BOUND_VARIABLE_1489272)))))))) (let ((_let_2049 (forall ((BOUND_VARIABLE_1489231 tptp.nat) (BOUND_VARIABLE_1489232 tptp.real)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7510 k_7509 tptp.one))) (let ((_let_5 (ho_7516 k_7521 _let_4))) (let ((_let_6 (ho_7516 (ho_7519 k_7523 _let_4) _let_5))) (let ((_let_7 (= BOUND_VARIABLE_1489232 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_7516 (ho_7512 k_7801 BOUND_VARIABLE_1489231) BOUND_VARIABLE_1489232) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_7) _let_6) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_6) BOUND_VARIABLE_1489232) _let_8)) _let_4) _let_5))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489232) _let_6) _let_8)) (ho_7516 k_7521 BOUND_VARIABLE_1489232)) BOUND_VARIABLE_1489232)) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1489231) _let_2))))))))))))))))) (let ((_let_2050 (forall ((BOUND_VARIABLE_1489204 tptp.nat) (BOUND_VARIABLE_1489205 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1489205 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_7802 BOUND_VARIABLE_1489204) BOUND_VARIABLE_1489205) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1489205) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1489205) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1489205)) BOUND_VARIABLE_1489205)) BOUND_VARIABLE_1489204))))))))))) (let ((_let_2051 (forall ((BOUND_VARIABLE_1489179 tptp.int) (BOUND_VARIABLE_1489180 tptp.int) (BOUND_VARIABLE_1489181 tptp.int) (BOUND_VARIABLE_1489182 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7803 BOUND_VARIABLE_1489179) BOUND_VARIABLE_1489180) BOUND_VARIABLE_1489181) BOUND_VARIABLE_1489182) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489180) BOUND_VARIABLE_1489182)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489179) BOUND_VARIABLE_1489181)))))))))) (let ((_let_2052 (forall ((BOUND_VARIABLE_1489154 tptp.int) (BOUND_VARIABLE_1489155 tptp.int) (BOUND_VARIABLE_1489156 tptp.int) (BOUND_VARIABLE_1489157 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7804 BOUND_VARIABLE_1489154) BOUND_VARIABLE_1489155) BOUND_VARIABLE_1489156) BOUND_VARIABLE_1489157) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489155) BOUND_VARIABLE_1489157)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489154) BOUND_VARIABLE_1489156)))))))))) (let ((_let_2053 (forall ((BOUND_VARIABLE_1489129 tptp.int) (BOUND_VARIABLE_1489130 tptp.int) (BOUND_VARIABLE_1489131 tptp.int) (BOUND_VARIABLE_1489132 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7805 BOUND_VARIABLE_1489129) BOUND_VARIABLE_1489130) BOUND_VARIABLE_1489131) BOUND_VARIABLE_1489132) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489130) BOUND_VARIABLE_1489132)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489129) BOUND_VARIABLE_1489131)))))))))) (let ((_let_2054 (forall ((BOUND_VARIABLE_1489104 tptp.int) (BOUND_VARIABLE_1489105 tptp.int) (BOUND_VARIABLE_1489106 tptp.int) (BOUND_VARIABLE_1489107 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7806 BOUND_VARIABLE_1489104) BOUND_VARIABLE_1489105) BOUND_VARIABLE_1489106) BOUND_VARIABLE_1489107) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489105) BOUND_VARIABLE_1489107)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489104) BOUND_VARIABLE_1489106)))))))))) (let ((_let_2055 (forall ((BOUND_VARIABLE_1489079 tptp.int) (BOUND_VARIABLE_1489080 tptp.int) (BOUND_VARIABLE_1489081 tptp.int) (BOUND_VARIABLE_1489082 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7807 BOUND_VARIABLE_1489079) BOUND_VARIABLE_1489080) BOUND_VARIABLE_1489081) BOUND_VARIABLE_1489082) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489080) BOUND_VARIABLE_1489082)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489079) BOUND_VARIABLE_1489081)))))))))) (let ((_let_2056 (forall ((BOUND_VARIABLE_1489054 tptp.int) (BOUND_VARIABLE_1489055 tptp.int) (BOUND_VARIABLE_1489056 tptp.int) (BOUND_VARIABLE_1489057 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7808 BOUND_VARIABLE_1489054) BOUND_VARIABLE_1489055) BOUND_VARIABLE_1489056) BOUND_VARIABLE_1489057) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489055) BOUND_VARIABLE_1489057)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489054) BOUND_VARIABLE_1489056)))))))))) (let ((_let_2057 (forall ((BOUND_VARIABLE_1489029 tptp.int) (BOUND_VARIABLE_1489030 tptp.int) (BOUND_VARIABLE_1489031 tptp.int) (BOUND_VARIABLE_1489032 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7809 BOUND_VARIABLE_1489029) BOUND_VARIABLE_1489030) BOUND_VARIABLE_1489031) BOUND_VARIABLE_1489032) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489030) BOUND_VARIABLE_1489032)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1489029) BOUND_VARIABLE_1489031)))))))))) (let ((_let_2058 (forall ((BOUND_VARIABLE_1489009 tptp.nat) (BOUND_VARIABLE_1489010 tptp.num)) (= (ho_7531 (ho_7812 (ho_7811 k_7810 (ho_7441 (ho_7476 k_7475 tptp.one) tptp.one)) (ho_7530 k_7529 BOUND_VARIABLE_1489010)) BOUND_VARIABLE_1489009) (ho_7441 (ho_7485 k_7813 BOUND_VARIABLE_1489009) BOUND_VARIABLE_1489010))))) (let ((_let_2059 (forall ((BOUND_VARIABLE_1489002 tptp.num)) (= (ho_7441 k_7814 BOUND_VARIABLE_1489002) (ho_7441 k_7444 (ho_7443 k_7442 BOUND_VARIABLE_1489002)))))) (let ((_let_2060 (forall ((BOUND_VARIABLE_1488985 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488986 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7815 BOUND_VARIABLE_1488985) BOUND_VARIABLE_1488986) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488986 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488985) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488985))))))))))) (let ((_let_2061 (forall ((BOUND_VARIABLE_1488968 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488969 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7823 BOUND_VARIABLE_1488968) BOUND_VARIABLE_1488969) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488969 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488968) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488968))))))))))) (let ((_let_2062 (forall ((BOUND_VARIABLE_1488951 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488952 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7824 BOUND_VARIABLE_1488951) BOUND_VARIABLE_1488952) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488952 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488951) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488951))))))))))) (let ((_let_2063 (forall ((BOUND_VARIABLE_1488934 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488935 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7825 BOUND_VARIABLE_1488934) BOUND_VARIABLE_1488935) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488935 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488934) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488934))))))))))) (let ((_let_2064 (forall ((BOUND_VARIABLE_1488917 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488918 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7826 BOUND_VARIABLE_1488917) BOUND_VARIABLE_1488918) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488918 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488917) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488917))))))))))) (let ((_let_2065 (forall ((BOUND_VARIABLE_1488900 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488901 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7827 BOUND_VARIABLE_1488900) BOUND_VARIABLE_1488901) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488901 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488900) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488900))))))))))) (let ((_let_2066 (forall ((BOUND_VARIABLE_1488883 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1488884 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_7828 BOUND_VARIABLE_1488883) BOUND_VARIABLE_1488884) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1488884 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1488883) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1488883))))))))))) (let ((_let_2067 (forall ((BOUND_VARIABLE_1488841 tptp.nat) (BOUND_VARIABLE_1488842 tptp.nat) (BOUND_VARIABLE_1488843 tptp.nat) (BOUND_VARIABLE_1488844 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488841) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488843) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488842) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488844) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7829 BOUND_VARIABLE_1488841) BOUND_VARIABLE_1488842) BOUND_VARIABLE_1488843) BOUND_VARIABLE_1488844)))))))) (let ((_let_2068 (forall ((BOUND_VARIABLE_1488799 tptp.nat) (BOUND_VARIABLE_1488800 tptp.nat) (BOUND_VARIABLE_1488801 tptp.nat) (BOUND_VARIABLE_1488802 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488799) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488802) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488800) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488801) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7830 BOUND_VARIABLE_1488799) BOUND_VARIABLE_1488800) BOUND_VARIABLE_1488801) BOUND_VARIABLE_1488802)))))))) (let ((_let_2069 (forall ((BOUND_VARIABLE_1488721 tptp.nat) (BOUND_VARIABLE_1488722 tptp.nat) (BOUND_VARIABLE_1488723 tptp.nat) (BOUND_VARIABLE_1488724 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488723) _let_2))) (let ((_let_5 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488722) _let_2)))) (let ((_let_6 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488724) _let_2))) (let ((_let_7 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488721) _let_2)))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_4))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_6))) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_6))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_4))) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7831 BOUND_VARIABLE_1488721) BOUND_VARIABLE_1488722) BOUND_VARIABLE_1488723) BOUND_VARIABLE_1488724)))))))))))) (let ((_let_2070 (forall ((BOUND_VARIABLE_1488674 tptp.nat) (BOUND_VARIABLE_1488675 tptp.nat) (BOUND_VARIABLE_1488676 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7537 BOUND_VARIABLE_1488674) BOUND_VARIABLE_1488675)) BOUND_VARIABLE_1488676) (ho_7834 (ho_7837 (ho_7836 k_7835 BOUND_VARIABLE_1488674) BOUND_VARIABLE_1488675) BOUND_VARIABLE_1488676))))) (let ((_let_2071 (forall ((BOUND_VARIABLE_1488627 tptp.nat) (BOUND_VARIABLE_1488628 tptp.nat) (BOUND_VARIABLE_1488629 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7543 BOUND_VARIABLE_1488627) BOUND_VARIABLE_1488628)) BOUND_VARIABLE_1488629) (ho_7834 (ho_7837 (ho_7836 k_7838 BOUND_VARIABLE_1488627) BOUND_VARIABLE_1488628) BOUND_VARIABLE_1488629))))) (let ((_let_2072 (forall ((BOUND_VARIABLE_1488585 tptp.nat) (BOUND_VARIABLE_1488586 tptp.nat) (BOUND_VARIABLE_1488587 tptp.nat) (BOUND_VARIABLE_1488588 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488585) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488588) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488586) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488587) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7839 BOUND_VARIABLE_1488585) BOUND_VARIABLE_1488586) BOUND_VARIABLE_1488587) BOUND_VARIABLE_1488588)))))))) (let ((_let_2073 (forall ((BOUND_VARIABLE_1488543 tptp.nat) (BOUND_VARIABLE_1488544 tptp.nat) (BOUND_VARIABLE_1488545 tptp.nat) (BOUND_VARIABLE_1488546 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488543) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488545) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488544) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488546) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7840 BOUND_VARIABLE_1488543) BOUND_VARIABLE_1488544) BOUND_VARIABLE_1488545) BOUND_VARIABLE_1488546)))))))) (let ((_let_2074 (forall ((BOUND_VARIABLE_1488497 tptp.nat) (BOUND_VARIABLE_1488498 tptp.nat) (BOUND_VARIABLE_1488499 tptp.nat) (BOUND_VARIABLE_1488500 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488497) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488500) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488499) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488498) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7841 BOUND_VARIABLE_1488497) BOUND_VARIABLE_1488498) BOUND_VARIABLE_1488499) BOUND_VARIABLE_1488500)))))))) (let ((_let_2075 (forall ((BOUND_VARIABLE_1488451 tptp.nat) (BOUND_VARIABLE_1488452 tptp.nat) (BOUND_VARIABLE_1488453 tptp.nat) (BOUND_VARIABLE_1488454 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488451) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488454) _let_2))))) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488453) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488452) _let_2))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_7842 BOUND_VARIABLE_1488451) BOUND_VARIABLE_1488452) BOUND_VARIABLE_1488453) BOUND_VARIABLE_1488454)))))))) (let ((_let_2076 (forall ((BOUND_VARIABLE_1488373 tptp.nat) (BOUND_VARIABLE_1488374 tptp.nat) (BOUND_VARIABLE_1488375 tptp.nat) (BOUND_VARIABLE_1488376 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488375) _let_2))) (let ((_let_5 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488374) _let_2)))) (let ((_let_6 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488376) _let_2))) (let ((_let_7 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1488373) _let_2)))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_4))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_6))) _let_2)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_7 _let_6))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 _let_5 _let_4))) _let_2)))) (ho_7641 (ho_7448 (ho_7644 (ho_7643 k_7843 BOUND_VARIABLE_1488373) BOUND_VARIABLE_1488374) BOUND_VARIABLE_1488375) BOUND_VARIABLE_1488376)))))))))))) (let ((_let_2077 (forall ((BOUND_VARIABLE_1488348 tptp.int) (BOUND_VARIABLE_1488349 tptp.int) (BOUND_VARIABLE_1488350 tptp.int) (BOUND_VARIABLE_1488351 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7844 BOUND_VARIABLE_1488348) BOUND_VARIABLE_1488349) BOUND_VARIABLE_1488350) BOUND_VARIABLE_1488351) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1488349) BOUND_VARIABLE_1488351)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1488348) BOUND_VARIABLE_1488350)))))))))) (let ((_let_2078 (forall ((BOUND_VARIABLE_1488334 tptp.code_integer)) (let ((_let_1 (ho_7846 k_7845 true))) (let ((_let_2 (ho_7848 k_7847 _let_1))) (let ((_let_3 (ho_7848 (ho_7850 k_7849 _let_2) _let_1))) (= (ho_7848 k_7856 BOUND_VARIABLE_1488334) (ho_7848 (ho_7850 (ho_7855 k_7854 (= BOUND_VARIABLE_1488334 _let_3)) _let_3) (ho_7848 (ho_7850 (ho_7855 k_7854 (ho_7853 (ho_7852 k_7851 BOUND_VARIABLE_1488334) _let_3)) _let_2) _let_1))))))))) (let ((_let_2079 (forall ((BOUND_VARIABLE_1488307 tptp.code_integer) (BOUND_VARIABLE_1488308 tptp.code_integer) (BOUND_VARIABLE_1488309 tptp.code_integer)) (let ((_let_1 (ho_7846 k_7845 true))) (let ((_let_2 (ho_7848 k_7847 _let_1))) (let ((_let_3 (ho_7848 (ho_7850 k_7849 _let_2) _let_1))) (let ((_let_4 (ho_7848 k_7847 BOUND_VARIABLE_1488308))) (= (ho_7859 (ho_7858 (ho_7865 k_7864 BOUND_VARIABLE_1488307) BOUND_VARIABLE_1488308) BOUND_VARIABLE_1488309) (ho_7863 (ho_7862 (ho_7861 k_7860 (= BOUND_VARIABLE_1488309 _let_3)) (ho_7859 (ho_7858 k_7857 _let_4) _let_3)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_7849 _let_4) _let_2)) (ho_7848 (ho_7850 k_7849 (ho_7848 (ho_7850 (ho_7855 k_7854 (ho_7853 (ho_7852 k_7851 BOUND_VARIABLE_1488307) _let_3)) (ho_7848 k_7847 BOUND_VARIABLE_1488307)) BOUND_VARIABLE_1488307)) (ho_7848 k_7847 BOUND_VARIABLE_1488309)))))))))))) (let ((_let_2080 (forall ((BOUND_VARIABLE_1488286 tptp.code_integer) (BOUND_VARIABLE_1488287 tptp.code_integer) (BOUND_VARIABLE_1488288 tptp.code_integer)) (let ((_let_1 (ho_7846 k_7845 true))) (let ((_let_2 (ho_7848 k_7847 _let_1))) (let ((_let_3 (ho_7848 k_7847 BOUND_VARIABLE_1488287))) (let ((_let_4 (ho_7848 (ho_7850 k_7849 _let_2) _let_1))) (= (ho_7859 (ho_7858 (ho_7865 k_7866 BOUND_VARIABLE_1488286) BOUND_VARIABLE_1488287) BOUND_VARIABLE_1488288) (ho_7863 (ho_7862 (ho_7861 k_7860 (= BOUND_VARIABLE_1488288 _let_4)) (ho_7859 (ho_7858 k_7857 _let_3) _let_4)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_7849 _let_3) _let_2)) (ho_7848 (ho_7850 k_7849 BOUND_VARIABLE_1488286) (ho_7848 k_7847 BOUND_VARIABLE_1488288)))))))))))) (let ((_let_2081 (forall ((BOUND_VARIABLE_1488264 tptp.code_integer) (BOUND_VARIABLE_1488265 tptp.code_integer) (BOUND_VARIABLE_1488266 tptp.code_integer)) (let ((_let_1 (ho_7846 k_7845 true))) (let ((_let_2 (ho_7848 k_7847 _let_1))) (let ((_let_3 (ho_7848 k_7847 BOUND_VARIABLE_1488265))) (let ((_let_4 (ho_7848 (ho_7850 k_7849 _let_2) _let_1))) (= (ho_7859 (ho_7858 (ho_7865 k_7867 BOUND_VARIABLE_1488264) BOUND_VARIABLE_1488265) BOUND_VARIABLE_1488266) (ho_7863 (ho_7862 (ho_7861 k_7860 (= BOUND_VARIABLE_1488266 _let_4)) (ho_7859 (ho_7858 k_7857 _let_3) _let_4)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_7849 _let_3) _let_2)) (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 BOUND_VARIABLE_1488264)) (ho_7848 k_7847 BOUND_VARIABLE_1488266)))))))))))) (let ((_let_2082 (forall ((BOUND_VARIABLE_1488246 tptp.code_integer) (BOUND_VARIABLE_1488247 tptp.code_integer) (BOUND_VARIABLE_1488248 tptp.code_integer)) (let ((_let_1 (ho_7846 k_7845 true))) (= (ho_7871 (ho_7870 (ho_7869 k_7868 BOUND_VARIABLE_1488246) BOUND_VARIABLE_1488247) BOUND_VARIABLE_1488248) (ho_7874 (ho_7873 k_7872 (ho_7848 (ho_7850 (ho_7855 k_7854 (ho_7853 (ho_7852 k_7851 (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 _let_1)) _let_1)) BOUND_VARIABLE_1488246)) BOUND_VARIABLE_1488247) (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 BOUND_VARIABLE_1488247)) (ho_7848 k_7847 BOUND_VARIABLE_1488248)))) (= BOUND_VARIABLE_1488248 _let_1))))))) (let ((_let_2083 (forall ((BOUND_VARIABLE_1488211 tptp.code_integer) (BOUND_VARIABLE_1488212 tptp.code_integer)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 (ho_7876 k_7875 BOUND_VARIABLE_1488211)) _let_2))) (let ((_let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_4) _let_4)))) (let ((_let_6 (ho_7846 k_7845 true))) (= (ho_7876 (ho_7880 k_7879 BOUND_VARIABLE_1488211) BOUND_VARIABLE_1488212) (ho_7466 (ho_7465 (ho_7878 k_7877 (= BOUND_VARIABLE_1488212 (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 _let_6)) _let_6))) _let_5) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_5) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))))))))))))) (let ((_let_2084 (forall ((BOUND_VARIABLE_1488196 tptp.code_integer) (BOUND_VARIABLE_1488197 tptp.code_integer)) (let ((_let_1 (ho_7882 k_7881 BOUND_VARIABLE_1488196))) (let ((_let_2 (ho_7443 (ho_7884 k_7883 _let_1) _let_1))) (let ((_let_3 (ho_7846 k_7845 true))) (= (ho_7882 (ho_7888 k_7887 BOUND_VARIABLE_1488196) BOUND_VARIABLE_1488197) (ho_7443 (ho_7884 (ho_7886 k_7885 (= BOUND_VARIABLE_1488197 (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 _let_3)) _let_3))) _let_2) (ho_7443 (ho_7884 k_7883 _let_2) tptp.one))))))))) (let ((_let_2085 (forall ((BOUND_VARIABLE_1488182 tptp.code_integer) (BOUND_VARIABLE_1488183 tptp.code_integer)) (let ((_let_1 (ho_7459 (ho_7461 k_7472 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))) (ho_7890 k_7889 BOUND_VARIABLE_1488182)))) (let ((_let_2 (ho_7846 k_7845 true))) (= (ho_7890 (ho_7894 k_7893 BOUND_VARIABLE_1488182) BOUND_VARIABLE_1488183) (ho_7459 (ho_7461 (ho_7892 k_7891 (= BOUND_VARIABLE_1488183 (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 _let_2)) _let_2))) _let_1) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7446 k_7445 tptp.one))))))))) (let ((_let_2086 (forall ((BOUND_VARIABLE_1488132 tptp.complex) (BOUND_VARIABLE_1488133 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1488133) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7730 k_7729 BOUND_VARIABLE_1488132)) _let_6)) (ho_7508 (ho_7896 k_7895 BOUND_VARIABLE_1488132) BOUND_VARIABLE_1488133)))))))))))))) (let ((_let_2087 (forall ((BOUND_VARIABLE_1488058 tptp.complex) (BOUND_VARIABLE_1488059 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1488059) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 (ho_7730 k_7733 BOUND_VARIABLE_1488058)))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7735 k_7897 BOUND_VARIABLE_1488058) BOUND_VARIABLE_1488059)))))))))))))))))))))) (let ((_let_2088 (forall ((BOUND_VARIABLE_1488035 tptp.num) (BOUND_VARIABLE_1488036 tptp.code_integer) (BOUND_VARIABLE_1488037 tptp.code_integer)) (let ((_let_1 (ho_7848 (ho_7850 k_7902 (ho_7901 k_7900 (ho_7443 k_7442 tptp.one))) BOUND_VARIABLE_1488036))) (let ((_let_2 (ho_7901 k_7900 BOUND_VARIABLE_1488035))) (= (ho_7859 (ho_7858 (ho_7899 k_7898 BOUND_VARIABLE_1488035) BOUND_VARIABLE_1488036) BOUND_VARIABLE_1488037) (ho_7863 (ho_7862 (ho_7861 k_7860 (ho_7853 (ho_7852 k_7903 _let_2) BOUND_VARIABLE_1488037)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_7849 _let_1) (ho_7846 k_7845 true))) (ho_7848 (ho_7850 k_7849 BOUND_VARIABLE_1488037) (ho_7848 k_7847 _let_2)))) (ho_7859 (ho_7858 k_7857 _let_1) BOUND_VARIABLE_1488037)))))))) (let ((_let_2089 (forall ((BOUND_VARIABLE_1488012 tptp.num) (BOUND_VARIABLE_1488013 tptp.code_integer) (BOUND_VARIABLE_1488014 tptp.code_integer)) (let ((_let_1 (ho_7848 (ho_7850 k_7902 (ho_7901 k_7900 (ho_7443 k_7442 tptp.one))) BOUND_VARIABLE_1488013))) (let ((_let_2 (ho_7901 k_7900 BOUND_VARIABLE_1488012))) (= (ho_7859 (ho_7858 (ho_7899 k_7904 BOUND_VARIABLE_1488012) BOUND_VARIABLE_1488013) BOUND_VARIABLE_1488014) (ho_7863 (ho_7862 (ho_7861 k_7860 (ho_7853 (ho_7852 k_7903 _let_2) BOUND_VARIABLE_1488014)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_7849 _let_1) (ho_7846 k_7845 true))) (ho_7848 (ho_7850 k_7849 BOUND_VARIABLE_1488014) (ho_7848 k_7847 _let_2)))) (ho_7859 (ho_7858 k_7857 _let_1) BOUND_VARIABLE_1488014)))))))) (let ((_let_2090 (forall ((BOUND_VARIABLE_1487964 tptp.rat) (BOUND_VARIABLE_1487965 tptp.int) (BOUND_VARIABLE_1487966 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7544 BOUND_VARIABLE_1487965) BOUND_VARIABLE_1487966)) (ho_7630 k_7629 BOUND_VARIABLE_1487964)) (ho_7496 (ho_7495 (ho_7635 k_7905 BOUND_VARIABLE_1487964) BOUND_VARIABLE_1487965) BOUND_VARIABLE_1487966))))) (let ((_let_2091 (forall ((BOUND_VARIABLE_1487523 tptp.int) (BOUND_VARIABLE_1487524 tptp.int) (BOUND_VARIABLE_1487525 tptp.int) (BOUND_VARIABLE_1487526 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 _let_2 _let_1))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_1) _let_3))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (let ((_let_6 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (let ((_let_9 (ho_7907 k_7906 _let_8))) (let ((_let_10 (ho_7907 k_7908 _let_8))) (let ((_let_11 (ho_7459 (ho_7461 k_7909 _let_10) _let_9))) (let ((_let_12 (ho_7459 _let_2 _let_11))) (let ((_let_13 (= _let_4 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_14)) (ho_7459 _let_2 _let_12)) _let_12)))) (let ((_let_16 (= _let_4 _let_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3))))))))) _let_17)) (ho_7459 _let_2 _let_9)) _let_9))))) (let ((_let_19 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_15)) _let_4))) (let ((_let_20 (ho_7461 (ho_7892 k_7891 _let_13) _let_4))) (let ((_let_21 (ho_7459 _let_20 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (not (= (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4))) (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_14)) _let_1) _let_3)))) (let ((_let_22 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (not (= (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526))) (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3))))))))) _let_17))) (let ((_let_23 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_16) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 _let_22) _let_1) _let_3)))) (let ((_let_24 (= _let_4 _let_10))) (let ((_let_25 (not _let_24))) (let ((_let_26 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3))))))))) _let_25)) (ho_7459 _let_2 _let_10)) _let_10))))) (let ((_let_27 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_15)) _let_4))) (let ((_let_28 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_24) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (not (= (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526))) (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3))))))))) _let_25)) _let_1) _let_3)))) (let ((_let_29 (= _let_4 _let_11))) (let ((_let_30 (not _let_29))) (let ((_let_31 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_30)) _let_12) _let_11)))) (let ((_let_32 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_31)) _let_4))) (let ((_let_33 (ho_7461 (ho_7892 k_7891 _let_29) _let_4))) (let ((_let_34 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (not (= (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4)) (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_30)) _let_1) _let_3)))) (let ((_let_35 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_31)) _let_4))) (= (ho_7698 (ho_7697 (ho_7912 (ho_7911 k_7910 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487526) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_22) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_28 _let_34)) _let_35) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_35) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_34 _let_23)) _let_32) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_32) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2)) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_16) (ho_7698 (ho_7697 k_7696 _let_4) _let_1)) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_20 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_28 _let_21)) _let_27) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_27) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_2 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_1 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (let ((_let_3 (ho_7907 k_7908 _let_2))) (not (= _let_3 (ho_7459 (ho_7461 k_7472 (ho_7459 _let_1 (ho_7459 (ho_7461 k_7909 _let_3) (ho_7907 k_7906 _let_2)))) K3)))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_20 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_21)) _let_19) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_19) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_2 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487523) BOUND_VARIABLE_1487526)) (ho_7459 _let_1 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487525) BOUND_VARIABLE_1487524)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487524) BOUND_VARIABLE_1487526)))) (let ((_let_3 (ho_7907 k_7906 _let_2))) (not (= _let_3 (ho_7459 (ho_7461 k_7472 (ho_7459 _let_1 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_2)) _let_3))) K3)))))))) _let_5) _let_6)) _let_4)))) _let_4)))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2092 (forall ((BOUND_VARIABLE_1487108 tptp.int) (BOUND_VARIABLE_1487109 tptp.int) (BOUND_VARIABLE_1487110 tptp.int) (BOUND_VARIABLE_1487111 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 _let_2 _let_1))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_1) _let_3))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (let ((_let_6 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_9 (ho_7907 k_7906 _let_8))) (let ((_let_10 (ho_7907 k_7908 _let_8))) (let ((_let_11 (ho_7459 (ho_7461 k_7909 _let_10) _let_9))) (let ((_let_12 (ho_7459 _let_2 _let_11))) (let ((_let_13 (= _let_4 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_14)) (ho_7459 _let_2 _let_12)) _let_12)))) (let ((_let_16 (= _let_4 _let_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)))))))) _let_17)) (ho_7459 _let_2 _let_9)) _let_9))))) (let ((_let_19 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_15)) _let_4))) (let ((_let_20 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111))))))))) _let_17))) (let ((_let_21 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_16) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 _let_20) _let_1) _let_3)))) (let ((_let_22 (ho_7461 (ho_7892 k_7891 _let_13) _let_4))) (let ((_let_23 (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_2 _let_3)))) (not (= (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_4)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))))) _let_14)) _let_1) _let_3)))) (let ((_let_24 (= _let_4 _let_10))) (let ((_let_25 (not _let_24))) (let ((_let_26 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)))))))) _let_25)) (ho_7459 _let_2 _let_10)) _let_10))))) (let ((_let_27 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_15)) _let_4))) (let ((_let_28 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_24) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111))))))))) _let_25)) _let_1) _let_3)))) (let ((_let_29 (= _let_4 _let_11))) (let ((_let_30 (not _let_29))) (let ((_let_31 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_3)) (ho_7907 k_7906 _let_3))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2))))))))) _let_30)) _let_12) _let_11)))) (let ((_let_32 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_31)) _let_4))) (let ((_let_33 (ho_7461 (ho_7892 k_7891 _let_29) _let_4))) (let ((_let_34 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (not (= (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)) (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))) _let_30)) _let_1) _let_3)))) (let ((_let_35 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_31)) _let_4))) (= (ho_7698 (ho_7697 (ho_7912 (ho_7911 k_7913 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487111) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_20) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_28 _let_34)) _let_35) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_35) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_21 _let_34)) _let_32) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_32) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2)) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_16) (ho_7698 (ho_7697 k_7696 _let_4) _let_1)) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_28)) _let_27) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_27) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1)))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_21)) _let_19) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_19) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487108) BOUND_VARIABLE_1487111)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487110) BOUND_VARIABLE_1487109))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1487109) BOUND_VARIABLE_1487111)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2093 (forall ((BOUND_VARIABLE_1486697 tptp.int) (BOUND_VARIABLE_1486698 tptp.int) (BOUND_VARIABLE_1486699 tptp.int) (BOUND_VARIABLE_1486700 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 _let_2 _let_1))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_1) _let_3))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (let ((_let_6 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_9 (ho_7907 k_7906 _let_8))) (let ((_let_10 (ho_7907 k_7908 _let_8))) (let ((_let_11 (ho_7459 (ho_7461 k_7909 _let_10) _let_9))) (let ((_let_12 (ho_7459 _let_2 _let_11))) (let ((_let_13 (= _let_4 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_14)) (ho_7459 _let_2 _let_12)) _let_12)))) (let ((_let_16 (= _let_4 _let_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)))))))) _let_17)) (ho_7459 _let_2 _let_9)) _let_9))))) (let ((_let_19 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_15)) _let_4))) (let ((_let_20 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699))))))))) _let_17))) (let ((_let_21 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_16) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 _let_20) _let_1) _let_3)))) (let ((_let_22 (ho_7461 (ho_7892 k_7891 _let_13) _let_4))) (let ((_let_23 (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_2 _let_3)))) (not (= (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_4)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))))) _let_14)) _let_1) _let_3)))) (let ((_let_24 (= _let_4 _let_10))) (let ((_let_25 (not _let_24))) (let ((_let_26 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)))))))) _let_25)) (ho_7459 _let_2 _let_10)) _let_10))))) (let ((_let_27 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_15)) _let_4))) (let ((_let_28 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_24) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699))))))))) _let_25)) _let_1) _let_3)))) (let ((_let_29 (= _let_4 _let_11))) (let ((_let_30 (not _let_29))) (let ((_let_31 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_3)) (ho_7907 k_7906 _let_3))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2))))))))) _let_30)) _let_12) _let_11)))) (let ((_let_32 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_31)) _let_4))) (let ((_let_33 (ho_7461 (ho_7892 k_7891 _let_29) _let_4))) (let ((_let_34 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (not (= (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)) (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))) _let_30)) _let_1) _let_3)))) (let ((_let_35 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_31)) _let_4))) (= (ho_7698 (ho_7697 (ho_7912 (ho_7911 k_7914 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699) BOUND_VARIABLE_1486700) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_20) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_28 _let_34)) _let_35) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_35) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_21 _let_34)) _let_32) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_32) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2)) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_16) (ho_7698 (ho_7697 k_7696 _let_4) _let_1)) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_28)) _let_27) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_27) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1)))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_21)) _let_19) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_19) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486697) BOUND_VARIABLE_1486700)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486698) BOUND_VARIABLE_1486699)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2094 (forall ((BOUND_VARIABLE_1486286 tptp.int) (BOUND_VARIABLE_1486287 tptp.int) (BOUND_VARIABLE_1486288 tptp.int) (BOUND_VARIABLE_1486289 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 _let_2 _let_1))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_1) _let_3))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (let ((_let_6 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_9 (ho_7907 k_7906 _let_8))) (let ((_let_10 (ho_7907 k_7908 _let_8))) (let ((_let_11 (ho_7459 (ho_7461 k_7909 _let_10) _let_9))) (let ((_let_12 (ho_7459 _let_2 _let_11))) (let ((_let_13 (= _let_4 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (not (= _let_3 (ho_7459 (ho_7461 k_7460 (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_4)) (ho_7907 k_7906 _let_4)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)))))))))) _let_14)) (ho_7459 _let_2 _let_12)) _let_12)))) (let ((_let_16 (= _let_4 _let_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)))))))) _let_17)) (ho_7459 _let_2 _let_9)) _let_9))))) (let ((_let_19 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_15)) _let_4))) (let ((_let_20 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7907 k_7906 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289))))))))) _let_17))) (let ((_let_21 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_16) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 _let_20) _let_1) _let_3)))) (let ((_let_22 (ho_7461 (ho_7892 k_7891 _let_13) _let_4))) (let ((_let_23 (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_2 _let_3)))) (not (= (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_4)) (ho_7459 _let_2 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))))) _let_14)) _let_1) _let_3)))) (let ((_let_24 (= _let_4 _let_10))) (let ((_let_25 (not _let_24))) (let ((_let_26 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)))))))) _let_25)) (ho_7459 _let_2 _let_10)) _let_10))))) (let ((_let_27 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_15)) _let_4))) (let ((_let_28 (ho_7459 (ho_7461 (ho_7892 k_7891 _let_24) _let_4) (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7907 k_7908 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289))))))))) _let_25)) _let_1) _let_3)))) (let ((_let_29 (= _let_4 _let_11))) (let ((_let_30 (not _let_29))) (let ((_let_31 (ho_7463 k_7462 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (not (= _let_2 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_3)) (ho_7907 k_7906 _let_3))) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2))))))))) _let_30)) _let_12) _let_11)))) (let ((_let_32 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_18 _let_31)) _let_4))) (let ((_let_33 (ho_7461 (ho_7892 k_7891 _let_29) _let_4))) (let ((_let_34 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (not (= (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)) (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))) _let_30)) _let_1) _let_3)))) (let ((_let_35 (ho_7459 (ho_7470 _let_7 (ho_7466 _let_26 _let_31)) _let_4))) (= (ho_7698 (ho_7697 (ho_7912 (ho_7911 k_7915 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486288) BOUND_VARIABLE_1486289) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_20) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_28 _let_34)) _let_35) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_35) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_33 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_21 _let_34)) _let_32) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_32) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2)) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))) (ho_7702 (ho_7701 (ho_7700 k_7699 _let_16) (ho_7698 (ho_7697 k_7696 _let_4) _let_1)) (ho_7698 (ho_7697 k_7696 (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_28)) _let_27) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_27) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_2 (ho_7907 k_7908 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7909 _let_2) (ho_7907 k_7906 _let_1)))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4))))) (ho_7459 _let_22 (ho_7459 (ho_7461 (ho_7892 k_7891 (= _let_23 _let_21)) _let_19) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_19) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 (ho_7878 k_7877 (forall ((K3 tptp.int)) (let ((_let_1 (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486286) BOUND_VARIABLE_1486288)) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486287) BOUND_VARIABLE_1486289)))) (let ((_let_2 (ho_7907 k_7906 _let_1))) (not (= _let_2 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7459 (ho_7461 k_7909 (ho_7907 k_7908 _let_1)) _let_2))) K3))))))) _let_5) _let_6)) _let_4)))) _let_4)))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2095 (forall ((BOUND_VARIABLE_1486261 tptp.int) (BOUND_VARIABLE_1486262 tptp.int) (BOUND_VARIABLE_1486263 tptp.int) (BOUND_VARIABLE_1486264 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7916 BOUND_VARIABLE_1486261) BOUND_VARIABLE_1486262) BOUND_VARIABLE_1486263) BOUND_VARIABLE_1486264) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486262) BOUND_VARIABLE_1486264)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486261) BOUND_VARIABLE_1486263)))))))))) (let ((_let_2096 (forall ((BOUND_VARIABLE_1486236 tptp.int) (BOUND_VARIABLE_1486237 tptp.int) (BOUND_VARIABLE_1486238 tptp.int) (BOUND_VARIABLE_1486239 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7917 BOUND_VARIABLE_1486236) BOUND_VARIABLE_1486237) BOUND_VARIABLE_1486238) BOUND_VARIABLE_1486239) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486237) BOUND_VARIABLE_1486239)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486236) BOUND_VARIABLE_1486238)))))))))) (let ((_let_2097 (forall ((BOUND_VARIABLE_1486211 tptp.int) (BOUND_VARIABLE_1486212 tptp.int) (BOUND_VARIABLE_1486213 tptp.int) (BOUND_VARIABLE_1486214 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7918 BOUND_VARIABLE_1486211) BOUND_VARIABLE_1486212) BOUND_VARIABLE_1486213) BOUND_VARIABLE_1486214) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486212) BOUND_VARIABLE_1486214)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1486211) BOUND_VARIABLE_1486213)))))))))) (let ((_let_2098 (forall ((BOUND_VARIABLE_1486191 tptp.int) (BOUND_VARIABLE_1486192 tptp.int) (BOUND_VARIABLE_1486193 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 k_7919 BOUND_VARIABLE_1486191) BOUND_VARIABLE_1486192) BOUND_VARIABLE_1486193) (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7922 (ho_7921 k_7920 BOUND_VARIABLE_1486191) BOUND_VARIABLE_1486192))) (or (not (= BOUND_VARIABLE_1486193 (ho_7927 (ho_7926 k_7925 _let_1) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7924 k_7923 _let_1)))))))))))) (let ((_let_2099 (forall ((BOUND_VARIABLE_1486169 tptp.int) (BOUND_VARIABLE_1486170 tptp.int) (BOUND_VARIABLE_1486171 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 k_7928 BOUND_VARIABLE_1486169) BOUND_VARIABLE_1486170) BOUND_VARIABLE_1486171) (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7922 (ho_7921 k_7920 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1486169) (ho_7446 k_7445 tptp.one))) BOUND_VARIABLE_1486170))) (or (not (= BOUND_VARIABLE_1486171 (ho_7927 (ho_7926 k_7925 _let_1) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7924 k_7923 _let_1)))))))))))) (let ((_let_2100 (forall ((BOUND_VARIABLE_1486106 tptp.real) (BOUND_VARIABLE_1486107 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1486107) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7929 BOUND_VARIABLE_1486106) BOUND_VARIABLE_1486107) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1486107 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1486107 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1486106) BOUND_VARIABLE_1486107))))))))))))))))) (let ((_let_2101 (forall ((BOUND_VARIABLE_1486051 tptp.real) (BOUND_VARIABLE_1486052 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7930 BOUND_VARIABLE_1486051) BOUND_VARIABLE_1486052) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1486052 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1486052) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1486052 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1486052) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1486051) BOUND_VARIABLE_1486052))))))))))))))) (let ((_let_2102 (forall ((BOUND_VARIABLE_1485988 tptp.real) (BOUND_VARIABLE_1485989 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1485989) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_7931 BOUND_VARIABLE_1485988) BOUND_VARIABLE_1485989) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1485989 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1485989 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1485988) BOUND_VARIABLE_1485989))))))))))))))))) (let ((_let_2103 (forall ((BOUND_VARIABLE_1485933 tptp.real) (BOUND_VARIABLE_1485934 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7932 BOUND_VARIABLE_1485933) BOUND_VARIABLE_1485934) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1485934 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1485934) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1485934 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1485934) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1485933) BOUND_VARIABLE_1485934))))))))))))))) (let ((_let_2104 (forall ((BOUND_VARIABLE_1485906 tptp.nat) (BOUND_VARIABLE_1485907 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1485907 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_7933 BOUND_VARIABLE_1485906) BOUND_VARIABLE_1485907) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1485907) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1485907) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1485907)) BOUND_VARIABLE_1485907)) BOUND_VARIABLE_1485906))))))))))) (let ((_let_2105 (forall ((BOUND_VARIABLE_1485807 tptp.complex) (BOUND_VARIABLE_1485808 tptp.nat) (BOUND_VARIABLE_1485809 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485809) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7516 (ho_7519 k_7523 _let_7) (ho_7516 k_7521 _let_7)))) (let ((_let_9 (ho_7728 k_7727 (ho_7516 (ho_7519 k_7522 (ho_7730 k_7934 BOUND_VARIABLE_1485807)) (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1485808) _let_8)))))) (let ((_let_10 (ho_7730 k_7729 _let_9))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 _let_8) _let_7))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7733 _let_11)))) (let ((_let_13 (ho_7730 k_7733 _let_9))) (let ((_let_14 (ho_7519 k_7522 (ho_7730 k_7729 _let_11)))) (let ((_let_15 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_10)) (ho_7516 k_7521 (ho_7516 _let_12 _let_13)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_13)) (ho_7516 _let_12 _let_10)))) _let_6))) (let ((_let_16 (ho_7463 k_7462 _let_1))) (let ((_let_17 (ho_7466 (ho_7465 k_7471 _let_16) _let_4))) (let ((_let_18 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_17 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_17) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_16) _let_3))))) _let_7)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_18 (ho_7730 k_7729 _let_15))) (ho_7516 _let_18 (ho_7730 k_7733 _let_15))) (ho_7736 (ho_7937 (ho_7936 k_7935 BOUND_VARIABLE_1485807) BOUND_VARIABLE_1485808) BOUND_VARIABLE_1485809))))))))))))))))))))))) (let ((_let_2106 (forall ((BOUND_VARIABLE_1485702 tptp.nat) (BOUND_VARIABLE_1485703 tptp.nat) (BOUND_VARIABLE_1485704 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7443 k_7442 tptp.one))) (let ((_let_5 (ho_7463 k_7462 (ho_7446 k_7445 _let_4)))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1485704) _let_3)) (ho_7459 (ho_7470 _let_6 _let_5) _let_3))))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7516 k_7521 _let_8))) (let ((_let_10 (ho_7516 (ho_7519 k_7523 _let_8) _let_9))) (let ((_let_11 (ho_7788 k_7787 k_7786))) (let ((_let_12 (ho_7728 k_7727 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 _let_4)) (ho_7516 k_7796 _let_9))) (ho_7516 (ho_7512 _let_11 BOUND_VARIABLE_1485702) _let_10))) (ho_7516 k_7520 (ho_7516 (ho_7512 _let_11 BOUND_VARIABLE_1485703) _let_10)))))) (let ((_let_13 (ho_7730 k_7729 _let_12))) (let ((_let_14 (ho_7728 (ho_7732 k_7731 _let_10) _let_8))) (let ((_let_15 (ho_7519 k_7522 (ho_7730 k_7733 _let_14)))) (let ((_let_16 (ho_7730 k_7733 _let_12))) (let ((_let_17 (ho_7519 k_7522 (ho_7730 k_7729 _let_14)))) (let ((_let_18 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_17 _let_13)) (ho_7516 k_7521 (ho_7516 _let_15 _let_16)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_17 _let_16)) (ho_7516 _let_15 _let_13)))) _let_7))) (let ((_let_19 (ho_7463 k_7462 _let_1))) (let ((_let_20 (ho_7466 (ho_7465 k_7471 _let_19) _let_5))) (let ((_let_21 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_20 _let_7)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_20) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 _let_7) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_6 _let_19) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_21 (ho_7730 k_7729 _let_18))) (ho_7516 _let_21 (ho_7730 k_7733 _let_18))) (ho_7736 (ho_7937 (ho_7939 k_7938 BOUND_VARIABLE_1485702) BOUND_VARIABLE_1485703) BOUND_VARIABLE_1485704)))))))))))))))))))))))))) (let ((_let_2107 (forall ((BOUND_VARIABLE_1485677 tptp.int) (BOUND_VARIABLE_1485678 tptp.int) (BOUND_VARIABLE_1485679 tptp.int) (BOUND_VARIABLE_1485680 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7940 BOUND_VARIABLE_1485677) BOUND_VARIABLE_1485678) BOUND_VARIABLE_1485679) BOUND_VARIABLE_1485680) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485678) BOUND_VARIABLE_1485680)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485677) BOUND_VARIABLE_1485679)))))))))) (let ((_let_2108 (forall ((BOUND_VARIABLE_1485652 tptp.int) (BOUND_VARIABLE_1485653 tptp.int) (BOUND_VARIABLE_1485654 tptp.int) (BOUND_VARIABLE_1485655 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7941 BOUND_VARIABLE_1485652) BOUND_VARIABLE_1485653) BOUND_VARIABLE_1485654) BOUND_VARIABLE_1485655) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485653) BOUND_VARIABLE_1485655)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485652) BOUND_VARIABLE_1485654)))))))))) (let ((_let_2109 (forall ((BOUND_VARIABLE_1485627 tptp.int) (BOUND_VARIABLE_1485628 tptp.int) (BOUND_VARIABLE_1485629 tptp.int) (BOUND_VARIABLE_1485630 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7942 BOUND_VARIABLE_1485627) BOUND_VARIABLE_1485628) BOUND_VARIABLE_1485629) BOUND_VARIABLE_1485630) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485628) BOUND_VARIABLE_1485630)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485627) BOUND_VARIABLE_1485629)))))))))) (let ((_let_2110 (forall ((BOUND_VARIABLE_1485602 tptp.int) (BOUND_VARIABLE_1485603 tptp.int) (BOUND_VARIABLE_1485604 tptp.int) (BOUND_VARIABLE_1485605 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7943 BOUND_VARIABLE_1485602) BOUND_VARIABLE_1485603) BOUND_VARIABLE_1485604) BOUND_VARIABLE_1485605) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485603) BOUND_VARIABLE_1485605)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485602) BOUND_VARIABLE_1485604)))))))))) (let ((_let_2111 (forall ((BOUND_VARIABLE_1485577 tptp.int) (BOUND_VARIABLE_1485578 tptp.int) (BOUND_VARIABLE_1485579 tptp.int) (BOUND_VARIABLE_1485580 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7944 BOUND_VARIABLE_1485577) BOUND_VARIABLE_1485578) BOUND_VARIABLE_1485579) BOUND_VARIABLE_1485580) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485578) BOUND_VARIABLE_1485580)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485577) BOUND_VARIABLE_1485579)))))))))) (let ((_let_2112 (forall ((BOUND_VARIABLE_1485552 tptp.int) (BOUND_VARIABLE_1485553 tptp.int) (BOUND_VARIABLE_1485554 tptp.int) (BOUND_VARIABLE_1485555 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7945 BOUND_VARIABLE_1485552) BOUND_VARIABLE_1485553) BOUND_VARIABLE_1485554) BOUND_VARIABLE_1485555) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485553) BOUND_VARIABLE_1485555)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485552) BOUND_VARIABLE_1485554)))))))))) (let ((_let_2113 (forall ((BOUND_VARIABLE_1485527 tptp.int) (BOUND_VARIABLE_1485528 tptp.int) (BOUND_VARIABLE_1485529 tptp.int) (BOUND_VARIABLE_1485530 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7946 BOUND_VARIABLE_1485527) BOUND_VARIABLE_1485528) BOUND_VARIABLE_1485529) BOUND_VARIABLE_1485530) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485528) BOUND_VARIABLE_1485530)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485527) BOUND_VARIABLE_1485529)))))))))) (let ((_let_2114 (forall ((BOUND_VARIABLE_1485502 tptp.int) (BOUND_VARIABLE_1485503 tptp.int) (BOUND_VARIABLE_1485504 tptp.int) (BOUND_VARIABLE_1485505 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7947 BOUND_VARIABLE_1485502) BOUND_VARIABLE_1485503) BOUND_VARIABLE_1485504) BOUND_VARIABLE_1485505) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485503) BOUND_VARIABLE_1485505)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485502) BOUND_VARIABLE_1485504)))))))))) (let ((_let_2115 (forall ((BOUND_VARIABLE_1485477 tptp.int) (BOUND_VARIABLE_1485478 tptp.int) (BOUND_VARIABLE_1485479 tptp.int) (BOUND_VARIABLE_1485480 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7948 BOUND_VARIABLE_1485477) BOUND_VARIABLE_1485478) BOUND_VARIABLE_1485479) BOUND_VARIABLE_1485480) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485478) BOUND_VARIABLE_1485480)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485477) BOUND_VARIABLE_1485479)))))))))) (let ((_let_2116 (forall ((BOUND_VARIABLE_1485452 tptp.int) (BOUND_VARIABLE_1485453 tptp.int) (BOUND_VARIABLE_1485454 tptp.int) (BOUND_VARIABLE_1485455 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7949 BOUND_VARIABLE_1485452) BOUND_VARIABLE_1485453) BOUND_VARIABLE_1485454) BOUND_VARIABLE_1485455) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485453) BOUND_VARIABLE_1485455)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485452) BOUND_VARIABLE_1485454)))))))))) (let ((_let_2117 (forall ((BOUND_VARIABLE_1485427 tptp.int) (BOUND_VARIABLE_1485428 tptp.int) (BOUND_VARIABLE_1485429 tptp.int) (BOUND_VARIABLE_1485430 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7950 BOUND_VARIABLE_1485427) BOUND_VARIABLE_1485428) BOUND_VARIABLE_1485429) BOUND_VARIABLE_1485430) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485428) BOUND_VARIABLE_1485430)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485427) BOUND_VARIABLE_1485429)))))))))) (let ((_let_2118 (forall ((BOUND_VARIABLE_1485402 tptp.int) (BOUND_VARIABLE_1485403 tptp.int) (BOUND_VARIABLE_1485404 tptp.int) (BOUND_VARIABLE_1485405 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7951 BOUND_VARIABLE_1485402) BOUND_VARIABLE_1485403) BOUND_VARIABLE_1485404) BOUND_VARIABLE_1485405) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485403) BOUND_VARIABLE_1485405)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485402) BOUND_VARIABLE_1485404)))))))))) (let ((_let_2119 (forall ((BOUND_VARIABLE_1485377 tptp.int) (BOUND_VARIABLE_1485378 tptp.int) (BOUND_VARIABLE_1485379 tptp.int) (BOUND_VARIABLE_1485380 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7952 BOUND_VARIABLE_1485377) BOUND_VARIABLE_1485378) BOUND_VARIABLE_1485379) BOUND_VARIABLE_1485380) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485378) BOUND_VARIABLE_1485380)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485377) BOUND_VARIABLE_1485379)))))))))) (let ((_let_2120 (forall ((BOUND_VARIABLE_1485352 tptp.int) (BOUND_VARIABLE_1485353 tptp.int) (BOUND_VARIABLE_1485354 tptp.int) (BOUND_VARIABLE_1485355 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_7953 BOUND_VARIABLE_1485352) BOUND_VARIABLE_1485353) BOUND_VARIABLE_1485354) BOUND_VARIABLE_1485355) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485353) BOUND_VARIABLE_1485355)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1485352) BOUND_VARIABLE_1485354)))))))))) (let ((_let_2121 (forall ((BOUND_VARIABLE_1485305 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485305) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 _let_7) _let_6)) (ho_7508 k_7954 BOUND_VARIABLE_1485305)))))))))))))) (let ((_let_2122 (forall ((BOUND_VARIABLE_1485258 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485258) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 _let_7) _let_6)) (ho_7508 k_7955 BOUND_VARIABLE_1485258)))))))))))))) (let ((_let_2123 (forall ((BOUND_VARIABLE_1485199 tptp.complex) (BOUND_VARIABLE_1485200 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485200) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1485199) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7956 BOUND_VARIABLE_1485199) BOUND_VARIABLE_1485200)))))))))))))))) (let ((_let_2124 (forall ((BOUND_VARIABLE_1485139 tptp.complex) (BOUND_VARIABLE_1485140 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485140) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7958 k_7957 BOUND_VARIABLE_1485139)) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7959 BOUND_VARIABLE_1485139) BOUND_VARIABLE_1485140)))))))))))))))) (let ((_let_2125 (forall ((BOUND_VARIABLE_1485080 tptp.complex) (BOUND_VARIABLE_1485081 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485081) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1485080) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7960 BOUND_VARIABLE_1485080) BOUND_VARIABLE_1485081)))))))))))))))) (let ((_let_2126 (forall ((BOUND_VARIABLE_1485020 tptp.complex) (BOUND_VARIABLE_1485021 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1485021) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7958 k_7957 BOUND_VARIABLE_1485020)) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7961 BOUND_VARIABLE_1485020) BOUND_VARIABLE_1485021)))))))))))))))) (let ((_let_2127 (forall ((BOUND_VARIABLE_1484971 tptp.real) (BOUND_VARIABLE_1484972 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484972) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484971) _let_6)) (ho_7508 (ho_7507 k_7962 BOUND_VARIABLE_1484971) BOUND_VARIABLE_1484972)))))))))))))) (let ((_let_2128 (forall ((BOUND_VARIABLE_1484921 tptp.real) (BOUND_VARIABLE_1484922 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484922) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 BOUND_VARIABLE_1484921)) _let_6)) (ho_7508 (ho_7507 k_7963 BOUND_VARIABLE_1484921) BOUND_VARIABLE_1484922)))))))))))))) (let ((_let_2129 (forall ((BOUND_VARIABLE_1484872 tptp.real) (BOUND_VARIABLE_1484873 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484873) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484872) _let_6)) (ho_7508 (ho_7507 k_7964 BOUND_VARIABLE_1484872) BOUND_VARIABLE_1484873)))))))))))))) (let ((_let_2130 (forall ((BOUND_VARIABLE_1484822 tptp.real) (BOUND_VARIABLE_1484823 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484823) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 BOUND_VARIABLE_1484822)) _let_6)) (ho_7508 (ho_7507 k_7965 BOUND_VARIABLE_1484822) BOUND_VARIABLE_1484823)))))))))))))) (let ((_let_2131 (forall ((BOUND_VARIABLE_1484775 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484775) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 _let_7) _let_6)) (ho_7508 k_7966 BOUND_VARIABLE_1484775)))))))))))))) (let ((_let_2132 (forall ((BOUND_VARIABLE_1484728 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484728) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 _let_7) _let_6)) (ho_7508 k_7967 BOUND_VARIABLE_1484728)))))))))))))) (let ((_let_2133 (forall ((BOUND_VARIABLE_1484669 tptp.complex) (BOUND_VARIABLE_1484670 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484670) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1484669) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7968 BOUND_VARIABLE_1484669) BOUND_VARIABLE_1484670)))))))))))))))) (let ((_let_2134 (forall ((BOUND_VARIABLE_1484609 tptp.complex) (BOUND_VARIABLE_1484610 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484610) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7958 k_7957 BOUND_VARIABLE_1484609)) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7969 BOUND_VARIABLE_1484609) BOUND_VARIABLE_1484610)))))))))))))))) (let ((_let_2135 (forall ((BOUND_VARIABLE_1484550 tptp.complex) (BOUND_VARIABLE_1484551 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484551) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1484550) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7970 BOUND_VARIABLE_1484550) BOUND_VARIABLE_1484551)))))))))))))))) (let ((_let_2136 (forall ((BOUND_VARIABLE_1484490 tptp.complex) (BOUND_VARIABLE_1484491 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484491) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7958 k_7957 BOUND_VARIABLE_1484490)) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7971 BOUND_VARIABLE_1484490) BOUND_VARIABLE_1484491)))))))))))))))) (let ((_let_2137 (forall ((BOUND_VARIABLE_1484441 tptp.real) (BOUND_VARIABLE_1484442 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484442) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484441) _let_6)) (ho_7508 (ho_7507 k_7972 BOUND_VARIABLE_1484441) BOUND_VARIABLE_1484442)))))))))))))) (let ((_let_2138 (forall ((BOUND_VARIABLE_1484391 tptp.real) (BOUND_VARIABLE_1484392 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484392) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 BOUND_VARIABLE_1484391)) _let_6)) (ho_7508 (ho_7507 k_7973 BOUND_VARIABLE_1484391) BOUND_VARIABLE_1484392)))))))))))))) (let ((_let_2139 (forall ((BOUND_VARIABLE_1484342 tptp.real) (BOUND_VARIABLE_1484343 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484343) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484342) _let_6)) (ho_7508 (ho_7507 k_7974 BOUND_VARIABLE_1484342) BOUND_VARIABLE_1484343)))))))))))))) (let ((_let_2140 (forall ((BOUND_VARIABLE_1484292 tptp.real) (BOUND_VARIABLE_1484293 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484293) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 BOUND_VARIABLE_1484292)) _let_6)) (ho_7508 (ho_7507 k_7975 BOUND_VARIABLE_1484292) BOUND_VARIABLE_1484293)))))))))))))) (let ((_let_2141 (forall ((BOUND_VARIABLE_1484237 tptp.real) (BOUND_VARIABLE_1484238 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7976 BOUND_VARIABLE_1484237) BOUND_VARIABLE_1484238) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1484238 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1484238) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1484238 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1484238) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484237) BOUND_VARIABLE_1484238))))))))))))))) (let ((_let_2142 (forall ((BOUND_VARIABLE_1484182 tptp.real) (BOUND_VARIABLE_1484183 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_7977 BOUND_VARIABLE_1484182) BOUND_VARIABLE_1484183) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1484183 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1484183) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1484183 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1484183) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484182) BOUND_VARIABLE_1484183))))))))))))))) (let ((_let_2143 (forall ((BOUND_VARIABLE_1484133 tptp.real) (BOUND_VARIABLE_1484134 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484134) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1484133) _let_6)) (ho_7508 (ho_7507 k_7978 BOUND_VARIABLE_1484133) BOUND_VARIABLE_1484134)))))))))))))) (let ((_let_2144 (forall ((BOUND_VARIABLE_1484083 tptp.real) (BOUND_VARIABLE_1484084 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484084) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 BOUND_VARIABLE_1484083)) _let_6)) (ho_7508 (ho_7507 k_7979 BOUND_VARIABLE_1484083) BOUND_VARIABLE_1484084)))))))))))))) (let ((_let_2145 (forall ((BOUND_VARIABLE_1484024 tptp.complex) (BOUND_VARIABLE_1484025 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1484025) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1484024) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7980 BOUND_VARIABLE_1484024) BOUND_VARIABLE_1484025)))))))))))))))) (let ((_let_2146 (forall ((BOUND_VARIABLE_1483964 tptp.complex) (BOUND_VARIABLE_1483965 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1483965) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7958 k_7957 BOUND_VARIABLE_1483964)) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7981 BOUND_VARIABLE_1483964) BOUND_VARIABLE_1483965)))))))))))))))) (let ((_let_2147 (forall ((BOUND_VARIABLE_1483905 tptp.complex) (BOUND_VARIABLE_1483906 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1483906) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483905) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7982 BOUND_VARIABLE_1483905) BOUND_VARIABLE_1483906)))))))))))))))) (let ((_let_2148 (forall ((BOUND_VARIABLE_1483845 tptp.complex) (BOUND_VARIABLE_1483846 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1483846) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7958 k_7957 BOUND_VARIABLE_1483845)) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_7983 BOUND_VARIABLE_1483845) BOUND_VARIABLE_1483846)))))))))))))))) (let ((_let_2149 (forall ((BOUND_VARIABLE_1483709 tptp.complex) (BOUND_VARIABLE_1483710 tptp.complex) (BOUND_VARIABLE_1483711 tptp.nat) (BOUND_VARIABLE_1483712 tptp.nat)) (let ((_let_1 (ho_7985 k_7984 tptp.one))) (let ((_let_2 (ho_7958 k_7957 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 _let_4 _let_3))) (let ((_let_6 (ho_7459 (ho_7461 k_7460 _let_3) _let_5))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1483711) _let_6)))) (let ((_let_9 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483710) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1483712) _let_6))))))) (let ((_let_10 (ho_7730 k_7729 _let_9))) (let ((_let_11 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483709) BOUND_VARIABLE_1483712))) (let ((_let_12 (ho_7510 k_7509 tptp.one))) (let ((_let_13 (ho_7463 k_7462 _let_3))) (let ((_let_14 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_15 (ho_7466 (ho_7465 k_7471 _let_13) _let_14))) (let ((_let_16 (ho_7519 k_7522 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7459 (ho_7461 k_7472 (ho_7927 (ho_7988 k_7987 _let_5) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1483711) _let_14))) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 k_7986 BOUND_VARIABLE_1483711) BOUND_VARIABLE_1483712)) _let_6)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1483711 _let_15)) _let_12) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_15) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_13) _let_6))))) _let_12)))))))) (let ((_let_17 (ho_7728 (ho_7732 k_7731 (ho_7516 _let_16 (ho_7730 k_7729 _let_11))) (ho_7516 _let_16 (ho_7730 k_7733 _let_11))))) (let ((_let_18 (ho_7519 k_7522 (ho_7730 k_7733 _let_17)))) (let ((_let_19 (ho_7730 k_7733 _let_9))) (let ((_let_20 (ho_7519 k_7522 (ho_7730 k_7729 _let_17)))) (= (ho_7736 (ho_7937 (ho_7936 (ho_7995 k_7994 BOUND_VARIABLE_1483709) BOUND_VARIABLE_1483710) BOUND_VARIABLE_1483711) BOUND_VARIABLE_1483712) (ho_7958 (ho_7993 (ho_7992 k_7991 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483711 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483712 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_10)) (ho_7516 k_7521 (ho_7516 _let_18 _let_19)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_19)) (ho_7516 _let_18 _let_10)))) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_1)) (ho_7730 k_7729 _let_2))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_1)) (ho_7730 k_7733 _let_2)))))))))))))))))))))))))))) (let ((_let_2150 (forall ((BOUND_VARIABLE_1483699 tptp.nat) (BOUND_VARIABLE_1483700 tptp.nat)) (= (ho_7541 (ho_7540 k_7996 BOUND_VARIABLE_1483699) BOUND_VARIABLE_1483700) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1483700)) (ho_7533 k_7532 BOUND_VARIABLE_1483699)))))) (let ((_let_2151 (forall ((BOUND_VARIABLE_1483601 tptp.real) (BOUND_VARIABLE_1483602 tptp.real) (BOUND_VARIABLE_1483603 tptp.nat) (BOUND_VARIABLE_1483604 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 _let_3 _let_2))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_2) _let_4))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1483603) _let_5)))) (let ((_let_8 (ho_7463 k_7462 _let_2))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_8) _let_9))) (= (ho_7508 (ho_7775 (ho_7999 (ho_7998 k_7997 BOUND_VARIABLE_1483601) BOUND_VARIABLE_1483602) BOUND_VARIABLE_1483603) BOUND_VARIABLE_1483604) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483603 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483604 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7459 (ho_7461 k_7472 (ho_7927 (ho_7988 k_7987 _let_4) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1483603) _let_9))) (ho_7459 (ho_7470 _let_6 (ho_7466 (ho_7465 k_7986 BOUND_VARIABLE_1483603) BOUND_VARIABLE_1483604)) _let_5)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1483603 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_7 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_8) _let_5))))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483601) BOUND_VARIABLE_1483604))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483602) (ho_7463 k_7462 (ho_7459 _let_7 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1483604) _let_5))))))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))))))))))))))) (let ((_let_2152 (forall ((BOUND_VARIABLE_1483591 tptp.nat) (BOUND_VARIABLE_1483592 tptp.nat)) (= (ho_7541 (ho_7540 k_8000 BOUND_VARIABLE_1483591) BOUND_VARIABLE_1483592) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1483592)) (ho_7533 k_7532 BOUND_VARIABLE_1483591)))))) (let ((_let_2153 (forall ((BOUND_VARIABLE_1483465 tptp.complex) (BOUND_VARIABLE_1483466 tptp.complex) (BOUND_VARIABLE_1483467 tptp.nat) (BOUND_VARIABLE_1483468 tptp.nat)) (let ((_let_1 (ho_7985 k_7984 tptp.one))) (let ((_let_2 (ho_7958 k_7957 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 _let_4 _let_3))) (let ((_let_6 (ho_7459 (ho_7461 k_7460 _let_3) _let_5))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1483467) _let_6)))) (let ((_let_9 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483466) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1483468) _let_6))))))) (let ((_let_10 (ho_7730 k_7729 _let_9))) (let ((_let_11 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483465) BOUND_VARIABLE_1483468))) (let ((_let_12 (ho_7510 k_7509 tptp.one))) (let ((_let_13 (ho_7463 k_7462 _let_3))) (let ((_let_14 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_15 (ho_7466 (ho_7465 k_7471 _let_13) _let_14))) (let ((_let_16 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7459 (ho_7461 k_7472 (ho_7927 (ho_7988 k_7987 _let_5) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1483467) _let_14))) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 k_7986 BOUND_VARIABLE_1483467) BOUND_VARIABLE_1483468)) _let_6)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1483467 _let_15)) _let_12) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_15) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_13) _let_6))))) _let_12))))))) (let ((_let_17 (ho_7728 (ho_7732 k_7731 (ho_7516 _let_16 (ho_7730 k_7729 _let_11))) (ho_7516 _let_16 (ho_7730 k_7733 _let_11))))) (let ((_let_18 (ho_7519 k_7522 (ho_7730 k_7733 _let_17)))) (let ((_let_19 (ho_7730 k_7733 _let_9))) (let ((_let_20 (ho_7519 k_7522 (ho_7730 k_7729 _let_17)))) (= (ho_7736 (ho_7937 (ho_7936 (ho_7995 k_8001 BOUND_VARIABLE_1483465) BOUND_VARIABLE_1483466) BOUND_VARIABLE_1483467) BOUND_VARIABLE_1483468) (ho_7958 (ho_7993 (ho_7992 k_7991 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483467 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_10)) (ho_7516 k_7521 (ho_7516 _let_18 _let_19)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_19)) (ho_7516 _let_18 _let_10)))) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_1)) (ho_7730 k_7729 _let_2))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_1)) (ho_7730 k_7733 _let_2)))))))))))))))))))))))))))) (let ((_let_2154 (forall ((BOUND_VARIABLE_1483455 tptp.nat) (BOUND_VARIABLE_1483456 tptp.nat)) (= (ho_7541 (ho_7540 k_8002 BOUND_VARIABLE_1483455) BOUND_VARIABLE_1483456) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1483456)) (ho_7533 k_7532 BOUND_VARIABLE_1483455)))))) (let ((_let_2155 (forall ((BOUND_VARIABLE_1483367 tptp.real) (BOUND_VARIABLE_1483368 tptp.real) (BOUND_VARIABLE_1483369 tptp.nat) (BOUND_VARIABLE_1483370 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 _let_3 _let_2))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_2) _let_4))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1483369) _let_5)))) (let ((_let_8 (ho_7463 k_7462 _let_2))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_8) _let_9))) (= (ho_7508 (ho_7775 (ho_7999 (ho_7998 k_8003 BOUND_VARIABLE_1483367) BOUND_VARIABLE_1483368) BOUND_VARIABLE_1483369) BOUND_VARIABLE_1483370) (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483369 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7459 (ho_7461 k_7472 (ho_7927 (ho_7988 k_7987 _let_4) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1483369) _let_9))) (ho_7459 (ho_7470 _let_6 (ho_7466 (ho_7465 k_7986 BOUND_VARIABLE_1483369) BOUND_VARIABLE_1483370)) _let_5)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1483369 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_7 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_8) _let_5))))) _let_1))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483367) BOUND_VARIABLE_1483370))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483368) (ho_7463 k_7462 (ho_7459 _let_7 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1483370) _let_5))))))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))))))))))))))) (let ((_let_2156 (forall ((BOUND_VARIABLE_1483357 tptp.nat) (BOUND_VARIABLE_1483358 tptp.nat)) (= (ho_7541 (ho_7540 k_8004 BOUND_VARIABLE_1483357) BOUND_VARIABLE_1483358) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1483358)) (ho_7533 k_7532 BOUND_VARIABLE_1483357)))))) (let ((_let_2157 (forall ((BOUND_VARIABLE_1483221 tptp.complex) (BOUND_VARIABLE_1483222 tptp.complex) (BOUND_VARIABLE_1483223 tptp.nat) (BOUND_VARIABLE_1483224 tptp.nat)) (let ((_let_1 (ho_7985 k_7984 tptp.one))) (let ((_let_2 (ho_7958 k_7957 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 _let_4 _let_3))) (let ((_let_6 (ho_7459 (ho_7461 k_7460 _let_3) _let_5))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1483223) _let_6)))) (let ((_let_9 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483222) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1483224) _let_6))))))) (let ((_let_10 (ho_7730 k_7729 _let_9))) (let ((_let_11 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1483221) BOUND_VARIABLE_1483224))) (let ((_let_12 (ho_7510 k_7509 tptp.one))) (let ((_let_13 (ho_7463 k_7462 _let_3))) (let ((_let_14 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_15 (ho_7466 (ho_7465 k_7471 _let_13) _let_14))) (let ((_let_16 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7459 (ho_7461 k_7472 (ho_7927 (ho_7988 k_7987 _let_5) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1483223) _let_14))) (ho_7459 (ho_7470 _let_7 (ho_7466 (ho_7465 k_7986 BOUND_VARIABLE_1483223) BOUND_VARIABLE_1483224)) _let_6)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1483223 _let_15)) _let_12) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_15) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_13) _let_6))))) _let_12))))))) (let ((_let_17 (ho_7728 (ho_7732 k_7731 (ho_7516 _let_16 (ho_7730 k_7729 _let_11))) (ho_7516 _let_16 (ho_7730 k_7733 _let_11))))) (let ((_let_18 (ho_7519 k_7522 (ho_7730 k_7733 _let_17)))) (let ((_let_19 (ho_7730 k_7733 _let_9))) (let ((_let_20 (ho_7519 k_7522 (ho_7730 k_7729 _let_17)))) (= (ho_7736 (ho_7937 (ho_7936 (ho_7995 k_8005 BOUND_VARIABLE_1483221) BOUND_VARIABLE_1483222) BOUND_VARIABLE_1483223) BOUND_VARIABLE_1483224) (ho_7958 (ho_7993 (ho_7992 k_7991 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483223 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))) (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483224 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))))) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_10)) (ho_7516 k_7521 (ho_7516 _let_18 _let_19)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_19)) (ho_7516 _let_18 _let_10)))) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_1)) (ho_7730 k_7729 _let_2))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_1)) (ho_7730 k_7733 _let_2)))))))))))))))))))))))))))) (let ((_let_2158 (forall ((BOUND_VARIABLE_1483211 tptp.nat) (BOUND_VARIABLE_1483212 tptp.nat)) (= (ho_7541 (ho_7540 k_8006 BOUND_VARIABLE_1483211) BOUND_VARIABLE_1483212) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1483212)) (ho_7533 k_7532 BOUND_VARIABLE_1483211)))))) (let ((_let_2159 (forall ((BOUND_VARIABLE_1483113 tptp.real) (BOUND_VARIABLE_1483114 tptp.real) (BOUND_VARIABLE_1483115 tptp.nat) (BOUND_VARIABLE_1483116 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 _let_3 _let_2))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_2) _let_4))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1483115) _let_5)))) (let ((_let_8 (ho_7463 k_7462 _let_2))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_8) _let_9))) (= (ho_7508 (ho_7775 (ho_7999 (ho_7998 k_8007 BOUND_VARIABLE_1483113) BOUND_VARIABLE_1483114) BOUND_VARIABLE_1483115) BOUND_VARIABLE_1483116) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483115 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))) (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1483116 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7459 (ho_7461 k_7472 (ho_7927 (ho_7988 k_7987 _let_4) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1483115) _let_9))) (ho_7459 (ho_7470 _let_6 (ho_7466 (ho_7465 k_7986 BOUND_VARIABLE_1483115) BOUND_VARIABLE_1483116)) _let_5)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1483115 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_7 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_8) _let_5))))) _let_1))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483113) BOUND_VARIABLE_1483116))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483114) (ho_7463 k_7462 (ho_7459 _let_7 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1483116) _let_5))))))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))))))))))))))) (let ((_let_2160 (forall ((BOUND_VARIABLE_1483103 tptp.nat) (BOUND_VARIABLE_1483104 tptp.nat)) (= (ho_7541 (ho_7540 k_8008 BOUND_VARIABLE_1483103) BOUND_VARIABLE_1483104) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1483104)) (ho_7533 k_7532 BOUND_VARIABLE_1483103)))))) (let ((_let_2161 (forall ((BOUND_VARIABLE_1526772 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1483061 tptp.real) (BOUND_VARIABLE_1483062 tptp.nat) (BOUND_VARIABLE_1483063 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1526772 BOUND_VARIABLE_1483063)) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1483061) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1483063) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1483062) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))))) (ho_7508 (ho_7775 (ho_7999 (ho_8010 k_8009 BOUND_VARIABLE_1526772) BOUND_VARIABLE_1483061) BOUND_VARIABLE_1483062) BOUND_VARIABLE_1483063))))))))) (let ((_let_2162 (forall ((BOUND_VARIABLE_1483009 tptp.nat) (BOUND_VARIABLE_1483010 tptp.nat) (BOUND_VARIABLE_1483011 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1483009) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1483010) _let_2)))))) (or (not (= BOUND_VARIABLE_1483011 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8011 BOUND_VARIABLE_1483009) BOUND_VARIABLE_1483010) BOUND_VARIABLE_1483011))))) (let ((_let_2163 (forall ((BOUND_VARIABLE_1526837 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1482967 tptp.int) (BOUND_VARIABLE_1482968 tptp.nat) (BOUND_VARIABLE_1482969 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7459 (ho_7461 k_7472 (ho_7927 BOUND_VARIABLE_1526837 BOUND_VARIABLE_1482969)) (ho_7927 (ho_7988 k_7987 BOUND_VARIABLE_1482967) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482969) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482968) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))))) (ho_7927 (ho_8015 (ho_8014 (ho_8013 k_8012 BOUND_VARIABLE_1526837) BOUND_VARIABLE_1482967) BOUND_VARIABLE_1482968) BOUND_VARIABLE_1482969))))))))) (let ((_let_2164 (forall ((BOUND_VARIABLE_1482915 tptp.nat) (BOUND_VARIABLE_1482916 tptp.nat) (BOUND_VARIABLE_1482917 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482915) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482916) _let_2)))))) (or (not (= BOUND_VARIABLE_1482917 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8016 BOUND_VARIABLE_1482915) BOUND_VARIABLE_1482916) BOUND_VARIABLE_1482917))))) (let ((_let_2165 (forall ((BOUND_VARIABLE_1526912 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1482872 tptp.rat) (BOUND_VARIABLE_1482873 tptp.nat) (BOUND_VARIABLE_1482874 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1526912 BOUND_VARIABLE_1482874)) (ho_7636 (ho_8018 k_8017 BOUND_VARIABLE_1482872) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482874) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482873) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))))) (ho_7636 (ho_8023 (ho_8022 (ho_8021 k_8020 BOUND_VARIABLE_1526912) BOUND_VARIABLE_1482872) BOUND_VARIABLE_1482873) BOUND_VARIABLE_1482874))))))))) (let ((_let_2166 (forall ((BOUND_VARIABLE_1482820 tptp.nat) (BOUND_VARIABLE_1482821 tptp.nat) (BOUND_VARIABLE_1482822 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482820) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482821) _let_2)))))) (or (not (= BOUND_VARIABLE_1482822 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8024 BOUND_VARIABLE_1482820) BOUND_VARIABLE_1482821) BOUND_VARIABLE_1482822))))) (let ((_let_2167 (forall ((BOUND_VARIABLE_1526986 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1482751 tptp.complex) (BOUND_VARIABLE_1482752 tptp.nat) (BOUND_VARIABLE_1482753 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1482751) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482753) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482752) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3))))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7736 BOUND_VARIABLE_1526986 BOUND_VARIABLE_1482753))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7733 _let_7)))) (let ((_let_9 (ho_7730 k_7733 _let_5))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7729 _let_7)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_6)) (ho_7516 k_7521 (ho_7516 _let_8 _let_9)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_9)) (ho_7516 _let_8 _let_6))) (ho_7736 (ho_7937 (ho_7936 (ho_8026 k_8025 BOUND_VARIABLE_1526986) BOUND_VARIABLE_1482751) BOUND_VARIABLE_1482752) BOUND_VARIABLE_1482753))))))))))))))) (let ((_let_2168 (forall ((BOUND_VARIABLE_1482699 tptp.nat) (BOUND_VARIABLE_1482700 tptp.nat) (BOUND_VARIABLE_1482701 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482699) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482700) _let_2)))))) (or (not (= BOUND_VARIABLE_1482701 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8027 BOUND_VARIABLE_1482699) BOUND_VARIABLE_1482700) BOUND_VARIABLE_1482701))))) (let ((_let_2169 (forall ((BOUND_VARIABLE_1482656 tptp.complex) (BOUND_VARIABLE_1482657 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1482656) BOUND_VARIABLE_1482657))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7466 (ho_7465 k_7471 _let_6) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_9 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1482657 _let_8)) _let_2) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_8) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1482657) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_2)))))) (= (ho_7736 (ho_7735 k_8028 BOUND_VARIABLE_1482656) BOUND_VARIABLE_1482657) (ho_7728 (ho_7732 k_7731 (ho_7516 _let_9 (ho_7730 k_7729 _let_1))) (ho_7516 _let_9 (ho_7730 k_7733 _let_1)))))))))))))))) (let ((_let_2170 (forall ((BOUND_VARIABLE_1482646 tptp.nat) (BOUND_VARIABLE_1482647 tptp.nat)) (= (ho_7541 (ho_7540 k_8029 BOUND_VARIABLE_1482646) BOUND_VARIABLE_1482647) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1482647)) (ho_7533 k_7532 BOUND_VARIABLE_1482646)))))) (let ((_let_2171 (forall ((BOUND_VARIABLE_1482582 tptp.complex) (BOUND_VARIABLE_1482583 tptp.nat) (BOUND_VARIABLE_1482584 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482584) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482583) _let_3))))) (let ((_let_6 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1482582) _let_5))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_10 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_5)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 _let_8) _let_3))))) _let_7)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_10 (ho_7730 k_7729 _let_6))) (ho_7516 _let_10 (ho_7730 k_7733 _let_6))) (ho_7736 (ho_7937 (ho_7936 k_8030 BOUND_VARIABLE_1482582) BOUND_VARIABLE_1482583) BOUND_VARIABLE_1482584))))))))))))))) (let ((_let_2172 (forall ((BOUND_VARIABLE_1482547 tptp.real) (BOUND_VARIABLE_1482548 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 k_8031 BOUND_VARIABLE_1482547) BOUND_VARIABLE_1482548) (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1482548 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1482548) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1482547) BOUND_VARIABLE_1482548))))))))))))) (let ((_let_2173 (forall ((BOUND_VARIABLE_1482537 tptp.nat) (BOUND_VARIABLE_1482538 tptp.nat)) (= (ho_7541 (ho_7540 k_8032 BOUND_VARIABLE_1482537) BOUND_VARIABLE_1482538) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1482538)) (ho_7533 k_7532 BOUND_VARIABLE_1482537)))))) (let ((_let_2174 (forall ((BOUND_VARIABLE_1482483 tptp.real) (BOUND_VARIABLE_1482484 tptp.nat) (BOUND_VARIABLE_1482485 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482485) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482484) _let_3))))) (let ((_let_6 (ho_7510 k_7509 tptp.one))) (let ((_let_7 (ho_7463 k_7462 _let_1))) (let ((_let_8 (ho_7466 (ho_7465 k_7471 _let_7) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_8 _let_5)) _let_6) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_8) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 _let_7) _let_3))))) _let_6)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1482483) _let_5)) (ho_7508 (ho_7775 (ho_7999 k_8033 BOUND_VARIABLE_1482483) BOUND_VARIABLE_1482484) BOUND_VARIABLE_1482485))))))))))))) (let ((_let_2175 (forall ((BOUND_VARIABLE_1527208 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1482435 tptp.real) (BOUND_VARIABLE_1482436 tptp.real) (BOUND_VARIABLE_1482437 tptp.nat) (BOUND_VARIABLE_1482438 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1527208 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482437) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1482438) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1482435) BOUND_VARIABLE_1482438))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1482436) BOUND_VARIABLE_1482437)) (ho_7508 (ho_7775 (ho_7999 (ho_7998 (ho_8035 k_8034 BOUND_VARIABLE_1527208) BOUND_VARIABLE_1482435) BOUND_VARIABLE_1482436) BOUND_VARIABLE_1482437) BOUND_VARIABLE_1482438)))))))) (let ((_let_2176 (forall ((BOUND_VARIABLE_1482403 tptp.nat) (BOUND_VARIABLE_1482404 tptp.nat) (BOUND_VARIABLE_1482405 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1482405)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482403) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482404) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8036 BOUND_VARIABLE_1482403) BOUND_VARIABLE_1482404) BOUND_VARIABLE_1482405))))))))) (let ((_let_2177 (forall ((BOUND_VARIABLE_1527269 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1482355 tptp.int) (BOUND_VARIABLE_1482356 tptp.int) (BOUND_VARIABLE_1482357 tptp.nat) (BOUND_VARIABLE_1482358 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7472 (ho_7927 BOUND_VARIABLE_1527269 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 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BOUND_VARIABLE_1482325)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482323) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482324) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8040 BOUND_VARIABLE_1482323) BOUND_VARIABLE_1482324) BOUND_VARIABLE_1482325))))))))) (let ((_let_2179 (forall ((BOUND_VARIABLE_1527333 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1482275 tptp.rat) (BOUND_VARIABLE_1482276 tptp.rat) (BOUND_VARIABLE_1482277 tptp.nat) (BOUND_VARIABLE_1482278 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019))) (= (ho_7711 (ho_7717 _let_4 (ho_7711 (ho_7717 _let_4 (ho_7636 BOUND_VARIABLE_1527333 (ho_7463 k_7462 (ho_7459 (ho_7461 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(ho_7533 k_7532 BOUND_VARIABLE_1482245)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482243) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482244) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8044 BOUND_VARIABLE_1482243) BOUND_VARIABLE_1482244) BOUND_VARIABLE_1482245))))))))) (let ((_let_2181 (forall ((BOUND_VARIABLE_1527399 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1482139 tptp.complex) (BOUND_VARIABLE_1482140 tptp.complex) (BOUND_VARIABLE_1482141 tptp.nat) (BOUND_VARIABLE_1482142 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1482140) BOUND_VARIABLE_1482141))) (let ((_let_2 (ho_7730 k_7729 _let_1))) (let ((_let_3 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1482139) BOUND_VARIABLE_1482142))) (let ((_let_4 (ho_7730 k_7729 _let_3))) (let ((_let_5 (ho_7446 k_7445 tptp.one))) (let ((_let_6 (ho_7459 (ho_7461 k_7460 _let_5) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_5)))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7736 BOUND_VARIABLE_1527399 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1482141) _let_6)) (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1482142) _let_6)))) _let_6)) (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 _let_5)) _let_6)))))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7733 _let_8)))) (let ((_let_10 (ho_7730 k_7733 _let_3))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7729 _let_8)))) (let ((_let_12 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_11 _let_4)) (ho_7516 k_7521 (ho_7516 _let_9 _let_10)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_11 _let_10)) (ho_7516 _let_9 _let_4))))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7733 _let_12)))) (let ((_let_14 (ho_7730 k_7733 _let_1))) (let ((_let_15 (ho_7519 k_7522 (ho_7730 k_7729 _let_12)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_15 _let_2)) (ho_7516 k_7521 (ho_7516 _let_13 _let_14)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_15 _let_14)) (ho_7516 _let_13 _let_2))) (ho_7736 (ho_7937 (ho_7936 (ho_7995 (ho_8046 k_8045 BOUND_VARIABLE_1527399) BOUND_VARIABLE_1482139) BOUND_VARIABLE_1482140) BOUND_VARIABLE_1482141) BOUND_VARIABLE_1482142)))))))))))))))))))) (let ((_let_2182 (forall ((BOUND_VARIABLE_1482107 tptp.nat) (BOUND_VARIABLE_1482108 tptp.nat) (BOUND_VARIABLE_1482109 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1482109)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482107) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1482108) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8047 BOUND_VARIABLE_1482107) BOUND_VARIABLE_1482108) BOUND_VARIABLE_1482109))))))))) (let ((_let_2183 (forall ((BOUND_VARIABLE_1482075 tptp.nat) (BOUND_VARIABLE_1482076 tptp.real) (BOUND_VARIABLE_1482077 tptp.nat) (BOUND_VARIABLE_1482078 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1482075) _let_2)) BOUND_VARIABLE_1482076))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1482077) _let_2))) BOUND_VARIABLE_1482078) (ho_7516 (ho_7512 (ho_8050 (ho_8049 k_8048 BOUND_VARIABLE_1482075) BOUND_VARIABLE_1482076) BOUND_VARIABLE_1482077) BOUND_VARIABLE_1482078)))))))) (let ((_let_2184 (forall ((BOUND_VARIABLE_1482039 tptp.nat) (BOUND_VARIABLE_1482040 tptp.real) (BOUND_VARIABLE_1482041 tptp.nat) (BOUND_VARIABLE_1482042 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7512 _let_4 BOUND_VARIABLE_1482039) _let_3)) BOUND_VARIABLE_1482040)) _let_2))) (ho_7516 (ho_7512 _let_4 BOUND_VARIABLE_1482041) _let_3))) BOUND_VARIABLE_1482042) (ho_7516 (ho_7512 (ho_8050 (ho_8049 k_8051 BOUND_VARIABLE_1482039) BOUND_VARIABLE_1482040) BOUND_VARIABLE_1482041) BOUND_VARIABLE_1482042))))))))) (let ((_let_2185 (forall ((BOUND_VARIABLE_1482007 tptp.nat) (BOUND_VARIABLE_1482008 tptp.rat) (BOUND_VARIABLE_1482009 tptp.nat) (BOUND_VARIABLE_1482010 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))) (let ((_let_9 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 (ho_7711 (ho_7717 _let_7 (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1482007) _let_8)) BOUND_VARIABLE_1482008))) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1482009) _let_8))) BOUND_VARIABLE_1482010) (ho_7711 (ho_8055 (ho_8058 (ho_8057 k_8056 BOUND_VARIABLE_1482007) BOUND_VARIABLE_1482008) BOUND_VARIABLE_1482009) BOUND_VARIABLE_1482010)))))))))))))) (let ((_let_2186 (forall ((BOUND_VARIABLE_1481971 tptp.nat) (BOUND_VARIABLE_1481972 tptp.rat) (BOUND_VARIABLE_1481973 tptp.nat) (BOUND_VARIABLE_1481974 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7711 _let_5 _let_3))) (let ((_let_7 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_8 (ho_7716 _let_7 k_7712))) (let ((_let_9 (ho_7711 (ho_7717 _let_8 _let_3) _let_6))) (let ((_let_10 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_7 k_8019) (ho_7711 (ho_7717 _let_8 (ho_7711 _let_5 (ho_7711 (ho_7717 _let_8 (ho_7711 (ho_7717 _let_8 (ho_7711 (ho_8055 _let_10 BOUND_VARIABLE_1481971) _let_9)) BOUND_VARIABLE_1481972)) _let_6))) (ho_7711 (ho_8055 _let_10 BOUND_VARIABLE_1481973) _let_9))) BOUND_VARIABLE_1481974) (ho_7711 (ho_8055 (ho_8058 (ho_8057 k_8059 BOUND_VARIABLE_1481971) BOUND_VARIABLE_1481972) BOUND_VARIABLE_1481973) BOUND_VARIABLE_1481974))))))))))))))) (let ((_let_2187 (forall ((BOUND_VARIABLE_1481881 tptp.nat) (BOUND_VARIABLE_1481882 tptp.complex) (BOUND_VARIABLE_1481883 tptp.nat) (BOUND_VARIABLE_1481884 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1481884))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3))))) (let ((_let_5 (ho_8062 k_8061 k_8060))) (let ((_let_6 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1481883) _let_4))) (let ((_let_7 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1481881) _let_4))) (let ((_let_8 (ho_7958 k_7957 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_7)) (ho_7730 k_7729 BOUND_VARIABLE_1481882))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_7)) (ho_7730 k_7733 BOUND_VARIABLE_1481882)))))) (let ((_let_9 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_8)) (ho_7730 k_7729 _let_6))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_8)) (ho_7730 k_7733 _let_6))))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7733 _let_9)))) (let ((_let_11 (ho_7730 k_7733 BOUND_VARIABLE_1481884))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7729 _let_9)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_12 _let_1)) (ho_7516 k_7521 (ho_7516 _let_10 _let_11)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_12 _let_11)) (ho_7516 _let_10 _let_1))) (ho_7958 (ho_8063 (ho_8066 (ho_8065 k_8064 BOUND_VARIABLE_1481881) BOUND_VARIABLE_1481882) BOUND_VARIABLE_1481883) BOUND_VARIABLE_1481884))))))))))))))))) (let ((_let_2188 (forall ((BOUND_VARIABLE_1481775 tptp.nat) (BOUND_VARIABLE_1481776 tptp.complex) (BOUND_VARIABLE_1481777 tptp.nat) (BOUND_VARIABLE_1481778 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1481778))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7730 k_7733 _let_3))) (let ((_let_5 (ho_7730 k_7729 _let_3))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) _let_5)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) _let_4)))) (let ((_let_7 (ho_8062 k_8061 k_8060))) (let ((_let_8 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1481777) _let_6))) (let ((_let_9 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1481775) _let_6))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_9)) (ho_7730 k_7729 BOUND_VARIABLE_1481776))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_9)) (ho_7730 k_7733 BOUND_VARIABLE_1481776))))) (let ((_let_11 (ho_7958 k_7957 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_10)) _let_5)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_10)) _let_4))))) (let ((_let_12 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_11)) (ho_7730 k_7729 _let_8))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_11)) (ho_7730 k_7733 _let_8))))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7733 _let_12)))) (let ((_let_14 (ho_7730 k_7733 BOUND_VARIABLE_1481778))) (let ((_let_15 (ho_7519 k_7522 (ho_7730 k_7729 _let_12)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_15 _let_1)) (ho_7516 k_7521 (ho_7516 _let_13 _let_14)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_15 _let_14)) (ho_7516 _let_13 _let_1))) (ho_7958 (ho_8063 (ho_8066 (ho_8065 k_8067 BOUND_VARIABLE_1481775) BOUND_VARIABLE_1481776) BOUND_VARIABLE_1481777) BOUND_VARIABLE_1481778)))))))))))))))))))) (let ((_let_2189 (forall ((BOUND_VARIABLE_1481733 tptp.nat) (BOUND_VARIABLE_1481734 tptp.nat) (BOUND_VARIABLE_1481735 tptp.nat) (BOUND_VARIABLE_1481736 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (let ((_let_4 (ho_7446 k_7445 tptp.one))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_4)))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7512 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1481733) _let_5)) (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1481734) _let_5)))) _let_2))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1481735) _let_2))) BOUND_VARIABLE_1481736) (ho_7516 (ho_7512 (ho_7515 (ho_8069 k_8068 BOUND_VARIABLE_1481733) BOUND_VARIABLE_1481734) BOUND_VARIABLE_1481735) BOUND_VARIABLE_1481736))))))))))) (let ((_let_2190 (forall ((BOUND_VARIABLE_1481691 tptp.nat) (BOUND_VARIABLE_1481692 tptp.nat) (BOUND_VARIABLE_1481693 tptp.nat) (BOUND_VARIABLE_1481694 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))) (let ((_let_9 (ho_8054 k_8053 k_8052))) (let ((_let_10 (ho_7469 k_7468 k_7467))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 (ho_7711 (ho_8055 _let_9 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_10 BOUND_VARIABLE_1481691) _let_2)) (ho_7459 (ho_7470 _let_10 BOUND_VARIABLE_1481692) _let_2)))) _let_8))) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1481693) _let_8))) BOUND_VARIABLE_1481694) (ho_7711 (ho_8055 (ho_8072 (ho_8071 k_8070 BOUND_VARIABLE_1481691) BOUND_VARIABLE_1481692) BOUND_VARIABLE_1481693) BOUND_VARIABLE_1481694))))))))))))))) (let ((_let_2191 (forall ((BOUND_VARIABLE_1481605 tptp.nat) (BOUND_VARIABLE_1481606 tptp.nat) (BOUND_VARIABLE_1481607 tptp.nat) (BOUND_VARIABLE_1481608 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1481608))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3))))) (let ((_let_5 (ho_8062 k_8061 k_8060))) (let ((_let_6 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1481607) _let_4))) (let ((_let_7 (ho_7446 k_7445 tptp.one))) (let ((_let_8 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_7)))) (let ((_let_9 (ho_7469 k_7468 k_7467))) (let ((_let_10 (ho_7958 k_7957 (ho_7958 (ho_8063 _let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_9 BOUND_VARIABLE_1481605) _let_8)) (ho_7459 (ho_7470 _let_9 BOUND_VARIABLE_1481606) _let_8)))) _let_4)))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_10)) (ho_7730 k_7729 _let_6))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_10)) (ho_7730 k_7733 _let_6))))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7733 _let_11)))) (let ((_let_13 (ho_7730 k_7733 BOUND_VARIABLE_1481608))) (let ((_let_14 (ho_7519 k_7522 (ho_7730 k_7729 _let_11)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_1)) (ho_7516 k_7521 (ho_7516 _let_12 _let_13)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_13)) (ho_7516 _let_12 _let_1))) (ho_7958 (ho_8063 (ho_8075 (ho_8074 k_8073 BOUND_VARIABLE_1481605) BOUND_VARIABLE_1481606) BOUND_VARIABLE_1481607) BOUND_VARIABLE_1481608))))))))))))))))))) (let ((_let_2192 (forall ((BOUND_VARIABLE_1481548 tptp.complex) (BOUND_VARIABLE_1481549 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (let ((_let_6 (ho_7459 (ho_7470 _let_4 _let_5) _let_3))) (let ((_let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_6) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481549) _let_3))))) (let ((_let_8 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1481548) _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_7)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_7) _let_3)) (ho_7459 _let_2 _let_6)))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_8))) (ho_7516 _let_11 (ho_7730 k_7733 _let_8))) (ho_7736 (ho_7735 k_8076 BOUND_VARIABLE_1481548) BOUND_VARIABLE_1481549)))))))))))))))) (let ((_let_2193 (forall ((BOUND_VARIABLE_1481501 tptp.real) (BOUND_VARIABLE_1481502 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (let ((_let_6 (ho_7459 (ho_7470 _let_4 _let_5) _let_3))) (let ((_let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_6) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481502) _let_3))))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_7)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_7) _let_3)) (ho_7459 _let_2 _let_6)))) _let_8)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1481501) _let_7)) (ho_7508 (ho_7507 k_8077 BOUND_VARIABLE_1481501) BOUND_VARIABLE_1481502)))))))))))))) (let ((_let_2194 (forall ((BOUND_VARIABLE_1481469 tptp.nat) (BOUND_VARIABLE_1481470 tptp.real) (BOUND_VARIABLE_1481471 tptp.nat) (BOUND_VARIABLE_1481472 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1481469) _let_2)) BOUND_VARIABLE_1481470))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1481471) _let_2))) BOUND_VARIABLE_1481472) (ho_7516 (ho_7512 (ho_8050 (ho_8049 k_8078 BOUND_VARIABLE_1481469) BOUND_VARIABLE_1481470) BOUND_VARIABLE_1481471) BOUND_VARIABLE_1481472)))))))) (let ((_let_2195 (forall ((BOUND_VARIABLE_1481447 tptp.real) (BOUND_VARIABLE_1481448 tptp.nat) (BOUND_VARIABLE_1481449 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 k_7521 BOUND_VARIABLE_1481447))) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1481448) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1481449) (ho_7516 (ho_7512 (ho_8050 k_8079 BOUND_VARIABLE_1481447) BOUND_VARIABLE_1481448) BOUND_VARIABLE_1481449)))))) (let ((_let_2196 (forall ((BOUND_VARIABLE_1481415 tptp.nat) (BOUND_VARIABLE_1481416 tptp.rat) (BOUND_VARIABLE_1481417 tptp.nat) (BOUND_VARIABLE_1481418 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))) (let ((_let_9 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 (ho_7711 (ho_7717 _let_7 (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1481415) _let_8)) BOUND_VARIABLE_1481416))) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1481417) _let_8))) BOUND_VARIABLE_1481418) (ho_7711 (ho_8055 (ho_8058 (ho_8057 k_8080 BOUND_VARIABLE_1481415) BOUND_VARIABLE_1481416) BOUND_VARIABLE_1481417) BOUND_VARIABLE_1481418)))))))))))))) (let ((_let_2197 (forall ((BOUND_VARIABLE_1481390 tptp.rat) (BOUND_VARIABLE_1481391 tptp.nat) (BOUND_VARIABLE_1481392 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 (ho_7711 _let_5 BOUND_VARIABLE_1481390))) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1481391) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3))))) BOUND_VARIABLE_1481392) (ho_7711 (ho_8055 (ho_8058 k_8081 BOUND_VARIABLE_1481390) BOUND_VARIABLE_1481391) BOUND_VARIABLE_1481392)))))))))))) (let ((_let_2198 (forall ((BOUND_VARIABLE_1481300 tptp.nat) (BOUND_VARIABLE_1481301 tptp.complex) (BOUND_VARIABLE_1481302 tptp.nat) (BOUND_VARIABLE_1481303 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1481303))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3))))) (let ((_let_5 (ho_8062 k_8061 k_8060))) (let ((_let_6 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1481302) _let_4))) (let ((_let_7 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1481300) _let_4))) (let ((_let_8 (ho_7958 k_7957 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_7)) (ho_7730 k_7729 BOUND_VARIABLE_1481301))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_7)) (ho_7730 k_7733 BOUND_VARIABLE_1481301)))))) (let ((_let_9 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_8)) (ho_7730 k_7729 _let_6))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_8)) (ho_7730 k_7733 _let_6))))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7733 _let_9)))) (let ((_let_11 (ho_7730 k_7733 BOUND_VARIABLE_1481303))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7729 _let_9)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_12 _let_1)) (ho_7516 k_7521 (ho_7516 _let_10 _let_11)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_12 _let_11)) (ho_7516 _let_10 _let_1))) (ho_7958 (ho_8063 (ho_8066 (ho_8065 k_8082 BOUND_VARIABLE_1481300) BOUND_VARIABLE_1481301) BOUND_VARIABLE_1481302) BOUND_VARIABLE_1481303))))))))))))))))) (let ((_let_2199 (forall ((BOUND_VARIABLE_1481237 tptp.complex) (BOUND_VARIABLE_1481238 tptp.nat) (BOUND_VARIABLE_1481239 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1481239))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1481238) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3)))))) (let ((_let_5 (ho_7958 k_7957 (ho_7958 k_7957 BOUND_VARIABLE_1481237)))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_5)) (ho_7730 k_7729 _let_4))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_5)) (ho_7730 k_7733 _let_4))))) (let ((_let_7 (ho_7519 k_7522 (ho_7730 k_7733 _let_6)))) (let ((_let_8 (ho_7730 k_7733 BOUND_VARIABLE_1481239))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7729 _let_6)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_1)) (ho_7516 k_7521 (ho_7516 _let_7 _let_8)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_8)) (ho_7516 _let_7 _let_1))) (ho_7958 (ho_8063 (ho_8066 k_8083 BOUND_VARIABLE_1481237) BOUND_VARIABLE_1481238) BOUND_VARIABLE_1481239)))))))))))))) (let ((_let_2200 (forall ((BOUND_VARIABLE_1528075 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1528073 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1481207 tptp.nat) (BOUND_VARIABLE_1481208 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1528075 BOUND_VARIABLE_1481208)) (ho_7508 BOUND_VARIABLE_1528073 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481207) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481208) _let_3)))))) (ho_7508 (ho_7775 (ho_7774 (ho_8085 k_8084 BOUND_VARIABLE_1528075) BOUND_VARIABLE_1528073) BOUND_VARIABLE_1481207) BOUND_VARIABLE_1481208))))))))) (let ((_let_2201 (forall ((BOUND_VARIABLE_1481195 tptp.nat) (BOUND_VARIABLE_1481196 tptp.nat)) (= (ho_7541 (ho_7540 k_8086 BOUND_VARIABLE_1481195) BOUND_VARIABLE_1481196) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1481196)) (ho_7533 k_7532 BOUND_VARIABLE_1481195)))))) (let ((_let_2202 (forall ((BOUND_VARIABLE_1528117 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1528114 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1481138 tptp.nat) (BOUND_VARIABLE_1481139 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7736 BOUND_VARIABLE_1528114 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481138) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481139) _let_3))))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7736 BOUND_VARIABLE_1528117 BOUND_VARIABLE_1481139))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7733 _let_7)))) (let ((_let_9 (ho_7730 k_7733 _let_5))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7729 _let_7)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_6)) (ho_7516 k_7521 (ho_7516 _let_8 _let_9)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_9)) (ho_7516 _let_8 _let_6))) (ho_7736 (ho_7937 (ho_8089 (ho_8088 k_8087 BOUND_VARIABLE_1528117) BOUND_VARIABLE_1528114) BOUND_VARIABLE_1481138) BOUND_VARIABLE_1481139))))))))))))))) (let ((_let_2203 (forall ((BOUND_VARIABLE_1481126 tptp.nat) (BOUND_VARIABLE_1481127 tptp.nat)) (= (ho_7541 (ho_7540 k_8090 BOUND_VARIABLE_1481126) BOUND_VARIABLE_1481127) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1481127)) (ho_7533 k_7532 BOUND_VARIABLE_1481126)))))) (let ((_let_2204 (forall ((BOUND_VARIABLE_1528178 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1528174 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1481085 tptp.nat) (BOUND_VARIABLE_1481086 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_4 (ho_7466 BOUND_VARIABLE_1528178 BOUND_VARIABLE_1481086)) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7466 BOUND_VARIABLE_1528174 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481085) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1481086) _let_3)))))) _let_3))) (ho_7466 (ho_7465 (ho_8093 (ho_8092 k_8091 BOUND_VARIABLE_1528178) BOUND_VARIABLE_1528174) BOUND_VARIABLE_1481085) BOUND_VARIABLE_1481086))))))))) (let ((_let_2205 (forall ((BOUND_VARIABLE_1481073 tptp.nat) (BOUND_VARIABLE_1481074 tptp.nat)) (= (ho_7541 (ho_7540 k_8094 BOUND_VARIABLE_1481073) BOUND_VARIABLE_1481074) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1481074)) (ho_7533 k_7532 BOUND_VARIABLE_1481073)))))) (let ((_let_2206 (forall ((BOUND_VARIABLE_1481053 tptp.real) (BOUND_VARIABLE_1481054 tptp.nat) (BOUND_VARIABLE_1481055 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1481053) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1481054) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1481055) (ho_7516 (ho_7512 (ho_8050 k_8095 BOUND_VARIABLE_1481053) BOUND_VARIABLE_1481054) BOUND_VARIABLE_1481055)))))) (let ((_let_2207 (forall ((BOUND_VARIABLE_1481033 tptp.real) (BOUND_VARIABLE_1481034 tptp.nat) (BOUND_VARIABLE_1481035 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1481033) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1481034) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1481035) (ho_7516 (ho_7512 (ho_8050 k_8096 BOUND_VARIABLE_1481033) BOUND_VARIABLE_1481034) BOUND_VARIABLE_1481035)))))) (let ((_let_2208 (forall ((BOUND_VARIABLE_1481012 tptp.rat) (BOUND_VARIABLE_1481013 tptp.nat) (BOUND_VARIABLE_1481014 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_6 (ho_7716 _let_5 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_5 k_8019) (ho_7711 (ho_7717 _let_6 BOUND_VARIABLE_1481012) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1481013) (ho_7711 (ho_7717 _let_6 _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3))))) BOUND_VARIABLE_1481014) (ho_7711 (ho_8055 (ho_8058 k_8097 BOUND_VARIABLE_1481012) BOUND_VARIABLE_1481013) BOUND_VARIABLE_1481014))))))))))) (let ((_let_2209 (forall ((BOUND_VARIABLE_1480991 tptp.rat) (BOUND_VARIABLE_1480992 tptp.nat) (BOUND_VARIABLE_1480993 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_6 (ho_7716 _let_5 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_5 k_8019) (ho_7711 (ho_7717 _let_6 BOUND_VARIABLE_1480991) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1480992) (ho_7711 (ho_7717 _let_6 _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3))))) BOUND_VARIABLE_1480993) (ho_7711 (ho_8055 (ho_8058 k_8098 BOUND_VARIABLE_1480991) BOUND_VARIABLE_1480992) BOUND_VARIABLE_1480993))))))))))) (let ((_let_2210 (forall ((BOUND_VARIABLE_1480971 tptp.int) (BOUND_VARIABLE_1480972 tptp.nat) (BOUND_VARIABLE_1480973 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1480971) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) BOUND_VARIABLE_1480972) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1))))) BOUND_VARIABLE_1480973) (ho_7459 (ho_7470 (ho_8100 k_8099 BOUND_VARIABLE_1480971) BOUND_VARIABLE_1480972) BOUND_VARIABLE_1480973)))))) (let ((_let_2211 (forall ((BOUND_VARIABLE_1480951 tptp.int) (BOUND_VARIABLE_1480952 tptp.nat) (BOUND_VARIABLE_1480953 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1480951) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) BOUND_VARIABLE_1480952) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1))))) BOUND_VARIABLE_1480953) (ho_7459 (ho_7470 (ho_8100 k_8101 BOUND_VARIABLE_1480951) BOUND_VARIABLE_1480952) BOUND_VARIABLE_1480953)))))) (let ((_let_2212 (forall ((BOUND_VARIABLE_1480930 tptp.real) (BOUND_VARIABLE_1480931 tptp.nat) (BOUND_VARIABLE_1480932 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 BOUND_VARIABLE_1480930)) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1480931) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1480932) (ho_7516 (ho_7512 (ho_8050 k_8102 BOUND_VARIABLE_1480930) BOUND_VARIABLE_1480931) BOUND_VARIABLE_1480932)))))) (let ((_let_2213 (forall ((BOUND_VARIABLE_1480907 tptp.rat) (BOUND_VARIABLE_1480908 tptp.nat) (BOUND_VARIABLE_1480909 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 BOUND_VARIABLE_1480907)) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1480908) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3))))) BOUND_VARIABLE_1480909) (ho_7711 (ho_8055 (ho_8058 k_8103 BOUND_VARIABLE_1480907) BOUND_VARIABLE_1480908) BOUND_VARIABLE_1480909)))))))))))) (let ((_let_2214 (forall ((BOUND_VARIABLE_1480845 tptp.complex) (BOUND_VARIABLE_1480846 tptp.nat) (BOUND_VARIABLE_1480847 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1480847))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1480846) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3)))))) (let ((_let_5 (ho_7958 k_7957 BOUND_VARIABLE_1480845))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_5)) (ho_7730 k_7729 _let_4))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_5)) (ho_7730 k_7733 _let_4))))) (let ((_let_7 (ho_7519 k_7522 (ho_7730 k_7733 _let_6)))) (let ((_let_8 (ho_7730 k_7733 BOUND_VARIABLE_1480847))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7729 _let_6)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_1)) (ho_7516 k_7521 (ho_7516 _let_7 _let_8)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_8)) (ho_7516 _let_7 _let_1))) (ho_7958 (ho_8063 (ho_8066 k_8104 BOUND_VARIABLE_1480845) BOUND_VARIABLE_1480846) BOUND_VARIABLE_1480847)))))))))))))) (let ((_let_2215 (forall ((BOUND_VARIABLE_1528390 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1528388 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1480815 tptp.nat) (BOUND_VARIABLE_1480816 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1528390 BOUND_VARIABLE_1480816)) (ho_7508 BOUND_VARIABLE_1528388 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480815) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480816) _let_3)))))) (ho_7508 (ho_7775 (ho_7774 (ho_8085 k_8105 BOUND_VARIABLE_1528390) BOUND_VARIABLE_1528388) BOUND_VARIABLE_1480815) BOUND_VARIABLE_1480816))))))))) (let ((_let_2216 (forall ((BOUND_VARIABLE_1480803 tptp.nat) (BOUND_VARIABLE_1480804 tptp.nat)) (= (ho_7541 (ho_7540 k_8106 BOUND_VARIABLE_1480803) BOUND_VARIABLE_1480804) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480804)) (ho_7533 k_7532 BOUND_VARIABLE_1480803)))))) (let ((_let_2217 (forall ((BOUND_VARIABLE_1528427 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1528425 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1480773 tptp.nat) (BOUND_VARIABLE_1480774 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7459 (ho_7461 k_7472 (ho_7927 BOUND_VARIABLE_1528427 BOUND_VARIABLE_1480774)) (ho_7927 BOUND_VARIABLE_1528425 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480773) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480774) _let_3)))))) (ho_7927 (ho_8015 (ho_8109 (ho_8108 k_8107 BOUND_VARIABLE_1528427) BOUND_VARIABLE_1528425) BOUND_VARIABLE_1480773) BOUND_VARIABLE_1480774))))))))) (let ((_let_2218 (forall ((BOUND_VARIABLE_1480761 tptp.nat) (BOUND_VARIABLE_1480762 tptp.nat)) (= (ho_7541 (ho_7540 k_8110 BOUND_VARIABLE_1480761) BOUND_VARIABLE_1480762) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480762)) (ho_7533 k_7532 BOUND_VARIABLE_1480761)))))) (let ((_let_2219 (forall ((BOUND_VARIABLE_1528472 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1528470 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1480730 tptp.nat) (BOUND_VARIABLE_1480731 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1528472 BOUND_VARIABLE_1480731)) (ho_7636 BOUND_VARIABLE_1528470 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480730) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480731) _let_3)))))) (ho_7636 (ho_8023 (ho_8113 (ho_8112 k_8111 BOUND_VARIABLE_1528472) BOUND_VARIABLE_1528470) BOUND_VARIABLE_1480730) BOUND_VARIABLE_1480731))))))))) (let ((_let_2220 (forall ((BOUND_VARIABLE_1480718 tptp.nat) (BOUND_VARIABLE_1480719 tptp.nat)) (= (ho_7541 (ho_7540 k_8114 BOUND_VARIABLE_1480718) BOUND_VARIABLE_1480719) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480719)) (ho_7533 k_7532 BOUND_VARIABLE_1480718)))))) (let ((_let_2221 (forall ((BOUND_VARIABLE_1528518 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1528515 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1480661 tptp.nat) (BOUND_VARIABLE_1480662 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7736 BOUND_VARIABLE_1528515 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480661) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480662) _let_3))))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7736 BOUND_VARIABLE_1528518 BOUND_VARIABLE_1480662))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7733 _let_7)))) (let ((_let_9 (ho_7730 k_7733 _let_5))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7729 _let_7)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_6)) (ho_7516 k_7521 (ho_7516 _let_8 _let_9)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_9)) (ho_7516 _let_8 _let_6))) (ho_7736 (ho_7937 (ho_8089 (ho_8088 k_8115 BOUND_VARIABLE_1528518) BOUND_VARIABLE_1528515) BOUND_VARIABLE_1480661) BOUND_VARIABLE_1480662))))))))))))))) (let ((_let_2222 (forall ((BOUND_VARIABLE_1480649 tptp.nat) (BOUND_VARIABLE_1480650 tptp.nat)) (= (ho_7541 (ho_7540 k_8116 BOUND_VARIABLE_1480649) BOUND_VARIABLE_1480650) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480650)) (ho_7533 k_7532 BOUND_VARIABLE_1480649)))))) (let ((_let_2223 (forall ((BOUND_VARIABLE_1528569 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1528567 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1480619 tptp.nat) (BOUND_VARIABLE_1480620 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1528569 BOUND_VARIABLE_1480620)) (ho_7508 BOUND_VARIABLE_1528567 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480619) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480620) _let_3)))))) (ho_7508 (ho_7775 (ho_7774 (ho_8085 k_8117 BOUND_VARIABLE_1528569) BOUND_VARIABLE_1528567) BOUND_VARIABLE_1480619) BOUND_VARIABLE_1480620))))))))) (let ((_let_2224 (forall ((BOUND_VARIABLE_1480607 tptp.nat) (BOUND_VARIABLE_1480608 tptp.nat)) (= (ho_7541 (ho_7540 k_8118 BOUND_VARIABLE_1480607) BOUND_VARIABLE_1480608) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480608)) (ho_7533 k_7532 BOUND_VARIABLE_1480607)))))) (let ((_let_2225 (forall ((BOUND_VARIABLE_1528607 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1528604 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1480550 tptp.nat) (BOUND_VARIABLE_1480551 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7736 BOUND_VARIABLE_1528604 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480550) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480551) _let_3))))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7736 BOUND_VARIABLE_1528607 BOUND_VARIABLE_1480551))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7733 _let_7)))) (let ((_let_9 (ho_7730 k_7733 _let_5))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7729 _let_7)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_6)) (ho_7516 k_7521 (ho_7516 _let_8 _let_9)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_9)) (ho_7516 _let_8 _let_6))) (ho_7736 (ho_7937 (ho_8089 (ho_8088 k_8119 BOUND_VARIABLE_1528607) BOUND_VARIABLE_1528604) BOUND_VARIABLE_1480550) BOUND_VARIABLE_1480551))))))))))))))) (let ((_let_2226 (forall ((BOUND_VARIABLE_1480538 tptp.nat) (BOUND_VARIABLE_1480539 tptp.nat)) (= (ho_7541 (ho_7540 k_8120 BOUND_VARIABLE_1480538) BOUND_VARIABLE_1480539) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480539)) (ho_7533 k_7532 BOUND_VARIABLE_1480538)))))) (let ((_let_2227 (forall ((BOUND_VARIABLE_1528658 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1528656 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1480508 tptp.nat) (BOUND_VARIABLE_1480509 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1528658 BOUND_VARIABLE_1480509)) (ho_7508 BOUND_VARIABLE_1528656 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480508) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480509) _let_3)))))) (ho_7508 (ho_7775 (ho_7774 (ho_8085 k_8121 BOUND_VARIABLE_1528658) BOUND_VARIABLE_1528656) BOUND_VARIABLE_1480508) BOUND_VARIABLE_1480509))))))))) (let ((_let_2228 (forall ((BOUND_VARIABLE_1480496 tptp.nat) (BOUND_VARIABLE_1480497 tptp.nat)) (= (ho_7541 (ho_7540 k_8122 BOUND_VARIABLE_1480496) BOUND_VARIABLE_1480497) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480497)) (ho_7533 k_7532 BOUND_VARIABLE_1480496)))))) (let ((_let_2229 (forall ((BOUND_VARIABLE_1528696 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1528693 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1480439 tptp.nat) (BOUND_VARIABLE_1480440 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7736 BOUND_VARIABLE_1528693 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480439) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480440) _let_3))))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7736 BOUND_VARIABLE_1528696 BOUND_VARIABLE_1480440))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7733 _let_7)))) (let ((_let_9 (ho_7730 k_7733 _let_5))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7729 _let_7)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_6)) (ho_7516 k_7521 (ho_7516 _let_8 _let_9)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_9)) (ho_7516 _let_8 _let_6))) (ho_7736 (ho_7937 (ho_8089 (ho_8088 k_8123 BOUND_VARIABLE_1528696) BOUND_VARIABLE_1528693) BOUND_VARIABLE_1480439) BOUND_VARIABLE_1480440))))))))))))))) (let ((_let_2230 (forall ((BOUND_VARIABLE_1480427 tptp.nat) (BOUND_VARIABLE_1480428 tptp.nat)) (= (ho_7541 (ho_7540 k_8124 BOUND_VARIABLE_1480427) BOUND_VARIABLE_1480428) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480428)) (ho_7533 k_7532 BOUND_VARIABLE_1480427)))))) (let ((_let_2231 (forall ((BOUND_VARIABLE_1528745 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1480400 tptp.nat) (BOUND_VARIABLE_1480401 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7927 (ho_8015 BOUND_VARIABLE_1528745 BOUND_VARIABLE_1480401) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480400) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480401) _let_3))))) (ho_7927 (ho_8015 (ho_8126 k_8125 BOUND_VARIABLE_1528745) BOUND_VARIABLE_1480400) BOUND_VARIABLE_1480401))))))))) (let ((_let_2232 (forall ((BOUND_VARIABLE_1480389 tptp.nat) (BOUND_VARIABLE_1480390 tptp.nat)) (= (ho_7541 (ho_7540 k_8127 BOUND_VARIABLE_1480389) BOUND_VARIABLE_1480390) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480390)) (ho_7533 k_7532 BOUND_VARIABLE_1480389)))))) (let ((_let_2233 (forall ((BOUND_VARIABLE_1528781 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1480362 tptp.nat) (BOUND_VARIABLE_1480363 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7466 (ho_7465 BOUND_VARIABLE_1528781 BOUND_VARIABLE_1480363) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480362) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480363) _let_3))))) (ho_7466 (ho_7465 (ho_8129 k_8128 BOUND_VARIABLE_1528781) BOUND_VARIABLE_1480362) BOUND_VARIABLE_1480363))))))))) (let ((_let_2234 (forall ((BOUND_VARIABLE_1480351 tptp.nat) (BOUND_VARIABLE_1480352 tptp.nat)) (= (ho_7541 (ho_7540 k_8130 BOUND_VARIABLE_1480351) BOUND_VARIABLE_1480352) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480352)) (ho_7533 k_7532 BOUND_VARIABLE_1480351)))))) (let ((_let_2235 (forall ((BOUND_VARIABLE_1528817 |u_(-> tptp.nat tptp.nat tptp.real)|) (BOUND_VARIABLE_1480324 tptp.nat) (BOUND_VARIABLE_1480325 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7508 (ho_7775 BOUND_VARIABLE_1528817 BOUND_VARIABLE_1480325) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480324) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480325) _let_3))))) (ho_7508 (ho_7775 (ho_8132 k_8131 BOUND_VARIABLE_1528817) BOUND_VARIABLE_1480324) BOUND_VARIABLE_1480325))))))))) (let ((_let_2236 (forall ((BOUND_VARIABLE_1480313 tptp.nat) (BOUND_VARIABLE_1480314 tptp.nat)) (= (ho_7541 (ho_7540 k_8133 BOUND_VARIABLE_1480313) BOUND_VARIABLE_1480314) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480314)) (ho_7533 k_7532 BOUND_VARIABLE_1480313)))))) (let ((_let_2237 (forall ((BOUND_VARIABLE_1528853 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1480286 tptp.nat) (BOUND_VARIABLE_1480287 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7466 (ho_7465 BOUND_VARIABLE_1528853 BOUND_VARIABLE_1480287) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480286) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1480287) _let_3))))) (ho_7466 (ho_7465 (ho_8129 k_8134 BOUND_VARIABLE_1528853) BOUND_VARIABLE_1480286) BOUND_VARIABLE_1480287))))))))) (let ((_let_2238 (forall ((BOUND_VARIABLE_1480275 tptp.nat) (BOUND_VARIABLE_1480276 tptp.nat)) (= (ho_7541 (ho_7540 k_8135 BOUND_VARIABLE_1480275) BOUND_VARIABLE_1480276) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480276)) (ho_7533 k_7532 BOUND_VARIABLE_1480275)))))) (let ((_let_2239 (forall ((BOUND_VARIABLE_1528880 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1480264 tptp.real) (BOUND_VARIABLE_1480265 tptp.nat)) (= (ho_7508 (ho_7507 (ho_7800 k_8136 BOUND_VARIABLE_1528880) BOUND_VARIABLE_1480264) BOUND_VARIABLE_1480265) (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1528880 BOUND_VARIABLE_1480265)) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1480264) BOUND_VARIABLE_1480265)))))) (let ((_let_2240 (forall ((BOUND_VARIABLE_1480253 tptp.nat) (BOUND_VARIABLE_1480254 tptp.nat)) (= (ho_7541 (ho_7540 k_8137 BOUND_VARIABLE_1480253) BOUND_VARIABLE_1480254) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480254)) (ho_7533 k_7532 BOUND_VARIABLE_1480253)))))) (let ((_let_2241 (forall ((BOUND_VARIABLE_1528907 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1480227 tptp.complex) (BOUND_VARIABLE_1480228 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1480227) BOUND_VARIABLE_1480228))) (let ((_let_2 (ho_7730 k_7729 _let_1))) (let ((_let_3 (ho_7736 BOUND_VARIABLE_1528907 BOUND_VARIABLE_1480228))) (let ((_let_4 (ho_7519 k_7522 (ho_7730 k_7733 _let_3)))) (let ((_let_5 (ho_7730 k_7733 _let_1))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7729 _let_3)))) (= (ho_7736 (ho_7735 (ho_8139 k_8138 BOUND_VARIABLE_1528907) BOUND_VARIABLE_1480227) BOUND_VARIABLE_1480228) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_2)) (ho_7516 k_7521 (ho_7516 _let_4 _let_5)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_5)) (ho_7516 _let_4 _let_2))))))))))))) (let ((_let_2242 (forall ((BOUND_VARIABLE_1480216 tptp.nat) (BOUND_VARIABLE_1480217 tptp.nat)) (= (ho_7541 (ho_7540 k_8140 BOUND_VARIABLE_1480216) BOUND_VARIABLE_1480217) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480217)) (ho_7533 k_7532 BOUND_VARIABLE_1480216)))))) (let ((_let_2243 (forall ((BOUND_VARIABLE_1528953 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1480205 tptp.real) (BOUND_VARIABLE_1480206 tptp.nat)) (= (ho_7508 (ho_7507 (ho_7800 k_8141 BOUND_VARIABLE_1528953) BOUND_VARIABLE_1480205) BOUND_VARIABLE_1480206) (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1528953 BOUND_VARIABLE_1480206)) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1480205) BOUND_VARIABLE_1480206)))))) (let ((_let_2244 (forall ((BOUND_VARIABLE_1480194 tptp.nat) (BOUND_VARIABLE_1480195 tptp.nat)) (= (ho_7541 (ho_7540 k_8142 BOUND_VARIABLE_1480194) BOUND_VARIABLE_1480195) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480195)) (ho_7533 k_7532 BOUND_VARIABLE_1480194)))))) (let ((_let_2245 (forall ((BOUND_VARIABLE_1528980 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1480168 tptp.complex) (BOUND_VARIABLE_1480169 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1480168) BOUND_VARIABLE_1480169))) (let ((_let_2 (ho_7730 k_7729 _let_1))) (let ((_let_3 (ho_7736 BOUND_VARIABLE_1528980 BOUND_VARIABLE_1480169))) (let ((_let_4 (ho_7519 k_7522 (ho_7730 k_7733 _let_3)))) (let ((_let_5 (ho_7730 k_7733 _let_1))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7729 _let_3)))) (= (ho_7736 (ho_7735 (ho_8139 k_8143 BOUND_VARIABLE_1528980) BOUND_VARIABLE_1480168) BOUND_VARIABLE_1480169) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_2)) (ho_7516 k_7521 (ho_7516 _let_4 _let_5)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_5)) (ho_7516 _let_4 _let_2))))))))))))) (let ((_let_2246 (forall ((BOUND_VARIABLE_1480157 tptp.nat) (BOUND_VARIABLE_1480158 tptp.nat)) (= (ho_7541 (ho_7540 k_8144 BOUND_VARIABLE_1480157) BOUND_VARIABLE_1480158) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1480158)) (ho_7533 k_7532 BOUND_VARIABLE_1480157)))))) (let ((_let_2247 (forall ((BOUND_VARIABLE_1480098 tptp.complex) (BOUND_VARIABLE_1480099 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1480099) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1480098) _let_6))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_4))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_6)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_9) _let_3))))) _let_8)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_7))) (ho_7516 _let_11 (ho_7730 k_7733 _let_7))) (ho_7736 (ho_7735 k_8145 BOUND_VARIABLE_1480098) BOUND_VARIABLE_1480099)))))))))))))))) (let ((_let_2248 (forall ((BOUND_VARIABLE_1480055 tptp.complex) (BOUND_VARIABLE_1480056 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1480055) BOUND_VARIABLE_1480056))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7466 (ho_7465 k_7471 _let_6) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (let ((_let_9 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1480056 _let_8)) _let_2) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_8) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1480056) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_2)))))) (= (ho_7736 (ho_7735 k_8146 BOUND_VARIABLE_1480055) BOUND_VARIABLE_1480056) (ho_7728 (ho_7732 k_7731 (ho_7516 _let_9 (ho_7730 k_7729 _let_1))) (ho_7516 _let_9 (ho_7730 k_7733 _let_1)))))))))))))))) (let ((_let_2249 (forall ((BOUND_VARIABLE_1480006 tptp.real) (BOUND_VARIABLE_1480007 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1480007) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1480006) _let_6)) (ho_7508 (ho_7507 k_8147 BOUND_VARIABLE_1480006) BOUND_VARIABLE_1480007)))))))))))))) (let ((_let_2250 (forall ((BOUND_VARIABLE_1479971 tptp.real) (BOUND_VARIABLE_1479972 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 k_8148 BOUND_VARIABLE_1479971) BOUND_VARIABLE_1479972) (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1479972 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1479972) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1479971) BOUND_VARIABLE_1479972))))))))))))) (let ((_let_2251 (forall ((BOUND_VARIABLE_1529139 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1479944 tptp.nat) (BOUND_VARIABLE_1479945 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7927 (ho_8015 BOUND_VARIABLE_1529139 BOUND_VARIABLE_1479945) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479944) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479945) _let_3))))) (ho_7927 (ho_8015 (ho_8126 k_8149 BOUND_VARIABLE_1529139) BOUND_VARIABLE_1479944) BOUND_VARIABLE_1479945))))))))) (let ((_let_2252 (forall ((BOUND_VARIABLE_1479933 tptp.nat) (BOUND_VARIABLE_1479934 tptp.nat)) (= (ho_7541 (ho_7540 k_8150 BOUND_VARIABLE_1479933) BOUND_VARIABLE_1479934) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1479934)) (ho_7533 k_7532 BOUND_VARIABLE_1479933)))))) (let ((_let_2253 (forall ((BOUND_VARIABLE_1529171 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1479906 tptp.nat) (BOUND_VARIABLE_1479907 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7466 (ho_7465 BOUND_VARIABLE_1529171 BOUND_VARIABLE_1479907) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479906) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479907) _let_3))))) (ho_7466 (ho_7465 (ho_8129 k_8151 BOUND_VARIABLE_1529171) BOUND_VARIABLE_1479906) BOUND_VARIABLE_1479907))))))))) (let ((_let_2254 (forall ((BOUND_VARIABLE_1479895 tptp.nat) (BOUND_VARIABLE_1479896 tptp.nat)) (= (ho_7541 (ho_7540 k_8152 BOUND_VARIABLE_1479895) BOUND_VARIABLE_1479896) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1479896)) (ho_7533 k_7532 BOUND_VARIABLE_1479895)))))) (let ((_let_2255 (forall ((BOUND_VARIABLE_1529203 |u_(-> tptp.nat tptp.nat tptp.real)|) (BOUND_VARIABLE_1479868 tptp.nat) (BOUND_VARIABLE_1479869 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7508 (ho_7775 BOUND_VARIABLE_1529203 BOUND_VARIABLE_1479869) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479868) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479869) _let_3))))) (ho_7508 (ho_7775 (ho_8132 k_8153 BOUND_VARIABLE_1529203) BOUND_VARIABLE_1479868) BOUND_VARIABLE_1479869))))))))) (let ((_let_2256 (forall ((BOUND_VARIABLE_1479857 tptp.nat) (BOUND_VARIABLE_1479858 tptp.nat)) (= (ho_7541 (ho_7540 k_8154 BOUND_VARIABLE_1479857) BOUND_VARIABLE_1479858) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1479858)) (ho_7533 k_7532 BOUND_VARIABLE_1479857)))))) (let ((_let_2257 (forall ((BOUND_VARIABLE_1529235 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1479830 tptp.nat) (BOUND_VARIABLE_1479831 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7466 (ho_7465 BOUND_VARIABLE_1529235 BOUND_VARIABLE_1479831) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479830) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1479831) _let_3))))) (ho_7466 (ho_7465 (ho_8129 k_8155 BOUND_VARIABLE_1529235) BOUND_VARIABLE_1479830) BOUND_VARIABLE_1479831))))))))) (let ((_let_2258 (forall ((BOUND_VARIABLE_1479819 tptp.nat) (BOUND_VARIABLE_1479820 tptp.nat)) (= (ho_7541 (ho_7540 k_8156 BOUND_VARIABLE_1479819) BOUND_VARIABLE_1479820) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1479820)) (ho_7533 k_7532 BOUND_VARIABLE_1479819)))))) (let ((_let_2259 (forall ((BOUND_VARIABLE_1479788 tptp.real) (BOUND_VARIABLE_1479789 tptp.nat) (BOUND_VARIABLE_1479790 tptp.nat) (BOUND_VARIABLE_1479791 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1479788) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1479789) _let_2)))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1479790) _let_2))) BOUND_VARIABLE_1479791) (ho_7516 (ho_7512 (ho_7515 (ho_8158 k_8157 BOUND_VARIABLE_1479788) BOUND_VARIABLE_1479789) BOUND_VARIABLE_1479790) BOUND_VARIABLE_1479791)))))))) (let ((_let_2260 (forall ((BOUND_VARIABLE_1479756 tptp.rat) (BOUND_VARIABLE_1479757 tptp.nat) (BOUND_VARIABLE_1479758 tptp.nat) (BOUND_VARIABLE_1479759 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))) (let ((_let_9 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 (ho_7711 (ho_7717 _let_7 BOUND_VARIABLE_1479756) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1479757) _let_8)))) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1479758) _let_8))) BOUND_VARIABLE_1479759) (ho_7711 (ho_8055 (ho_8072 (ho_8160 k_8159 BOUND_VARIABLE_1479756) BOUND_VARIABLE_1479757) BOUND_VARIABLE_1479758) BOUND_VARIABLE_1479759)))))))))))))) (let ((_let_2261 (forall ((BOUND_VARIABLE_1479668 tptp.complex) (BOUND_VARIABLE_1479669 tptp.nat) (BOUND_VARIABLE_1479670 tptp.nat) (BOUND_VARIABLE_1479671 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1479671))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3))))) (let ((_let_5 (ho_8062 k_8061 k_8060))) (let ((_let_6 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1479670) _let_4))) (let ((_let_7 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1479669) _let_4))) (let ((_let_8 (ho_7958 k_7957 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 BOUND_VARIABLE_1479668)) (ho_7730 k_7729 _let_7))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 BOUND_VARIABLE_1479668)) (ho_7730 k_7733 _let_7)))))) (let ((_let_9 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_8)) (ho_7730 k_7729 _let_6))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_8)) (ho_7730 k_7733 _let_6))))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7733 _let_9)))) (let ((_let_11 (ho_7730 k_7733 BOUND_VARIABLE_1479671))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7729 _let_9)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_12 _let_1)) (ho_7516 k_7521 (ho_7516 _let_10 _let_11)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_12 _let_11)) (ho_7516 _let_10 _let_1))) (ho_7958 (ho_8063 (ho_8075 (ho_8162 k_8161 BOUND_VARIABLE_1479668) BOUND_VARIABLE_1479669) BOUND_VARIABLE_1479670) BOUND_VARIABLE_1479671))))))))))))))))) (let ((_let_2262 (forall ((BOUND_VARIABLE_1479658 tptp.nat) (BOUND_VARIABLE_1479659 tptp.nat)) (= (ho_7541 (ho_7540 k_8163 BOUND_VARIABLE_1479658) BOUND_VARIABLE_1479659) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1479659)) (ho_7533 k_7532 BOUND_VARIABLE_1479658)))))) (let ((_let_2263 (forall ((BOUND_VARIABLE_1529379 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1479650 tptp.nat) (BOUND_VARIABLE_1479651 tptp.nat)) (= (ho_7927 (ho_8015 (ho_8126 k_8164 BOUND_VARIABLE_1529379) BOUND_VARIABLE_1479650) BOUND_VARIABLE_1479651) (ho_7927 (ho_8015 BOUND_VARIABLE_1529379 BOUND_VARIABLE_1479651) BOUND_VARIABLE_1479650))))) (let ((_let_2264 (forall ((BOUND_VARIABLE_1479598 tptp.nat) (BOUND_VARIABLE_1479599 tptp.nat) (BOUND_VARIABLE_1479600 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479598) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479599) _let_2)))))) (or (not (= BOUND_VARIABLE_1479600 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8165 BOUND_VARIABLE_1479598) BOUND_VARIABLE_1479599) BOUND_VARIABLE_1479600))))) (let ((_let_2265 (forall ((BOUND_VARIABLE_1479588 tptp.nat) (BOUND_VARIABLE_1479589 tptp.nat)) (= (ho_7541 (ho_7540 k_8166 BOUND_VARIABLE_1479588) BOUND_VARIABLE_1479589) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1479589)) (ho_7533 k_7532 BOUND_VARIABLE_1479588)))))) (let ((_let_2266 (forall ((BOUND_VARIABLE_1529433 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1479580 tptp.nat) (BOUND_VARIABLE_1479581 tptp.nat)) (= (ho_7466 (ho_7465 (ho_8129 k_8167 BOUND_VARIABLE_1529433) BOUND_VARIABLE_1479580) BOUND_VARIABLE_1479581) (ho_7466 (ho_7465 BOUND_VARIABLE_1529433 BOUND_VARIABLE_1479581) BOUND_VARIABLE_1479580))))) (let ((_let_2267 (forall ((BOUND_VARIABLE_1479528 tptp.nat) (BOUND_VARIABLE_1479529 tptp.nat) (BOUND_VARIABLE_1479530 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479528) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479529) _let_2)))))) (or (not (= BOUND_VARIABLE_1479530 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8168 BOUND_VARIABLE_1479528) BOUND_VARIABLE_1479529) BOUND_VARIABLE_1479530))))) (let ((_let_2268 (forall ((BOUND_VARIABLE_1479518 tptp.nat) (BOUND_VARIABLE_1479519 tptp.nat)) (= (ho_7541 (ho_7540 k_8169 BOUND_VARIABLE_1479518) BOUND_VARIABLE_1479519) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1479519)) (ho_7533 k_7532 BOUND_VARIABLE_1479518)))))) (let ((_let_2269 (forall ((BOUND_VARIABLE_1529487 |u_(-> tptp.nat tptp.nat tptp.real)|) (BOUND_VARIABLE_1479510 tptp.nat) (BOUND_VARIABLE_1479511 tptp.nat)) (= (ho_7508 (ho_7775 (ho_8132 k_8170 BOUND_VARIABLE_1529487) BOUND_VARIABLE_1479510) BOUND_VARIABLE_1479511) (ho_7508 (ho_7775 BOUND_VARIABLE_1529487 BOUND_VARIABLE_1479511) BOUND_VARIABLE_1479510))))) (let ((_let_2270 (forall ((BOUND_VARIABLE_1479458 tptp.nat) (BOUND_VARIABLE_1479459 tptp.nat) (BOUND_VARIABLE_1479460 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479458) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479459) _let_2)))))) (or (not (= BOUND_VARIABLE_1479460 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8171 BOUND_VARIABLE_1479458) BOUND_VARIABLE_1479459) BOUND_VARIABLE_1479460))))) (let ((_let_2271 (forall ((BOUND_VARIABLE_1479448 tptp.nat) (BOUND_VARIABLE_1479449 tptp.nat)) (= (ho_7541 (ho_7540 k_8172 BOUND_VARIABLE_1479448) BOUND_VARIABLE_1479449) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1479449)) (ho_7533 k_7532 BOUND_VARIABLE_1479448)))))) (let ((_let_2272 (forall ((BOUND_VARIABLE_1529541 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1479440 tptp.nat) (BOUND_VARIABLE_1479441 tptp.nat)) (= (ho_7466 (ho_7465 (ho_8129 k_8173 BOUND_VARIABLE_1529541) BOUND_VARIABLE_1479440) BOUND_VARIABLE_1479441) (ho_7466 (ho_7465 BOUND_VARIABLE_1529541 BOUND_VARIABLE_1479441) BOUND_VARIABLE_1479440))))) (let ((_let_2273 (forall ((BOUND_VARIABLE_1479388 tptp.nat) (BOUND_VARIABLE_1479389 tptp.nat) (BOUND_VARIABLE_1479390 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479388) _let_2)))) (ho_7463 k_7462 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1479389) _let_2)))))) (or (not (= BOUND_VARIABLE_1479390 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 (ho_7539 k_8174 BOUND_VARIABLE_1479388) BOUND_VARIABLE_1479389) BOUND_VARIABLE_1479390))))) (let ((_let_2274 (forall ((BOUND_VARIABLE_1479363 tptp.int) (BOUND_VARIABLE_1479364 tptp.int) (BOUND_VARIABLE_1479365 tptp.int) (BOUND_VARIABLE_1479366 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8175 BOUND_VARIABLE_1479363) BOUND_VARIABLE_1479364) BOUND_VARIABLE_1479365) BOUND_VARIABLE_1479366) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479364) BOUND_VARIABLE_1479366)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479363) BOUND_VARIABLE_1479365)))))))))) (let ((_let_2275 (forall ((BOUND_VARIABLE_1479321 tptp.rat) (BOUND_VARIABLE_1479322 tptp.int) (BOUND_VARIABLE_1479323 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7545 BOUND_VARIABLE_1479323) BOUND_VARIABLE_1479322)) (ho_7630 k_7629 BOUND_VARIABLE_1479321)) (ho_7496 (ho_7495 (ho_7635 k_8176 BOUND_VARIABLE_1479321) BOUND_VARIABLE_1479322) BOUND_VARIABLE_1479323))))) (let ((_let_2276 (forall ((BOUND_VARIABLE_1479279 tptp.rat) (BOUND_VARIABLE_1479280 tptp.int) (BOUND_VARIABLE_1479281 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7546 BOUND_VARIABLE_1479281) BOUND_VARIABLE_1479280)) (ho_7630 k_7629 BOUND_VARIABLE_1479279)) (ho_7496 (ho_7495 (ho_7635 k_8177 BOUND_VARIABLE_1479279) BOUND_VARIABLE_1479280) BOUND_VARIABLE_1479281))))) (let ((_let_2277 (forall ((BOUND_VARIABLE_1479254 tptp.int) (BOUND_VARIABLE_1479255 tptp.int) (BOUND_VARIABLE_1479256 tptp.int) (BOUND_VARIABLE_1479257 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8178 BOUND_VARIABLE_1479254) BOUND_VARIABLE_1479255) BOUND_VARIABLE_1479256) BOUND_VARIABLE_1479257) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479255) BOUND_VARIABLE_1479257)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479254) BOUND_VARIABLE_1479256)))))))))) (let ((_let_2278 (forall ((BOUND_VARIABLE_1479229 tptp.int) (BOUND_VARIABLE_1479230 tptp.int) (BOUND_VARIABLE_1479231 tptp.int) (BOUND_VARIABLE_1479232 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8179 BOUND_VARIABLE_1479229) BOUND_VARIABLE_1479230) BOUND_VARIABLE_1479231) BOUND_VARIABLE_1479232) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479230) BOUND_VARIABLE_1479232)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479229) BOUND_VARIABLE_1479231)))))))))) (let ((_let_2279 (forall ((BOUND_VARIABLE_1479187 tptp.rat) (BOUND_VARIABLE_1479188 tptp.int) (BOUND_VARIABLE_1479189 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7547 BOUND_VARIABLE_1479189) BOUND_VARIABLE_1479188)) (ho_7630 k_7629 BOUND_VARIABLE_1479187)) (ho_7496 (ho_7495 (ho_7635 k_8180 BOUND_VARIABLE_1479187) BOUND_VARIABLE_1479188) BOUND_VARIABLE_1479189))))) (let ((_let_2280 (forall ((BOUND_VARIABLE_1479162 tptp.int) (BOUND_VARIABLE_1479163 tptp.int) (BOUND_VARIABLE_1479164 tptp.int) (BOUND_VARIABLE_1479165 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8181 BOUND_VARIABLE_1479162) BOUND_VARIABLE_1479163) BOUND_VARIABLE_1479164) BOUND_VARIABLE_1479165) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479163) BOUND_VARIABLE_1479165)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479162) BOUND_VARIABLE_1479164)))))))))) (let ((_let_2281 (forall ((BOUND_VARIABLE_1479120 tptp.rat) (BOUND_VARIABLE_1479121 tptp.int) (BOUND_VARIABLE_1479122 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7548 BOUND_VARIABLE_1479122) BOUND_VARIABLE_1479121)) (ho_7630 k_7629 BOUND_VARIABLE_1479120)) (ho_7496 (ho_7495 (ho_7635 k_8182 BOUND_VARIABLE_1479120) BOUND_VARIABLE_1479121) BOUND_VARIABLE_1479122))))) (let ((_let_2282 (forall ((BOUND_VARIABLE_1479078 tptp.rat) (BOUND_VARIABLE_1479079 tptp.int) (BOUND_VARIABLE_1479080 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7549 BOUND_VARIABLE_1479080) BOUND_VARIABLE_1479079)) (ho_7630 k_7629 BOUND_VARIABLE_1479078)) (ho_7496 (ho_7495 (ho_7635 k_8183 BOUND_VARIABLE_1479078) BOUND_VARIABLE_1479079) BOUND_VARIABLE_1479080))))) (let ((_let_2283 (forall ((BOUND_VARIABLE_1479053 tptp.int) (BOUND_VARIABLE_1479054 tptp.int) (BOUND_VARIABLE_1479055 tptp.int) (BOUND_VARIABLE_1479056 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8184 BOUND_VARIABLE_1479053) BOUND_VARIABLE_1479054) BOUND_VARIABLE_1479055) BOUND_VARIABLE_1479056) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479054) BOUND_VARIABLE_1479056)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1479053) BOUND_VARIABLE_1479055)))))))))) (let ((_let_2284 (forall ((BOUND_VARIABLE_1479011 tptp.rat) (BOUND_VARIABLE_1479012 tptp.int) (BOUND_VARIABLE_1479013 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7550 BOUND_VARIABLE_1479013) BOUND_VARIABLE_1479012)) (ho_7630 k_7629 BOUND_VARIABLE_1479011)) (ho_7496 (ho_7495 (ho_7635 k_8185 BOUND_VARIABLE_1479011) BOUND_VARIABLE_1479012) BOUND_VARIABLE_1479013))))) (let ((_let_2285 (forall ((BOUND_VARIABLE_1478978 tptp.nat) (BOUND_VARIABLE_1478979 tptp.nat) (BOUND_VARIABLE_1478980 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1478978) _let_2))) _let_1))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1478979) _let_2))) BOUND_VARIABLE_1478980) (ho_7516 (ho_7512 (ho_7515 k_8186 BOUND_VARIABLE_1478978) BOUND_VARIABLE_1478979) BOUND_VARIABLE_1478980)))))))) (let ((_let_2286 (forall ((BOUND_VARIABLE_1478945 tptp.nat) (BOUND_VARIABLE_1478946 tptp.nat) (BOUND_VARIABLE_1478947 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)))) (let ((_let_4 (ho_7704 k_7703 (ho_7702 _let_3 (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_5 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_6 (ho_7710 _let_5 k_7705))) (let ((_let_7 (ho_7715 (ho_7714 k_7713 k_7706) _let_5))) (let ((_let_8 (ho_7716 _let_7 k_7712))) (let ((_let_9 (ho_7711 (ho_7717 _let_8 _let_4) (ho_7711 _let_6 _let_4)))) (let ((_let_10 (ho_8054 k_8053 k_8052))) (let ((_let_11 (ho_7716 _let_7 k_8019))) (= (ho_7711 (ho_7717 _let_11 (ho_7711 (ho_7717 _let_8 (ho_7711 _let_6 (ho_7711 (ho_7717 _let_8 (ho_7711 (ho_7717 _let_11 (ho_7704 k_7703 (ho_7702 _let_3 (ho_7698 (ho_7697 k_7696 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))) _let_1)))) (ho_7711 (ho_8055 _let_10 BOUND_VARIABLE_1478945) _let_9))) _let_4))) (ho_7711 (ho_8055 _let_10 BOUND_VARIABLE_1478946) _let_9))) BOUND_VARIABLE_1478947) (ho_7711 (ho_8055 (ho_8072 k_8187 BOUND_VARIABLE_1478945) BOUND_VARIABLE_1478946) BOUND_VARIABLE_1478947)))))))))))))))) (let ((_let_2287 (forall ((BOUND_VARIABLE_1478832 tptp.nat) (BOUND_VARIABLE_1478833 tptp.nat) (BOUND_VARIABLE_1478834 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478834))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7730 k_7733 _let_2))) (let ((_let_5 (ho_7730 k_7729 _let_2))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_5) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 _let_4) (ho_7730 k_7733 _let_3))))) (let ((_let_7 (ho_8062 k_8061 k_8060))) (let ((_let_8 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1478833) _let_6))) (let ((_let_9 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1478832) _let_6))) (let ((_let_10 (ho_7730 k_7729 _let_9))) (let ((_let_11 (ho_7985 k_7984 (ho_7443 k_7442 tptp.one)))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7733 _let_11)))) (let ((_let_13 (ho_7730 k_7733 _let_9))) (let ((_let_14 (ho_7519 k_7522 (ho_7730 k_7729 _let_11)))) (let ((_let_15 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_10)) (ho_7516 k_7521 (ho_7516 _let_12 _let_13)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_13)) (ho_7516 _let_12 _let_10))))) (let ((_let_16 (ho_7958 k_7957 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_15)) _let_5)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_15)) _let_4))))) (let ((_let_17 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_16)) (ho_7730 k_7729 _let_8))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_16)) (ho_7730 k_7733 _let_8))))) (let ((_let_18 (ho_7519 k_7522 (ho_7730 k_7733 _let_17)))) (let ((_let_19 (ho_7730 k_7733 BOUND_VARIABLE_1478834))) (let ((_let_20 (ho_7519 k_7522 (ho_7730 k_7729 _let_17)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_1)) (ho_7516 k_7521 (ho_7516 _let_18 _let_19)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_20 _let_19)) (ho_7516 _let_18 _let_1))) (ho_7958 (ho_8063 (ho_8075 k_8188 BOUND_VARIABLE_1478832) BOUND_VARIABLE_1478833) BOUND_VARIABLE_1478834))))))))))))))))))))))))) (let ((_let_2288 (forall ((BOUND_VARIABLE_1478811 tptp.real) (BOUND_VARIABLE_1478812 tptp.nat) (BOUND_VARIABLE_1478813 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 BOUND_VARIABLE_1478811)) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1478812) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1478813) (ho_7516 (ho_7512 (ho_8050 k_8189 BOUND_VARIABLE_1478811) BOUND_VARIABLE_1478812) BOUND_VARIABLE_1478813)))))) (let ((_let_2289 (forall ((BOUND_VARIABLE_1478788 tptp.rat) (BOUND_VARIABLE_1478789 tptp.nat) (BOUND_VARIABLE_1478790 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 BOUND_VARIABLE_1478788)) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1478789) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3))))) BOUND_VARIABLE_1478790) (ho_7711 (ho_8055 (ho_8058 k_8190 BOUND_VARIABLE_1478788) BOUND_VARIABLE_1478789) BOUND_VARIABLE_1478790)))))))))))) (let ((_let_2290 (forall ((BOUND_VARIABLE_1478726 tptp.complex) (BOUND_VARIABLE_1478727 tptp.nat) (BOUND_VARIABLE_1478728 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478728))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1478727) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3)))))) (let ((_let_5 (ho_7958 k_7957 BOUND_VARIABLE_1478726))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_5)) (ho_7730 k_7729 _let_4))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_5)) (ho_7730 k_7733 _let_4))))) (let ((_let_7 (ho_7519 k_7522 (ho_7730 k_7733 _let_6)))) (let ((_let_8 (ho_7730 k_7733 BOUND_VARIABLE_1478728))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7729 _let_6)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_1)) (ho_7516 k_7521 (ho_7516 _let_7 _let_8)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_8)) (ho_7516 _let_7 _let_1))) (ho_7958 (ho_8063 (ho_8066 k_8191 BOUND_VARIABLE_1478726) BOUND_VARIABLE_1478727) BOUND_VARIABLE_1478728)))))))))))))) (let ((_let_2291 (forall ((BOUND_VARIABLE_1478704 tptp.real) (BOUND_VARIABLE_1478705 tptp.nat) (BOUND_VARIABLE_1478706 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1478704) (ho_7516 k_7521 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1478705) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))))) BOUND_VARIABLE_1478706) (ho_7516 (ho_7512 (ho_8050 k_8192 BOUND_VARIABLE_1478704) BOUND_VARIABLE_1478705) BOUND_VARIABLE_1478706)))))) (let ((_let_2292 (forall ((BOUND_VARIABLE_1478681 tptp.rat) (BOUND_VARIABLE_1478682 tptp.nat) (BOUND_VARIABLE_1478683 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 BOUND_VARIABLE_1478681) (ho_7711 _let_5 (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1478682) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))))) BOUND_VARIABLE_1478683) (ho_7711 (ho_8055 (ho_8058 k_8193 BOUND_VARIABLE_1478681) BOUND_VARIABLE_1478682) BOUND_VARIABLE_1478683)))))))))))) (let ((_let_2293 (forall ((BOUND_VARIABLE_1478618 tptp.complex) (BOUND_VARIABLE_1478619 tptp.nat) (BOUND_VARIABLE_1478620 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478620))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7958 k_7957 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1478619) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3))))))) (let ((_let_5 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 BOUND_VARIABLE_1478618)) (ho_7730 k_7729 _let_4))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 BOUND_VARIABLE_1478618)) (ho_7730 k_7733 _let_4))))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7733 _let_5)))) (let ((_let_7 (ho_7730 k_7733 BOUND_VARIABLE_1478620))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7729 _let_5)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_8 _let_1)) (ho_7516 k_7521 (ho_7516 _let_6 _let_7)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_8 _let_7)) (ho_7516 _let_6 _let_1))) (ho_7958 (ho_8063 (ho_8066 k_8194 BOUND_VARIABLE_1478618) BOUND_VARIABLE_1478619) BOUND_VARIABLE_1478620))))))))))))) (let ((_let_2294 (forall ((BOUND_VARIABLE_1478591 tptp.nat) (BOUND_VARIABLE_1478592 tptp.nat) (BOUND_VARIABLE_1478593 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1478591) _let_2))) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1478592) _let_2))) BOUND_VARIABLE_1478593) (ho_7516 (ho_7512 (ho_7515 k_8195 BOUND_VARIABLE_1478591) BOUND_VARIABLE_1478592) BOUND_VARIABLE_1478593)))))))) (let ((_let_2295 (forall ((BOUND_VARIABLE_1478564 tptp.nat) (BOUND_VARIABLE_1478565 tptp.nat) (BOUND_VARIABLE_1478566 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))) (let ((_let_9 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1478564) _let_8))) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1478565) _let_8))) BOUND_VARIABLE_1478566) (ho_7711 (ho_8055 (ho_8072 k_8196 BOUND_VARIABLE_1478564) BOUND_VARIABLE_1478565) BOUND_VARIABLE_1478566)))))))))))))) (let ((_let_2296 (forall ((BOUND_VARIABLE_1478493 tptp.nat) (BOUND_VARIABLE_1478494 tptp.nat) (BOUND_VARIABLE_1478495 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478495))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3))))) (let ((_let_5 (ho_8062 k_8061 k_8060))) (let ((_let_6 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1478494) _let_4))) (let ((_let_7 (ho_7958 k_7957 (ho_7958 (ho_8063 _let_5 BOUND_VARIABLE_1478493) _let_4)))) (let ((_let_8 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_7)) (ho_7730 k_7729 _let_6))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_7)) (ho_7730 k_7733 _let_6))))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7733 _let_8)))) (let ((_let_10 (ho_7730 k_7733 BOUND_VARIABLE_1478495))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7729 _let_8)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_11 _let_1)) (ho_7516 k_7521 (ho_7516 _let_9 _let_10)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_11 _let_10)) (ho_7516 _let_9 _let_1))) (ho_7958 (ho_8063 (ho_8075 k_8197 BOUND_VARIABLE_1478493) BOUND_VARIABLE_1478494) BOUND_VARIABLE_1478495)))))))))))))))) (let ((_let_2297 (forall ((BOUND_VARIABLE_1478458 tptp.real) (BOUND_VARIABLE_1478459 tptp.nat) (BOUND_VARIABLE_1478460 tptp.nat) (BOUND_VARIABLE_1478461 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (let ((_let_3 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1478458) (ho_7516 k_7521 (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1478459) _let_2)))) _let_1)) (ho_7516 (ho_7512 _let_3 BOUND_VARIABLE_1478460) _let_2))) BOUND_VARIABLE_1478461) (ho_7516 (ho_7512 (ho_7515 (ho_8158 k_8198 BOUND_VARIABLE_1478458) BOUND_VARIABLE_1478459) BOUND_VARIABLE_1478460) BOUND_VARIABLE_1478461)))))))) (let ((_let_2298 (forall ((BOUND_VARIABLE_1478422 tptp.rat) (BOUND_VARIABLE_1478423 tptp.nat) (BOUND_VARIABLE_1478424 tptp.nat) (BOUND_VARIABLE_1478425 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3)))) (let ((_let_9 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 (ho_7717 _let_7 (ho_7711 (ho_7717 _let_7 BOUND_VARIABLE_1478422) (ho_7711 _let_5 (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1478423) _let_8)))) _let_3)) (ho_7711 (ho_8055 _let_9 BOUND_VARIABLE_1478424) _let_8))) BOUND_VARIABLE_1478425) (ho_7711 (ho_8055 (ho_8072 (ho_8160 k_8199 BOUND_VARIABLE_1478422) BOUND_VARIABLE_1478423) BOUND_VARIABLE_1478424) BOUND_VARIABLE_1478425)))))))))))))) (let ((_let_2299 (forall ((BOUND_VARIABLE_1478318 tptp.complex) (BOUND_VARIABLE_1478319 tptp.nat) (BOUND_VARIABLE_1478320 tptp.nat) (BOUND_VARIABLE_1478321 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478321))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7730 k_7733 _let_2))) (let ((_let_5 (ho_7730 k_7729 _let_2))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_5) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 _let_4) (ho_7730 k_7733 _let_3))))) (let ((_let_7 (ho_8062 k_8061 k_8060))) (let ((_let_8 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1478320) _let_6))) (let ((_let_9 (ho_7958 k_7957 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1478319) _let_6)))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 BOUND_VARIABLE_1478318)) (ho_7730 k_7729 _let_9))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 BOUND_VARIABLE_1478318)) (ho_7730 k_7733 _let_9))))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_10)) _let_5)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_10)) _let_4)))) (let ((_let_12 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_11)) (ho_7730 k_7729 _let_8))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_11)) (ho_7730 k_7733 _let_8))))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7733 _let_12)))) (let ((_let_14 (ho_7730 k_7733 BOUND_VARIABLE_1478321))) (let ((_let_15 (ho_7519 k_7522 (ho_7730 k_7729 _let_12)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_15 _let_1)) (ho_7516 k_7521 (ho_7516 _let_13 _let_14)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_15 _let_14)) (ho_7516 _let_13 _let_1))) (ho_7958 (ho_8063 (ho_8075 (ho_8162 k_8200 BOUND_VARIABLE_1478318) BOUND_VARIABLE_1478319) BOUND_VARIABLE_1478320) BOUND_VARIABLE_1478321)))))))))))))))))))) (let ((_let_2300 (forall ((BOUND_VARIABLE_1478295 tptp.rat) (BOUND_VARIABLE_1478296 tptp.nat) (BOUND_VARIABLE_1478297 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 BOUND_VARIABLE_1478295)) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1478296) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3))))) BOUND_VARIABLE_1478297) (ho_7711 (ho_8055 (ho_8058 k_8201 BOUND_VARIABLE_1478295) BOUND_VARIABLE_1478296) BOUND_VARIABLE_1478297)))))))))))) (let ((_let_2301 (forall ((BOUND_VARIABLE_1478257 tptp.nat) (BOUND_VARIABLE_1478258 tptp.rat) (BOUND_VARIABLE_1478259 tptp.nat) (BOUND_VARIABLE_1478260 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7711 _let_5 _let_3))) (let ((_let_7 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_8 (ho_7716 _let_7 k_7712))) (let ((_let_9 (ho_7711 (ho_7717 _let_8 _let_3) _let_6))) (let ((_let_10 (ho_8054 k_8053 k_8052))) (= (ho_7711 (ho_7717 (ho_7716 _let_7 k_8019) (ho_7711 (ho_7717 _let_8 (ho_7711 _let_5 (ho_7711 (ho_7717 _let_8 (ho_7711 (ho_7717 _let_8 (ho_7711 (ho_8055 _let_10 BOUND_VARIABLE_1478257) _let_9)) (ho_7711 _let_5 BOUND_VARIABLE_1478258))) _let_6))) (ho_7711 (ho_8055 _let_10 BOUND_VARIABLE_1478259) _let_9))) BOUND_VARIABLE_1478260) (ho_7711 (ho_8055 (ho_8058 (ho_8057 k_8202 BOUND_VARIABLE_1478257) BOUND_VARIABLE_1478258) BOUND_VARIABLE_1478259) BOUND_VARIABLE_1478260))))))))))))))) (let ((_let_2302 (forall ((BOUND_VARIABLE_1478236 tptp.real) (BOUND_VARIABLE_1478237 tptp.nat) (BOUND_VARIABLE_1478238 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 BOUND_VARIABLE_1478236)) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1478237) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1478238) (ho_7516 (ho_7512 (ho_8050 k_8203 BOUND_VARIABLE_1478236) BOUND_VARIABLE_1478237) BOUND_VARIABLE_1478238)))))) (let ((_let_2303 (forall ((BOUND_VARIABLE_1478199 tptp.nat) (BOUND_VARIABLE_1478200 tptp.real) (BOUND_VARIABLE_1478201 tptp.nat) (BOUND_VARIABLE_1478202 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (ho_7788 k_7787 k_7786))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7512 _let_4 BOUND_VARIABLE_1478199) _let_3)) (ho_7516 k_7521 BOUND_VARIABLE_1478200))) _let_2))) (ho_7516 (ho_7512 _let_4 BOUND_VARIABLE_1478201) _let_3))) BOUND_VARIABLE_1478202) (ho_7516 (ho_7512 (ho_8050 (ho_8049 k_8204 BOUND_VARIABLE_1478199) BOUND_VARIABLE_1478200) BOUND_VARIABLE_1478201) BOUND_VARIABLE_1478202))))))))) (let ((_let_2304 (forall ((BOUND_VARIABLE_1478137 tptp.complex) (BOUND_VARIABLE_1478138 tptp.nat) (BOUND_VARIABLE_1478139 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478139))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1478138) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3)))))) (let ((_let_5 (ho_7958 k_7957 BOUND_VARIABLE_1478137))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_5)) (ho_7730 k_7729 _let_4))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_5)) (ho_7730 k_7733 _let_4))))) (let ((_let_7 (ho_7519 k_7522 (ho_7730 k_7733 _let_6)))) (let ((_let_8 (ho_7730 k_7733 BOUND_VARIABLE_1478139))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7729 _let_6)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_1)) (ho_7516 k_7521 (ho_7516 _let_7 _let_8)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_8)) (ho_7516 _let_7 _let_1))) (ho_7958 (ho_8063 (ho_8066 k_8205 BOUND_VARIABLE_1478137) BOUND_VARIABLE_1478138) BOUND_VARIABLE_1478139)))))))))))))) (let ((_let_2305 (forall ((BOUND_VARIABLE_1478030 tptp.nat) (BOUND_VARIABLE_1478031 tptp.complex) (BOUND_VARIABLE_1478032 tptp.nat) (BOUND_VARIABLE_1478033 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1478033))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7730 k_7733 _let_3))) (let ((_let_5 (ho_7730 k_7729 _let_3))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) _let_5)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) _let_4)))) (let ((_let_7 (ho_8062 k_8061 k_8060))) (let ((_let_8 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1478032) _let_6))) (let ((_let_9 (ho_7958 k_7957 BOUND_VARIABLE_1478031))) (let ((_let_10 (ho_7958 (ho_8063 _let_7 BOUND_VARIABLE_1478030) _let_6))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_10)) (ho_7730 k_7729 _let_9))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_10)) (ho_7730 k_7733 _let_9))))) (let ((_let_12 (ho_7958 k_7957 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_11)) _let_5)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_11)) _let_4))))) (let ((_let_13 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_12)) (ho_7730 k_7729 _let_8))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_12)) (ho_7730 k_7733 _let_8))))) (let ((_let_14 (ho_7519 k_7522 (ho_7730 k_7733 _let_13)))) (let ((_let_15 (ho_7730 k_7733 BOUND_VARIABLE_1478033))) (let ((_let_16 (ho_7519 k_7522 (ho_7730 k_7729 _let_13)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_16 _let_1)) (ho_7516 k_7521 (ho_7516 _let_14 _let_15)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_16 _let_15)) (ho_7516 _let_14 _let_1))) (ho_7958 (ho_8063 (ho_8066 (ho_8065 k_8206 BOUND_VARIABLE_1478030) BOUND_VARIABLE_1478031) BOUND_VARIABLE_1478032) BOUND_VARIABLE_1478033))))))))))))))))))))) (let ((_let_2306 (forall ((BOUND_VARIABLE_1478005 tptp.int) (BOUND_VARIABLE_1478006 tptp.int) (BOUND_VARIABLE_1478007 tptp.int) (BOUND_VARIABLE_1478008 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8207 BOUND_VARIABLE_1478005) BOUND_VARIABLE_1478006) BOUND_VARIABLE_1478007) BOUND_VARIABLE_1478008) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1478006) BOUND_VARIABLE_1478008)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1478005) BOUND_VARIABLE_1478007)))))))))) (let ((_let_2307 (forall ((BOUND_VARIABLE_1477980 tptp.int) (BOUND_VARIABLE_1477981 tptp.int) (BOUND_VARIABLE_1477982 tptp.int) (BOUND_VARIABLE_1477983 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8208 BOUND_VARIABLE_1477980) BOUND_VARIABLE_1477981) BOUND_VARIABLE_1477982) BOUND_VARIABLE_1477983) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477981) BOUND_VARIABLE_1477983)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477980) BOUND_VARIABLE_1477982)))))))))) (let ((_let_2308 (forall ((BOUND_VARIABLE_1477955 tptp.int) (BOUND_VARIABLE_1477956 tptp.int) (BOUND_VARIABLE_1477957 tptp.int) (BOUND_VARIABLE_1477958 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8209 BOUND_VARIABLE_1477955) BOUND_VARIABLE_1477956) BOUND_VARIABLE_1477957) BOUND_VARIABLE_1477958) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477956) BOUND_VARIABLE_1477958)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477955) BOUND_VARIABLE_1477957)))))))))) (let ((_let_2309 (forall ((BOUND_VARIABLE_1477930 tptp.int) (BOUND_VARIABLE_1477931 tptp.int) (BOUND_VARIABLE_1477932 tptp.int) (BOUND_VARIABLE_1477933 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8210 BOUND_VARIABLE_1477930) BOUND_VARIABLE_1477931) BOUND_VARIABLE_1477932) BOUND_VARIABLE_1477933) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477931) BOUND_VARIABLE_1477933)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477930) BOUND_VARIABLE_1477932)))))))))) (let ((_let_2310 (forall ((BOUND_VARIABLE_1477907 tptp.rat) (BOUND_VARIABLE_1477908 tptp.nat) (BOUND_VARIABLE_1477909 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 BOUND_VARIABLE_1477907)) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1477908) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3))))) BOUND_VARIABLE_1477909) (ho_7711 (ho_8055 (ho_8058 k_8211 BOUND_VARIABLE_1477907) BOUND_VARIABLE_1477908) BOUND_VARIABLE_1477909)))))))))))) (let ((_let_2311 (forall ((BOUND_VARIABLE_1477882 tptp.int) (BOUND_VARIABLE_1477883 tptp.int) (BOUND_VARIABLE_1477884 tptp.int) (BOUND_VARIABLE_1477885 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8212 BOUND_VARIABLE_1477882) BOUND_VARIABLE_1477883) BOUND_VARIABLE_1477884) BOUND_VARIABLE_1477885) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477883) BOUND_VARIABLE_1477885)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477882) BOUND_VARIABLE_1477884)))))))))) (let ((_let_2312 (forall ((BOUND_VARIABLE_1477857 tptp.int) (BOUND_VARIABLE_1477858 tptp.int) (BOUND_VARIABLE_1477859 tptp.int) (BOUND_VARIABLE_1477860 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8213 BOUND_VARIABLE_1477857) BOUND_VARIABLE_1477858) BOUND_VARIABLE_1477859) BOUND_VARIABLE_1477860) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477858) BOUND_VARIABLE_1477860)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477857) BOUND_VARIABLE_1477859)))))))))) (let ((_let_2313 (forall ((BOUND_VARIABLE_1477832 tptp.int) (BOUND_VARIABLE_1477833 tptp.int) (BOUND_VARIABLE_1477834 tptp.int) (BOUND_VARIABLE_1477835 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8214 BOUND_VARIABLE_1477832) BOUND_VARIABLE_1477833) BOUND_VARIABLE_1477834) BOUND_VARIABLE_1477835) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477833) BOUND_VARIABLE_1477835)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477832) BOUND_VARIABLE_1477834)))))))))) (let ((_let_2314 (forall ((BOUND_VARIABLE_1477807 tptp.int) (BOUND_VARIABLE_1477808 tptp.int) (BOUND_VARIABLE_1477809 tptp.int) (BOUND_VARIABLE_1477810 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8215 BOUND_VARIABLE_1477807) BOUND_VARIABLE_1477808) BOUND_VARIABLE_1477809) BOUND_VARIABLE_1477810) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477808) BOUND_VARIABLE_1477810)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477807) BOUND_VARIABLE_1477809)))))))))) (let ((_let_2315 (forall ((BOUND_VARIABLE_1477782 tptp.int) (BOUND_VARIABLE_1477783 tptp.int) (BOUND_VARIABLE_1477784 tptp.int) (BOUND_VARIABLE_1477785 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8216 BOUND_VARIABLE_1477782) BOUND_VARIABLE_1477783) BOUND_VARIABLE_1477784) BOUND_VARIABLE_1477785) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477783) BOUND_VARIABLE_1477785)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477782) BOUND_VARIABLE_1477784)))))))))) (let ((_let_2316 (forall ((BOUND_VARIABLE_1477757 tptp.int) (BOUND_VARIABLE_1477758 tptp.int) (BOUND_VARIABLE_1477759 tptp.int) (BOUND_VARIABLE_1477760 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8217 BOUND_VARIABLE_1477757) BOUND_VARIABLE_1477758) BOUND_VARIABLE_1477759) BOUND_VARIABLE_1477760) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477758) BOUND_VARIABLE_1477760)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477757) BOUND_VARIABLE_1477759)))))))))) (let ((_let_2317 (forall ((BOUND_VARIABLE_1477732 tptp.int) (BOUND_VARIABLE_1477733 tptp.int) (BOUND_VARIABLE_1477734 tptp.int) (BOUND_VARIABLE_1477735 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8218 BOUND_VARIABLE_1477732) BOUND_VARIABLE_1477733) BOUND_VARIABLE_1477734) BOUND_VARIABLE_1477735) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477733) BOUND_VARIABLE_1477735)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477732) BOUND_VARIABLE_1477734)))))))))) (let ((_let_2318 (forall ((BOUND_VARIABLE_1477707 tptp.int) (BOUND_VARIABLE_1477708 tptp.int) (BOUND_VARIABLE_1477709 tptp.int) (BOUND_VARIABLE_1477710 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8219 BOUND_VARIABLE_1477707) BOUND_VARIABLE_1477708) BOUND_VARIABLE_1477709) BOUND_VARIABLE_1477710) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477708) BOUND_VARIABLE_1477710)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477707) BOUND_VARIABLE_1477709)))))))))) (let ((_let_2319 (forall ((BOUND_VARIABLE_1477682 tptp.int) (BOUND_VARIABLE_1477683 tptp.int) (BOUND_VARIABLE_1477684 tptp.int) (BOUND_VARIABLE_1477685 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8220 BOUND_VARIABLE_1477682) BOUND_VARIABLE_1477683) BOUND_VARIABLE_1477684) BOUND_VARIABLE_1477685) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477683) BOUND_VARIABLE_1477685)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477682) BOUND_VARIABLE_1477684)))))))))) (let ((_let_2320 (forall ((BOUND_VARIABLE_1477657 tptp.int) (BOUND_VARIABLE_1477658 tptp.int) (BOUND_VARIABLE_1477659 tptp.int) (BOUND_VARIABLE_1477660 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8221 BOUND_VARIABLE_1477657) BOUND_VARIABLE_1477658) BOUND_VARIABLE_1477659) BOUND_VARIABLE_1477660) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477658) BOUND_VARIABLE_1477660)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477657) BOUND_VARIABLE_1477659)))))))))) (let ((_let_2321 (forall ((BOUND_VARIABLE_1477632 tptp.int) (BOUND_VARIABLE_1477633 tptp.int) (BOUND_VARIABLE_1477634 tptp.int) (BOUND_VARIABLE_1477635 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8222 BOUND_VARIABLE_1477632) BOUND_VARIABLE_1477633) BOUND_VARIABLE_1477634) BOUND_VARIABLE_1477635) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477633) BOUND_VARIABLE_1477635)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477632) BOUND_VARIABLE_1477634)))))))))) (let ((_let_2322 (forall ((BOUND_VARIABLE_1477607 tptp.int) (BOUND_VARIABLE_1477608 tptp.int) (BOUND_VARIABLE_1477609 tptp.int) (BOUND_VARIABLE_1477610 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8223 BOUND_VARIABLE_1477607) BOUND_VARIABLE_1477608) BOUND_VARIABLE_1477609) BOUND_VARIABLE_1477610) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477608) BOUND_VARIABLE_1477610)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477607) BOUND_VARIABLE_1477609)))))))))) (let ((_let_2323 (forall ((BOUND_VARIABLE_1477582 tptp.int) (BOUND_VARIABLE_1477583 tptp.int) (BOUND_VARIABLE_1477584 tptp.int) (BOUND_VARIABLE_1477585 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8224 BOUND_VARIABLE_1477582) BOUND_VARIABLE_1477583) BOUND_VARIABLE_1477584) BOUND_VARIABLE_1477585) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477583) BOUND_VARIABLE_1477585)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477582) BOUND_VARIABLE_1477584)))))))))) (let ((_let_2324 (forall ((BOUND_VARIABLE_1477557 tptp.int) (BOUND_VARIABLE_1477558 tptp.int) (BOUND_VARIABLE_1477559 tptp.int) (BOUND_VARIABLE_1477560 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8225 BOUND_VARIABLE_1477557) BOUND_VARIABLE_1477558) BOUND_VARIABLE_1477559) BOUND_VARIABLE_1477560) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477558) BOUND_VARIABLE_1477560)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477557) BOUND_VARIABLE_1477559)))))))))) (let ((_let_2325 (forall ((BOUND_VARIABLE_1477532 tptp.int) (BOUND_VARIABLE_1477533 tptp.int) (BOUND_VARIABLE_1477534 tptp.int) (BOUND_VARIABLE_1477535 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8226 BOUND_VARIABLE_1477532) BOUND_VARIABLE_1477533) BOUND_VARIABLE_1477534) BOUND_VARIABLE_1477535) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477533) BOUND_VARIABLE_1477535)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477532) BOUND_VARIABLE_1477534)))))))))) (let ((_let_2326 (forall ((BOUND_VARIABLE_1477507 tptp.int) (BOUND_VARIABLE_1477508 tptp.int) (BOUND_VARIABLE_1477509 tptp.int) (BOUND_VARIABLE_1477510 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8227 BOUND_VARIABLE_1477507) BOUND_VARIABLE_1477508) BOUND_VARIABLE_1477509) BOUND_VARIABLE_1477510) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477508) BOUND_VARIABLE_1477510)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477507) BOUND_VARIABLE_1477509)))))))))) (let ((_let_2327 (forall ((BOUND_VARIABLE_1477482 tptp.int) (BOUND_VARIABLE_1477483 tptp.int) (BOUND_VARIABLE_1477484 tptp.int) (BOUND_VARIABLE_1477485 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8228 BOUND_VARIABLE_1477482) BOUND_VARIABLE_1477483) BOUND_VARIABLE_1477484) BOUND_VARIABLE_1477485) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477483) BOUND_VARIABLE_1477485)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477482) BOUND_VARIABLE_1477484)))))))))) (let ((_let_2328 (forall ((BOUND_VARIABLE_1477457 tptp.int) (BOUND_VARIABLE_1477458 tptp.int) (BOUND_VARIABLE_1477459 tptp.int) (BOUND_VARIABLE_1477460 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8229 BOUND_VARIABLE_1477457) BOUND_VARIABLE_1477458) BOUND_VARIABLE_1477459) BOUND_VARIABLE_1477460) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477458) BOUND_VARIABLE_1477460)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477457) BOUND_VARIABLE_1477459)))))))))) (let ((_let_2329 (forall ((BOUND_VARIABLE_1477432 tptp.int) (BOUND_VARIABLE_1477433 tptp.int) (BOUND_VARIABLE_1477434 tptp.int) (BOUND_VARIABLE_1477435 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8230 BOUND_VARIABLE_1477432) BOUND_VARIABLE_1477433) BOUND_VARIABLE_1477434) BOUND_VARIABLE_1477435) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477433) BOUND_VARIABLE_1477435)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477432) BOUND_VARIABLE_1477434)))))))))) (let ((_let_2330 (forall ((BOUND_VARIABLE_1477407 tptp.int) (BOUND_VARIABLE_1477408 tptp.int) (BOUND_VARIABLE_1477409 tptp.int) (BOUND_VARIABLE_1477410 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8231 BOUND_VARIABLE_1477407) BOUND_VARIABLE_1477408) BOUND_VARIABLE_1477409) BOUND_VARIABLE_1477410) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477408) BOUND_VARIABLE_1477410)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477407) BOUND_VARIABLE_1477409)))))))))) (let ((_let_2331 (forall ((BOUND_VARIABLE_1477382 tptp.int) (BOUND_VARIABLE_1477383 tptp.int) (BOUND_VARIABLE_1477384 tptp.int) (BOUND_VARIABLE_1477385 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8232 BOUND_VARIABLE_1477382) BOUND_VARIABLE_1477383) BOUND_VARIABLE_1477384) BOUND_VARIABLE_1477385) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477383) BOUND_VARIABLE_1477385)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477382) BOUND_VARIABLE_1477384)))))))))) (let ((_let_2332 (forall ((BOUND_VARIABLE_1477357 tptp.int) (BOUND_VARIABLE_1477358 tptp.int) (BOUND_VARIABLE_1477359 tptp.int) (BOUND_VARIABLE_1477360 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8233 BOUND_VARIABLE_1477357) BOUND_VARIABLE_1477358) BOUND_VARIABLE_1477359) BOUND_VARIABLE_1477360) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477358) BOUND_VARIABLE_1477360)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477357) BOUND_VARIABLE_1477359)))))))))) (let ((_let_2333 (forall ((BOUND_VARIABLE_1477332 tptp.int) (BOUND_VARIABLE_1477333 tptp.int) (BOUND_VARIABLE_1477334 tptp.int) (BOUND_VARIABLE_1477335 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8234 BOUND_VARIABLE_1477332) BOUND_VARIABLE_1477333) BOUND_VARIABLE_1477334) BOUND_VARIABLE_1477335) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477333) BOUND_VARIABLE_1477335)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477332) BOUND_VARIABLE_1477334)))))))))) (let ((_let_2334 (forall ((BOUND_VARIABLE_1477307 tptp.int) (BOUND_VARIABLE_1477308 tptp.int) (BOUND_VARIABLE_1477309 tptp.int) (BOUND_VARIABLE_1477310 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8235 BOUND_VARIABLE_1477307) BOUND_VARIABLE_1477308) BOUND_VARIABLE_1477309) BOUND_VARIABLE_1477310) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477308) BOUND_VARIABLE_1477310)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477307) BOUND_VARIABLE_1477309)))))))))) (let ((_let_2335 (forall ((BOUND_VARIABLE_1477282 tptp.int) (BOUND_VARIABLE_1477283 tptp.int) (BOUND_VARIABLE_1477284 tptp.int) (BOUND_VARIABLE_1477285 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8236 BOUND_VARIABLE_1477282) BOUND_VARIABLE_1477283) BOUND_VARIABLE_1477284) BOUND_VARIABLE_1477285) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477283) BOUND_VARIABLE_1477285)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477282) BOUND_VARIABLE_1477284)))))))))) (let ((_let_2336 (forall ((BOUND_VARIABLE_1477257 tptp.int) (BOUND_VARIABLE_1477258 tptp.int) (BOUND_VARIABLE_1477259 tptp.int) (BOUND_VARIABLE_1477260 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8237 BOUND_VARIABLE_1477257) BOUND_VARIABLE_1477258) BOUND_VARIABLE_1477259) BOUND_VARIABLE_1477260) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477258) BOUND_VARIABLE_1477260)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477257) BOUND_VARIABLE_1477259)))))))))) (let ((_let_2337 (forall ((BOUND_VARIABLE_1477232 tptp.int) (BOUND_VARIABLE_1477233 tptp.int) (BOUND_VARIABLE_1477234 tptp.int) (BOUND_VARIABLE_1477235 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8238 BOUND_VARIABLE_1477232) BOUND_VARIABLE_1477233) BOUND_VARIABLE_1477234) BOUND_VARIABLE_1477235) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477233) BOUND_VARIABLE_1477235)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477232) BOUND_VARIABLE_1477234)))))))))) (let ((_let_2338 (forall ((BOUND_VARIABLE_1477207 tptp.int) (BOUND_VARIABLE_1477208 tptp.int) (BOUND_VARIABLE_1477209 tptp.int) (BOUND_VARIABLE_1477210 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8239 BOUND_VARIABLE_1477207) BOUND_VARIABLE_1477208) BOUND_VARIABLE_1477209) BOUND_VARIABLE_1477210) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477208) BOUND_VARIABLE_1477210)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477207) BOUND_VARIABLE_1477209)))))))))) (let ((_let_2339 (forall ((BOUND_VARIABLE_1477182 tptp.int) (BOUND_VARIABLE_1477183 tptp.int) (BOUND_VARIABLE_1477184 tptp.int) (BOUND_VARIABLE_1477185 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8240 BOUND_VARIABLE_1477182) BOUND_VARIABLE_1477183) BOUND_VARIABLE_1477184) BOUND_VARIABLE_1477185) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477183) BOUND_VARIABLE_1477185)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477182) BOUND_VARIABLE_1477184)))))))))) (let ((_let_2340 (forall ((BOUND_VARIABLE_1477157 tptp.int) (BOUND_VARIABLE_1477158 tptp.int) (BOUND_VARIABLE_1477159 tptp.int) (BOUND_VARIABLE_1477160 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8241 BOUND_VARIABLE_1477157) BOUND_VARIABLE_1477158) BOUND_VARIABLE_1477159) BOUND_VARIABLE_1477160) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477158) BOUND_VARIABLE_1477160)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477157) BOUND_VARIABLE_1477159)))))))))) (let ((_let_2341 (forall ((BOUND_VARIABLE_1477132 tptp.int) (BOUND_VARIABLE_1477133 tptp.int) (BOUND_VARIABLE_1477134 tptp.int) (BOUND_VARIABLE_1477135 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8242 BOUND_VARIABLE_1477132) BOUND_VARIABLE_1477133) BOUND_VARIABLE_1477134) BOUND_VARIABLE_1477135) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477133) BOUND_VARIABLE_1477135)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477132) BOUND_VARIABLE_1477134)))))))))) (let ((_let_2342 (forall ((BOUND_VARIABLE_1477107 tptp.int) (BOUND_VARIABLE_1477108 tptp.int) (BOUND_VARIABLE_1477109 tptp.int) (BOUND_VARIABLE_1477110 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8243 BOUND_VARIABLE_1477107) BOUND_VARIABLE_1477108) BOUND_VARIABLE_1477109) BOUND_VARIABLE_1477110) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477108) BOUND_VARIABLE_1477110)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477107) BOUND_VARIABLE_1477109)))))))))) (let ((_let_2343 (forall ((BOUND_VARIABLE_1477082 tptp.int) (BOUND_VARIABLE_1477083 tptp.int) (BOUND_VARIABLE_1477084 tptp.int) (BOUND_VARIABLE_1477085 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8244 BOUND_VARIABLE_1477082) BOUND_VARIABLE_1477083) BOUND_VARIABLE_1477084) BOUND_VARIABLE_1477085) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477083) BOUND_VARIABLE_1477085)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477082) BOUND_VARIABLE_1477084)))))))))) (let ((_let_2344 (forall ((BOUND_VARIABLE_1477057 tptp.int) (BOUND_VARIABLE_1477058 tptp.int) (BOUND_VARIABLE_1477059 tptp.int) (BOUND_VARIABLE_1477060 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8245 BOUND_VARIABLE_1477057) BOUND_VARIABLE_1477058) BOUND_VARIABLE_1477059) BOUND_VARIABLE_1477060) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477058) BOUND_VARIABLE_1477060)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477057) BOUND_VARIABLE_1477059)))))))))) (let ((_let_2345 (forall ((BOUND_VARIABLE_1477032 tptp.int) (BOUND_VARIABLE_1477033 tptp.int) (BOUND_VARIABLE_1477034 tptp.int) (BOUND_VARIABLE_1477035 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8246 BOUND_VARIABLE_1477032) BOUND_VARIABLE_1477033) BOUND_VARIABLE_1477034) BOUND_VARIABLE_1477035) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477033) BOUND_VARIABLE_1477035)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477032) BOUND_VARIABLE_1477034)))))))))) (let ((_let_2346 (forall ((BOUND_VARIABLE_1477007 tptp.int) (BOUND_VARIABLE_1477008 tptp.int) (BOUND_VARIABLE_1477009 tptp.int) (BOUND_VARIABLE_1477010 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8247 BOUND_VARIABLE_1477007) BOUND_VARIABLE_1477008) BOUND_VARIABLE_1477009) BOUND_VARIABLE_1477010) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477008) BOUND_VARIABLE_1477010)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1477007) BOUND_VARIABLE_1477009)))))))))) (let ((_let_2347 (forall ((BOUND_VARIABLE_1476982 tptp.int) (BOUND_VARIABLE_1476983 tptp.int) (BOUND_VARIABLE_1476984 tptp.int) (BOUND_VARIABLE_1476985 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8248 BOUND_VARIABLE_1476982) BOUND_VARIABLE_1476983) BOUND_VARIABLE_1476984) BOUND_VARIABLE_1476985) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476983) BOUND_VARIABLE_1476985)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476982) BOUND_VARIABLE_1476984)))))))))) (let ((_let_2348 (forall ((BOUND_VARIABLE_1476957 tptp.int) (BOUND_VARIABLE_1476958 tptp.int) (BOUND_VARIABLE_1476959 tptp.int) (BOUND_VARIABLE_1476960 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8249 BOUND_VARIABLE_1476957) BOUND_VARIABLE_1476958) BOUND_VARIABLE_1476959) BOUND_VARIABLE_1476960) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476958) BOUND_VARIABLE_1476960)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476957) BOUND_VARIABLE_1476959)))))))))) (let ((_let_2349 (forall ((BOUND_VARIABLE_1476932 tptp.int) (BOUND_VARIABLE_1476933 tptp.int) (BOUND_VARIABLE_1476934 tptp.int) (BOUND_VARIABLE_1476935 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8250 BOUND_VARIABLE_1476932) BOUND_VARIABLE_1476933) BOUND_VARIABLE_1476934) BOUND_VARIABLE_1476935) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476933) BOUND_VARIABLE_1476935)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476932) BOUND_VARIABLE_1476934)))))))))) (let ((_let_2350 (forall ((BOUND_VARIABLE_1476907 tptp.int) (BOUND_VARIABLE_1476908 tptp.int) (BOUND_VARIABLE_1476909 tptp.int) (BOUND_VARIABLE_1476910 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8251 BOUND_VARIABLE_1476907) BOUND_VARIABLE_1476908) BOUND_VARIABLE_1476909) BOUND_VARIABLE_1476910) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476908) BOUND_VARIABLE_1476910)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476907) BOUND_VARIABLE_1476909)))))))))) (let ((_let_2351 (forall ((BOUND_VARIABLE_1476882 tptp.int) (BOUND_VARIABLE_1476883 tptp.int) (BOUND_VARIABLE_1476884 tptp.int) (BOUND_VARIABLE_1476885 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8252 BOUND_VARIABLE_1476882) BOUND_VARIABLE_1476883) BOUND_VARIABLE_1476884) BOUND_VARIABLE_1476885) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476883) BOUND_VARIABLE_1476885)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476882) BOUND_VARIABLE_1476884)))))))))) (let ((_let_2352 (forall ((BOUND_VARIABLE_1476857 tptp.int) (BOUND_VARIABLE_1476858 tptp.int) (BOUND_VARIABLE_1476859 tptp.int) (BOUND_VARIABLE_1476860 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8253 BOUND_VARIABLE_1476857) BOUND_VARIABLE_1476858) BOUND_VARIABLE_1476859) BOUND_VARIABLE_1476860) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476858) BOUND_VARIABLE_1476860)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476857) BOUND_VARIABLE_1476859)))))))))) (let ((_let_2353 (forall ((BOUND_VARIABLE_1476832 tptp.int) (BOUND_VARIABLE_1476833 tptp.int) (BOUND_VARIABLE_1476834 tptp.int) (BOUND_VARIABLE_1476835 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8254 BOUND_VARIABLE_1476832) BOUND_VARIABLE_1476833) BOUND_VARIABLE_1476834) BOUND_VARIABLE_1476835) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476833) BOUND_VARIABLE_1476835)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476832) BOUND_VARIABLE_1476834)))))))))) (let ((_let_2354 (forall ((BOUND_VARIABLE_1476807 tptp.int) (BOUND_VARIABLE_1476808 tptp.int) (BOUND_VARIABLE_1476809 tptp.int) (BOUND_VARIABLE_1476810 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8255 BOUND_VARIABLE_1476807) BOUND_VARIABLE_1476808) BOUND_VARIABLE_1476809) BOUND_VARIABLE_1476810) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476808) BOUND_VARIABLE_1476810)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476807) BOUND_VARIABLE_1476809)))))))))) (let ((_let_2355 (forall ((BOUND_VARIABLE_1476782 tptp.int) (BOUND_VARIABLE_1476783 tptp.int) (BOUND_VARIABLE_1476784 tptp.int) (BOUND_VARIABLE_1476785 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8256 BOUND_VARIABLE_1476782) BOUND_VARIABLE_1476783) BOUND_VARIABLE_1476784) BOUND_VARIABLE_1476785) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476783) BOUND_VARIABLE_1476785)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476782) BOUND_VARIABLE_1476784)))))))))) (let ((_let_2356 (forall ((BOUND_VARIABLE_1476757 tptp.int) (BOUND_VARIABLE_1476758 tptp.int) (BOUND_VARIABLE_1476759 tptp.int) (BOUND_VARIABLE_1476760 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8257 BOUND_VARIABLE_1476757) BOUND_VARIABLE_1476758) BOUND_VARIABLE_1476759) BOUND_VARIABLE_1476760) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476758) BOUND_VARIABLE_1476760)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476757) BOUND_VARIABLE_1476759)))))))))) (let ((_let_2357 (forall ((BOUND_VARIABLE_1476732 tptp.int) (BOUND_VARIABLE_1476733 tptp.int) (BOUND_VARIABLE_1476734 tptp.int) (BOUND_VARIABLE_1476735 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8258 BOUND_VARIABLE_1476732) BOUND_VARIABLE_1476733) BOUND_VARIABLE_1476734) BOUND_VARIABLE_1476735) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476733) BOUND_VARIABLE_1476735)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476732) BOUND_VARIABLE_1476734)))))))))) (let ((_let_2358 (forall ((BOUND_VARIABLE_1476707 tptp.int) (BOUND_VARIABLE_1476708 tptp.int) (BOUND_VARIABLE_1476709 tptp.int) (BOUND_VARIABLE_1476710 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8259 BOUND_VARIABLE_1476707) BOUND_VARIABLE_1476708) BOUND_VARIABLE_1476709) BOUND_VARIABLE_1476710) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476708) BOUND_VARIABLE_1476710)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476707) BOUND_VARIABLE_1476709)))))))))) (let ((_let_2359 (forall ((BOUND_VARIABLE_1476682 tptp.int) (BOUND_VARIABLE_1476683 tptp.int) (BOUND_VARIABLE_1476684 tptp.int) (BOUND_VARIABLE_1476685 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8260 BOUND_VARIABLE_1476682) BOUND_VARIABLE_1476683) BOUND_VARIABLE_1476684) BOUND_VARIABLE_1476685) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476683) BOUND_VARIABLE_1476685)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476682) BOUND_VARIABLE_1476684)))))))))) (let ((_let_2360 (forall ((BOUND_VARIABLE_1476657 tptp.int) (BOUND_VARIABLE_1476658 tptp.int) (BOUND_VARIABLE_1476659 tptp.int) (BOUND_VARIABLE_1476660 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8261 BOUND_VARIABLE_1476657) BOUND_VARIABLE_1476658) BOUND_VARIABLE_1476659) BOUND_VARIABLE_1476660) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476658) BOUND_VARIABLE_1476660)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476657) BOUND_VARIABLE_1476659)))))))))) (let ((_let_2361 (forall ((BOUND_VARIABLE_1476632 tptp.int) (BOUND_VARIABLE_1476633 tptp.int) (BOUND_VARIABLE_1476634 tptp.int) (BOUND_VARIABLE_1476635 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8262 BOUND_VARIABLE_1476632) BOUND_VARIABLE_1476633) BOUND_VARIABLE_1476634) BOUND_VARIABLE_1476635) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476633) BOUND_VARIABLE_1476635)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476632) BOUND_VARIABLE_1476634)))))))))) (let ((_let_2362 (forall ((BOUND_VARIABLE_1476607 tptp.int) (BOUND_VARIABLE_1476608 tptp.int) (BOUND_VARIABLE_1476609 tptp.int) (BOUND_VARIABLE_1476610 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8263 BOUND_VARIABLE_1476607) BOUND_VARIABLE_1476608) BOUND_VARIABLE_1476609) BOUND_VARIABLE_1476610) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476608) BOUND_VARIABLE_1476610)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476607) BOUND_VARIABLE_1476609)))))))))) (let ((_let_2363 (forall ((BOUND_VARIABLE_1476582 tptp.int) (BOUND_VARIABLE_1476583 tptp.int) (BOUND_VARIABLE_1476584 tptp.int) (BOUND_VARIABLE_1476585 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8264 BOUND_VARIABLE_1476582) BOUND_VARIABLE_1476583) BOUND_VARIABLE_1476584) BOUND_VARIABLE_1476585) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476583) BOUND_VARIABLE_1476585)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476582) BOUND_VARIABLE_1476584)))))))))) (let ((_let_2364 (forall ((BOUND_VARIABLE_1476557 tptp.int) (BOUND_VARIABLE_1476558 tptp.int) (BOUND_VARIABLE_1476559 tptp.int) (BOUND_VARIABLE_1476560 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8265 BOUND_VARIABLE_1476557) BOUND_VARIABLE_1476558) BOUND_VARIABLE_1476559) BOUND_VARIABLE_1476560) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476558) BOUND_VARIABLE_1476560)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476557) BOUND_VARIABLE_1476559)))))))))) (let ((_let_2365 (forall ((BOUND_VARIABLE_1476532 tptp.int) (BOUND_VARIABLE_1476533 tptp.int) (BOUND_VARIABLE_1476534 tptp.int) (BOUND_VARIABLE_1476535 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8266 BOUND_VARIABLE_1476532) BOUND_VARIABLE_1476533) BOUND_VARIABLE_1476534) BOUND_VARIABLE_1476535) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476533) BOUND_VARIABLE_1476535)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1476532) BOUND_VARIABLE_1476534)))))))))) (let ((_let_2366 (forall ((BOUND_VARIABLE_1476511 tptp.real) (BOUND_VARIABLE_1476512 tptp.nat) (BOUND_VARIABLE_1476513 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 (ho_7516 k_7521 BOUND_VARIABLE_1476511)) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1476512) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1476513) (ho_7516 (ho_7512 (ho_8050 k_8267 BOUND_VARIABLE_1476511) BOUND_VARIABLE_1476512) BOUND_VARIABLE_1476513)))))) (let ((_let_2367 (forall ((BOUND_VARIABLE_1476488 tptp.rat) (BOUND_VARIABLE_1476489 tptp.nat) (BOUND_VARIABLE_1476490 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7710 _let_4 k_7705))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7711 (ho_7717 _let_7 (ho_7711 _let_5 BOUND_VARIABLE_1476488)) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1476489) (ho_7711 (ho_7717 _let_7 _let_3) (ho_7711 _let_5 _let_3))))) BOUND_VARIABLE_1476490) (ho_7711 (ho_8055 (ho_8058 k_8268 BOUND_VARIABLE_1476488) BOUND_VARIABLE_1476489) BOUND_VARIABLE_1476490)))))))))))) (let ((_let_2368 (forall ((BOUND_VARIABLE_1476426 tptp.complex) (BOUND_VARIABLE_1476427 tptp.nat) (BOUND_VARIABLE_1476428 tptp.complex)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1476428))) (let ((_let_2 (ho_7985 k_7984 tptp.one))) (let ((_let_3 (ho_7958 k_7957 _let_2))) (let ((_let_4 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1476427) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_2)) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_2)) (ho_7730 k_7733 _let_3)))))) (let ((_let_5 (ho_7958 k_7957 BOUND_VARIABLE_1476426))) (let ((_let_6 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_5)) (ho_7730 k_7729 _let_4))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_5)) (ho_7730 k_7733 _let_4))))) (let ((_let_7 (ho_7519 k_7522 (ho_7730 k_7733 _let_6)))) (let ((_let_8 (ho_7730 k_7733 BOUND_VARIABLE_1476428))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7729 _let_6)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_1)) (ho_7516 k_7521 (ho_7516 _let_7 _let_8)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_9 _let_8)) (ho_7516 _let_7 _let_1))) (ho_7958 (ho_8063 (ho_8066 k_8269 BOUND_VARIABLE_1476426) BOUND_VARIABLE_1476427) BOUND_VARIABLE_1476428)))))))))))))) (let ((_let_2369 (forall ((BOUND_VARIABLE_1476363 tptp.real) (BOUND_VARIABLE_1476364 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1476364) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8270 BOUND_VARIABLE_1476363) BOUND_VARIABLE_1476364) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1476364 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1476364 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1476363) BOUND_VARIABLE_1476364))))))))))))))))) (let ((_let_2370 (forall ((BOUND_VARIABLE_1476300 tptp.real) (BOUND_VARIABLE_1476301 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1476301) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8271 BOUND_VARIABLE_1476300) BOUND_VARIABLE_1476301) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1476301 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1476301 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1476300) BOUND_VARIABLE_1476301))))))))))))))))) (let ((_let_2371 (forall ((BOUND_VARIABLE_1476237 tptp.real) (BOUND_VARIABLE_1476238 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1476238) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8272 BOUND_VARIABLE_1476237) BOUND_VARIABLE_1476238) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1476238 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1476238 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1476237) BOUND_VARIABLE_1476238))))))))))))))))) (let ((_let_2372 (forall ((BOUND_VARIABLE_1476208 tptp.real) (BOUND_VARIABLE_1476209 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (and (ho_7781 (ho_7780 k_7779 (ho_7516 k_7521 _let_1)) BOUND_VARIABLE_1476209) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1476209) _let_1) (= BOUND_VARIABLE_1476208 (ho_7795 k_7794 (ho_7507 k_7551 BOUND_VARIABLE_1476209)))) (ho_7781 (ho_7780 k_8273 BOUND_VARIABLE_1476208) BOUND_VARIABLE_1476209)))))) (let ((_let_2373 (forall ((BOUND_VARIABLE_1476145 tptp.real) (BOUND_VARIABLE_1476146 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1476146) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8274 BOUND_VARIABLE_1476145) BOUND_VARIABLE_1476146) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1476146 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1476146 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1476145) BOUND_VARIABLE_1476146))))))))))))))))) (let ((_let_2374 (forall ((BOUND_VARIABLE_1476116 tptp.real) (BOUND_VARIABLE_1476117 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (and (ho_7781 (ho_7780 k_7779 (ho_7516 k_7521 _let_1)) BOUND_VARIABLE_1476117) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1476117) _let_1) (= BOUND_VARIABLE_1476116 (ho_7795 k_7794 (ho_7507 k_7552 BOUND_VARIABLE_1476117)))) (ho_7781 (ho_7780 k_8275 BOUND_VARIABLE_1476116) BOUND_VARIABLE_1476117)))))) (let ((_let_2375 (forall ((BOUND_VARIABLE_1476053 tptp.real) (BOUND_VARIABLE_1476054 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1476054) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8276 BOUND_VARIABLE_1476053) BOUND_VARIABLE_1476054) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 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((BOUND_VARIABLE_1475990 tptp.real) (BOUND_VARIABLE_1475991 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1475991) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8277 BOUND_VARIABLE_1475990) BOUND_VARIABLE_1475991) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1475991 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1475991 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1475990) BOUND_VARIABLE_1475991))))))))))))))))) (let ((_let_2377 (forall ((BOUND_VARIABLE_1475927 tptp.real) (BOUND_VARIABLE_1475928 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1475928) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8278 BOUND_VARIABLE_1475927) BOUND_VARIABLE_1475928) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1475928 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1475928 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1475927) BOUND_VARIABLE_1475928))))))))))))))))) (let ((_let_2378 (forall ((BOUND_VARIABLE_1475864 tptp.real) (BOUND_VARIABLE_1475865 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1475865) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8279 BOUND_VARIABLE_1475864) BOUND_VARIABLE_1475865) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1475865 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1475865 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1475864) BOUND_VARIABLE_1475865))))))))))))))))) (let ((_let_2379 (forall ((BOUND_VARIABLE_1475801 tptp.real) (BOUND_VARIABLE_1475802 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1475802) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8280 BOUND_VARIABLE_1475801) BOUND_VARIABLE_1475802) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1475802 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1475802 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1475801) BOUND_VARIABLE_1475802))))))))))))))))) (let ((_let_2380 (forall ((BOUND_VARIABLE_1475738 tptp.real) (BOUND_VARIABLE_1475739 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1475739) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8281 BOUND_VARIABLE_1475738) BOUND_VARIABLE_1475739) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1475739 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1475739 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1475738) BOUND_VARIABLE_1475739))))))))))))))))) (let ((_let_2381 (forall ((BOUND_VARIABLE_1475718 tptp.int) (BOUND_VARIABLE_1475719 tptp.nat) (BOUND_VARIABLE_1475720 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1475718) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) BOUND_VARIABLE_1475719) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1))))) BOUND_VARIABLE_1475720) (ho_7459 (ho_7470 (ho_8100 k_8282 BOUND_VARIABLE_1475718) BOUND_VARIABLE_1475719) BOUND_VARIABLE_1475720)))))) (let ((_let_2382 (forall ((BOUND_VARIABLE_1475686 tptp.int) (BOUND_VARIABLE_1475687 tptp.nat) (BOUND_VARIABLE_1475688 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1475686) (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1475687) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1475688) _let_3))))) _let_3)) (ho_7927 (ho_8015 (ho_8014 k_8283 BOUND_VARIABLE_1475686) BOUND_VARIABLE_1475687) BOUND_VARIABLE_1475688))))))))) (let ((_let_2383 (forall ((BOUND_VARIABLE_1475646 tptp.nat) (BOUND_VARIABLE_1475647 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1475646) _let_2)))))) (or (not (= BOUND_VARIABLE_1475647 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8284 BOUND_VARIABLE_1475646) BOUND_VARIABLE_1475647))))) (let ((_let_2384 (forall ((BOUND_VARIABLE_1475605 tptp.nat) (BOUND_VARIABLE_1475606 tptp.nat) (BOUND_VARIABLE_1475607 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1475605) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7466 (ho_7465 (ho_8093 k_8286 k_8285) BOUND_VARIABLE_1475606) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 _let_1)) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1475607) _let_2))) (ho_7466 (ho_7465 (ho_8288 k_8287 BOUND_VARIABLE_1475605) BOUND_VARIABLE_1475606) BOUND_VARIABLE_1475607)))))))) (let ((_let_2385 (forall ((BOUND_VARIABLE_1475562 tptp.nat) (BOUND_VARIABLE_1475563 tptp.nat) (BOUND_VARIABLE_1475564 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1475562) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7466 (ho_7465 (ho_8093 k_8286 k_8285) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1475563) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1475564) _let_3))))) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 _let_1)) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) _let_3))) (ho_7466 (ho_7465 (ho_8288 k_8289 BOUND_VARIABLE_1475562) BOUND_VARIABLE_1475563) BOUND_VARIABLE_1475564))))))))) (let ((_let_2386 (forall ((BOUND_VARIABLE_1475522 tptp.nat) (BOUND_VARIABLE_1475523 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1475522) _let_2)))))) (or (not (= BOUND_VARIABLE_1475523 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8290 BOUND_VARIABLE_1475522) BOUND_VARIABLE_1475523))))) (let ((_let_2387 (forall ((BOUND_VARIABLE_1475501 tptp.rat) (BOUND_VARIABLE_1475502 tptp.nat) (BOUND_VARIABLE_1475503 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_6 (ho_7716 _let_5 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_5 k_8019) (ho_7711 (ho_7717 _let_6 BOUND_VARIABLE_1475501) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1475502) (ho_7711 (ho_7717 _let_6 _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3))))) BOUND_VARIABLE_1475503) (ho_7711 (ho_8055 (ho_8058 k_8291 BOUND_VARIABLE_1475501) BOUND_VARIABLE_1475502) BOUND_VARIABLE_1475503))))))))))) (let ((_let_2388 (forall ((BOUND_VARIABLE_1475468 tptp.rat) (BOUND_VARIABLE_1475469 tptp.nat) (BOUND_VARIABLE_1475470 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_3)) (ho_7698 (ho_7697 k_7696 _let_3) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_5 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_6 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_5) k_7712))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (= (ho_7711 (ho_7717 _let_6 BOUND_VARIABLE_1475468) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1475469) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1475470) _let_3))))) (ho_7711 (ho_7717 _let_6 _let_4) (ho_7711 (ho_7710 _let_5 k_7705) _let_4)))) (ho_7636 (ho_8023 (ho_8022 k_8292 BOUND_VARIABLE_1475468) BOUND_VARIABLE_1475469) BOUND_VARIABLE_1475470)))))))))))) (let ((_let_2389 (forall ((BOUND_VARIABLE_1475428 tptp.nat) (BOUND_VARIABLE_1475429 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1475428) _let_2)))))) (or (not (= BOUND_VARIABLE_1475429 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8293 BOUND_VARIABLE_1475428) BOUND_VARIABLE_1475429))))) (let ((_let_2390 (forall ((BOUND_VARIABLE_1475408 tptp.real) (BOUND_VARIABLE_1475409 tptp.nat) (BOUND_VARIABLE_1475410 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1475408) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1475409) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) BOUND_VARIABLE_1475410) (ho_7516 (ho_7512 (ho_8050 k_8294 BOUND_VARIABLE_1475408) BOUND_VARIABLE_1475409) BOUND_VARIABLE_1475410)))))) (let ((_let_2391 (forall ((BOUND_VARIABLE_1475376 tptp.real) (BOUND_VARIABLE_1475377 tptp.nat) (BOUND_VARIABLE_1475378 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1475376) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1475377) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1475378) _let_4))))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (ho_7508 (ho_7775 (ho_7999 k_8295 BOUND_VARIABLE_1475376) BOUND_VARIABLE_1475377) BOUND_VARIABLE_1475378)))))))))) (let ((_let_2392 (forall ((BOUND_VARIABLE_1475336 tptp.nat) (BOUND_VARIABLE_1475337 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1475336) _let_2)))))) (or (not (= BOUND_VARIABLE_1475337 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8296 BOUND_VARIABLE_1475336) BOUND_VARIABLE_1475337))))) (let ((_let_2393 (forall ((BOUND_VARIABLE_1475307 tptp.real) (BOUND_VARIABLE_1475308 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (and (ho_7781 (ho_7780 k_7779 (ho_7516 k_7521 _let_1)) BOUND_VARIABLE_1475308) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1475308) _let_1) (= BOUND_VARIABLE_1475307 (ho_7795 k_7794 (ho_7507 k_7553 BOUND_VARIABLE_1475308)))) (ho_7781 (ho_7780 k_8297 BOUND_VARIABLE_1475307) BOUND_VARIABLE_1475308)))))) (let ((_let_2394 (forall ((BOUND_VARIABLE_1475282 tptp.int) (BOUND_VARIABLE_1475283 tptp.int) (BOUND_VARIABLE_1475284 tptp.int) (BOUND_VARIABLE_1475285 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8298 BOUND_VARIABLE_1475282) BOUND_VARIABLE_1475283) BOUND_VARIABLE_1475284) BOUND_VARIABLE_1475285) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475283) BOUND_VARIABLE_1475285)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475282) BOUND_VARIABLE_1475284)))))))))) (let ((_let_2395 (forall ((BOUND_VARIABLE_1475257 tptp.int) (BOUND_VARIABLE_1475258 tptp.int) (BOUND_VARIABLE_1475259 tptp.int) (BOUND_VARIABLE_1475260 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8299 BOUND_VARIABLE_1475257) BOUND_VARIABLE_1475258) BOUND_VARIABLE_1475259) BOUND_VARIABLE_1475260) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475258) BOUND_VARIABLE_1475260)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475257) BOUND_VARIABLE_1475259)))))))))) (let ((_let_2396 (forall ((BOUND_VARIABLE_1475232 tptp.int) (BOUND_VARIABLE_1475233 tptp.int) (BOUND_VARIABLE_1475234 tptp.int) (BOUND_VARIABLE_1475235 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8300 BOUND_VARIABLE_1475232) BOUND_VARIABLE_1475233) BOUND_VARIABLE_1475234) BOUND_VARIABLE_1475235) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475233) BOUND_VARIABLE_1475235)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475232) BOUND_VARIABLE_1475234)))))))))) (let ((_let_2397 (forall ((BOUND_VARIABLE_1475207 tptp.int) (BOUND_VARIABLE_1475208 tptp.int) (BOUND_VARIABLE_1475209 tptp.int) (BOUND_VARIABLE_1475210 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8301 BOUND_VARIABLE_1475207) BOUND_VARIABLE_1475208) BOUND_VARIABLE_1475209) BOUND_VARIABLE_1475210) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475208) BOUND_VARIABLE_1475210)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475207) BOUND_VARIABLE_1475209)))))))))) (let ((_let_2398 (forall ((BOUND_VARIABLE_1475182 tptp.int) (BOUND_VARIABLE_1475183 tptp.int) (BOUND_VARIABLE_1475184 tptp.int) (BOUND_VARIABLE_1475185 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8302 BOUND_VARIABLE_1475182) BOUND_VARIABLE_1475183) BOUND_VARIABLE_1475184) BOUND_VARIABLE_1475185) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475183) BOUND_VARIABLE_1475185)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475182) BOUND_VARIABLE_1475184)))))))))) (let ((_let_2399 (forall ((BOUND_VARIABLE_1475157 tptp.int) (BOUND_VARIABLE_1475158 tptp.int) (BOUND_VARIABLE_1475159 tptp.int) (BOUND_VARIABLE_1475160 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8303 BOUND_VARIABLE_1475157) BOUND_VARIABLE_1475158) BOUND_VARIABLE_1475159) BOUND_VARIABLE_1475160) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475158) BOUND_VARIABLE_1475160)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475157) BOUND_VARIABLE_1475159)))))))))) (let ((_let_2400 (forall ((BOUND_VARIABLE_1475132 tptp.int) (BOUND_VARIABLE_1475133 tptp.int) (BOUND_VARIABLE_1475134 tptp.int) (BOUND_VARIABLE_1475135 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8304 BOUND_VARIABLE_1475132) BOUND_VARIABLE_1475133) BOUND_VARIABLE_1475134) BOUND_VARIABLE_1475135) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475133) BOUND_VARIABLE_1475135)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475132) BOUND_VARIABLE_1475134)))))))))) (let ((_let_2401 (forall ((BOUND_VARIABLE_1475107 tptp.int) (BOUND_VARIABLE_1475108 tptp.int) (BOUND_VARIABLE_1475109 tptp.int) (BOUND_VARIABLE_1475110 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8305 BOUND_VARIABLE_1475107) BOUND_VARIABLE_1475108) BOUND_VARIABLE_1475109) BOUND_VARIABLE_1475110) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475108) BOUND_VARIABLE_1475110)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475107) BOUND_VARIABLE_1475109)))))))))) (let ((_let_2402 (forall ((BOUND_VARIABLE_1475082 tptp.int) (BOUND_VARIABLE_1475083 tptp.int) (BOUND_VARIABLE_1475084 tptp.int) (BOUND_VARIABLE_1475085 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8306 BOUND_VARIABLE_1475082) BOUND_VARIABLE_1475083) BOUND_VARIABLE_1475084) BOUND_VARIABLE_1475085) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475083) BOUND_VARIABLE_1475085)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475082) BOUND_VARIABLE_1475084)))))))))) (let ((_let_2403 (forall ((BOUND_VARIABLE_1475057 tptp.int) (BOUND_VARIABLE_1475058 tptp.int) (BOUND_VARIABLE_1475059 tptp.int) (BOUND_VARIABLE_1475060 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8307 BOUND_VARIABLE_1475057) BOUND_VARIABLE_1475058) BOUND_VARIABLE_1475059) BOUND_VARIABLE_1475060) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475058) BOUND_VARIABLE_1475060)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475057) BOUND_VARIABLE_1475059)))))))))) (let ((_let_2404 (forall ((BOUND_VARIABLE_1475032 tptp.int) (BOUND_VARIABLE_1475033 tptp.int) (BOUND_VARIABLE_1475034 tptp.int) (BOUND_VARIABLE_1475035 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8308 BOUND_VARIABLE_1475032) BOUND_VARIABLE_1475033) BOUND_VARIABLE_1475034) BOUND_VARIABLE_1475035) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475033) BOUND_VARIABLE_1475035)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475032) BOUND_VARIABLE_1475034)))))))))) (let ((_let_2405 (forall ((BOUND_VARIABLE_1475007 tptp.int) (BOUND_VARIABLE_1475008 tptp.int) (BOUND_VARIABLE_1475009 tptp.int) (BOUND_VARIABLE_1475010 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8309 BOUND_VARIABLE_1475007) BOUND_VARIABLE_1475008) BOUND_VARIABLE_1475009) BOUND_VARIABLE_1475010) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475008) BOUND_VARIABLE_1475010)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1475007) BOUND_VARIABLE_1475009)))))))))) (let ((_let_2406 (forall ((BOUND_VARIABLE_1474944 tptp.real) (BOUND_VARIABLE_1474945 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474945) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8310 BOUND_VARIABLE_1474944) BOUND_VARIABLE_1474945) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474945 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474945 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474944) BOUND_VARIABLE_1474945))))))))))))))))) (let ((_let_2407 (forall ((BOUND_VARIABLE_1474881 tptp.real) (BOUND_VARIABLE_1474882 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474882) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8311 BOUND_VARIABLE_1474881) BOUND_VARIABLE_1474882) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474882 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474882 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474881) BOUND_VARIABLE_1474882))))))))))))))))) (let ((_let_2408 (forall ((BOUND_VARIABLE_1474818 tptp.real) (BOUND_VARIABLE_1474819 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474819) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8312 BOUND_VARIABLE_1474818) BOUND_VARIABLE_1474819) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474819 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474819 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474818) BOUND_VARIABLE_1474819))))))))))))))))) (let ((_let_2409 (forall ((BOUND_VARIABLE_1474755 tptp.real) (BOUND_VARIABLE_1474756 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474756) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8313 BOUND_VARIABLE_1474755) BOUND_VARIABLE_1474756) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474756 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474756 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474755) BOUND_VARIABLE_1474756))))))))))))))))) (let ((_let_2410 (forall ((BOUND_VARIABLE_1474730 tptp.int) (BOUND_VARIABLE_1474731 tptp.int) (BOUND_VARIABLE_1474732 tptp.int) (BOUND_VARIABLE_1474733 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8314 BOUND_VARIABLE_1474730) BOUND_VARIABLE_1474731) BOUND_VARIABLE_1474732) BOUND_VARIABLE_1474733) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474731) BOUND_VARIABLE_1474733)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474730) BOUND_VARIABLE_1474732)))))))))) (let ((_let_2411 (forall ((BOUND_VARIABLE_1474705 tptp.int) (BOUND_VARIABLE_1474706 tptp.int) (BOUND_VARIABLE_1474707 tptp.int) (BOUND_VARIABLE_1474708 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8315 BOUND_VARIABLE_1474705) BOUND_VARIABLE_1474706) BOUND_VARIABLE_1474707) BOUND_VARIABLE_1474708) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474706) BOUND_VARIABLE_1474708)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474705) BOUND_VARIABLE_1474707)))))))))) (let ((_let_2412 (forall ((BOUND_VARIABLE_1474680 tptp.int) (BOUND_VARIABLE_1474681 tptp.int) (BOUND_VARIABLE_1474682 tptp.int) (BOUND_VARIABLE_1474683 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8316 BOUND_VARIABLE_1474680) BOUND_VARIABLE_1474681) BOUND_VARIABLE_1474682) BOUND_VARIABLE_1474683) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474681) BOUND_VARIABLE_1474683)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474680) BOUND_VARIABLE_1474682)))))))))) (let ((_let_2413 (forall ((BOUND_VARIABLE_1474655 tptp.int) (BOUND_VARIABLE_1474656 tptp.int) (BOUND_VARIABLE_1474657 tptp.int) (BOUND_VARIABLE_1474658 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8317 BOUND_VARIABLE_1474655) BOUND_VARIABLE_1474656) BOUND_VARIABLE_1474657) BOUND_VARIABLE_1474658) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474656) BOUND_VARIABLE_1474658)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474655) BOUND_VARIABLE_1474657)))))))))) (let ((_let_2414 (forall ((BOUND_VARIABLE_1474630 tptp.int) (BOUND_VARIABLE_1474631 tptp.int) (BOUND_VARIABLE_1474632 tptp.int) (BOUND_VARIABLE_1474633 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8318 BOUND_VARIABLE_1474630) BOUND_VARIABLE_1474631) BOUND_VARIABLE_1474632) BOUND_VARIABLE_1474633) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474631) BOUND_VARIABLE_1474633)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474630) BOUND_VARIABLE_1474632)))))))))) (let ((_let_2415 (forall ((BOUND_VARIABLE_1474605 tptp.int) (BOUND_VARIABLE_1474606 tptp.int) (BOUND_VARIABLE_1474607 tptp.int) (BOUND_VARIABLE_1474608 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8319 BOUND_VARIABLE_1474605) BOUND_VARIABLE_1474606) BOUND_VARIABLE_1474607) BOUND_VARIABLE_1474608) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474606) BOUND_VARIABLE_1474608)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474605) BOUND_VARIABLE_1474607)))))))))) (let ((_let_2416 (forall ((BOUND_VARIABLE_1474580 tptp.int) (BOUND_VARIABLE_1474581 tptp.int) (BOUND_VARIABLE_1474582 tptp.int) (BOUND_VARIABLE_1474583 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8320 BOUND_VARIABLE_1474580) BOUND_VARIABLE_1474581) BOUND_VARIABLE_1474582) BOUND_VARIABLE_1474583) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474581) BOUND_VARIABLE_1474583)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474580) BOUND_VARIABLE_1474582)))))))))) (let ((_let_2417 (forall ((BOUND_VARIABLE_1474555 tptp.int) (BOUND_VARIABLE_1474556 tptp.int) (BOUND_VARIABLE_1474557 tptp.int) (BOUND_VARIABLE_1474558 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8321 BOUND_VARIABLE_1474555) BOUND_VARIABLE_1474556) BOUND_VARIABLE_1474557) BOUND_VARIABLE_1474558) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474556) BOUND_VARIABLE_1474558)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474555) BOUND_VARIABLE_1474557)))))))))) (let ((_let_2418 (forall ((BOUND_VARIABLE_1474530 tptp.int) (BOUND_VARIABLE_1474531 tptp.int) (BOUND_VARIABLE_1474532 tptp.int) (BOUND_VARIABLE_1474533 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8322 BOUND_VARIABLE_1474530) BOUND_VARIABLE_1474531) BOUND_VARIABLE_1474532) BOUND_VARIABLE_1474533) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474531) BOUND_VARIABLE_1474533)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474530) BOUND_VARIABLE_1474532)))))))))) (let ((_let_2419 (forall ((BOUND_VARIABLE_1474505 tptp.int) (BOUND_VARIABLE_1474506 tptp.int) (BOUND_VARIABLE_1474507 tptp.int) (BOUND_VARIABLE_1474508 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8323 BOUND_VARIABLE_1474505) BOUND_VARIABLE_1474506) BOUND_VARIABLE_1474507) BOUND_VARIABLE_1474508) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474506) BOUND_VARIABLE_1474508)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474505) BOUND_VARIABLE_1474507)))))))))) (let ((_let_2420 (forall ((BOUND_VARIABLE_1474480 tptp.int) (BOUND_VARIABLE_1474481 tptp.int) (BOUND_VARIABLE_1474482 tptp.int) (BOUND_VARIABLE_1474483 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8324 BOUND_VARIABLE_1474480) BOUND_VARIABLE_1474481) BOUND_VARIABLE_1474482) BOUND_VARIABLE_1474483) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474481) BOUND_VARIABLE_1474483)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474480) BOUND_VARIABLE_1474482)))))))))) (let ((_let_2421 (forall ((BOUND_VARIABLE_1474455 tptp.int) (BOUND_VARIABLE_1474456 tptp.int) (BOUND_VARIABLE_1474457 tptp.int) (BOUND_VARIABLE_1474458 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8325 BOUND_VARIABLE_1474455) BOUND_VARIABLE_1474456) BOUND_VARIABLE_1474457) BOUND_VARIABLE_1474458) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474456) BOUND_VARIABLE_1474458)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1474455) BOUND_VARIABLE_1474457)))))))))) (let ((_let_2422 (forall ((BOUND_VARIABLE_1474450 tptp.nat)) (= BOUND_VARIABLE_1474450 (ho_7466 k_8326 BOUND_VARIABLE_1474450))))) (let ((_let_2423 (forall ((BOUND_VARIABLE_1474410 tptp.nat) (BOUND_VARIABLE_1474411 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1474410) _let_2)))))) (or (not (= BOUND_VARIABLE_1474411 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8327 BOUND_VARIABLE_1474410) BOUND_VARIABLE_1474411))))) (let ((_let_2424 (forall ((BOUND_VARIABLE_1474405 tptp.nat)) (= BOUND_VARIABLE_1474405 (ho_7466 k_8328 BOUND_VARIABLE_1474405))))) (let ((_let_2425 (forall ((BOUND_VARIABLE_1474365 tptp.nat) (BOUND_VARIABLE_1474366 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1474365) _let_2)))))) (or (not (= BOUND_VARIABLE_1474366 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8329 BOUND_VARIABLE_1474365) BOUND_VARIABLE_1474366))))) (let ((_let_2426 (forall ((BOUND_VARIABLE_1474360 tptp.nat)) (= BOUND_VARIABLE_1474360 (ho_7466 k_8330 BOUND_VARIABLE_1474360))))) (let ((_let_2427 (forall ((BOUND_VARIABLE_1474320 tptp.nat) (BOUND_VARIABLE_1474321 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1474320) _let_2)))))) (or (not (= BOUND_VARIABLE_1474321 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8331 BOUND_VARIABLE_1474320) BOUND_VARIABLE_1474321))))) (let ((_let_2428 (forall ((BOUND_VARIABLE_1474315 tptp.nat)) (= BOUND_VARIABLE_1474315 (ho_7466 k_8332 BOUND_VARIABLE_1474315))))) (let ((_let_2429 (forall ((BOUND_VARIABLE_1474275 tptp.nat) (BOUND_VARIABLE_1474276 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7750 (ho_7749 k_7748 _let_4) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 _let_4) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1474275) _let_2)))))) (or (not (= BOUND_VARIABLE_1474276 (ho_7466 (ho_7754 k_7753 _let_5) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_5)))))))))))) (ho_7541 (ho_7540 k_8333 BOUND_VARIABLE_1474275) BOUND_VARIABLE_1474276))))) (let ((_let_2430 (forall ((BOUND_VARIABLE_1474212 tptp.real) (BOUND_VARIABLE_1474213 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474213) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8334 BOUND_VARIABLE_1474212) BOUND_VARIABLE_1474213) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474213 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474213 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474212) BOUND_VARIABLE_1474213))))))))))))))))) (let ((_let_2431 (forall ((BOUND_VARIABLE_1474149 tptp.real) (BOUND_VARIABLE_1474150 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474150) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8335 BOUND_VARIABLE_1474149) BOUND_VARIABLE_1474150) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474150 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474150 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474149) BOUND_VARIABLE_1474150))))))))))))))))) (let ((_let_2432 (forall ((BOUND_VARIABLE_1474086 tptp.real) (BOUND_VARIABLE_1474087 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474087) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8336 BOUND_VARIABLE_1474086) BOUND_VARIABLE_1474087) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474087 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474087 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474086) BOUND_VARIABLE_1474087))))))))))))))))) (let ((_let_2433 (forall ((BOUND_VARIABLE_1474023 tptp.real) (BOUND_VARIABLE_1474024 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1474024) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8337 BOUND_VARIABLE_1474023) BOUND_VARIABLE_1474024) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1474024 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1474024 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1474023) BOUND_VARIABLE_1474024))))))))))))))))) (let ((_let_2434 (forall ((BOUND_VARIABLE_1473960 tptp.real) (BOUND_VARIABLE_1473961 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1473961) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8338 BOUND_VARIABLE_1473960) BOUND_VARIABLE_1473961) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1473961 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1473961 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1473960) BOUND_VARIABLE_1473961))))))))))))))))) (let ((_let_2435 (forall ((BOUND_VARIABLE_1473897 tptp.real) (BOUND_VARIABLE_1473898 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1473898) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8339 BOUND_VARIABLE_1473897) BOUND_VARIABLE_1473898) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1473898 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1473898 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1473897) BOUND_VARIABLE_1473898))))))))))))))))) (let ((_let_2436 (forall ((BOUND_VARIABLE_1473834 tptp.real) (BOUND_VARIABLE_1473835 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1473835) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8340 BOUND_VARIABLE_1473834) BOUND_VARIABLE_1473835) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1473835 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1473835 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1473834) BOUND_VARIABLE_1473835))))))))))))))))) (let ((_let_2437 (forall ((BOUND_VARIABLE_1473771 tptp.real) (BOUND_VARIABLE_1473772 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1473772) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8341 BOUND_VARIABLE_1473771) BOUND_VARIABLE_1473772) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1473772 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1473772 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1473771) BOUND_VARIABLE_1473772))))))))))))))))) (let ((_let_2438 (forall ((BOUND_VARIABLE_1473746 tptp.int) (BOUND_VARIABLE_1473747 tptp.int) (BOUND_VARIABLE_1473748 tptp.int) (BOUND_VARIABLE_1473749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8342 BOUND_VARIABLE_1473746) BOUND_VARIABLE_1473747) BOUND_VARIABLE_1473748) BOUND_VARIABLE_1473749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473747) BOUND_VARIABLE_1473749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473746) BOUND_VARIABLE_1473748)))))))))) (let ((_let_2439 (forall ((BOUND_VARIABLE_1473721 tptp.int) (BOUND_VARIABLE_1473722 tptp.int) (BOUND_VARIABLE_1473723 tptp.int) (BOUND_VARIABLE_1473724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8343 BOUND_VARIABLE_1473721) BOUND_VARIABLE_1473722) BOUND_VARIABLE_1473723) BOUND_VARIABLE_1473724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473722) BOUND_VARIABLE_1473724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473721) BOUND_VARIABLE_1473723)))))))))) (let ((_let_2440 (forall ((BOUND_VARIABLE_1473696 tptp.int) (BOUND_VARIABLE_1473697 tptp.int) (BOUND_VARIABLE_1473698 tptp.int) (BOUND_VARIABLE_1473699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8344 BOUND_VARIABLE_1473696) BOUND_VARIABLE_1473697) BOUND_VARIABLE_1473698) BOUND_VARIABLE_1473699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473697) BOUND_VARIABLE_1473699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473696) BOUND_VARIABLE_1473698)))))))))) (let ((_let_2441 (forall ((BOUND_VARIABLE_1473671 tptp.int) (BOUND_VARIABLE_1473672 tptp.int) (BOUND_VARIABLE_1473673 tptp.int) (BOUND_VARIABLE_1473674 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8345 BOUND_VARIABLE_1473671) BOUND_VARIABLE_1473672) BOUND_VARIABLE_1473673) BOUND_VARIABLE_1473674) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473672) BOUND_VARIABLE_1473674)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473671) BOUND_VARIABLE_1473673)))))))))) (let ((_let_2442 (forall ((BOUND_VARIABLE_1473646 tptp.int) (BOUND_VARIABLE_1473647 tptp.int) (BOUND_VARIABLE_1473648 tptp.int) (BOUND_VARIABLE_1473649 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8346 BOUND_VARIABLE_1473646) BOUND_VARIABLE_1473647) BOUND_VARIABLE_1473648) BOUND_VARIABLE_1473649) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473647) BOUND_VARIABLE_1473649)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473646) BOUND_VARIABLE_1473648)))))))))) (let ((_let_2443 (forall ((BOUND_VARIABLE_1473621 tptp.int) (BOUND_VARIABLE_1473622 tptp.int) (BOUND_VARIABLE_1473623 tptp.int) (BOUND_VARIABLE_1473624 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8347 BOUND_VARIABLE_1473621) BOUND_VARIABLE_1473622) BOUND_VARIABLE_1473623) BOUND_VARIABLE_1473624) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473622) BOUND_VARIABLE_1473624)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473621) BOUND_VARIABLE_1473623)))))))))) (let ((_let_2444 (forall ((BOUND_VARIABLE_1473596 tptp.int) (BOUND_VARIABLE_1473597 tptp.int) (BOUND_VARIABLE_1473598 tptp.int) (BOUND_VARIABLE_1473599 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8348 BOUND_VARIABLE_1473596) BOUND_VARIABLE_1473597) BOUND_VARIABLE_1473598) BOUND_VARIABLE_1473599) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473597) BOUND_VARIABLE_1473599)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473596) BOUND_VARIABLE_1473598)))))))))) (let ((_let_2445 (forall ((BOUND_VARIABLE_1473571 tptp.int) (BOUND_VARIABLE_1473572 tptp.int) (BOUND_VARIABLE_1473573 tptp.int) (BOUND_VARIABLE_1473574 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8349 BOUND_VARIABLE_1473571) BOUND_VARIABLE_1473572) BOUND_VARIABLE_1473573) BOUND_VARIABLE_1473574) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473572) BOUND_VARIABLE_1473574)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473571) BOUND_VARIABLE_1473573)))))))))) (let ((_let_2446 (forall ((BOUND_VARIABLE_1473546 tptp.int) (BOUND_VARIABLE_1473547 tptp.int) (BOUND_VARIABLE_1473548 tptp.int) (BOUND_VARIABLE_1473549 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8350 BOUND_VARIABLE_1473546) BOUND_VARIABLE_1473547) BOUND_VARIABLE_1473548) BOUND_VARIABLE_1473549) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473547) BOUND_VARIABLE_1473549)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473546) BOUND_VARIABLE_1473548)))))))))) (let ((_let_2447 (forall ((BOUND_VARIABLE_1473521 tptp.int) (BOUND_VARIABLE_1473522 tptp.int) (BOUND_VARIABLE_1473523 tptp.int) (BOUND_VARIABLE_1473524 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8351 BOUND_VARIABLE_1473521) BOUND_VARIABLE_1473522) BOUND_VARIABLE_1473523) BOUND_VARIABLE_1473524) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473522) BOUND_VARIABLE_1473524)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473521) BOUND_VARIABLE_1473523)))))))))) (let ((_let_2448 (forall ((BOUND_VARIABLE_1473496 tptp.int) (BOUND_VARIABLE_1473497 tptp.int) (BOUND_VARIABLE_1473498 tptp.int) (BOUND_VARIABLE_1473499 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8352 BOUND_VARIABLE_1473496) BOUND_VARIABLE_1473497) BOUND_VARIABLE_1473498) BOUND_VARIABLE_1473499) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473497) BOUND_VARIABLE_1473499)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473496) BOUND_VARIABLE_1473498)))))))))) (let ((_let_2449 (forall ((BOUND_VARIABLE_1473471 tptp.int) (BOUND_VARIABLE_1473472 tptp.int) (BOUND_VARIABLE_1473473 tptp.int) (BOUND_VARIABLE_1473474 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8353 BOUND_VARIABLE_1473471) BOUND_VARIABLE_1473472) BOUND_VARIABLE_1473473) BOUND_VARIABLE_1473474) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473472) BOUND_VARIABLE_1473474)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473471) BOUND_VARIABLE_1473473)))))))))) (let ((_let_2450 (forall ((BOUND_VARIABLE_1473446 tptp.int) (BOUND_VARIABLE_1473447 tptp.int) (BOUND_VARIABLE_1473448 tptp.int) (BOUND_VARIABLE_1473449 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8354 BOUND_VARIABLE_1473446) BOUND_VARIABLE_1473447) BOUND_VARIABLE_1473448) BOUND_VARIABLE_1473449) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473447) BOUND_VARIABLE_1473449)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473446) BOUND_VARIABLE_1473448)))))))))) (let ((_let_2451 (forall ((BOUND_VARIABLE_1473421 tptp.int) (BOUND_VARIABLE_1473422 tptp.int) (BOUND_VARIABLE_1473423 tptp.int) (BOUND_VARIABLE_1473424 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8355 BOUND_VARIABLE_1473421) BOUND_VARIABLE_1473422) BOUND_VARIABLE_1473423) BOUND_VARIABLE_1473424) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473422) BOUND_VARIABLE_1473424)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473421) BOUND_VARIABLE_1473423)))))))))) (let ((_let_2452 (forall ((BOUND_VARIABLE_1473396 tptp.int) (BOUND_VARIABLE_1473397 tptp.int) (BOUND_VARIABLE_1473398 tptp.int) (BOUND_VARIABLE_1473399 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8356 BOUND_VARIABLE_1473396) BOUND_VARIABLE_1473397) BOUND_VARIABLE_1473398) BOUND_VARIABLE_1473399) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473397) BOUND_VARIABLE_1473399)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473396) BOUND_VARIABLE_1473398)))))))))) (let ((_let_2453 (forall ((BOUND_VARIABLE_1473371 tptp.int) (BOUND_VARIABLE_1473372 tptp.int) (BOUND_VARIABLE_1473373 tptp.int) (BOUND_VARIABLE_1473374 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8357 BOUND_VARIABLE_1473371) BOUND_VARIABLE_1473372) BOUND_VARIABLE_1473373) BOUND_VARIABLE_1473374) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473372) BOUND_VARIABLE_1473374)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473371) BOUND_VARIABLE_1473373)))))))))) (let ((_let_2454 (forall ((BOUND_VARIABLE_1473346 tptp.int) (BOUND_VARIABLE_1473347 tptp.int) (BOUND_VARIABLE_1473348 tptp.int) (BOUND_VARIABLE_1473349 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8358 BOUND_VARIABLE_1473346) BOUND_VARIABLE_1473347) BOUND_VARIABLE_1473348) BOUND_VARIABLE_1473349) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473347) BOUND_VARIABLE_1473349)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473346) BOUND_VARIABLE_1473348)))))))))) (let ((_let_2455 (forall ((BOUND_VARIABLE_1473321 tptp.int) (BOUND_VARIABLE_1473322 tptp.int) (BOUND_VARIABLE_1473323 tptp.int) (BOUND_VARIABLE_1473324 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8359 BOUND_VARIABLE_1473321) BOUND_VARIABLE_1473322) BOUND_VARIABLE_1473323) BOUND_VARIABLE_1473324) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473322) BOUND_VARIABLE_1473324)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473321) BOUND_VARIABLE_1473323)))))))))) (let ((_let_2456 (forall ((BOUND_VARIABLE_1473296 tptp.int) (BOUND_VARIABLE_1473297 tptp.int) (BOUND_VARIABLE_1473298 tptp.int) (BOUND_VARIABLE_1473299 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8360 BOUND_VARIABLE_1473296) BOUND_VARIABLE_1473297) BOUND_VARIABLE_1473298) BOUND_VARIABLE_1473299) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473297) BOUND_VARIABLE_1473299)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473296) BOUND_VARIABLE_1473298)))))))))) (let ((_let_2457 (forall ((BOUND_VARIABLE_1473271 tptp.int) (BOUND_VARIABLE_1473272 tptp.int) (BOUND_VARIABLE_1473273 tptp.int) (BOUND_VARIABLE_1473274 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8361 BOUND_VARIABLE_1473271) BOUND_VARIABLE_1473272) BOUND_VARIABLE_1473273) BOUND_VARIABLE_1473274) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473272) BOUND_VARIABLE_1473274)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473271) BOUND_VARIABLE_1473273)))))))))) (let ((_let_2458 (forall ((BOUND_VARIABLE_1473246 tptp.int) (BOUND_VARIABLE_1473247 tptp.int) (BOUND_VARIABLE_1473248 tptp.int) (BOUND_VARIABLE_1473249 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8362 BOUND_VARIABLE_1473246) BOUND_VARIABLE_1473247) BOUND_VARIABLE_1473248) BOUND_VARIABLE_1473249) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473247) BOUND_VARIABLE_1473249)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473246) BOUND_VARIABLE_1473248)))))))))) (let ((_let_2459 (forall ((BOUND_VARIABLE_1473221 tptp.int) (BOUND_VARIABLE_1473222 tptp.int) (BOUND_VARIABLE_1473223 tptp.int) (BOUND_VARIABLE_1473224 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8363 BOUND_VARIABLE_1473221) BOUND_VARIABLE_1473222) BOUND_VARIABLE_1473223) BOUND_VARIABLE_1473224) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473222) BOUND_VARIABLE_1473224)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473221) BOUND_VARIABLE_1473223)))))))))) (let ((_let_2460 (forall ((BOUND_VARIABLE_1473196 tptp.int) (BOUND_VARIABLE_1473197 tptp.int) (BOUND_VARIABLE_1473198 tptp.int) (BOUND_VARIABLE_1473199 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8364 BOUND_VARIABLE_1473196) BOUND_VARIABLE_1473197) BOUND_VARIABLE_1473198) BOUND_VARIABLE_1473199) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473197) BOUND_VARIABLE_1473199)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473196) BOUND_VARIABLE_1473198)))))))))) (let ((_let_2461 (forall ((BOUND_VARIABLE_1473171 tptp.int) (BOUND_VARIABLE_1473172 tptp.int) (BOUND_VARIABLE_1473173 tptp.int) (BOUND_VARIABLE_1473174 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8365 BOUND_VARIABLE_1473171) BOUND_VARIABLE_1473172) BOUND_VARIABLE_1473173) BOUND_VARIABLE_1473174) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473172) BOUND_VARIABLE_1473174)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473171) BOUND_VARIABLE_1473173)))))))))) (let ((_let_2462 (forall ((BOUND_VARIABLE_1473146 tptp.int) (BOUND_VARIABLE_1473147 tptp.int) (BOUND_VARIABLE_1473148 tptp.int) (BOUND_VARIABLE_1473149 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8366 BOUND_VARIABLE_1473146) BOUND_VARIABLE_1473147) BOUND_VARIABLE_1473148) BOUND_VARIABLE_1473149) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473147) BOUND_VARIABLE_1473149)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473146) BOUND_VARIABLE_1473148)))))))))) (let ((_let_2463 (forall ((BOUND_VARIABLE_1473121 tptp.int) (BOUND_VARIABLE_1473122 tptp.int) (BOUND_VARIABLE_1473123 tptp.int) (BOUND_VARIABLE_1473124 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8367 BOUND_VARIABLE_1473121) BOUND_VARIABLE_1473122) BOUND_VARIABLE_1473123) BOUND_VARIABLE_1473124) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473122) BOUND_VARIABLE_1473124)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473121) BOUND_VARIABLE_1473123)))))))))) (let ((_let_2464 (forall ((BOUND_VARIABLE_1473096 tptp.int) (BOUND_VARIABLE_1473097 tptp.int) (BOUND_VARIABLE_1473098 tptp.int) (BOUND_VARIABLE_1473099 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8368 BOUND_VARIABLE_1473096) BOUND_VARIABLE_1473097) BOUND_VARIABLE_1473098) BOUND_VARIABLE_1473099) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473097) BOUND_VARIABLE_1473099)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473096) BOUND_VARIABLE_1473098)))))))))) (let ((_let_2465 (forall ((BOUND_VARIABLE_1473071 tptp.int) (BOUND_VARIABLE_1473072 tptp.int) (BOUND_VARIABLE_1473073 tptp.int) (BOUND_VARIABLE_1473074 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8369 BOUND_VARIABLE_1473071) BOUND_VARIABLE_1473072) BOUND_VARIABLE_1473073) BOUND_VARIABLE_1473074) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473072) BOUND_VARIABLE_1473074)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473071) BOUND_VARIABLE_1473073)))))))))) (let ((_let_2466 (forall ((BOUND_VARIABLE_1473046 tptp.int) (BOUND_VARIABLE_1473047 tptp.int) (BOUND_VARIABLE_1473048 tptp.int) (BOUND_VARIABLE_1473049 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8370 BOUND_VARIABLE_1473046) BOUND_VARIABLE_1473047) BOUND_VARIABLE_1473048) BOUND_VARIABLE_1473049) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473047) BOUND_VARIABLE_1473049)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473046) BOUND_VARIABLE_1473048)))))))))) (let ((_let_2467 (forall ((BOUND_VARIABLE_1473021 tptp.int) (BOUND_VARIABLE_1473022 tptp.int) (BOUND_VARIABLE_1473023 tptp.int) (BOUND_VARIABLE_1473024 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8371 BOUND_VARIABLE_1473021) BOUND_VARIABLE_1473022) BOUND_VARIABLE_1473023) BOUND_VARIABLE_1473024) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473022) BOUND_VARIABLE_1473024)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1473021) BOUND_VARIABLE_1473023)))))))))) (let ((_let_2468 (forall ((BOUND_VARIABLE_1472996 tptp.int) (BOUND_VARIABLE_1472997 tptp.int) (BOUND_VARIABLE_1472998 tptp.int) (BOUND_VARIABLE_1472999 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8372 BOUND_VARIABLE_1472996) BOUND_VARIABLE_1472997) BOUND_VARIABLE_1472998) BOUND_VARIABLE_1472999) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472997) BOUND_VARIABLE_1472999)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472996) BOUND_VARIABLE_1472998)))))))))) (let ((_let_2469 (forall ((BOUND_VARIABLE_1472971 tptp.int) (BOUND_VARIABLE_1472972 tptp.int) (BOUND_VARIABLE_1472973 tptp.int) (BOUND_VARIABLE_1472974 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8373 BOUND_VARIABLE_1472971) BOUND_VARIABLE_1472972) BOUND_VARIABLE_1472973) BOUND_VARIABLE_1472974) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472972) BOUND_VARIABLE_1472974)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472971) BOUND_VARIABLE_1472973)))))))))) (let ((_let_2470 (forall ((BOUND_VARIABLE_1472946 tptp.int) (BOUND_VARIABLE_1472947 tptp.int) (BOUND_VARIABLE_1472948 tptp.int) (BOUND_VARIABLE_1472949 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8374 BOUND_VARIABLE_1472946) BOUND_VARIABLE_1472947) BOUND_VARIABLE_1472948) BOUND_VARIABLE_1472949) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472947) BOUND_VARIABLE_1472949)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472946) BOUND_VARIABLE_1472948)))))))))) (let ((_let_2471 (forall ((BOUND_VARIABLE_1472921 tptp.int) (BOUND_VARIABLE_1472922 tptp.int) (BOUND_VARIABLE_1472923 tptp.int) (BOUND_VARIABLE_1472924 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8375 BOUND_VARIABLE_1472921) BOUND_VARIABLE_1472922) BOUND_VARIABLE_1472923) BOUND_VARIABLE_1472924) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472922) BOUND_VARIABLE_1472924)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472921) BOUND_VARIABLE_1472923)))))))))) (let ((_let_2472 (forall ((BOUND_VARIABLE_1472896 tptp.int) (BOUND_VARIABLE_1472897 tptp.int) (BOUND_VARIABLE_1472898 tptp.int) (BOUND_VARIABLE_1472899 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8376 BOUND_VARIABLE_1472896) BOUND_VARIABLE_1472897) BOUND_VARIABLE_1472898) BOUND_VARIABLE_1472899) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472897) BOUND_VARIABLE_1472899)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472896) BOUND_VARIABLE_1472898)))))))))) (let ((_let_2473 (forall ((BOUND_VARIABLE_1472871 tptp.int) (BOUND_VARIABLE_1472872 tptp.int) (BOUND_VARIABLE_1472873 tptp.int) (BOUND_VARIABLE_1472874 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8377 BOUND_VARIABLE_1472871) BOUND_VARIABLE_1472872) BOUND_VARIABLE_1472873) BOUND_VARIABLE_1472874) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472872) BOUND_VARIABLE_1472874)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472871) BOUND_VARIABLE_1472873)))))))))) (let ((_let_2474 (forall ((BOUND_VARIABLE_1472846 tptp.int) (BOUND_VARIABLE_1472847 tptp.int) (BOUND_VARIABLE_1472848 tptp.int) (BOUND_VARIABLE_1472849 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8378 BOUND_VARIABLE_1472846) BOUND_VARIABLE_1472847) BOUND_VARIABLE_1472848) BOUND_VARIABLE_1472849) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472847) BOUND_VARIABLE_1472849)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472846) BOUND_VARIABLE_1472848)))))))))) (let ((_let_2475 (forall ((BOUND_VARIABLE_1472821 tptp.int) (BOUND_VARIABLE_1472822 tptp.int) (BOUND_VARIABLE_1472823 tptp.int) (BOUND_VARIABLE_1472824 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8379 BOUND_VARIABLE_1472821) BOUND_VARIABLE_1472822) BOUND_VARIABLE_1472823) BOUND_VARIABLE_1472824) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472822) BOUND_VARIABLE_1472824)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472821) BOUND_VARIABLE_1472823)))))))))) (let ((_let_2476 (forall ((BOUND_VARIABLE_1472796 tptp.int) (BOUND_VARIABLE_1472797 tptp.int) (BOUND_VARIABLE_1472798 tptp.int) (BOUND_VARIABLE_1472799 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8380 BOUND_VARIABLE_1472796) BOUND_VARIABLE_1472797) BOUND_VARIABLE_1472798) BOUND_VARIABLE_1472799) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472797) BOUND_VARIABLE_1472799)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472796) BOUND_VARIABLE_1472798)))))))))) (let ((_let_2477 (forall ((BOUND_VARIABLE_1472771 tptp.int) (BOUND_VARIABLE_1472772 tptp.int) (BOUND_VARIABLE_1472773 tptp.int) (BOUND_VARIABLE_1472774 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8381 BOUND_VARIABLE_1472771) BOUND_VARIABLE_1472772) BOUND_VARIABLE_1472773) BOUND_VARIABLE_1472774) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472772) BOUND_VARIABLE_1472774)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472771) BOUND_VARIABLE_1472773)))))))))) (let ((_let_2478 (forall ((BOUND_VARIABLE_1472746 tptp.int) (BOUND_VARIABLE_1472747 tptp.int) (BOUND_VARIABLE_1472748 tptp.int) (BOUND_VARIABLE_1472749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8382 BOUND_VARIABLE_1472746) BOUND_VARIABLE_1472747) BOUND_VARIABLE_1472748) BOUND_VARIABLE_1472749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472747) BOUND_VARIABLE_1472749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472746) BOUND_VARIABLE_1472748)))))))))) (let ((_let_2479 (forall ((BOUND_VARIABLE_1472721 tptp.int) (BOUND_VARIABLE_1472722 tptp.int) (BOUND_VARIABLE_1472723 tptp.int) (BOUND_VARIABLE_1472724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8383 BOUND_VARIABLE_1472721) BOUND_VARIABLE_1472722) BOUND_VARIABLE_1472723) BOUND_VARIABLE_1472724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472722) BOUND_VARIABLE_1472724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472721) BOUND_VARIABLE_1472723)))))))))) (let ((_let_2480 (forall ((BOUND_VARIABLE_1472696 tptp.int) (BOUND_VARIABLE_1472697 tptp.int) (BOUND_VARIABLE_1472698 tptp.int) (BOUND_VARIABLE_1472699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8384 BOUND_VARIABLE_1472696) BOUND_VARIABLE_1472697) BOUND_VARIABLE_1472698) BOUND_VARIABLE_1472699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472697) BOUND_VARIABLE_1472699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472696) BOUND_VARIABLE_1472698)))))))))) (let ((_let_2481 (forall ((BOUND_VARIABLE_1472671 tptp.int) (BOUND_VARIABLE_1472672 tptp.int) (BOUND_VARIABLE_1472673 tptp.int) (BOUND_VARIABLE_1472674 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8385 BOUND_VARIABLE_1472671) BOUND_VARIABLE_1472672) BOUND_VARIABLE_1472673) BOUND_VARIABLE_1472674) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472672) BOUND_VARIABLE_1472674)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472671) BOUND_VARIABLE_1472673)))))))))) (let ((_let_2482 (forall ((BOUND_VARIABLE_1472608 tptp.real) (BOUND_VARIABLE_1472609 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1472609) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8386 BOUND_VARIABLE_1472608) BOUND_VARIABLE_1472609) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1472609 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1472609 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1472608) BOUND_VARIABLE_1472609))))))))))))))))) (let ((_let_2483 (forall ((BOUND_VARIABLE_1472545 tptp.real) (BOUND_VARIABLE_1472546 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1472546) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8387 BOUND_VARIABLE_1472545) BOUND_VARIABLE_1472546) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1472546 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1472546 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1472545) BOUND_VARIABLE_1472546))))))))))))))))) (let ((_let_2484 (forall ((BOUND_VARIABLE_1472516 tptp.real) (BOUND_VARIABLE_1472517 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (and (ho_7781 (ho_7780 k_7779 (ho_7516 k_7521 _let_1)) BOUND_VARIABLE_1472517) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1472517) _let_1) (= BOUND_VARIABLE_1472516 (ho_7795 k_7794 (ho_7507 k_7554 BOUND_VARIABLE_1472517)))) (ho_7781 (ho_7780 k_8388 BOUND_VARIABLE_1472516) BOUND_VARIABLE_1472517)))))) (let ((_let_2485 (forall ((BOUND_VARIABLE_1472487 tptp.real) (BOUND_VARIABLE_1472488 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (and (ho_7781 (ho_7780 k_7779 (ho_7516 k_7521 _let_1)) BOUND_VARIABLE_1472488) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1472488) _let_1) (= BOUND_VARIABLE_1472487 (ho_7795 k_7794 (ho_7507 k_7555 BOUND_VARIABLE_1472488)))) (ho_7781 (ho_7780 k_8389 BOUND_VARIABLE_1472487) BOUND_VARIABLE_1472488)))))) (let ((_let_2486 (forall ((BOUND_VARIABLE_1472438 tptp.real) (BOUND_VARIABLE_1472439 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1472439) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1472438) _let_6)) (ho_7508 (ho_7507 k_8390 BOUND_VARIABLE_1472438) BOUND_VARIABLE_1472439)))))))))))))) (let ((_let_2487 (forall ((BOUND_VARIABLE_1472388 tptp.real) (BOUND_VARIABLE_1472389 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1472389) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 BOUND_VARIABLE_1472388)) _let_6)) (ho_7508 (ho_7507 k_8391 BOUND_VARIABLE_1472388) BOUND_VARIABLE_1472389)))))))))))))) (let ((_let_2488 (forall ((BOUND_VARIABLE_1472338 tptp.real) (BOUND_VARIABLE_1472339 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7443 k_7442 tptp.one))) (let ((_let_5 (ho_7463 k_7462 (ho_7446 k_7445 _let_4)))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1472339) _let_3)) (ho_7459 (ho_7470 _let_6 _let_5) _let_3))))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7463 k_7462 _let_1))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_9) _let_5))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_10 _let_7)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 _let_7) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_6 _let_9) _let_3))))) _let_8)))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7521 (ho_7510 k_7509 _let_4))) BOUND_VARIABLE_1472338)) _let_7)) (ho_7508 (ho_7507 k_8392 BOUND_VARIABLE_1472338) BOUND_VARIABLE_1472339))))))))))))))) (let ((_let_2489 (forall ((BOUND_VARIABLE_1472286 tptp.real) (BOUND_VARIABLE_1472287 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (= (ho_7781 (ho_7780 k_8393 BOUND_VARIABLE_1472286) BOUND_VARIABLE_1472287) (and (= BOUND_VARIABLE_1472286 (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7556 BOUND_VARIABLE_1472287))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7557 BOUND_VARIABLE_1472287))))) (ho_7781 (ho_7780 k_7779 _let_2) BOUND_VARIABLE_1472287) (not (= BOUND_VARIABLE_1472287 _let_2)) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1472287) _let_1) (not (= BOUND_VARIABLE_1472287 _let_1))))))))) (let ((_let_2490 (forall ((BOUND_VARIABLE_1472220 tptp.real) (BOUND_VARIABLE_1472221 tptp.real)) (let ((_let_1 (ho_7443 k_7442 tptp.one))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7516 k_7521 _let_2))) (let ((_let_4 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 _let_3)) (ho_7516 k_7520 (ho_7510 k_7509 _let_1))))) (let ((_let_5 (ho_7516 k_7521 _let_4))) (let ((_let_6 (ho_7463 k_7462 (ho_7446 k_7445 _let_1)))) (let ((_let_7 (ho_7519 k_7523 _let_2))) (= (ho_7781 (ho_7780 k_8398 BOUND_VARIABLE_1472220) BOUND_VARIABLE_1472221) (and (= (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7558 BOUND_VARIABLE_1472221))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7559 BOUND_VARIABLE_1472221)))) (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1472220) (ho_7516 k_7520 (ho_7516 _let_7 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_6 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) _let_6))) (ho_7516 _let_7 _let_3)) (ho_7516 (ho_8397 (ho_8396 k_8395 tptp.top_top_set_real) k_8394) (ho_7516 _let_7 (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1472220) _let_6)))))))) (ho_7781 (ho_7780 k_7779 _let_5) BOUND_VARIABLE_1472221) (not (= BOUND_VARIABLE_1472221 _let_5)) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1472221) _let_4) (not (= BOUND_VARIABLE_1472221 _let_4)))))))))))))) (let ((_let_2491 (forall ((BOUND_VARIABLE_1472168 tptp.real) (BOUND_VARIABLE_1472169 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (= (ho_7781 (ho_7780 k_8399 BOUND_VARIABLE_1472168) BOUND_VARIABLE_1472169) (and (= BOUND_VARIABLE_1472168 (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7560 BOUND_VARIABLE_1472169))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7561 BOUND_VARIABLE_1472169))))) (ho_7781 (ho_7780 k_7779 _let_2) BOUND_VARIABLE_1472169) (not (= BOUND_VARIABLE_1472169 _let_2)) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1472169) _let_1) (not (= BOUND_VARIABLE_1472169 _let_1))))))))) (let ((_let_2492 (forall ((BOUND_VARIABLE_1472116 tptp.real) (BOUND_VARIABLE_1472117 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (= (ho_7781 (ho_7780 k_8400 BOUND_VARIABLE_1472116) BOUND_VARIABLE_1472117) (and (= BOUND_VARIABLE_1472116 (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7562 BOUND_VARIABLE_1472117))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7563 BOUND_VARIABLE_1472117))))) (ho_7781 (ho_7780 k_7779 _let_2) BOUND_VARIABLE_1472117) (not (= BOUND_VARIABLE_1472117 _let_2)) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1472117) _let_1) (not (= BOUND_VARIABLE_1472117 _let_1))))))))) (let ((_let_2493 (forall ((BOUND_VARIABLE_1472091 tptp.int) (BOUND_VARIABLE_1472092 tptp.int) (BOUND_VARIABLE_1472093 tptp.int) (BOUND_VARIABLE_1472094 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8401 BOUND_VARIABLE_1472091) BOUND_VARIABLE_1472092) BOUND_VARIABLE_1472093) BOUND_VARIABLE_1472094) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472092) BOUND_VARIABLE_1472094)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472091) BOUND_VARIABLE_1472093)))))))))) (let ((_let_2494 (forall ((BOUND_VARIABLE_1472066 tptp.int) (BOUND_VARIABLE_1472067 tptp.int) (BOUND_VARIABLE_1472068 tptp.int) (BOUND_VARIABLE_1472069 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8402 BOUND_VARIABLE_1472066) BOUND_VARIABLE_1472067) BOUND_VARIABLE_1472068) BOUND_VARIABLE_1472069) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472067) BOUND_VARIABLE_1472069)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472066) BOUND_VARIABLE_1472068)))))))))) (let ((_let_2495 (forall ((BOUND_VARIABLE_1472045 tptp.rat) (BOUND_VARIABLE_1472046 tptp.nat) (BOUND_VARIABLE_1472047 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_6 (ho_7716 _let_5 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_5 k_8019) (ho_7711 (ho_7717 _let_6 BOUND_VARIABLE_1472045) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1472046) (ho_7711 (ho_7717 _let_6 _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3))))) BOUND_VARIABLE_1472047) (ho_7711 (ho_8055 (ho_8058 k_8403 BOUND_VARIABLE_1472045) BOUND_VARIABLE_1472046) BOUND_VARIABLE_1472047))))))))))) (let ((_let_2496 (forall ((BOUND_VARIABLE_1472020 tptp.int) (BOUND_VARIABLE_1472021 tptp.int) (BOUND_VARIABLE_1472022 tptp.int) (BOUND_VARIABLE_1472023 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8404 BOUND_VARIABLE_1472020) BOUND_VARIABLE_1472021) BOUND_VARIABLE_1472022) BOUND_VARIABLE_1472023) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472021) BOUND_VARIABLE_1472023)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1472020) BOUND_VARIABLE_1472022)))))))))) (let ((_let_2497 (forall ((BOUND_VARIABLE_1471995 tptp.int) (BOUND_VARIABLE_1471996 tptp.int) (BOUND_VARIABLE_1471997 tptp.int) (BOUND_VARIABLE_1471998 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8405 BOUND_VARIABLE_1471995) BOUND_VARIABLE_1471996) BOUND_VARIABLE_1471997) BOUND_VARIABLE_1471998) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1471996) BOUND_VARIABLE_1471998)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1471995) BOUND_VARIABLE_1471997)))))))))) (let ((_let_2498 (forall ((BOUND_VARIABLE_1471974 tptp.rat) (BOUND_VARIABLE_1471975 tptp.nat) (BOUND_VARIABLE_1471976 tptp.rat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7715 (ho_7714 k_7713 k_7706) _let_4))) (let ((_let_6 (ho_7716 _let_5 k_7712))) (= (ho_7711 (ho_7717 (ho_7716 _let_5 k_8019) (ho_7711 (ho_7717 _let_6 BOUND_VARIABLE_1471974) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1471975) (ho_7711 (ho_7717 _let_6 _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3))))) BOUND_VARIABLE_1471976) (ho_7711 (ho_8055 (ho_8058 k_8406 BOUND_VARIABLE_1471974) BOUND_VARIABLE_1471975) BOUND_VARIABLE_1471976))))))))))) (let ((_let_2499 (forall ((BOUND_VARIABLE_1471911 tptp.real) (BOUND_VARIABLE_1471912 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1471912) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8407 BOUND_VARIABLE_1471911) BOUND_VARIABLE_1471912) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471912 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471912 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471911) BOUND_VARIABLE_1471912))))))))))))))))) (let ((_let_2500 (forall ((BOUND_VARIABLE_1471856 tptp.real) (BOUND_VARIABLE_1471857 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8408 BOUND_VARIABLE_1471856) BOUND_VARIABLE_1471857) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471857 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1471857) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471857 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1471857) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471856) BOUND_VARIABLE_1471857))))))))))))))) (let ((_let_2501 (forall ((BOUND_VARIABLE_1471792 tptp.real) (BOUND_VARIABLE_1471793 tptp.nat)) (let ((_let_1 (ho_7443 k_7442 tptp.one))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))) (let ((_let_9 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1471793) _let_5)))) (let ((_let_10 (ho_7463 k_7462 (ho_7446 k_7445 _let_1)))) (let ((_let_11 (ho_7466 (ho_7465 k_7471 _let_6) _let_10))) (let ((_let_12 (ho_7516 k_7521 _let_2))) (= (ho_7508 (ho_7507 k_8409 BOUND_VARIABLE_1471792) BOUND_VARIABLE_1471793) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471793 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_2) _let_12)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_12) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_9 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_8) (ho_7459 (ho_7470 _let_7 _let_11) _let_5)))) _let_5))))) _let_10))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471793 _let_11)) _let_2) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_11) (ho_7463 k_7462 (ho_7459 _let_9 (ho_7459 _let_4 _let_8)))) _let_2)))))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 _let_1)) BOUND_VARIABLE_1471792)) BOUND_VARIABLE_1471793)))))))))))))))))) (let ((_let_2502 (forall ((BOUND_VARIABLE_1471736 tptp.real) (BOUND_VARIABLE_1471737 tptp.nat)) (let ((_let_1 (ho_7443 k_7442 tptp.one))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7516 k_7521 _let_2))) (let ((_let_4 (ho_7446 k_7445 tptp.one))) (let ((_let_5 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_6 (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 _let_5 _let_4)))) (let ((_let_7 (ho_7463 k_7462 _let_4))) (let ((_let_8 (ho_7469 k_7468 k_7467))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 _let_1)))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_7) _let_9))) (= (ho_7508 (ho_7507 k_8410 BOUND_VARIABLE_1471736) BOUND_VARIABLE_1471737) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471737 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_3) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1471737) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471737 _let_10)) _let_2) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_8 BOUND_VARIABLE_1471737) _let_6)) (ho_7459 _let_5 (ho_7459 (ho_7470 _let_8 _let_7) _let_6))))) _let_2))))) (ho_7516 (ho_7519 k_7523 _let_2) _let_3))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 _let_1)) BOUND_VARIABLE_1471736)) BOUND_VARIABLE_1471737)))))))))))))))) (let ((_let_2503 (forall ((BOUND_VARIABLE_1471665 tptp.complex) (BOUND_VARIABLE_1471666 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1471665) BOUND_VARIABLE_1471666))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))) (let ((_let_9 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1471666) _let_5)))) (let ((_let_10 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_11 (ho_7466 (ho_7465 k_7471 _let_6) _let_10))) (let ((_let_12 (ho_7516 k_7521 _let_2))) (let ((_let_13 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471666 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_2) _let_12)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_12) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_9 (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_8) (ho_7459 (ho_7470 _let_7 _let_11) _let_5)))) _let_5))))) _let_10))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471666 _let_11)) _let_2) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_11) (ho_7463 k_7462 (ho_7459 _let_9 (ho_7459 _let_4 _let_8)))) _let_2)))))))) (= (ho_7736 (ho_7735 k_8411 BOUND_VARIABLE_1471665) BOUND_VARIABLE_1471666) (ho_7728 (ho_7732 k_7731 (ho_7516 _let_13 (ho_7730 k_7729 _let_1))) (ho_7516 _let_13 (ho_7730 k_7733 _let_1)))))))))))))))))))) (let ((_let_2504 (forall ((BOUND_VARIABLE_1471602 tptp.complex) (BOUND_VARIABLE_1471603 tptp.nat)) (let ((_let_1 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1471602) BOUND_VARIABLE_1471603))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7516 k_7521 _let_2))) (let ((_let_4 (ho_7446 k_7445 tptp.one))) (let ((_let_5 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_6 (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 _let_5 _let_4)))) (let ((_let_7 (ho_7463 k_7462 _let_4))) (let ((_let_8 (ho_7469 k_7468 k_7467))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_7) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471603 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_3) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1471603) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471603 _let_10)) _let_2) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_8 BOUND_VARIABLE_1471603) _let_6)) (ho_7459 _let_5 (ho_7459 (ho_7470 _let_8 _let_7) _let_6))))) _let_2))))) (ho_7516 (ho_7519 k_7523 _let_2) _let_3))))) (= (ho_7736 (ho_7735 k_8412 BOUND_VARIABLE_1471602) BOUND_VARIABLE_1471603) (ho_7728 (ho_7732 k_7731 (ho_7516 _let_11 (ho_7730 k_7729 _let_1))) (ho_7516 _let_11 (ho_7730 k_7733 _let_1)))))))))))))))))) (let ((_let_2505 (forall ((BOUND_VARIABLE_1471518 tptp.complex) (BOUND_VARIABLE_1471519 tptp.nat)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1471518))) (let ((_let_2 (ho_7443 k_7442 tptp.one))) (let ((_let_3 (ho_7985 k_7984 _let_2))) (let ((_let_4 (ho_7519 k_7522 (ho_7730 k_7733 _let_3)))) (let ((_let_5 (ho_7730 k_7733 BOUND_VARIABLE_1471518))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7729 _let_3)))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_1)) (ho_7516 k_7521 (ho_7516 _let_4 _let_5)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_5)) (ho_7516 _let_4 _let_1)))) BOUND_VARIABLE_1471519))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7446 k_7445 tptp.one))) (let ((_let_10 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_11 (ho_7459 (ho_7461 k_7460 _let_9) (ho_7459 _let_10 _let_9)))) (let ((_let_12 (ho_7463 k_7462 _let_9))) (let ((_let_13 (ho_7469 k_7468 k_7467))) (let ((_let_14 (ho_7459 (ho_7470 _let_13 _let_12) _let_11))) (let ((_let_15 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_13 BOUND_VARIABLE_1471519) _let_11)))) (let ((_let_16 (ho_7463 k_7462 (ho_7446 k_7445 _let_2)))) (let ((_let_17 (ho_7466 (ho_7465 k_7471 _let_12) _let_16))) (let ((_let_18 (ho_7516 k_7521 _let_8))) (let ((_let_19 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471519 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_8) _let_18)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_18) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_15 (ho_7459 _let_10 (ho_7459 (ho_7470 _let_13 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_14) (ho_7459 (ho_7470 _let_13 _let_17) _let_11)))) _let_11))))) _let_16))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471519 _let_17)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_17) (ho_7463 k_7462 (ho_7459 _let_15 (ho_7459 _let_10 _let_14)))) _let_8)))))))) (= (ho_7736 (ho_7735 k_8413 BOUND_VARIABLE_1471518) BOUND_VARIABLE_1471519) (ho_7728 (ho_7732 k_7731 (ho_7516 _let_19 (ho_7730 k_7729 _let_7))) (ho_7516 _let_19 (ho_7730 k_7733 _let_7)))))))))))))))))))))))))) (let ((_let_2506 (forall ((BOUND_VARIABLE_1471442 tptp.complex) (BOUND_VARIABLE_1471443 tptp.nat)) (let ((_let_1 (ho_7730 k_7729 BOUND_VARIABLE_1471442))) (let ((_let_2 (ho_7443 k_7442 tptp.one))) (let ((_let_3 (ho_7985 k_7984 _let_2))) (let ((_let_4 (ho_7519 k_7522 (ho_7730 k_7733 _let_3)))) (let ((_let_5 (ho_7730 k_7733 BOUND_VARIABLE_1471442))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7729 _let_3)))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_1)) (ho_7516 k_7521 (ho_7516 _let_4 _let_5)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_5)) (ho_7516 _let_4 _let_1)))) BOUND_VARIABLE_1471443))) (let ((_let_8 (ho_7510 k_7509 tptp.one))) (let ((_let_9 (ho_7516 k_7521 _let_8))) (let ((_let_10 (ho_7446 k_7445 tptp.one))) (let ((_let_11 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_12 (ho_7459 (ho_7461 k_7460 _let_10) (ho_7459 _let_11 _let_10)))) (let ((_let_13 (ho_7463 k_7462 _let_10))) (let ((_let_14 (ho_7469 k_7468 k_7467))) (let ((_let_15 (ho_7463 k_7462 (ho_7446 k_7445 _let_2)))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_13) _let_15))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471443 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_9) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1471443) _let_15))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471443 _let_16)) _let_8) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_14 BOUND_VARIABLE_1471443) _let_12)) (ho_7459 _let_11 (ho_7459 (ho_7470 _let_14 _let_13) _let_12))))) _let_8))))) (ho_7516 (ho_7519 k_7523 _let_8) _let_9))))) (= (ho_7736 (ho_7735 k_8414 BOUND_VARIABLE_1471442) BOUND_VARIABLE_1471443) (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_7))) (ho_7516 _let_17 (ho_7730 k_7733 _let_7)))))))))))))))))))))))) (let ((_let_2507 (forall ((BOUND_VARIABLE_1471390 tptp.real) (BOUND_VARIABLE_1471391 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (= (ho_7781 (ho_7780 k_8415 BOUND_VARIABLE_1471390) BOUND_VARIABLE_1471391) (and (= BOUND_VARIABLE_1471390 (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7564 BOUND_VARIABLE_1471391))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7565 BOUND_VARIABLE_1471391))))) (ho_7781 (ho_7780 k_7779 _let_2) BOUND_VARIABLE_1471391) (not (= BOUND_VARIABLE_1471391 _let_2)) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1471391) _let_1) (not (= BOUND_VARIABLE_1471391 _let_1))))))))) (let ((_let_2508 (forall ((BOUND_VARIABLE_1471338 tptp.real) (BOUND_VARIABLE_1471339 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (= (ho_7781 (ho_7780 k_8416 BOUND_VARIABLE_1471338) BOUND_VARIABLE_1471339) (and (= BOUND_VARIABLE_1471338 (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7566 BOUND_VARIABLE_1471339))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7567 BOUND_VARIABLE_1471339))))) (ho_7781 (ho_7780 k_7779 _let_2) BOUND_VARIABLE_1471339) (not (= BOUND_VARIABLE_1471339 _let_2)) (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1471339) _let_1) (not (= BOUND_VARIABLE_1471339 _let_1))))))))) (let ((_let_2509 (forall ((BOUND_VARIABLE_1471275 tptp.real) (BOUND_VARIABLE_1471276 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1471276) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8417 BOUND_VARIABLE_1471275) BOUND_VARIABLE_1471276) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471276 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471276 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471275) BOUND_VARIABLE_1471276))))))))))))))))) (let ((_let_2510 (forall ((BOUND_VARIABLE_1471220 tptp.real) (BOUND_VARIABLE_1471221 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8418 BOUND_VARIABLE_1471220) BOUND_VARIABLE_1471221) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471221 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1471221) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471221 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1471221) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471220) BOUND_VARIABLE_1471221))))))))))))))) (let ((_let_2511 (forall ((BOUND_VARIABLE_1471157 tptp.real) (BOUND_VARIABLE_1471158 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1471158) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8419 BOUND_VARIABLE_1471157) BOUND_VARIABLE_1471158) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471158 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471158 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471157) BOUND_VARIABLE_1471158))))))))))))))))) (let ((_let_2512 (forall ((BOUND_VARIABLE_1471102 tptp.real) (BOUND_VARIABLE_1471103 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8420 BOUND_VARIABLE_1471102) BOUND_VARIABLE_1471103) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471103 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1471103) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471103 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1471103) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471102) BOUND_VARIABLE_1471103))))))))))))))) (let ((_let_2513 (forall ((BOUND_VARIABLE_1471039 tptp.real) (BOUND_VARIABLE_1471040 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1471040) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8421 BOUND_VARIABLE_1471039) BOUND_VARIABLE_1471040) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1471040 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1471040 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1471039) BOUND_VARIABLE_1471040))))))))))))))))) (let ((_let_2514 (forall ((BOUND_VARIABLE_1470984 tptp.real) (BOUND_VARIABLE_1470985 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8422 BOUND_VARIABLE_1470984) BOUND_VARIABLE_1470985) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470985 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1470985) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470985 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1470985) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470984) BOUND_VARIABLE_1470985))))))))))))))) (let ((_let_2515 (forall ((BOUND_VARIABLE_1470921 tptp.real) (BOUND_VARIABLE_1470922 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1470922) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8423 BOUND_VARIABLE_1470921) BOUND_VARIABLE_1470922) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470922 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470922 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470921) BOUND_VARIABLE_1470922))))))))))))))))) (let ((_let_2516 (forall ((BOUND_VARIABLE_1470866 tptp.real) (BOUND_VARIABLE_1470867 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8424 BOUND_VARIABLE_1470866) BOUND_VARIABLE_1470867) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470867 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1470867) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470867 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1470867) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470866) BOUND_VARIABLE_1470867))))))))))))))) (let ((_let_2517 (forall ((BOUND_VARIABLE_1470803 tptp.real) (BOUND_VARIABLE_1470804 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1470804) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8425 BOUND_VARIABLE_1470803) BOUND_VARIABLE_1470804) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470804 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470804 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470803) BOUND_VARIABLE_1470804))))))))))))))))) (let ((_let_2518 (forall ((BOUND_VARIABLE_1470748 tptp.real) (BOUND_VARIABLE_1470749 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8426 BOUND_VARIABLE_1470748) BOUND_VARIABLE_1470749) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470749 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1470749) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470749 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1470749) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470748) BOUND_VARIABLE_1470749))))))))))))))) (let ((_let_2519 (forall ((BOUND_VARIABLE_1470685 tptp.real) (BOUND_VARIABLE_1470686 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1470686) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8427 BOUND_VARIABLE_1470685) BOUND_VARIABLE_1470686) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470686 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470686 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470685) BOUND_VARIABLE_1470686))))))))))))))))) (let ((_let_2520 (forall ((BOUND_VARIABLE_1470630 tptp.real) (BOUND_VARIABLE_1470631 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8428 BOUND_VARIABLE_1470630) BOUND_VARIABLE_1470631) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470631 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1470631) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470631 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1470631) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470630) BOUND_VARIABLE_1470631))))))))))))))) (let ((_let_2521 (forall ((BOUND_VARIABLE_1470567 tptp.real) (BOUND_VARIABLE_1470568 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1470568) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8429 BOUND_VARIABLE_1470567) BOUND_VARIABLE_1470568) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470568 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470568 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470567) BOUND_VARIABLE_1470568))))))))))))))))) (let ((_let_2522 (forall ((BOUND_VARIABLE_1470512 tptp.real) (BOUND_VARIABLE_1470513 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8430 BOUND_VARIABLE_1470512) BOUND_VARIABLE_1470513) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470513 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1470513) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470513 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1470513) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470512) BOUND_VARIABLE_1470513))))))))))))))) (let ((_let_2523 (forall ((BOUND_VARIABLE_1470449 tptp.real) (BOUND_VARIABLE_1470450 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1470450) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8431 BOUND_VARIABLE_1470449) BOUND_VARIABLE_1470450) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470450 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470450 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470449) BOUND_VARIABLE_1470450))))))))))))))))) (let ((_let_2524 (forall ((BOUND_VARIABLE_1470394 tptp.real) (BOUND_VARIABLE_1470395 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8432 BOUND_VARIABLE_1470394) BOUND_VARIABLE_1470395) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1470395 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1470395) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1470395 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1470395) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1470394) BOUND_VARIABLE_1470395))))))))))))))) (let ((_let_2525 (forall ((BOUND_VARIABLE_1470369 tptp.int) (BOUND_VARIABLE_1470370 tptp.int) (BOUND_VARIABLE_1470371 tptp.int) (BOUND_VARIABLE_1470372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8433 BOUND_VARIABLE_1470369) BOUND_VARIABLE_1470370) BOUND_VARIABLE_1470371) BOUND_VARIABLE_1470372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470370) BOUND_VARIABLE_1470372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470369) BOUND_VARIABLE_1470371)))))))))) (let ((_let_2526 (forall ((BOUND_VARIABLE_1470344 tptp.int) (BOUND_VARIABLE_1470345 tptp.int) (BOUND_VARIABLE_1470346 tptp.int) (BOUND_VARIABLE_1470347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8434 BOUND_VARIABLE_1470344) BOUND_VARIABLE_1470345) BOUND_VARIABLE_1470346) BOUND_VARIABLE_1470347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470345) BOUND_VARIABLE_1470347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470344) BOUND_VARIABLE_1470346)))))))))) (let ((_let_2527 (forall ((BOUND_VARIABLE_1470319 tptp.int) (BOUND_VARIABLE_1470320 tptp.int) (BOUND_VARIABLE_1470321 tptp.int) (BOUND_VARIABLE_1470322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8435 BOUND_VARIABLE_1470319) BOUND_VARIABLE_1470320) BOUND_VARIABLE_1470321) BOUND_VARIABLE_1470322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470320) BOUND_VARIABLE_1470322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470319) BOUND_VARIABLE_1470321)))))))))) (let ((_let_2528 (forall ((BOUND_VARIABLE_1470294 tptp.int) (BOUND_VARIABLE_1470295 tptp.int) (BOUND_VARIABLE_1470296 tptp.int) (BOUND_VARIABLE_1470297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8436 BOUND_VARIABLE_1470294) BOUND_VARIABLE_1470295) BOUND_VARIABLE_1470296) BOUND_VARIABLE_1470297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470295) BOUND_VARIABLE_1470297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470294) BOUND_VARIABLE_1470296)))))))))) (let ((_let_2529 (forall ((BOUND_VARIABLE_1470269 tptp.int) (BOUND_VARIABLE_1470270 tptp.int) (BOUND_VARIABLE_1470271 tptp.int) (BOUND_VARIABLE_1470272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8437 BOUND_VARIABLE_1470269) BOUND_VARIABLE_1470270) BOUND_VARIABLE_1470271) BOUND_VARIABLE_1470272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470270) BOUND_VARIABLE_1470272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470269) BOUND_VARIABLE_1470271)))))))))) (let ((_let_2530 (forall ((BOUND_VARIABLE_1470244 tptp.int) (BOUND_VARIABLE_1470245 tptp.int) (BOUND_VARIABLE_1470246 tptp.int) (BOUND_VARIABLE_1470247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8438 BOUND_VARIABLE_1470244) BOUND_VARIABLE_1470245) BOUND_VARIABLE_1470246) BOUND_VARIABLE_1470247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470245) BOUND_VARIABLE_1470247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470244) BOUND_VARIABLE_1470246)))))))))) (let ((_let_2531 (forall ((BOUND_VARIABLE_1535878 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1470201 tptp.nat) (BOUND_VARIABLE_1470202 tptp.int) (BOUND_VARIABLE_1470203 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7568 BOUND_VARIABLE_1470203) BOUND_VARIABLE_1470202)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1535878 BOUND_VARIABLE_1470201))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_8439 BOUND_VARIABLE_1535878) BOUND_VARIABLE_1470201) BOUND_VARIABLE_1470202) BOUND_VARIABLE_1470203))))) (let ((_let_2532 (forall ((BOUND_VARIABLE_1535897 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1470157 tptp.nat) (BOUND_VARIABLE_1470158 tptp.int) (BOUND_VARIABLE_1470159 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7569 BOUND_VARIABLE_1470159) BOUND_VARIABLE_1470158)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1535897 BOUND_VARIABLE_1470157))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_8440 BOUND_VARIABLE_1535897) BOUND_VARIABLE_1470157) BOUND_VARIABLE_1470158) BOUND_VARIABLE_1470159))))) (let ((_let_2533 (forall ((BOUND_VARIABLE_1535920 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1470103 tptp.nat) (BOUND_VARIABLE_1470104 tptp.int) (BOUND_VARIABLE_1470105 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7570 BOUND_VARIABLE_1470105) BOUND_VARIABLE_1470104)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1535920 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1470103) _let_2)))))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_8441 BOUND_VARIABLE_1535920) BOUND_VARIABLE_1470103) BOUND_VARIABLE_1470104) BOUND_VARIABLE_1470105)))))))) (let ((_let_2534 (forall ((BOUND_VARIABLE_1535939 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1470059 tptp.nat) (BOUND_VARIABLE_1470060 tptp.int) (BOUND_VARIABLE_1470061 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7571 BOUND_VARIABLE_1470061) BOUND_VARIABLE_1470060)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1535939 BOUND_VARIABLE_1470059))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_8442 BOUND_VARIABLE_1535939) BOUND_VARIABLE_1470059) BOUND_VARIABLE_1470060) BOUND_VARIABLE_1470061))))) (let ((_let_2535 (forall ((BOUND_VARIABLE_1470033 tptp.int) (BOUND_VARIABLE_1470034 tptp.int) (BOUND_VARIABLE_1470035 tptp.int) (BOUND_VARIABLE_1470036 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8443 BOUND_VARIABLE_1470033) BOUND_VARIABLE_1470034) BOUND_VARIABLE_1470035) BOUND_VARIABLE_1470036) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470034) BOUND_VARIABLE_1470036)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470033) BOUND_VARIABLE_1470035)))))))))) (let ((_let_2536 (forall ((BOUND_VARIABLE_1470008 tptp.int) (BOUND_VARIABLE_1470009 tptp.int) (BOUND_VARIABLE_1470010 tptp.int) (BOUND_VARIABLE_1470011 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8444 BOUND_VARIABLE_1470008) BOUND_VARIABLE_1470009) BOUND_VARIABLE_1470010) BOUND_VARIABLE_1470011) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470009) BOUND_VARIABLE_1470011)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1470008) BOUND_VARIABLE_1470010)))))))))) (let ((_let_2537 (forall ((BOUND_VARIABLE_1469983 tptp.int) (BOUND_VARIABLE_1469984 tptp.int) (BOUND_VARIABLE_1469985 tptp.int) (BOUND_VARIABLE_1469986 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8445 BOUND_VARIABLE_1469983) BOUND_VARIABLE_1469984) BOUND_VARIABLE_1469985) BOUND_VARIABLE_1469986) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469984) BOUND_VARIABLE_1469986)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469983) BOUND_VARIABLE_1469985)))))))))) (let ((_let_2538 (forall ((BOUND_VARIABLE_1469958 tptp.int) (BOUND_VARIABLE_1469959 tptp.int) (BOUND_VARIABLE_1469960 tptp.int) (BOUND_VARIABLE_1469961 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8446 BOUND_VARIABLE_1469958) BOUND_VARIABLE_1469959) BOUND_VARIABLE_1469960) BOUND_VARIABLE_1469961) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469959) BOUND_VARIABLE_1469961)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469958) BOUND_VARIABLE_1469960)))))))))) (let ((_let_2539 (forall ((BOUND_VARIABLE_1469933 tptp.int) (BOUND_VARIABLE_1469934 tptp.int) (BOUND_VARIABLE_1469935 tptp.int) (BOUND_VARIABLE_1469936 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8447 BOUND_VARIABLE_1469933) BOUND_VARIABLE_1469934) BOUND_VARIABLE_1469935) BOUND_VARIABLE_1469936) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469934) BOUND_VARIABLE_1469936)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469933) BOUND_VARIABLE_1469935)))))))))) (let ((_let_2540 (forall ((BOUND_VARIABLE_1469908 tptp.int) (BOUND_VARIABLE_1469909 tptp.int) (BOUND_VARIABLE_1469910 tptp.int) (BOUND_VARIABLE_1469911 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8448 BOUND_VARIABLE_1469908) BOUND_VARIABLE_1469909) BOUND_VARIABLE_1469910) BOUND_VARIABLE_1469911) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469909) BOUND_VARIABLE_1469911)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469908) BOUND_VARIABLE_1469910)))))))))) (let ((_let_2541 (forall ((BOUND_VARIABLE_1469883 tptp.int) (BOUND_VARIABLE_1469884 tptp.int) (BOUND_VARIABLE_1469885 tptp.int) (BOUND_VARIABLE_1469886 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8449 BOUND_VARIABLE_1469883) BOUND_VARIABLE_1469884) BOUND_VARIABLE_1469885) BOUND_VARIABLE_1469886) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469884) BOUND_VARIABLE_1469886)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469883) BOUND_VARIABLE_1469885)))))))))) (let ((_let_2542 (forall ((BOUND_VARIABLE_1469858 tptp.int) (BOUND_VARIABLE_1469859 tptp.int) (BOUND_VARIABLE_1469860 tptp.int) (BOUND_VARIABLE_1469861 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8450 BOUND_VARIABLE_1469858) BOUND_VARIABLE_1469859) BOUND_VARIABLE_1469860) BOUND_VARIABLE_1469861) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469859) BOUND_VARIABLE_1469861)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469858) BOUND_VARIABLE_1469860)))))))))) (let ((_let_2543 (forall ((BOUND_VARIABLE_1469833 tptp.int) (BOUND_VARIABLE_1469834 tptp.int) (BOUND_VARIABLE_1469835 tptp.int) (BOUND_VARIABLE_1469836 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8451 BOUND_VARIABLE_1469833) BOUND_VARIABLE_1469834) BOUND_VARIABLE_1469835) BOUND_VARIABLE_1469836) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469834) BOUND_VARIABLE_1469836)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469833) BOUND_VARIABLE_1469835)))))))))) (let ((_let_2544 (forall ((BOUND_VARIABLE_1469808 tptp.int) (BOUND_VARIABLE_1469809 tptp.int) (BOUND_VARIABLE_1469810 tptp.int) (BOUND_VARIABLE_1469811 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8452 BOUND_VARIABLE_1469808) BOUND_VARIABLE_1469809) BOUND_VARIABLE_1469810) BOUND_VARIABLE_1469811) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469809) BOUND_VARIABLE_1469811)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469808) BOUND_VARIABLE_1469810)))))))))) (let ((_let_2545 (forall ((BOUND_VARIABLE_1469783 tptp.int) (BOUND_VARIABLE_1469784 tptp.int) (BOUND_VARIABLE_1469785 tptp.int) (BOUND_VARIABLE_1469786 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8453 BOUND_VARIABLE_1469783) BOUND_VARIABLE_1469784) BOUND_VARIABLE_1469785) BOUND_VARIABLE_1469786) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469784) BOUND_VARIABLE_1469786)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469783) BOUND_VARIABLE_1469785)))))))))) (let ((_let_2546 (forall ((BOUND_VARIABLE_1469758 tptp.int) (BOUND_VARIABLE_1469759 tptp.int) (BOUND_VARIABLE_1469760 tptp.int) (BOUND_VARIABLE_1469761 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8454 BOUND_VARIABLE_1469758) BOUND_VARIABLE_1469759) BOUND_VARIABLE_1469760) BOUND_VARIABLE_1469761) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469759) BOUND_VARIABLE_1469761)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1469758) BOUND_VARIABLE_1469760)))))))))) (let ((_let_2547 (forall ((BOUND_VARIABLE_1469695 tptp.real) (BOUND_VARIABLE_1469696 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1469696) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8455 BOUND_VARIABLE_1469695) BOUND_VARIABLE_1469696) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469696 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469696 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469695) BOUND_VARIABLE_1469696))))))))))))))))) (let ((_let_2548 (forall ((BOUND_VARIABLE_1469640 tptp.real) (BOUND_VARIABLE_1469641 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8456 BOUND_VARIABLE_1469640) BOUND_VARIABLE_1469641) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469641 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1469641) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469641 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1469641) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469640) BOUND_VARIABLE_1469641))))))))))))))) (let ((_let_2549 (forall ((BOUND_VARIABLE_1469577 tptp.real) (BOUND_VARIABLE_1469578 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1469578) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8457 BOUND_VARIABLE_1469577) BOUND_VARIABLE_1469578) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469578 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469578 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469577) BOUND_VARIABLE_1469578))))))))))))))))) (let ((_let_2550 (forall ((BOUND_VARIABLE_1469522 tptp.real) (BOUND_VARIABLE_1469523 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8458 BOUND_VARIABLE_1469522) BOUND_VARIABLE_1469523) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469523 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1469523) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469523 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1469523) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469522) BOUND_VARIABLE_1469523))))))))))))))) (let ((_let_2551 (forall ((BOUND_VARIABLE_1469459 tptp.real) (BOUND_VARIABLE_1469460 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1469460) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8459 BOUND_VARIABLE_1469459) BOUND_VARIABLE_1469460) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469460 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469460 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469459) BOUND_VARIABLE_1469460))))))))))))))))) (let ((_let_2552 (forall ((BOUND_VARIABLE_1469404 tptp.real) (BOUND_VARIABLE_1469405 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8460 BOUND_VARIABLE_1469404) BOUND_VARIABLE_1469405) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469405 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1469405) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469405 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1469405) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469404) BOUND_VARIABLE_1469405))))))))))))))) (let ((_let_2553 (forall ((BOUND_VARIABLE_1469341 tptp.real) (BOUND_VARIABLE_1469342 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1469342) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8461 BOUND_VARIABLE_1469341) BOUND_VARIABLE_1469342) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469342 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469342 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469341) BOUND_VARIABLE_1469342))))))))))))))))) (let ((_let_2554 (forall ((BOUND_VARIABLE_1469286 tptp.real) (BOUND_VARIABLE_1469287 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8462 BOUND_VARIABLE_1469286) BOUND_VARIABLE_1469287) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469287 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1469287) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469287 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1469287) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469286) BOUND_VARIABLE_1469287))))))))))))))) (let ((_let_2555 (forall ((BOUND_VARIABLE_1469223 tptp.real) (BOUND_VARIABLE_1469224 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1469224) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8463 BOUND_VARIABLE_1469223) BOUND_VARIABLE_1469224) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469224 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469224 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469223) BOUND_VARIABLE_1469224))))))))))))))))) (let ((_let_2556 (forall ((BOUND_VARIABLE_1469168 tptp.real) (BOUND_VARIABLE_1469169 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8464 BOUND_VARIABLE_1469168) BOUND_VARIABLE_1469169) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469169 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1469169) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469169 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1469169) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469168) BOUND_VARIABLE_1469169))))))))))))))) (let ((_let_2557 (forall ((BOUND_VARIABLE_1469105 tptp.real) (BOUND_VARIABLE_1469106 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1469106) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8465 BOUND_VARIABLE_1469105) BOUND_VARIABLE_1469106) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469106 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469106 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469105) BOUND_VARIABLE_1469106))))))))))))))))) (let ((_let_2558 (forall ((BOUND_VARIABLE_1469050 tptp.real) (BOUND_VARIABLE_1469051 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8466 BOUND_VARIABLE_1469050) BOUND_VARIABLE_1469051) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1469051 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1469051) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1469051 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1469051) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1469050) BOUND_VARIABLE_1469051))))))))))))))) (let ((_let_2559 (forall ((BOUND_VARIABLE_1468987 tptp.real) (BOUND_VARIABLE_1468988 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468988) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8467 BOUND_VARIABLE_1468987) BOUND_VARIABLE_1468988) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468988 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468988 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468987) BOUND_VARIABLE_1468988))))))))))))))))) (let ((_let_2560 (forall ((BOUND_VARIABLE_1468932 tptp.real) (BOUND_VARIABLE_1468933 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8468 BOUND_VARIABLE_1468932) BOUND_VARIABLE_1468933) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468933 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468933) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468933 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468933) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468932) BOUND_VARIABLE_1468933))))))))))))))) (let ((_let_2561 (forall ((BOUND_VARIABLE_1468869 tptp.real) (BOUND_VARIABLE_1468870 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468870) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8469 BOUND_VARIABLE_1468869) BOUND_VARIABLE_1468870) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468870 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468870 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468869) BOUND_VARIABLE_1468870))))))))))))))))) (let ((_let_2562 (forall ((BOUND_VARIABLE_1468814 tptp.real) (BOUND_VARIABLE_1468815 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8470 BOUND_VARIABLE_1468814) BOUND_VARIABLE_1468815) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468815 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468815) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468815 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468815) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468814) BOUND_VARIABLE_1468815))))))))))))))) (let ((_let_2563 (forall ((BOUND_VARIABLE_1468751 tptp.real) (BOUND_VARIABLE_1468752 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468752) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8471 BOUND_VARIABLE_1468751) BOUND_VARIABLE_1468752) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468752 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468752 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468751) BOUND_VARIABLE_1468752))))))))))))))))) (let ((_let_2564 (forall ((BOUND_VARIABLE_1468696 tptp.real) (BOUND_VARIABLE_1468697 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8472 BOUND_VARIABLE_1468696) BOUND_VARIABLE_1468697) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468697 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468697) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468697 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468697) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468696) BOUND_VARIABLE_1468697))))))))))))))) (let ((_let_2565 (forall ((BOUND_VARIABLE_1468633 tptp.real) (BOUND_VARIABLE_1468634 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468634) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8473 BOUND_VARIABLE_1468633) BOUND_VARIABLE_1468634) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468634 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468634 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468633) BOUND_VARIABLE_1468634))))))))))))))))) (let ((_let_2566 (forall ((BOUND_VARIABLE_1468578 tptp.real) (BOUND_VARIABLE_1468579 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8474 BOUND_VARIABLE_1468578) BOUND_VARIABLE_1468579) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468579 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468579) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468579 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468579) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468578) BOUND_VARIABLE_1468579))))))))))))))) (let ((_let_2567 (forall ((BOUND_VARIABLE_1468515 tptp.real) (BOUND_VARIABLE_1468516 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468516) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8475 BOUND_VARIABLE_1468515) BOUND_VARIABLE_1468516) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468516 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468516 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468515) BOUND_VARIABLE_1468516))))))))))))))))) (let ((_let_2568 (forall ((BOUND_VARIABLE_1468460 tptp.real) (BOUND_VARIABLE_1468461 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8476 BOUND_VARIABLE_1468460) BOUND_VARIABLE_1468461) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468461 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468461) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468461 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468461) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468460) BOUND_VARIABLE_1468461))))))))))))))) (let ((_let_2569 (forall ((BOUND_VARIABLE_1468397 tptp.real) (BOUND_VARIABLE_1468398 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468398) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8477 BOUND_VARIABLE_1468397) BOUND_VARIABLE_1468398) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468398 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468398 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468397) BOUND_VARIABLE_1468398))))))))))))))))) (let ((_let_2570 (forall ((BOUND_VARIABLE_1468342 tptp.real) (BOUND_VARIABLE_1468343 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8478 BOUND_VARIABLE_1468342) BOUND_VARIABLE_1468343) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468343 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468343) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468343 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468343) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468342) BOUND_VARIABLE_1468343))))))))))))))) (let ((_let_2571 (forall ((BOUND_VARIABLE_1468279 tptp.real) (BOUND_VARIABLE_1468280 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1468280) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8479 BOUND_VARIABLE_1468279) BOUND_VARIABLE_1468280) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468280 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468280 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468279) BOUND_VARIABLE_1468280))))))))))))))))) (let ((_let_2572 (forall ((BOUND_VARIABLE_1468224 tptp.real) (BOUND_VARIABLE_1468225 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8480 BOUND_VARIABLE_1468224) BOUND_VARIABLE_1468225) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1468225 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1468225) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1468225 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1468225) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1468224) BOUND_VARIABLE_1468225))))))))))))))) (let ((_let_2573 (forall ((BOUND_VARIABLE_1468199 tptp.int) (BOUND_VARIABLE_1468200 tptp.int) (BOUND_VARIABLE_1468201 tptp.int) (BOUND_VARIABLE_1468202 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8481 BOUND_VARIABLE_1468199) BOUND_VARIABLE_1468200) BOUND_VARIABLE_1468201) BOUND_VARIABLE_1468202) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468200) BOUND_VARIABLE_1468202)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468199) BOUND_VARIABLE_1468201)))))))))) (let ((_let_2574 (forall ((BOUND_VARIABLE_1468174 tptp.int) (BOUND_VARIABLE_1468175 tptp.int) (BOUND_VARIABLE_1468176 tptp.int) (BOUND_VARIABLE_1468177 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8482 BOUND_VARIABLE_1468174) BOUND_VARIABLE_1468175) BOUND_VARIABLE_1468176) BOUND_VARIABLE_1468177) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468175) BOUND_VARIABLE_1468177)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468174) BOUND_VARIABLE_1468176)))))))))) (let ((_let_2575 (forall ((BOUND_VARIABLE_1468149 tptp.int) (BOUND_VARIABLE_1468150 tptp.int) (BOUND_VARIABLE_1468151 tptp.int) (BOUND_VARIABLE_1468152 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8483 BOUND_VARIABLE_1468149) BOUND_VARIABLE_1468150) BOUND_VARIABLE_1468151) BOUND_VARIABLE_1468152) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468150) BOUND_VARIABLE_1468152)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468149) BOUND_VARIABLE_1468151)))))))))) (let ((_let_2576 (forall ((BOUND_VARIABLE_1468124 tptp.int) (BOUND_VARIABLE_1468125 tptp.int) (BOUND_VARIABLE_1468126 tptp.int) (BOUND_VARIABLE_1468127 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8484 BOUND_VARIABLE_1468124) BOUND_VARIABLE_1468125) BOUND_VARIABLE_1468126) BOUND_VARIABLE_1468127) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468125) BOUND_VARIABLE_1468127)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468124) BOUND_VARIABLE_1468126)))))))))) (let ((_let_2577 (forall ((BOUND_VARIABLE_1468099 tptp.int) (BOUND_VARIABLE_1468100 tptp.int) (BOUND_VARIABLE_1468101 tptp.int) (BOUND_VARIABLE_1468102 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8485 BOUND_VARIABLE_1468099) BOUND_VARIABLE_1468100) BOUND_VARIABLE_1468101) BOUND_VARIABLE_1468102) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468100) BOUND_VARIABLE_1468102)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468099) BOUND_VARIABLE_1468101)))))))))) (let ((_let_2578 (forall ((BOUND_VARIABLE_1468074 tptp.int) (BOUND_VARIABLE_1468075 tptp.int) (BOUND_VARIABLE_1468076 tptp.int) (BOUND_VARIABLE_1468077 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8486 BOUND_VARIABLE_1468074) BOUND_VARIABLE_1468075) BOUND_VARIABLE_1468076) BOUND_VARIABLE_1468077) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468075) BOUND_VARIABLE_1468077)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468074) BOUND_VARIABLE_1468076)))))))))) (let ((_let_2579 (forall ((BOUND_VARIABLE_1468049 tptp.int) (BOUND_VARIABLE_1468050 tptp.int) (BOUND_VARIABLE_1468051 tptp.int) (BOUND_VARIABLE_1468052 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8487 BOUND_VARIABLE_1468049) BOUND_VARIABLE_1468050) BOUND_VARIABLE_1468051) BOUND_VARIABLE_1468052) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468050) BOUND_VARIABLE_1468052)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1468049) BOUND_VARIABLE_1468051)))))))))) (let ((_let_2580 (forall ((BOUND_VARIABLE_1468009 tptp.int) (BOUND_VARIABLE_1468010 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7572 BOUND_VARIABLE_1468010) BOUND_VARIABLE_1468009)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8488 BOUND_VARIABLE_1468009) BOUND_VARIABLE_1468010))))))))) (let ((_let_2581 (forall ((BOUND_VARIABLE_1467984 tptp.int) (BOUND_VARIABLE_1467985 tptp.int) (BOUND_VARIABLE_1467986 tptp.int) (BOUND_VARIABLE_1467987 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8489 BOUND_VARIABLE_1467984) BOUND_VARIABLE_1467985) BOUND_VARIABLE_1467986) BOUND_VARIABLE_1467987) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467985) BOUND_VARIABLE_1467987)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467984) BOUND_VARIABLE_1467986)))))))))) (let ((_let_2582 (forall ((BOUND_VARIABLE_1467959 tptp.int) (BOUND_VARIABLE_1467960 tptp.int) (BOUND_VARIABLE_1467961 tptp.int) (BOUND_VARIABLE_1467962 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8490 BOUND_VARIABLE_1467959) BOUND_VARIABLE_1467960) BOUND_VARIABLE_1467961) BOUND_VARIABLE_1467962) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467960) BOUND_VARIABLE_1467962)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467959) BOUND_VARIABLE_1467961)))))))))) (let ((_let_2583 (forall ((BOUND_VARIABLE_1467917 tptp.rat) (BOUND_VARIABLE_1467918 tptp.int) (BOUND_VARIABLE_1467919 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7573 BOUND_VARIABLE_1467919) BOUND_VARIABLE_1467918)) (ho_7630 k_7629 BOUND_VARIABLE_1467917)) (ho_7496 (ho_7495 (ho_7635 k_8491 BOUND_VARIABLE_1467917) BOUND_VARIABLE_1467918) BOUND_VARIABLE_1467919))))) (let ((_let_2584 (forall ((BOUND_VARIABLE_1467875 tptp.rat) (BOUND_VARIABLE_1467876 tptp.int) (BOUND_VARIABLE_1467877 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7574 BOUND_VARIABLE_1467877) BOUND_VARIABLE_1467876)) (ho_7630 k_7629 BOUND_VARIABLE_1467875)) (ho_7496 (ho_7495 (ho_7635 k_8492 BOUND_VARIABLE_1467875) BOUND_VARIABLE_1467876) BOUND_VARIABLE_1467877))))) (let ((_let_2585 (forall ((BOUND_VARIABLE_1467850 tptp.int) (BOUND_VARIABLE_1467851 tptp.int) (BOUND_VARIABLE_1467852 tptp.int) (BOUND_VARIABLE_1467853 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8493 BOUND_VARIABLE_1467850) BOUND_VARIABLE_1467851) BOUND_VARIABLE_1467852) BOUND_VARIABLE_1467853) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467851) BOUND_VARIABLE_1467853)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467850) BOUND_VARIABLE_1467852)))))))))) (let ((_let_2586 (forall ((BOUND_VARIABLE_1467808 tptp.rat) (BOUND_VARIABLE_1467809 tptp.int) (BOUND_VARIABLE_1467810 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7575 BOUND_VARIABLE_1467810) BOUND_VARIABLE_1467809)) (ho_7630 k_7629 BOUND_VARIABLE_1467808)) (ho_7496 (ho_7495 (ho_7635 k_8494 BOUND_VARIABLE_1467808) BOUND_VARIABLE_1467809) BOUND_VARIABLE_1467810))))) (let ((_let_2587 (forall ((BOUND_VARIABLE_1467766 tptp.rat) (BOUND_VARIABLE_1467767 tptp.int) (BOUND_VARIABLE_1467768 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7576 BOUND_VARIABLE_1467768) BOUND_VARIABLE_1467767)) (ho_7630 k_7629 BOUND_VARIABLE_1467766)) (ho_7496 (ho_7495 (ho_7635 k_8495 BOUND_VARIABLE_1467766) BOUND_VARIABLE_1467767) BOUND_VARIABLE_1467768))))) (let ((_let_2588 (forall ((BOUND_VARIABLE_1467741 tptp.int) (BOUND_VARIABLE_1467742 tptp.int) (BOUND_VARIABLE_1467743 tptp.int) (BOUND_VARIABLE_1467744 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8496 BOUND_VARIABLE_1467741) BOUND_VARIABLE_1467742) BOUND_VARIABLE_1467743) BOUND_VARIABLE_1467744) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467742) BOUND_VARIABLE_1467744)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467741) BOUND_VARIABLE_1467743)))))))))) (let ((_let_2589 (forall ((BOUND_VARIABLE_1467699 tptp.rat) (BOUND_VARIABLE_1467700 tptp.int) (BOUND_VARIABLE_1467701 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7577 BOUND_VARIABLE_1467701) BOUND_VARIABLE_1467700)) (ho_7630 k_7629 BOUND_VARIABLE_1467699)) (ho_7496 (ho_7495 (ho_7635 k_8497 BOUND_VARIABLE_1467699) BOUND_VARIABLE_1467700) BOUND_VARIABLE_1467701))))) (let ((_let_2590 (forall ((BOUND_VARIABLE_1467653 tptp.real) (BOUND_VARIABLE_1467654 tptp.real) (BOUND_VARIABLE_1467655 tptp.nat) (BOUND_VARIABLE_1467656 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1467654) BOUND_VARIABLE_1467653)) BOUND_VARIABLE_1467656)) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1467654) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467655) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467656) _let_3)))))) (ho_7508 (ho_7775 (ho_7999 (ho_7998 k_8498 BOUND_VARIABLE_1467653) BOUND_VARIABLE_1467654) BOUND_VARIABLE_1467655) BOUND_VARIABLE_1467656))))))))) (let ((_let_2591 (forall ((BOUND_VARIABLE_1467612 tptp.nat) (BOUND_VARIABLE_1467613 tptp.nat) (BOUND_VARIABLE_1467614 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1467614)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467612) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) _let_3)))) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467613) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8499 BOUND_VARIABLE_1467612) BOUND_VARIABLE_1467613) BOUND_VARIABLE_1467614)))))))))) (let ((_let_2592 (forall ((BOUND_VARIABLE_1467561 tptp.rat) (BOUND_VARIABLE_1467562 tptp.rat) (BOUND_VARIABLE_1467563 tptp.nat) (BOUND_VARIABLE_1467564 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)))) (= (ho_7711 (ho_7717 (ho_7716 _let_5 k_8019) (ho_7636 (ho_8018 k_8017 (ho_7711 (ho_7717 (ho_7716 _let_5 k_7712) BOUND_VARIABLE_1467562) BOUND_VARIABLE_1467561)) BOUND_VARIABLE_1467564)) (ho_7636 (ho_8018 k_8017 BOUND_VARIABLE_1467562) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467563) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467564) _let_3)))))) (ho_7636 (ho_8023 (ho_8022 (ho_8043 k_8500 BOUND_VARIABLE_1467561) BOUND_VARIABLE_1467562) BOUND_VARIABLE_1467563) BOUND_VARIABLE_1467564)))))))))) (let ((_let_2593 (forall ((BOUND_VARIABLE_1467520 tptp.nat) (BOUND_VARIABLE_1467521 tptp.nat) (BOUND_VARIABLE_1467522 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1467522)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467520) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) _let_3)))) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467521) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8501 BOUND_VARIABLE_1467520) BOUND_VARIABLE_1467521) BOUND_VARIABLE_1467522)))))))))) (let ((_let_2594 (forall ((BOUND_VARIABLE_1467439 tptp.complex) (BOUND_VARIABLE_1467440 tptp.complex) (BOUND_VARIABLE_1467441 tptp.nat) (BOUND_VARIABLE_1467442 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7736 (ho_7735 k_7734 BOUND_VARIABLE_1467440) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467441) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467442) _let_3))))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 BOUND_VARIABLE_1467440)) (ho_7730 k_7729 BOUND_VARIABLE_1467439))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 BOUND_VARIABLE_1467440)) (ho_7730 k_7733 BOUND_VARIABLE_1467439)))) BOUND_VARIABLE_1467442))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7733 _let_7)))) (let ((_let_9 (ho_7730 k_7733 _let_5))) (let ((_let_10 (ho_7519 k_7522 (ho_7730 k_7729 _let_7)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_6)) (ho_7516 k_7521 (ho_7516 _let_8 _let_9)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_10 _let_9)) (ho_7516 _let_8 _let_6))) (ho_7736 (ho_7937 (ho_7936 (ho_7995 k_8502 BOUND_VARIABLE_1467439) BOUND_VARIABLE_1467440) BOUND_VARIABLE_1467441) BOUND_VARIABLE_1467442))))))))))))))) (let ((_let_2595 (forall ((BOUND_VARIABLE_1467398 tptp.nat) (BOUND_VARIABLE_1467399 tptp.nat) (BOUND_VARIABLE_1467400 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 _let_1))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1467400)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467398) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) _let_3)))) _let_3))))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1467399) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_8503 BOUND_VARIABLE_1467398) BOUND_VARIABLE_1467399) BOUND_VARIABLE_1467400)))))))))) (let ((_let_2596 (forall ((BOUND_VARIABLE_1467373 tptp.int) (BOUND_VARIABLE_1467374 tptp.int) (BOUND_VARIABLE_1467375 tptp.int) (BOUND_VARIABLE_1467376 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8504 BOUND_VARIABLE_1467373) BOUND_VARIABLE_1467374) BOUND_VARIABLE_1467375) BOUND_VARIABLE_1467376) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467374) BOUND_VARIABLE_1467376)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467373) BOUND_VARIABLE_1467375)))))))))) (let ((_let_2597 (forall ((BOUND_VARIABLE_1467348 tptp.int) (BOUND_VARIABLE_1467349 tptp.int) (BOUND_VARIABLE_1467350 tptp.int) (BOUND_VARIABLE_1467351 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8505 BOUND_VARIABLE_1467348) BOUND_VARIABLE_1467349) BOUND_VARIABLE_1467350) BOUND_VARIABLE_1467351) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467349) BOUND_VARIABLE_1467351)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467348) BOUND_VARIABLE_1467350)))))))))) (let ((_let_2598 (forall ((BOUND_VARIABLE_1467285 tptp.real) (BOUND_VARIABLE_1467286 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1467286) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8506 BOUND_VARIABLE_1467285) BOUND_VARIABLE_1467286) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1467286 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1467286 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1467285) BOUND_VARIABLE_1467286))))))))))))))))) (let ((_let_2599 (forall ((BOUND_VARIABLE_1467230 tptp.real) (BOUND_VARIABLE_1467231 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8507 BOUND_VARIABLE_1467230) BOUND_VARIABLE_1467231) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1467231 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1467231) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1467231 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1467231) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1467230) BOUND_VARIABLE_1467231))))))))))))))) (let ((_let_2600 (forall ((BOUND_VARIABLE_1467210 tptp.nat) (BOUND_VARIABLE_1467211 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1467210) _let_2)))) BOUND_VARIABLE_1467211) (ho_7641 (ho_7448 k_8508 BOUND_VARIABLE_1467210) BOUND_VARIABLE_1467211)))))))) (let ((_let_2601 (forall ((BOUND_VARIABLE_1467186 tptp.nat) (BOUND_VARIABLE_1467187 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)))) (let ((_let_4 (ho_7704 k_7703 (ho_7702 _let_3 (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_5 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_6 (ho_7715 (ho_7714 k_7713 k_7706) _let_5))) (let ((_let_7 (ho_7716 _let_6 k_7712))) (let ((_let_8 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) (let ((_let_9 (ho_7711 (ho_7717 (ho_7716 _let_6 k_8019) (ho_7704 k_7703 (ho_7702 _let_3 (ho_7698 (ho_7697 k_7696 _let_8) _let_1)))) (ho_7711 (ho_8055 (ho_8054 k_8053 k_8052) BOUND_VARIABLE_1467186) (ho_7711 (ho_7717 _let_7 _let_4) (ho_7711 (ho_7710 _let_5 k_7705) _let_4)))))) (= (ho_7636 (ho_8023 k_8511 BOUND_VARIABLE_1467186) BOUND_VARIABLE_1467187) (ho_7711 (ho_7717 (ho_8510 k_8509 (= BOUND_VARIABLE_1467187 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 _let_1)) (ho_7463 k_7462 _let_8)))) _let_9) (ho_7711 (ho_7717 _let_7 _let_9) _let_4))))))))))))))) (let ((_let_2602 (forall ((BOUND_VARIABLE_1467150 tptp.nat) (BOUND_VARIABLE_1467151 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7463 k_7462 _let_1))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_6 (ho_7466 (ho_7465 k_7471 _let_3) _let_5))) (let ((_let_7 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_4 _let_5) _let_2)) (ho_7459 (ho_7470 _let_4 (ho_7466 (ho_7465 (ho_8093 k_8286 k_8285) BOUND_VARIABLE_1467150) _let_6)) _let_2))))) (= (ho_7466 (ho_7465 k_8512 BOUND_VARIABLE_1467150) BOUND_VARIABLE_1467151) (ho_7466 (ho_7465 (ho_7878 k_7877 (= BOUND_VARIABLE_1467151 _let_6)) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_7) _let_2)) (ho_7459 (ho_7470 _let_4 _let_3) _let_2))))))))))))))) (let ((_let_2603 (forall ((BOUND_VARIABLE_1467126 tptp.nat) (BOUND_VARIABLE_1467127 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7443 k_7442 tptp.one))) (let ((_let_3 (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 _let_2)) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1467126) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))))) (= (ho_7508 (ho_7775 k_8513 BOUND_VARIABLE_1467126) BOUND_VARIABLE_1467127) (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1467127 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 _let_2))))) _let_3) (ho_7516 (ho_7519 k_7523 _let_3) _let_1))))))))) (let ((_let_2604 (forall ((BOUND_VARIABLE_1467102 tptp.nat) (BOUND_VARIABLE_1467103 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) (let ((_let_3 (ho_7459 (ho_7461 k_7472 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) BOUND_VARIABLE_1467102) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))))) (= (ho_7927 (ho_8015 k_8514 BOUND_VARIABLE_1467102) BOUND_VARIABLE_1467103) (ho_7459 (ho_7461 (ho_7892 k_7891 (= BOUND_VARIABLE_1467103 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 _let_1)) (ho_7463 k_7462 _let_2)))) _let_3) (ho_7459 (ho_7461 k_7460 _let_3) _let_1))))))))) (let ((_let_2605 (forall ((BOUND_VARIABLE_1467042 tptp.nat) (BOUND_VARIABLE_1467043 tptp.nat)) (let ((_let_1 (ho_7985 k_7984 tptp.one))) (let ((_let_2 (ho_7730 k_7733 _let_1))) (let ((_let_3 (ho_7958 k_7957 _let_1))) (let ((_let_4 (ho_7730 k_7729 _let_1))) (let ((_let_5 (ho_7958 (ho_8063 (ho_8062 k_8061 k_8060) BOUND_VARIABLE_1467042) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_4) (ho_7730 k_7729 _let_3))) (ho_7516 (ho_7519 k_7523 _let_2) (ho_7730 k_7733 _let_3)))))) (let ((_let_6 (ho_7730 k_7729 _let_5))) (let ((_let_7 (ho_7443 k_7442 tptp.one))) (let ((_let_8 (ho_7985 k_7984 _let_7))) (let ((_let_9 (ho_7519 k_7522 (ho_7730 k_7733 _let_8)))) (let ((_let_10 (ho_7730 k_7733 _let_5))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7729 _let_8)))) (let ((_let_12 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_11 _let_6)) (ho_7516 k_7521 (ho_7516 _let_9 _let_10)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_11 _let_10)) (ho_7516 _let_9 _let_6))))) (= (ho_7736 (ho_7937 k_8515 BOUND_VARIABLE_1467042) BOUND_VARIABLE_1467043) (ho_7958 (ho_7993 (ho_7992 k_7991 (= BOUND_VARIABLE_1467043 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 _let_7))))) _let_12) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_12)) _let_4)) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_12)) _let_2))))))))))))))))))) (let ((_let_2606 (forall ((BOUND_VARIABLE_1467017 tptp.int) (BOUND_VARIABLE_1467018 tptp.int) (BOUND_VARIABLE_1467019 tptp.int) (BOUND_VARIABLE_1467020 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8516 BOUND_VARIABLE_1467017) BOUND_VARIABLE_1467018) BOUND_VARIABLE_1467019) BOUND_VARIABLE_1467020) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467018) BOUND_VARIABLE_1467020)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1467017) BOUND_VARIABLE_1467019)))))))))) (let ((_let_2607 (forall ((BOUND_VARIABLE_1466992 tptp.int) (BOUND_VARIABLE_1466993 tptp.int) (BOUND_VARIABLE_1466994 tptp.int) (BOUND_VARIABLE_1466995 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8517 BOUND_VARIABLE_1466992) BOUND_VARIABLE_1466993) BOUND_VARIABLE_1466994) BOUND_VARIABLE_1466995) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466993) BOUND_VARIABLE_1466995)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466992) BOUND_VARIABLE_1466994)))))))))) (let ((_let_2608 (forall ((BOUND_VARIABLE_1466967 tptp.int) (BOUND_VARIABLE_1466968 tptp.int) (BOUND_VARIABLE_1466969 tptp.int) (BOUND_VARIABLE_1466970 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8518 BOUND_VARIABLE_1466967) BOUND_VARIABLE_1466968) BOUND_VARIABLE_1466969) BOUND_VARIABLE_1466970) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466968) BOUND_VARIABLE_1466970)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466967) BOUND_VARIABLE_1466969)))))))))) (let ((_let_2609 (forall ((BOUND_VARIABLE_1466942 tptp.int) (BOUND_VARIABLE_1466943 tptp.int) (BOUND_VARIABLE_1466944 tptp.int) (BOUND_VARIABLE_1466945 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8519 BOUND_VARIABLE_1466942) BOUND_VARIABLE_1466943) BOUND_VARIABLE_1466944) BOUND_VARIABLE_1466945) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466943) BOUND_VARIABLE_1466945)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466942) BOUND_VARIABLE_1466944)))))))))) (let ((_let_2610 (forall ((BOUND_VARIABLE_1466917 tptp.int) (BOUND_VARIABLE_1466918 tptp.int) (BOUND_VARIABLE_1466919 tptp.int) (BOUND_VARIABLE_1466920 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8520 BOUND_VARIABLE_1466917) BOUND_VARIABLE_1466918) BOUND_VARIABLE_1466919) BOUND_VARIABLE_1466920) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466918) BOUND_VARIABLE_1466920)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466917) BOUND_VARIABLE_1466919)))))))))) (let ((_let_2611 (forall ((BOUND_VARIABLE_1466892 tptp.int) (BOUND_VARIABLE_1466893 tptp.int) (BOUND_VARIABLE_1466894 tptp.int) (BOUND_VARIABLE_1466895 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8521 BOUND_VARIABLE_1466892) BOUND_VARIABLE_1466893) BOUND_VARIABLE_1466894) BOUND_VARIABLE_1466895) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466893) BOUND_VARIABLE_1466895)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466892) BOUND_VARIABLE_1466894)))))))))) (let ((_let_2612 (forall ((BOUND_VARIABLE_1466867 tptp.int) (BOUND_VARIABLE_1466868 tptp.int) (BOUND_VARIABLE_1466869 tptp.int) (BOUND_VARIABLE_1466870 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8522 BOUND_VARIABLE_1466867) BOUND_VARIABLE_1466868) BOUND_VARIABLE_1466869) BOUND_VARIABLE_1466870) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466868) BOUND_VARIABLE_1466870)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466867) BOUND_VARIABLE_1466869)))))))))) (let ((_let_2613 (forall ((BOUND_VARIABLE_1466842 tptp.int) (BOUND_VARIABLE_1466843 tptp.int) (BOUND_VARIABLE_1466844 tptp.int) (BOUND_VARIABLE_1466845 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8523 BOUND_VARIABLE_1466842) BOUND_VARIABLE_1466843) BOUND_VARIABLE_1466844) BOUND_VARIABLE_1466845) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466843) BOUND_VARIABLE_1466845)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466842) BOUND_VARIABLE_1466844)))))))))) (let ((_let_2614 (forall ((BOUND_VARIABLE_1466817 tptp.int) (BOUND_VARIABLE_1466818 tptp.int) (BOUND_VARIABLE_1466819 tptp.int) (BOUND_VARIABLE_1466820 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8524 BOUND_VARIABLE_1466817) BOUND_VARIABLE_1466818) BOUND_VARIABLE_1466819) BOUND_VARIABLE_1466820) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466818) BOUND_VARIABLE_1466820)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466817) BOUND_VARIABLE_1466819)))))))))) (let ((_let_2615 (forall ((BOUND_VARIABLE_1466792 tptp.int) (BOUND_VARIABLE_1466793 tptp.int) (BOUND_VARIABLE_1466794 tptp.int) (BOUND_VARIABLE_1466795 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8525 BOUND_VARIABLE_1466792) BOUND_VARIABLE_1466793) BOUND_VARIABLE_1466794) BOUND_VARIABLE_1466795) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466793) BOUND_VARIABLE_1466795)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466792) BOUND_VARIABLE_1466794)))))))))) (let ((_let_2616 (forall ((BOUND_VARIABLE_1466767 tptp.int) (BOUND_VARIABLE_1466768 tptp.int) (BOUND_VARIABLE_1466769 tptp.int) (BOUND_VARIABLE_1466770 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8526 BOUND_VARIABLE_1466767) BOUND_VARIABLE_1466768) BOUND_VARIABLE_1466769) BOUND_VARIABLE_1466770) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466768) BOUND_VARIABLE_1466770)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466767) BOUND_VARIABLE_1466769)))))))))) (let ((_let_2617 (forall ((BOUND_VARIABLE_1466742 tptp.int) (BOUND_VARIABLE_1466743 tptp.int) (BOUND_VARIABLE_1466744 tptp.int) (BOUND_VARIABLE_1466745 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8527 BOUND_VARIABLE_1466742) BOUND_VARIABLE_1466743) BOUND_VARIABLE_1466744) BOUND_VARIABLE_1466745) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466743) BOUND_VARIABLE_1466745)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466742) BOUND_VARIABLE_1466744)))))))))) (let ((_let_2618 (forall ((BOUND_VARIABLE_1466717 tptp.int) (BOUND_VARIABLE_1466718 tptp.int) (BOUND_VARIABLE_1466719 tptp.int) (BOUND_VARIABLE_1466720 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8528 BOUND_VARIABLE_1466717) BOUND_VARIABLE_1466718) BOUND_VARIABLE_1466719) BOUND_VARIABLE_1466720) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466718) BOUND_VARIABLE_1466720)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466717) BOUND_VARIABLE_1466719)))))))))) (let ((_let_2619 (forall ((BOUND_VARIABLE_1466677 tptp.num) (BOUND_VARIABLE_1466678 tptp.int) (BOUND_VARIABLE_1466679 tptp.int)) (let ((_let_1 (ho_7459 (ho_7461 k_7472 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))) BOUND_VARIABLE_1466678))) (= (ho_7702 (ho_7701 (ho_7700 k_7699 (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= BOUND_VARIABLE_1466679 (ho_7459 (ho_7461 k_7460 (ho_7446 k_7445 BOUND_VARIABLE_1466677)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))))))))) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7446 k_7445 tptp.one))) (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1466679) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7446 k_7445 BOUND_VARIABLE_1466677))))) (ho_7698 (ho_7697 k_7696 _let_1) BOUND_VARIABLE_1466679)) (ho_7698 (ho_7697 (ho_8530 k_8529 BOUND_VARIABLE_1466677) BOUND_VARIABLE_1466678) BOUND_VARIABLE_1466679)))))) (let ((_let_2620 (forall ((BOUND_VARIABLE_1466637 tptp.num) (BOUND_VARIABLE_1466638 tptp.int) (BOUND_VARIABLE_1466639 tptp.int)) (let ((_let_1 (ho_7459 (ho_7461 k_7472 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))) BOUND_VARIABLE_1466638))) (= (ho_7702 (ho_7701 (ho_7700 k_7699 (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= BOUND_VARIABLE_1466639 (ho_7459 (ho_7461 k_7460 (ho_7446 k_7445 BOUND_VARIABLE_1466637)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))))))))) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7446 k_7445 tptp.one))) (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1466639) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7446 k_7445 BOUND_VARIABLE_1466637))))) (ho_7698 (ho_7697 k_7696 _let_1) BOUND_VARIABLE_1466639)) (ho_7698 (ho_7697 (ho_8530 k_8531 BOUND_VARIABLE_1466637) BOUND_VARIABLE_1466638) BOUND_VARIABLE_1466639)))))) (let ((_let_2621 (forall ((BOUND_VARIABLE_1466575 tptp.num) (BOUND_VARIABLE_1466576 tptp.nat) (BOUND_VARIABLE_1466577 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1466576) _let_3))))) (let ((_let_6 (ho_7463 k_7462 (ho_7446 k_7445 BOUND_VARIABLE_1466575)))) (= (ho_8535 (ho_8534 (ho_8533 k_8532 (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 _let_6)) (ho_7533 k_7532 BOUND_VARIABLE_1466577))) (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1466577) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 _let_6) _let_3)))))) (ho_7641 (ho_7448 k_7640 _let_5) BOUND_VARIABLE_1466577)) (ho_7641 (ho_7448 (ho_8537 k_8536 BOUND_VARIABLE_1466575) BOUND_VARIABLE_1466576) BOUND_VARIABLE_1466577))))))))))) (let ((_let_2622 (forall ((BOUND_VARIABLE_1466513 tptp.num) (BOUND_VARIABLE_1466514 tptp.nat) (BOUND_VARIABLE_1466515 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1466514) _let_3))))) (let ((_let_6 (ho_7463 k_7462 (ho_7446 k_7445 BOUND_VARIABLE_1466513)))) (= (ho_8535 (ho_8534 (ho_8533 k_8532 (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 _let_6)) (ho_7533 k_7532 BOUND_VARIABLE_1466515))) (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1466515) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 _let_6) _let_3)))))) (ho_7641 (ho_7448 k_7640 _let_5) BOUND_VARIABLE_1466515)) (ho_7641 (ho_7448 (ho_8537 k_8538 BOUND_VARIABLE_1466513) BOUND_VARIABLE_1466514) BOUND_VARIABLE_1466515))))))))))) (let ((_let_2623 (forall ((BOUND_VARIABLE_1466488 tptp.int) (BOUND_VARIABLE_1466489 tptp.int) (BOUND_VARIABLE_1466490 tptp.int) (BOUND_VARIABLE_1466491 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8539 BOUND_VARIABLE_1466488) BOUND_VARIABLE_1466489) BOUND_VARIABLE_1466490) BOUND_VARIABLE_1466491) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466489) BOUND_VARIABLE_1466491)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466488) BOUND_VARIABLE_1466490)))))))))) (let ((_let_2624 (forall ((BOUND_VARIABLE_1466463 tptp.int) (BOUND_VARIABLE_1466464 tptp.int) (BOUND_VARIABLE_1466465 tptp.int) (BOUND_VARIABLE_1466466 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8540 BOUND_VARIABLE_1466463) BOUND_VARIABLE_1466464) BOUND_VARIABLE_1466465) BOUND_VARIABLE_1466466) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466464) BOUND_VARIABLE_1466466)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466463) BOUND_VARIABLE_1466465)))))))))) (let ((_let_2625 (forall ((BOUND_VARIABLE_1466438 tptp.int) (BOUND_VARIABLE_1466439 tptp.int) (BOUND_VARIABLE_1466440 tptp.int) (BOUND_VARIABLE_1466441 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8541 BOUND_VARIABLE_1466438) BOUND_VARIABLE_1466439) BOUND_VARIABLE_1466440) BOUND_VARIABLE_1466441) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466439) BOUND_VARIABLE_1466441)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466438) BOUND_VARIABLE_1466440)))))))))) (let ((_let_2626 (forall ((BOUND_VARIABLE_1466413 tptp.int) (BOUND_VARIABLE_1466414 tptp.int) (BOUND_VARIABLE_1466415 tptp.int) (BOUND_VARIABLE_1466416 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8542 BOUND_VARIABLE_1466413) BOUND_VARIABLE_1466414) BOUND_VARIABLE_1466415) BOUND_VARIABLE_1466416) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466414) BOUND_VARIABLE_1466416)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466413) BOUND_VARIABLE_1466415)))))))))) (let ((_let_2627 (forall ((BOUND_VARIABLE_1466388 tptp.int) (BOUND_VARIABLE_1466389 tptp.int) (BOUND_VARIABLE_1466390 tptp.int) (BOUND_VARIABLE_1466391 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8543 BOUND_VARIABLE_1466388) BOUND_VARIABLE_1466389) BOUND_VARIABLE_1466390) BOUND_VARIABLE_1466391) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466389) BOUND_VARIABLE_1466391)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466388) BOUND_VARIABLE_1466390)))))))))) (let ((_let_2628 (forall ((BOUND_VARIABLE_1466363 tptp.int) (BOUND_VARIABLE_1466364 tptp.int) (BOUND_VARIABLE_1466365 tptp.int) (BOUND_VARIABLE_1466366 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8544 BOUND_VARIABLE_1466363) BOUND_VARIABLE_1466364) BOUND_VARIABLE_1466365) BOUND_VARIABLE_1466366) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466364) BOUND_VARIABLE_1466366)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466363) BOUND_VARIABLE_1466365)))))))))) (let ((_let_2629 (forall ((BOUND_VARIABLE_1466338 tptp.int) (BOUND_VARIABLE_1466339 tptp.int) (BOUND_VARIABLE_1466340 tptp.int) (BOUND_VARIABLE_1466341 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8545 BOUND_VARIABLE_1466338) BOUND_VARIABLE_1466339) BOUND_VARIABLE_1466340) BOUND_VARIABLE_1466341) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466339) BOUND_VARIABLE_1466341)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466338) BOUND_VARIABLE_1466340)))))))))) (let ((_let_2630 (forall ((BOUND_VARIABLE_1466313 tptp.int) (BOUND_VARIABLE_1466314 tptp.int) (BOUND_VARIABLE_1466315 tptp.int) (BOUND_VARIABLE_1466316 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8546 BOUND_VARIABLE_1466313) BOUND_VARIABLE_1466314) BOUND_VARIABLE_1466315) BOUND_VARIABLE_1466316) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466314) BOUND_VARIABLE_1466316)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466313) BOUND_VARIABLE_1466315)))))))))) (let ((_let_2631 (forall ((BOUND_VARIABLE_1466288 tptp.int) (BOUND_VARIABLE_1466289 tptp.int) (BOUND_VARIABLE_1466290 tptp.int) (BOUND_VARIABLE_1466291 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8547 BOUND_VARIABLE_1466288) BOUND_VARIABLE_1466289) BOUND_VARIABLE_1466290) BOUND_VARIABLE_1466291) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466289) BOUND_VARIABLE_1466291)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466288) BOUND_VARIABLE_1466290)))))))))) (let ((_let_2632 (forall ((BOUND_VARIABLE_1466263 tptp.int) (BOUND_VARIABLE_1466264 tptp.int) (BOUND_VARIABLE_1466265 tptp.int) (BOUND_VARIABLE_1466266 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8548 BOUND_VARIABLE_1466263) BOUND_VARIABLE_1466264) BOUND_VARIABLE_1466265) BOUND_VARIABLE_1466266) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466264) BOUND_VARIABLE_1466266)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466263) BOUND_VARIABLE_1466265)))))))))) (let ((_let_2633 (forall ((BOUND_VARIABLE_1466238 tptp.int) (BOUND_VARIABLE_1466239 tptp.int) (BOUND_VARIABLE_1466240 tptp.int) (BOUND_VARIABLE_1466241 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8549 BOUND_VARIABLE_1466238) BOUND_VARIABLE_1466239) BOUND_VARIABLE_1466240) BOUND_VARIABLE_1466241) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466239) BOUND_VARIABLE_1466241)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466238) BOUND_VARIABLE_1466240)))))))))) (let ((_let_2634 (forall ((BOUND_VARIABLE_1466213 tptp.int) (BOUND_VARIABLE_1466214 tptp.int) (BOUND_VARIABLE_1466215 tptp.int) (BOUND_VARIABLE_1466216 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8550 BOUND_VARIABLE_1466213) BOUND_VARIABLE_1466214) BOUND_VARIABLE_1466215) BOUND_VARIABLE_1466216) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466214) BOUND_VARIABLE_1466216)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466213) BOUND_VARIABLE_1466215)))))))))) (let ((_let_2635 (forall ((BOUND_VARIABLE_1466188 tptp.int) (BOUND_VARIABLE_1466189 tptp.int) (BOUND_VARIABLE_1466190 tptp.int) (BOUND_VARIABLE_1466191 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8551 BOUND_VARIABLE_1466188) BOUND_VARIABLE_1466189) BOUND_VARIABLE_1466190) BOUND_VARIABLE_1466191) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466189) BOUND_VARIABLE_1466191)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466188) BOUND_VARIABLE_1466190)))))))))) (let ((_let_2636 (forall ((BOUND_VARIABLE_1466163 tptp.int) (BOUND_VARIABLE_1466164 tptp.int) (BOUND_VARIABLE_1466165 tptp.int) (BOUND_VARIABLE_1466166 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8552 BOUND_VARIABLE_1466163) BOUND_VARIABLE_1466164) BOUND_VARIABLE_1466165) BOUND_VARIABLE_1466166) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466164) BOUND_VARIABLE_1466166)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466163) BOUND_VARIABLE_1466165)))))))))) (let ((_let_2637 (forall ((BOUND_VARIABLE_1466138 tptp.int) (BOUND_VARIABLE_1466139 tptp.int) (BOUND_VARIABLE_1466140 tptp.int) (BOUND_VARIABLE_1466141 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8553 BOUND_VARIABLE_1466138) BOUND_VARIABLE_1466139) BOUND_VARIABLE_1466140) BOUND_VARIABLE_1466141) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466139) BOUND_VARIABLE_1466141)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466138) BOUND_VARIABLE_1466140)))))))))) (let ((_let_2638 (forall ((BOUND_VARIABLE_1466113 tptp.int) (BOUND_VARIABLE_1466114 tptp.int) (BOUND_VARIABLE_1466115 tptp.int) (BOUND_VARIABLE_1466116 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8554 BOUND_VARIABLE_1466113) BOUND_VARIABLE_1466114) BOUND_VARIABLE_1466115) BOUND_VARIABLE_1466116) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466114) BOUND_VARIABLE_1466116)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466113) BOUND_VARIABLE_1466115)))))))))) (let ((_let_2639 (forall ((BOUND_VARIABLE_1466088 tptp.int) (BOUND_VARIABLE_1466089 tptp.int) (BOUND_VARIABLE_1466090 tptp.int) (BOUND_VARIABLE_1466091 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8555 BOUND_VARIABLE_1466088) BOUND_VARIABLE_1466089) BOUND_VARIABLE_1466090) BOUND_VARIABLE_1466091) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466089) BOUND_VARIABLE_1466091)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466088) BOUND_VARIABLE_1466090)))))))))) (let ((_let_2640 (forall ((BOUND_VARIABLE_1466063 tptp.int) (BOUND_VARIABLE_1466064 tptp.int) (BOUND_VARIABLE_1466065 tptp.int) (BOUND_VARIABLE_1466066 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8556 BOUND_VARIABLE_1466063) BOUND_VARIABLE_1466064) BOUND_VARIABLE_1466065) BOUND_VARIABLE_1466066) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466064) BOUND_VARIABLE_1466066)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466063) BOUND_VARIABLE_1466065)))))))))) (let ((_let_2641 (forall ((BOUND_VARIABLE_1466038 tptp.int) (BOUND_VARIABLE_1466039 tptp.int) (BOUND_VARIABLE_1466040 tptp.int) (BOUND_VARIABLE_1466041 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8557 BOUND_VARIABLE_1466038) BOUND_VARIABLE_1466039) BOUND_VARIABLE_1466040) BOUND_VARIABLE_1466041) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466039) BOUND_VARIABLE_1466041)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466038) BOUND_VARIABLE_1466040)))))))))) (let ((_let_2642 (forall ((BOUND_VARIABLE_1466013 tptp.int) (BOUND_VARIABLE_1466014 tptp.int) (BOUND_VARIABLE_1466015 tptp.int) (BOUND_VARIABLE_1466016 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8558 BOUND_VARIABLE_1466013) BOUND_VARIABLE_1466014) BOUND_VARIABLE_1466015) BOUND_VARIABLE_1466016) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466014) BOUND_VARIABLE_1466016)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1466013) BOUND_VARIABLE_1466015)))))))))) (let ((_let_2643 (forall ((BOUND_VARIABLE_1465988 tptp.int) (BOUND_VARIABLE_1465989 tptp.int) (BOUND_VARIABLE_1465990 tptp.int) (BOUND_VARIABLE_1465991 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8559 BOUND_VARIABLE_1465988) BOUND_VARIABLE_1465989) BOUND_VARIABLE_1465990) BOUND_VARIABLE_1465991) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465989) BOUND_VARIABLE_1465991)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465988) BOUND_VARIABLE_1465990)))))))))) (let ((_let_2644 (forall ((BOUND_VARIABLE_1465963 tptp.int) (BOUND_VARIABLE_1465964 tptp.int) (BOUND_VARIABLE_1465965 tptp.int) (BOUND_VARIABLE_1465966 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8560 BOUND_VARIABLE_1465963) BOUND_VARIABLE_1465964) BOUND_VARIABLE_1465965) BOUND_VARIABLE_1465966) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465964) BOUND_VARIABLE_1465966)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465963) BOUND_VARIABLE_1465965)))))))))) (let ((_let_2645 (forall ((BOUND_VARIABLE_1465938 tptp.int) (BOUND_VARIABLE_1465939 tptp.int) (BOUND_VARIABLE_1465940 tptp.int) (BOUND_VARIABLE_1465941 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8561 BOUND_VARIABLE_1465938) BOUND_VARIABLE_1465939) BOUND_VARIABLE_1465940) BOUND_VARIABLE_1465941) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465939) BOUND_VARIABLE_1465941)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465938) BOUND_VARIABLE_1465940)))))))))) (let ((_let_2646 (forall ((BOUND_VARIABLE_1465913 tptp.int) (BOUND_VARIABLE_1465914 tptp.int) (BOUND_VARIABLE_1465915 tptp.int) (BOUND_VARIABLE_1465916 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8562 BOUND_VARIABLE_1465913) BOUND_VARIABLE_1465914) BOUND_VARIABLE_1465915) BOUND_VARIABLE_1465916) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465914) BOUND_VARIABLE_1465916)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465913) BOUND_VARIABLE_1465915)))))))))) (let ((_let_2647 (forall ((BOUND_VARIABLE_1465888 tptp.int) (BOUND_VARIABLE_1465889 tptp.int) (BOUND_VARIABLE_1465890 tptp.int) (BOUND_VARIABLE_1465891 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8563 BOUND_VARIABLE_1465888) BOUND_VARIABLE_1465889) BOUND_VARIABLE_1465890) BOUND_VARIABLE_1465891) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465889) BOUND_VARIABLE_1465891)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465888) BOUND_VARIABLE_1465890)))))))))) (let ((_let_2648 (forall ((BOUND_VARIABLE_1465863 tptp.int) (BOUND_VARIABLE_1465864 tptp.int) (BOUND_VARIABLE_1465865 tptp.int) (BOUND_VARIABLE_1465866 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8564 BOUND_VARIABLE_1465863) BOUND_VARIABLE_1465864) BOUND_VARIABLE_1465865) BOUND_VARIABLE_1465866) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465864) BOUND_VARIABLE_1465866)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465863) BOUND_VARIABLE_1465865)))))))))) (let ((_let_2649 (forall ((BOUND_VARIABLE_1465838 tptp.int) (BOUND_VARIABLE_1465839 tptp.int) (BOUND_VARIABLE_1465840 tptp.int) (BOUND_VARIABLE_1465841 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8565 BOUND_VARIABLE_1465838) BOUND_VARIABLE_1465839) BOUND_VARIABLE_1465840) BOUND_VARIABLE_1465841) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465839) BOUND_VARIABLE_1465841)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465838) BOUND_VARIABLE_1465840)))))))))) (let ((_let_2650 (forall ((BOUND_VARIABLE_1465813 tptp.int) (BOUND_VARIABLE_1465814 tptp.int) (BOUND_VARIABLE_1465815 tptp.int) (BOUND_VARIABLE_1465816 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8566 BOUND_VARIABLE_1465813) BOUND_VARIABLE_1465814) BOUND_VARIABLE_1465815) BOUND_VARIABLE_1465816) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465814) BOUND_VARIABLE_1465816)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465813) BOUND_VARIABLE_1465815)))))))))) (let ((_let_2651 (forall ((BOUND_VARIABLE_1465788 tptp.int) (BOUND_VARIABLE_1465789 tptp.int) (BOUND_VARIABLE_1465790 tptp.int) (BOUND_VARIABLE_1465791 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8567 BOUND_VARIABLE_1465788) BOUND_VARIABLE_1465789) BOUND_VARIABLE_1465790) BOUND_VARIABLE_1465791) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465789) BOUND_VARIABLE_1465791)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465788) BOUND_VARIABLE_1465790)))))))))) (let ((_let_2652 (forall ((BOUND_VARIABLE_1465763 tptp.int) (BOUND_VARIABLE_1465764 tptp.int) (BOUND_VARIABLE_1465765 tptp.int) (BOUND_VARIABLE_1465766 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8568 BOUND_VARIABLE_1465763) BOUND_VARIABLE_1465764) BOUND_VARIABLE_1465765) BOUND_VARIABLE_1465766) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465764) BOUND_VARIABLE_1465766)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465763) BOUND_VARIABLE_1465765)))))))))) (let ((_let_2653 (forall ((BOUND_VARIABLE_1465738 tptp.int) (BOUND_VARIABLE_1465739 tptp.int) (BOUND_VARIABLE_1465740 tptp.int) (BOUND_VARIABLE_1465741 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8569 BOUND_VARIABLE_1465738) BOUND_VARIABLE_1465739) BOUND_VARIABLE_1465740) BOUND_VARIABLE_1465741) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465739) BOUND_VARIABLE_1465741)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465738) BOUND_VARIABLE_1465740)))))))))) (let ((_let_2654 (forall ((BOUND_VARIABLE_1465713 tptp.int) (BOUND_VARIABLE_1465714 tptp.int) (BOUND_VARIABLE_1465715 tptp.int) (BOUND_VARIABLE_1465716 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8570 BOUND_VARIABLE_1465713) BOUND_VARIABLE_1465714) BOUND_VARIABLE_1465715) BOUND_VARIABLE_1465716) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465714) BOUND_VARIABLE_1465716)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465713) BOUND_VARIABLE_1465715)))))))))) (let ((_let_2655 (forall ((BOUND_VARIABLE_1465688 tptp.int) (BOUND_VARIABLE_1465689 tptp.int) (BOUND_VARIABLE_1465690 tptp.int) (BOUND_VARIABLE_1465691 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8571 BOUND_VARIABLE_1465688) BOUND_VARIABLE_1465689) BOUND_VARIABLE_1465690) BOUND_VARIABLE_1465691) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465689) BOUND_VARIABLE_1465691)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465688) BOUND_VARIABLE_1465690)))))))))) (let ((_let_2656 (forall ((BOUND_VARIABLE_1465663 tptp.int) (BOUND_VARIABLE_1465664 tptp.int) (BOUND_VARIABLE_1465665 tptp.int) (BOUND_VARIABLE_1465666 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8572 BOUND_VARIABLE_1465663) BOUND_VARIABLE_1465664) BOUND_VARIABLE_1465665) BOUND_VARIABLE_1465666) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465664) BOUND_VARIABLE_1465666)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465663) BOUND_VARIABLE_1465665)))))))))) (let ((_let_2657 (forall ((BOUND_VARIABLE_1465638 tptp.int) (BOUND_VARIABLE_1465639 tptp.int) (BOUND_VARIABLE_1465640 tptp.int) (BOUND_VARIABLE_1465641 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8573 BOUND_VARIABLE_1465638) BOUND_VARIABLE_1465639) BOUND_VARIABLE_1465640) BOUND_VARIABLE_1465641) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465639) BOUND_VARIABLE_1465641)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465638) BOUND_VARIABLE_1465640)))))))))) (let ((_let_2658 (forall ((BOUND_VARIABLE_1465613 tptp.int) (BOUND_VARIABLE_1465614 tptp.int) (BOUND_VARIABLE_1465615 tptp.int) (BOUND_VARIABLE_1465616 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8574 BOUND_VARIABLE_1465613) BOUND_VARIABLE_1465614) BOUND_VARIABLE_1465615) BOUND_VARIABLE_1465616) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465614) BOUND_VARIABLE_1465616)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465613) BOUND_VARIABLE_1465615)))))))))) (let ((_let_2659 (forall ((BOUND_VARIABLE_1465588 tptp.int) (BOUND_VARIABLE_1465589 tptp.int) (BOUND_VARIABLE_1465590 tptp.int) (BOUND_VARIABLE_1465591 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8575 BOUND_VARIABLE_1465588) BOUND_VARIABLE_1465589) BOUND_VARIABLE_1465590) BOUND_VARIABLE_1465591) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465589) BOUND_VARIABLE_1465591)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465588) BOUND_VARIABLE_1465590)))))))))) (let ((_let_2660 (forall ((BOUND_VARIABLE_1465563 tptp.int) (BOUND_VARIABLE_1465564 tptp.int) (BOUND_VARIABLE_1465565 tptp.int) (BOUND_VARIABLE_1465566 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8576 BOUND_VARIABLE_1465563) BOUND_VARIABLE_1465564) BOUND_VARIABLE_1465565) BOUND_VARIABLE_1465566) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465564) BOUND_VARIABLE_1465566)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465563) BOUND_VARIABLE_1465565)))))))))) (let ((_let_2661 (forall ((BOUND_VARIABLE_1465538 tptp.int) (BOUND_VARIABLE_1465539 tptp.int) (BOUND_VARIABLE_1465540 tptp.int) (BOUND_VARIABLE_1465541 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8577 BOUND_VARIABLE_1465538) BOUND_VARIABLE_1465539) BOUND_VARIABLE_1465540) BOUND_VARIABLE_1465541) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465539) BOUND_VARIABLE_1465541)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465538) BOUND_VARIABLE_1465540)))))))))) (let ((_let_2662 (forall ((BOUND_VARIABLE_1465513 tptp.int) (BOUND_VARIABLE_1465514 tptp.int) (BOUND_VARIABLE_1465515 tptp.int) (BOUND_VARIABLE_1465516 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8578 BOUND_VARIABLE_1465513) BOUND_VARIABLE_1465514) BOUND_VARIABLE_1465515) BOUND_VARIABLE_1465516) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465514) BOUND_VARIABLE_1465516)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465513) BOUND_VARIABLE_1465515)))))))))) (let ((_let_2663 (forall ((BOUND_VARIABLE_1465488 tptp.int) (BOUND_VARIABLE_1465489 tptp.int) (BOUND_VARIABLE_1465490 tptp.int) (BOUND_VARIABLE_1465491 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8579 BOUND_VARIABLE_1465488) BOUND_VARIABLE_1465489) BOUND_VARIABLE_1465490) BOUND_VARIABLE_1465491) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465489) BOUND_VARIABLE_1465491)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465488) BOUND_VARIABLE_1465490)))))))))) (let ((_let_2664 (forall ((BOUND_VARIABLE_1465463 tptp.int) (BOUND_VARIABLE_1465464 tptp.int) (BOUND_VARIABLE_1465465 tptp.int) (BOUND_VARIABLE_1465466 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8580 BOUND_VARIABLE_1465463) BOUND_VARIABLE_1465464) BOUND_VARIABLE_1465465) BOUND_VARIABLE_1465466) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465464) BOUND_VARIABLE_1465466)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465463) BOUND_VARIABLE_1465465)))))))))) (let ((_let_2665 (forall ((BOUND_VARIABLE_1465438 tptp.int) (BOUND_VARIABLE_1465439 tptp.int) (BOUND_VARIABLE_1465440 tptp.int) (BOUND_VARIABLE_1465441 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8581 BOUND_VARIABLE_1465438) BOUND_VARIABLE_1465439) BOUND_VARIABLE_1465440) BOUND_VARIABLE_1465441) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465439) BOUND_VARIABLE_1465441)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465438) BOUND_VARIABLE_1465440)))))))))) (let ((_let_2666 (forall ((BOUND_VARIABLE_1465413 tptp.int) (BOUND_VARIABLE_1465414 tptp.int) (BOUND_VARIABLE_1465415 tptp.int) (BOUND_VARIABLE_1465416 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8582 BOUND_VARIABLE_1465413) BOUND_VARIABLE_1465414) BOUND_VARIABLE_1465415) BOUND_VARIABLE_1465416) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465414) BOUND_VARIABLE_1465416)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465413) BOUND_VARIABLE_1465415)))))))))) (let ((_let_2667 (forall ((BOUND_VARIABLE_1465388 tptp.int) (BOUND_VARIABLE_1465389 tptp.int) (BOUND_VARIABLE_1465390 tptp.int) (BOUND_VARIABLE_1465391 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8583 BOUND_VARIABLE_1465388) BOUND_VARIABLE_1465389) BOUND_VARIABLE_1465390) BOUND_VARIABLE_1465391) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465389) BOUND_VARIABLE_1465391)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1465388) BOUND_VARIABLE_1465390)))))))))) (let ((_let_2668 (forall ((BOUND_VARIABLE_1465365 tptp.num) (BOUND_VARIABLE_1465366 tptp.code_integer) (BOUND_VARIABLE_1465367 tptp.code_integer)) (let ((_let_1 (ho_7848 (ho_7850 k_7902 (ho_7901 k_7900 (ho_7443 k_7442 tptp.one))) BOUND_VARIABLE_1465366))) (let ((_let_2 (ho_7901 k_7900 BOUND_VARIABLE_1465365))) (= (ho_7859 (ho_7858 (ho_7899 k_8584 BOUND_VARIABLE_1465365) BOUND_VARIABLE_1465366) BOUND_VARIABLE_1465367) (ho_7863 (ho_7862 (ho_7861 k_7860 (ho_7853 (ho_7852 k_7903 _let_2) BOUND_VARIABLE_1465367)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_7849 _let_1) (ho_7846 k_7845 true))) (ho_7848 (ho_7850 k_7849 BOUND_VARIABLE_1465367) (ho_7848 k_7847 _let_2)))) (ho_7859 (ho_7858 k_7857 _let_1) BOUND_VARIABLE_1465367)))))))) (let ((_let_2669 (forall ((BOUND_VARIABLE_1465325 tptp.num) (BOUND_VARIABLE_1465326 tptp.int) (BOUND_VARIABLE_1465327 tptp.int)) (let ((_let_1 (ho_7459 (ho_7461 k_7472 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))) BOUND_VARIABLE_1465326))) (= (ho_7702 (ho_7701 (ho_7700 k_7699 (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= BOUND_VARIABLE_1465327 (ho_7459 (ho_7461 k_7460 (ho_7446 k_7445 BOUND_VARIABLE_1465325)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))))))))) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7446 k_7445 tptp.one))) (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1465327) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7446 k_7445 BOUND_VARIABLE_1465325))))) (ho_7698 (ho_7697 k_7696 _let_1) BOUND_VARIABLE_1465327)) (ho_7698 (ho_7697 (ho_8530 k_8585 BOUND_VARIABLE_1465325) BOUND_VARIABLE_1465326) BOUND_VARIABLE_1465327)))))) (let ((_let_2670 (forall ((BOUND_VARIABLE_1465263 tptp.num) (BOUND_VARIABLE_1465264 tptp.nat) (BOUND_VARIABLE_1465265 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1465264) _let_3))))) (let ((_let_6 (ho_7463 k_7462 (ho_7446 k_7445 BOUND_VARIABLE_1465263)))) (= (ho_8535 (ho_8534 (ho_8533 k_8532 (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 _let_6)) (ho_7533 k_7532 BOUND_VARIABLE_1465265))) (ho_7641 (ho_7448 k_7640 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 _let_5) _let_3)) (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1465265) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 _let_6) _let_3)))))) (ho_7641 (ho_7448 k_7640 _let_5) BOUND_VARIABLE_1465265)) (ho_7641 (ho_7448 (ho_8537 k_8586 BOUND_VARIABLE_1465263) BOUND_VARIABLE_1465264) BOUND_VARIABLE_1465265))))))))))) (let ((_let_2671 (forall ((BOUND_VARIABLE_1465200 tptp.real) (BOUND_VARIABLE_1465201 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1465201) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8587 BOUND_VARIABLE_1465200) BOUND_VARIABLE_1465201) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1465201 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1465201 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1465200) BOUND_VARIABLE_1465201))))))))))))))))) (let ((_let_2672 (forall ((BOUND_VARIABLE_1465145 tptp.real) (BOUND_VARIABLE_1465146 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8588 BOUND_VARIABLE_1465145) BOUND_VARIABLE_1465146) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1465146 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1465146) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1465146 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1465146) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1465145) BOUND_VARIABLE_1465146))))))))))))))) (let ((_let_2673 (forall ((BOUND_VARIABLE_1465082 tptp.real) (BOUND_VARIABLE_1465083 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1465083) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8589 BOUND_VARIABLE_1465082) BOUND_VARIABLE_1465083) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1465083 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1465083 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1465082) BOUND_VARIABLE_1465083))))))))))))))))) (let ((_let_2674 (forall ((BOUND_VARIABLE_1465027 tptp.real) (BOUND_VARIABLE_1465028 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8590 BOUND_VARIABLE_1465027) BOUND_VARIABLE_1465028) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1465028 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1465028) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1465028 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1465028) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1465027) BOUND_VARIABLE_1465028))))))))))))))) (let ((_let_2675 (forall ((BOUND_VARIABLE_1464964 tptp.real) (BOUND_VARIABLE_1464965 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1464965) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8591 BOUND_VARIABLE_1464964) BOUND_VARIABLE_1464965) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1464965 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1464965 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1464964) BOUND_VARIABLE_1464965))))))))))))))))) (let ((_let_2676 (forall ((BOUND_VARIABLE_1464909 tptp.real) (BOUND_VARIABLE_1464910 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8592 BOUND_VARIABLE_1464909) BOUND_VARIABLE_1464910) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1464910 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1464910) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1464910 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1464910) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1464909) BOUND_VARIABLE_1464910))))))))))))))) (let ((_let_2677 (forall ((BOUND_VARIABLE_1464846 tptp.real) (BOUND_VARIABLE_1464847 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1464847) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8593 BOUND_VARIABLE_1464846) BOUND_VARIABLE_1464847) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1464847 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1464847 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1464846) BOUND_VARIABLE_1464847))))))))))))))))) (let ((_let_2678 (forall ((BOUND_VARIABLE_1464791 tptp.real) (BOUND_VARIABLE_1464792 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8594 BOUND_VARIABLE_1464791) BOUND_VARIABLE_1464792) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1464792 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1464792) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1464792 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1464792) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1464791) BOUND_VARIABLE_1464792))))))))))))))) (let ((_let_2679 (forall ((BOUND_VARIABLE_1464728 tptp.real) (BOUND_VARIABLE_1464729 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1464729) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_8595 BOUND_VARIABLE_1464728) BOUND_VARIABLE_1464729) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1464729 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1464729 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1464728) BOUND_VARIABLE_1464729))))))))))))))))) (let ((_let_2680 (forall ((BOUND_VARIABLE_1464673 tptp.real) (BOUND_VARIABLE_1464674 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_8596 BOUND_VARIABLE_1464673) BOUND_VARIABLE_1464674) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1464674 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1464674) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1464674 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1464674) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1464673) BOUND_VARIABLE_1464674))))))))))))))) (let ((_let_2681 (forall ((BOUND_VARIABLE_1464648 tptp.int) (BOUND_VARIABLE_1464649 tptp.int) (BOUND_VARIABLE_1464650 tptp.int) (BOUND_VARIABLE_1464651 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8597 BOUND_VARIABLE_1464648) BOUND_VARIABLE_1464649) BOUND_VARIABLE_1464650) BOUND_VARIABLE_1464651) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464649) BOUND_VARIABLE_1464651)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464648) BOUND_VARIABLE_1464650)))))))))) (let ((_let_2682 (forall ((BOUND_VARIABLE_1464623 tptp.int) (BOUND_VARIABLE_1464624 tptp.int) (BOUND_VARIABLE_1464625 tptp.int) (BOUND_VARIABLE_1464626 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8598 BOUND_VARIABLE_1464623) BOUND_VARIABLE_1464624) BOUND_VARIABLE_1464625) BOUND_VARIABLE_1464626) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464624) BOUND_VARIABLE_1464626)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464623) BOUND_VARIABLE_1464625)))))))))) (let ((_let_2683 (forall ((BOUND_VARIABLE_1464598 tptp.int) (BOUND_VARIABLE_1464599 tptp.int) (BOUND_VARIABLE_1464600 tptp.int) (BOUND_VARIABLE_1464601 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8599 BOUND_VARIABLE_1464598) BOUND_VARIABLE_1464599) BOUND_VARIABLE_1464600) BOUND_VARIABLE_1464601) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464599) BOUND_VARIABLE_1464601)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464598) BOUND_VARIABLE_1464600)))))))))) (let ((_let_2684 (forall ((BOUND_VARIABLE_1464573 tptp.int) (BOUND_VARIABLE_1464574 tptp.int) (BOUND_VARIABLE_1464575 tptp.int) (BOUND_VARIABLE_1464576 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8600 BOUND_VARIABLE_1464573) BOUND_VARIABLE_1464574) BOUND_VARIABLE_1464575) BOUND_VARIABLE_1464576) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464574) BOUND_VARIABLE_1464576)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464573) BOUND_VARIABLE_1464575)))))))))) (let ((_let_2685 (forall ((BOUND_VARIABLE_1464548 tptp.int) (BOUND_VARIABLE_1464549 tptp.int) (BOUND_VARIABLE_1464550 tptp.int) (BOUND_VARIABLE_1464551 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8601 BOUND_VARIABLE_1464548) BOUND_VARIABLE_1464549) BOUND_VARIABLE_1464550) BOUND_VARIABLE_1464551) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464549) BOUND_VARIABLE_1464551)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464548) BOUND_VARIABLE_1464550)))))))))) (let ((_let_2686 (forall ((BOUND_VARIABLE_1464523 tptp.int) (BOUND_VARIABLE_1464524 tptp.int) (BOUND_VARIABLE_1464525 tptp.int) (BOUND_VARIABLE_1464526 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8602 BOUND_VARIABLE_1464523) BOUND_VARIABLE_1464524) BOUND_VARIABLE_1464525) BOUND_VARIABLE_1464526) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464524) BOUND_VARIABLE_1464526)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464523) BOUND_VARIABLE_1464525)))))))))) (let ((_let_2687 (forall ((BOUND_VARIABLE_1464498 tptp.int) (BOUND_VARIABLE_1464499 tptp.int) (BOUND_VARIABLE_1464500 tptp.int) (BOUND_VARIABLE_1464501 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8603 BOUND_VARIABLE_1464498) BOUND_VARIABLE_1464499) BOUND_VARIABLE_1464500) BOUND_VARIABLE_1464501) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464499) BOUND_VARIABLE_1464501)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464498) BOUND_VARIABLE_1464500)))))))))) (let ((_let_2688 (forall ((BOUND_VARIABLE_1464458 tptp.int) (BOUND_VARIABLE_1464459 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7578 BOUND_VARIABLE_1464459) BOUND_VARIABLE_1464458)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8604 BOUND_VARIABLE_1464458) BOUND_VARIABLE_1464459))))))))) (let ((_let_2689 (forall ((BOUND_VARIABLE_1464433 tptp.int) (BOUND_VARIABLE_1464434 tptp.int) (BOUND_VARIABLE_1464435 tptp.int) (BOUND_VARIABLE_1464436 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8605 BOUND_VARIABLE_1464433) BOUND_VARIABLE_1464434) BOUND_VARIABLE_1464435) BOUND_VARIABLE_1464436) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464434) BOUND_VARIABLE_1464436)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464433) BOUND_VARIABLE_1464435)))))))))) (let ((_let_2690 (forall ((BOUND_VARIABLE_1464408 tptp.int) (BOUND_VARIABLE_1464409 tptp.int) (BOUND_VARIABLE_1464410 tptp.int) (BOUND_VARIABLE_1464411 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8606 BOUND_VARIABLE_1464408) BOUND_VARIABLE_1464409) BOUND_VARIABLE_1464410) BOUND_VARIABLE_1464411) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464409) BOUND_VARIABLE_1464411)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464408) BOUND_VARIABLE_1464410)))))))))) (let ((_let_2691 (forall ((BOUND_VARIABLE_1464383 tptp.int) (BOUND_VARIABLE_1464384 tptp.int) (BOUND_VARIABLE_1464385 tptp.int) (BOUND_VARIABLE_1464386 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8607 BOUND_VARIABLE_1464383) BOUND_VARIABLE_1464384) BOUND_VARIABLE_1464385) BOUND_VARIABLE_1464386) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464384) BOUND_VARIABLE_1464386)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464383) BOUND_VARIABLE_1464385)))))))))) (let ((_let_2692 (forall ((BOUND_VARIABLE_1464358 tptp.int) (BOUND_VARIABLE_1464359 tptp.int) (BOUND_VARIABLE_1464360 tptp.int) (BOUND_VARIABLE_1464361 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8608 BOUND_VARIABLE_1464358) BOUND_VARIABLE_1464359) BOUND_VARIABLE_1464360) BOUND_VARIABLE_1464361) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464359) BOUND_VARIABLE_1464361)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464358) BOUND_VARIABLE_1464360)))))))))) (let ((_let_2693 (forall ((BOUND_VARIABLE_1464333 tptp.int) (BOUND_VARIABLE_1464334 tptp.int) (BOUND_VARIABLE_1464335 tptp.int) (BOUND_VARIABLE_1464336 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8609 BOUND_VARIABLE_1464333) BOUND_VARIABLE_1464334) BOUND_VARIABLE_1464335) BOUND_VARIABLE_1464336) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464334) BOUND_VARIABLE_1464336)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464333) BOUND_VARIABLE_1464335)))))))))) (let ((_let_2694 (forall ((BOUND_VARIABLE_1464308 tptp.int) (BOUND_VARIABLE_1464309 tptp.int) (BOUND_VARIABLE_1464310 tptp.int) (BOUND_VARIABLE_1464311 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8610 BOUND_VARIABLE_1464308) BOUND_VARIABLE_1464309) BOUND_VARIABLE_1464310) BOUND_VARIABLE_1464311) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464309) BOUND_VARIABLE_1464311)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464308) BOUND_VARIABLE_1464310)))))))))) (let ((_let_2695 (forall ((BOUND_VARIABLE_1464268 tptp.int) (BOUND_VARIABLE_1464269 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7579 BOUND_VARIABLE_1464269) BOUND_VARIABLE_1464268)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8611 BOUND_VARIABLE_1464268) BOUND_VARIABLE_1464269))))))))) (let ((_let_2696 (forall ((BOUND_VARIABLE_1464243 tptp.int) (BOUND_VARIABLE_1464244 tptp.int) (BOUND_VARIABLE_1464245 tptp.int) (BOUND_VARIABLE_1464246 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8612 BOUND_VARIABLE_1464243) BOUND_VARIABLE_1464244) BOUND_VARIABLE_1464245) BOUND_VARIABLE_1464246) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464244) BOUND_VARIABLE_1464246)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464243) BOUND_VARIABLE_1464245)))))))))) (let ((_let_2697 (forall ((BOUND_VARIABLE_1464203 tptp.int) (BOUND_VARIABLE_1464204 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7580 BOUND_VARIABLE_1464204) BOUND_VARIABLE_1464203)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8613 BOUND_VARIABLE_1464203) BOUND_VARIABLE_1464204))))))))) (let ((_let_2698 (forall ((BOUND_VARIABLE_1464178 tptp.int) (BOUND_VARIABLE_1464179 tptp.int) (BOUND_VARIABLE_1464180 tptp.int) (BOUND_VARIABLE_1464181 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8614 BOUND_VARIABLE_1464178) BOUND_VARIABLE_1464179) BOUND_VARIABLE_1464180) BOUND_VARIABLE_1464181) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464179) BOUND_VARIABLE_1464181)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464178) BOUND_VARIABLE_1464180)))))))))) (let ((_let_2699 (forall ((BOUND_VARIABLE_1464153 tptp.int) (BOUND_VARIABLE_1464154 tptp.int) (BOUND_VARIABLE_1464155 tptp.int) (BOUND_VARIABLE_1464156 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8615 BOUND_VARIABLE_1464153) BOUND_VARIABLE_1464154) BOUND_VARIABLE_1464155) BOUND_VARIABLE_1464156) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464154) BOUND_VARIABLE_1464156)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464153) BOUND_VARIABLE_1464155)))))))))) (let ((_let_2700 (forall ((BOUND_VARIABLE_1464128 tptp.int) (BOUND_VARIABLE_1464129 tptp.int) (BOUND_VARIABLE_1464130 tptp.int) (BOUND_VARIABLE_1464131 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8616 BOUND_VARIABLE_1464128) BOUND_VARIABLE_1464129) BOUND_VARIABLE_1464130) BOUND_VARIABLE_1464131) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464129) BOUND_VARIABLE_1464131)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464128) BOUND_VARIABLE_1464130)))))))))) (let ((_let_2701 (forall ((BOUND_VARIABLE_1464103 tptp.int) (BOUND_VARIABLE_1464104 tptp.int) (BOUND_VARIABLE_1464105 tptp.int) (BOUND_VARIABLE_1464106 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8617 BOUND_VARIABLE_1464103) BOUND_VARIABLE_1464104) BOUND_VARIABLE_1464105) BOUND_VARIABLE_1464106) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464104) BOUND_VARIABLE_1464106)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464103) BOUND_VARIABLE_1464105)))))))))) (let ((_let_2702 (forall ((BOUND_VARIABLE_1464078 tptp.int) (BOUND_VARIABLE_1464079 tptp.int) (BOUND_VARIABLE_1464080 tptp.int) (BOUND_VARIABLE_1464081 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8618 BOUND_VARIABLE_1464078) BOUND_VARIABLE_1464079) BOUND_VARIABLE_1464080) BOUND_VARIABLE_1464081) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464079) BOUND_VARIABLE_1464081)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464078) BOUND_VARIABLE_1464080)))))))))) (let ((_let_2703 (forall ((BOUND_VARIABLE_1464053 tptp.int) (BOUND_VARIABLE_1464054 tptp.int) (BOUND_VARIABLE_1464055 tptp.int) (BOUND_VARIABLE_1464056 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8619 BOUND_VARIABLE_1464053) BOUND_VARIABLE_1464054) BOUND_VARIABLE_1464055) BOUND_VARIABLE_1464056) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464054) BOUND_VARIABLE_1464056)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464053) BOUND_VARIABLE_1464055)))))))))) (let ((_let_2704 (forall ((BOUND_VARIABLE_1464028 tptp.int) (BOUND_VARIABLE_1464029 tptp.int) (BOUND_VARIABLE_1464030 tptp.int) (BOUND_VARIABLE_1464031 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8620 BOUND_VARIABLE_1464028) BOUND_VARIABLE_1464029) BOUND_VARIABLE_1464030) BOUND_VARIABLE_1464031) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464029) BOUND_VARIABLE_1464031)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1464028) BOUND_VARIABLE_1464030)))))))))) (let ((_let_2705 (forall ((BOUND_VARIABLE_1463988 tptp.int) (BOUND_VARIABLE_1463989 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7581 BOUND_VARIABLE_1463989) BOUND_VARIABLE_1463988)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8621 BOUND_VARIABLE_1463988) BOUND_VARIABLE_1463989))))))))) (let ((_let_2706 (forall ((BOUND_VARIABLE_1463963 tptp.int) (BOUND_VARIABLE_1463964 tptp.int) (BOUND_VARIABLE_1463965 tptp.int) (BOUND_VARIABLE_1463966 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8622 BOUND_VARIABLE_1463963) BOUND_VARIABLE_1463964) BOUND_VARIABLE_1463965) BOUND_VARIABLE_1463966) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463964) BOUND_VARIABLE_1463966)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463963) BOUND_VARIABLE_1463965)))))))))) (let ((_let_2707 (forall ((BOUND_VARIABLE_1463923 tptp.int) (BOUND_VARIABLE_1463924 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7582 BOUND_VARIABLE_1463924) BOUND_VARIABLE_1463923)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8623 BOUND_VARIABLE_1463923) BOUND_VARIABLE_1463924))))))))) (let ((_let_2708 (forall ((BOUND_VARIABLE_1463898 tptp.int) (BOUND_VARIABLE_1463899 tptp.int) (BOUND_VARIABLE_1463900 tptp.int) (BOUND_VARIABLE_1463901 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8624 BOUND_VARIABLE_1463898) BOUND_VARIABLE_1463899) BOUND_VARIABLE_1463900) BOUND_VARIABLE_1463901) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463899) BOUND_VARIABLE_1463901)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463898) BOUND_VARIABLE_1463900)))))))))) (let ((_let_2709 (forall ((BOUND_VARIABLE_1463858 tptp.int) (BOUND_VARIABLE_1463859 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7583 BOUND_VARIABLE_1463859) BOUND_VARIABLE_1463858)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8625 BOUND_VARIABLE_1463858) BOUND_VARIABLE_1463859))))))))) (let ((_let_2710 (forall ((BOUND_VARIABLE_1463833 tptp.int) (BOUND_VARIABLE_1463834 tptp.int) (BOUND_VARIABLE_1463835 tptp.int) (BOUND_VARIABLE_1463836 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8626 BOUND_VARIABLE_1463833) BOUND_VARIABLE_1463834) BOUND_VARIABLE_1463835) BOUND_VARIABLE_1463836) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463834) BOUND_VARIABLE_1463836)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463833) BOUND_VARIABLE_1463835)))))))))) (let ((_let_2711 (forall ((BOUND_VARIABLE_1463808 tptp.int) (BOUND_VARIABLE_1463809 tptp.int) (BOUND_VARIABLE_1463810 tptp.int) (BOUND_VARIABLE_1463811 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8627 BOUND_VARIABLE_1463808) BOUND_VARIABLE_1463809) BOUND_VARIABLE_1463810) BOUND_VARIABLE_1463811) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463809) BOUND_VARIABLE_1463811)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463808) BOUND_VARIABLE_1463810)))))))))) (let ((_let_2712 (forall ((BOUND_VARIABLE_1463783 tptp.int) (BOUND_VARIABLE_1463784 tptp.int) (BOUND_VARIABLE_1463785 tptp.int) (BOUND_VARIABLE_1463786 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8628 BOUND_VARIABLE_1463783) BOUND_VARIABLE_1463784) BOUND_VARIABLE_1463785) BOUND_VARIABLE_1463786) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463784) BOUND_VARIABLE_1463786)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463783) BOUND_VARIABLE_1463785)))))))))) (let ((_let_2713 (forall ((BOUND_VARIABLE_1463758 tptp.int) (BOUND_VARIABLE_1463759 tptp.int) (BOUND_VARIABLE_1463760 tptp.int) (BOUND_VARIABLE_1463761 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8629 BOUND_VARIABLE_1463758) BOUND_VARIABLE_1463759) BOUND_VARIABLE_1463760) BOUND_VARIABLE_1463761) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463759) BOUND_VARIABLE_1463761)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463758) BOUND_VARIABLE_1463760)))))))))) (let ((_let_2714 (forall ((BOUND_VARIABLE_1463733 tptp.int) (BOUND_VARIABLE_1463734 tptp.int) (BOUND_VARIABLE_1463735 tptp.int) (BOUND_VARIABLE_1463736 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8630 BOUND_VARIABLE_1463733) BOUND_VARIABLE_1463734) BOUND_VARIABLE_1463735) BOUND_VARIABLE_1463736) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463734) BOUND_VARIABLE_1463736)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463733) BOUND_VARIABLE_1463735)))))))))) (let ((_let_2715 (forall ((BOUND_VARIABLE_1463708 tptp.int) (BOUND_VARIABLE_1463709 tptp.int) (BOUND_VARIABLE_1463710 tptp.int) (BOUND_VARIABLE_1463711 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8631 BOUND_VARIABLE_1463708) BOUND_VARIABLE_1463709) BOUND_VARIABLE_1463710) BOUND_VARIABLE_1463711) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463709) BOUND_VARIABLE_1463711)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463708) BOUND_VARIABLE_1463710)))))))))) (let ((_let_2716 (forall ((BOUND_VARIABLE_1463683 tptp.int) (BOUND_VARIABLE_1463684 tptp.int) (BOUND_VARIABLE_1463685 tptp.int) (BOUND_VARIABLE_1463686 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8632 BOUND_VARIABLE_1463683) BOUND_VARIABLE_1463684) BOUND_VARIABLE_1463685) BOUND_VARIABLE_1463686) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463684) BOUND_VARIABLE_1463686)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463683) BOUND_VARIABLE_1463685)))))))))) (let ((_let_2717 (forall ((BOUND_VARIABLE_1463658 tptp.int) (BOUND_VARIABLE_1463659 tptp.int) (BOUND_VARIABLE_1463660 tptp.int) (BOUND_VARIABLE_1463661 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8633 BOUND_VARIABLE_1463658) BOUND_VARIABLE_1463659) BOUND_VARIABLE_1463660) BOUND_VARIABLE_1463661) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463659) BOUND_VARIABLE_1463661)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463658) BOUND_VARIABLE_1463660)))))))))) (let ((_let_2718 (forall ((BOUND_VARIABLE_1463633 tptp.int) (BOUND_VARIABLE_1463634 tptp.int) (BOUND_VARIABLE_1463635 tptp.int) (BOUND_VARIABLE_1463636 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8634 BOUND_VARIABLE_1463633) BOUND_VARIABLE_1463634) BOUND_VARIABLE_1463635) BOUND_VARIABLE_1463636) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463634) BOUND_VARIABLE_1463636)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463633) BOUND_VARIABLE_1463635)))))))))) (let ((_let_2719 (forall ((BOUND_VARIABLE_1463608 tptp.int) (BOUND_VARIABLE_1463609 tptp.int) (BOUND_VARIABLE_1463610 tptp.int) (BOUND_VARIABLE_1463611 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8635 BOUND_VARIABLE_1463608) BOUND_VARIABLE_1463609) BOUND_VARIABLE_1463610) BOUND_VARIABLE_1463611) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463609) BOUND_VARIABLE_1463611)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463608) BOUND_VARIABLE_1463610)))))))))) (let ((_let_2720 (forall ((BOUND_VARIABLE_1463583 tptp.int) (BOUND_VARIABLE_1463584 tptp.int) (BOUND_VARIABLE_1463585 tptp.int) (BOUND_VARIABLE_1463586 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8636 BOUND_VARIABLE_1463583) BOUND_VARIABLE_1463584) BOUND_VARIABLE_1463585) BOUND_VARIABLE_1463586) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463584) BOUND_VARIABLE_1463586)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463583) BOUND_VARIABLE_1463585)))))))))) (let ((_let_2721 (forall ((BOUND_VARIABLE_1463558 tptp.int) (BOUND_VARIABLE_1463559 tptp.int) (BOUND_VARIABLE_1463560 tptp.int) (BOUND_VARIABLE_1463561 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8637 BOUND_VARIABLE_1463558) BOUND_VARIABLE_1463559) BOUND_VARIABLE_1463560) BOUND_VARIABLE_1463561) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463559) BOUND_VARIABLE_1463561)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463558) BOUND_VARIABLE_1463560)))))))))) (let ((_let_2722 (forall ((BOUND_VARIABLE_1463518 tptp.int) (BOUND_VARIABLE_1463519 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7584 BOUND_VARIABLE_1463519) BOUND_VARIABLE_1463518)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8638 BOUND_VARIABLE_1463518) BOUND_VARIABLE_1463519))))))))) (let ((_let_2723 (forall ((BOUND_VARIABLE_1463493 tptp.int) (BOUND_VARIABLE_1463494 tptp.int) (BOUND_VARIABLE_1463495 tptp.int) (BOUND_VARIABLE_1463496 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8639 BOUND_VARIABLE_1463493) BOUND_VARIABLE_1463494) BOUND_VARIABLE_1463495) BOUND_VARIABLE_1463496) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463494) BOUND_VARIABLE_1463496)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463493) BOUND_VARIABLE_1463495)))))))))) (let ((_let_2724 (forall ((BOUND_VARIABLE_1463453 tptp.int) (BOUND_VARIABLE_1463454 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7585 BOUND_VARIABLE_1463454) BOUND_VARIABLE_1463453)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8640 BOUND_VARIABLE_1463453) BOUND_VARIABLE_1463454))))))))) (let ((_let_2725 (forall ((BOUND_VARIABLE_1463428 tptp.int) (BOUND_VARIABLE_1463429 tptp.int) (BOUND_VARIABLE_1463430 tptp.int) (BOUND_VARIABLE_1463431 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8641 BOUND_VARIABLE_1463428) BOUND_VARIABLE_1463429) BOUND_VARIABLE_1463430) BOUND_VARIABLE_1463431) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463429) BOUND_VARIABLE_1463431)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463428) BOUND_VARIABLE_1463430)))))))))) (let ((_let_2726 (forall ((BOUND_VARIABLE_1463388 tptp.int) (BOUND_VARIABLE_1463389 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7586 BOUND_VARIABLE_1463389) BOUND_VARIABLE_1463388)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8642 BOUND_VARIABLE_1463388) BOUND_VARIABLE_1463389))))))))) (let ((_let_2727 (forall ((BOUND_VARIABLE_1463363 tptp.int) (BOUND_VARIABLE_1463364 tptp.int) (BOUND_VARIABLE_1463365 tptp.int) (BOUND_VARIABLE_1463366 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8643 BOUND_VARIABLE_1463363) BOUND_VARIABLE_1463364) BOUND_VARIABLE_1463365) BOUND_VARIABLE_1463366) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463364) BOUND_VARIABLE_1463366)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463363) BOUND_VARIABLE_1463365)))))))))) (let ((_let_2728 (forall ((BOUND_VARIABLE_1463323 tptp.int) (BOUND_VARIABLE_1463324 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7587 BOUND_VARIABLE_1463324) BOUND_VARIABLE_1463323)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8644 BOUND_VARIABLE_1463323) BOUND_VARIABLE_1463324))))))))) (let ((_let_2729 (forall ((BOUND_VARIABLE_1463298 tptp.int) (BOUND_VARIABLE_1463299 tptp.int) (BOUND_VARIABLE_1463300 tptp.int) (BOUND_VARIABLE_1463301 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8645 BOUND_VARIABLE_1463298) BOUND_VARIABLE_1463299) BOUND_VARIABLE_1463300) BOUND_VARIABLE_1463301) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463299) BOUND_VARIABLE_1463301)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463298) BOUND_VARIABLE_1463300)))))))))) (let ((_let_2730 (forall ((BOUND_VARIABLE_1463273 tptp.int) (BOUND_VARIABLE_1463274 tptp.int) (BOUND_VARIABLE_1463275 tptp.int) (BOUND_VARIABLE_1463276 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8646 BOUND_VARIABLE_1463273) BOUND_VARIABLE_1463274) BOUND_VARIABLE_1463275) BOUND_VARIABLE_1463276) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463274) BOUND_VARIABLE_1463276)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463273) BOUND_VARIABLE_1463275)))))))))) (let ((_let_2731 (forall ((BOUND_VARIABLE_1463248 tptp.int) (BOUND_VARIABLE_1463249 tptp.int) (BOUND_VARIABLE_1463250 tptp.int) (BOUND_VARIABLE_1463251 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8647 BOUND_VARIABLE_1463248) BOUND_VARIABLE_1463249) BOUND_VARIABLE_1463250) BOUND_VARIABLE_1463251) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463249) BOUND_VARIABLE_1463251)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463248) BOUND_VARIABLE_1463250)))))))))) (let ((_let_2732 (forall ((BOUND_VARIABLE_1463223 tptp.int) (BOUND_VARIABLE_1463224 tptp.int) (BOUND_VARIABLE_1463225 tptp.int) (BOUND_VARIABLE_1463226 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8648 BOUND_VARIABLE_1463223) BOUND_VARIABLE_1463224) BOUND_VARIABLE_1463225) BOUND_VARIABLE_1463226) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463224) BOUND_VARIABLE_1463226)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463223) BOUND_VARIABLE_1463225)))))))))) (let ((_let_2733 (forall ((BOUND_VARIABLE_1463183 tptp.int) (BOUND_VARIABLE_1463184 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7588 BOUND_VARIABLE_1463184) BOUND_VARIABLE_1463183)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8649 BOUND_VARIABLE_1463183) BOUND_VARIABLE_1463184))))))))) (let ((_let_2734 (forall ((BOUND_VARIABLE_1463158 tptp.int) (BOUND_VARIABLE_1463159 tptp.int) (BOUND_VARIABLE_1463160 tptp.int) (BOUND_VARIABLE_1463161 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8650 BOUND_VARIABLE_1463158) BOUND_VARIABLE_1463159) BOUND_VARIABLE_1463160) BOUND_VARIABLE_1463161) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463159) BOUND_VARIABLE_1463161)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463158) BOUND_VARIABLE_1463160)))))))))) (let ((_let_2735 (forall ((BOUND_VARIABLE_1463133 tptp.int) (BOUND_VARIABLE_1463134 tptp.int) (BOUND_VARIABLE_1463135 tptp.int) (BOUND_VARIABLE_1463136 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8651 BOUND_VARIABLE_1463133) BOUND_VARIABLE_1463134) BOUND_VARIABLE_1463135) BOUND_VARIABLE_1463136) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463134) BOUND_VARIABLE_1463136)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463133) BOUND_VARIABLE_1463135)))))))))) (let ((_let_2736 (forall ((BOUND_VARIABLE_1463093 tptp.int) (BOUND_VARIABLE_1463094 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7589 BOUND_VARIABLE_1463094) BOUND_VARIABLE_1463093)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8652 BOUND_VARIABLE_1463093) BOUND_VARIABLE_1463094))))))))) (let ((_let_2737 (forall ((BOUND_VARIABLE_1463068 tptp.int) (BOUND_VARIABLE_1463069 tptp.int) (BOUND_VARIABLE_1463070 tptp.int) (BOUND_VARIABLE_1463071 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8653 BOUND_VARIABLE_1463068) BOUND_VARIABLE_1463069) BOUND_VARIABLE_1463070) BOUND_VARIABLE_1463071) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463069) BOUND_VARIABLE_1463071)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463068) BOUND_VARIABLE_1463070)))))))))) (let ((_let_2738 (forall ((BOUND_VARIABLE_1463028 tptp.int) (BOUND_VARIABLE_1463029 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7590 BOUND_VARIABLE_1463029) BOUND_VARIABLE_1463028)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8654 BOUND_VARIABLE_1463028) BOUND_VARIABLE_1463029))))))))) (let ((_let_2739 (forall ((BOUND_VARIABLE_1463003 tptp.int) (BOUND_VARIABLE_1463004 tptp.int) (BOUND_VARIABLE_1463005 tptp.int) (BOUND_VARIABLE_1463006 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8655 BOUND_VARIABLE_1463003) BOUND_VARIABLE_1463004) BOUND_VARIABLE_1463005) BOUND_VARIABLE_1463006) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463004) BOUND_VARIABLE_1463006)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1463003) BOUND_VARIABLE_1463005)))))))))) (let ((_let_2740 (forall ((BOUND_VARIABLE_1462978 tptp.int) (BOUND_VARIABLE_1462979 tptp.int) (BOUND_VARIABLE_1462980 tptp.int) (BOUND_VARIABLE_1462981 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8656 BOUND_VARIABLE_1462978) BOUND_VARIABLE_1462979) BOUND_VARIABLE_1462980) BOUND_VARIABLE_1462981) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462979) BOUND_VARIABLE_1462981)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462978) BOUND_VARIABLE_1462980)))))))))) (let ((_let_2741 (forall ((BOUND_VARIABLE_1462938 tptp.int) (BOUND_VARIABLE_1462939 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7591 BOUND_VARIABLE_1462939) BOUND_VARIABLE_1462938)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8657 BOUND_VARIABLE_1462938) BOUND_VARIABLE_1462939))))))))) (let ((_let_2742 (forall ((BOUND_VARIABLE_1462913 tptp.int) (BOUND_VARIABLE_1462914 tptp.int) (BOUND_VARIABLE_1462915 tptp.int) (BOUND_VARIABLE_1462916 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8658 BOUND_VARIABLE_1462913) BOUND_VARIABLE_1462914) BOUND_VARIABLE_1462915) BOUND_VARIABLE_1462916) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462914) BOUND_VARIABLE_1462916)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462913) BOUND_VARIABLE_1462915)))))))))) (let ((_let_2743 (forall ((BOUND_VARIABLE_1462888 tptp.int) (BOUND_VARIABLE_1462889 tptp.int) (BOUND_VARIABLE_1462890 tptp.int) (BOUND_VARIABLE_1462891 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8659 BOUND_VARIABLE_1462888) BOUND_VARIABLE_1462889) BOUND_VARIABLE_1462890) BOUND_VARIABLE_1462891) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462889) BOUND_VARIABLE_1462891)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462888) BOUND_VARIABLE_1462890)))))))))) (let ((_let_2744 (forall ((BOUND_VARIABLE_1462848 tptp.int) (BOUND_VARIABLE_1462849 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7592 BOUND_VARIABLE_1462849) BOUND_VARIABLE_1462848)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8660 BOUND_VARIABLE_1462848) BOUND_VARIABLE_1462849))))))))) (let ((_let_2745 (forall ((BOUND_VARIABLE_1462823 tptp.int) (BOUND_VARIABLE_1462824 tptp.int) (BOUND_VARIABLE_1462825 tptp.int) (BOUND_VARIABLE_1462826 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8661 BOUND_VARIABLE_1462823) BOUND_VARIABLE_1462824) BOUND_VARIABLE_1462825) BOUND_VARIABLE_1462826) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462824) BOUND_VARIABLE_1462826)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462823) BOUND_VARIABLE_1462825)))))))))) (let ((_let_2746 (forall ((BOUND_VARIABLE_1462783 tptp.int) (BOUND_VARIABLE_1462784 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7593 BOUND_VARIABLE_1462784) BOUND_VARIABLE_1462783)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (ho_7496 (ho_7495 k_8662 BOUND_VARIABLE_1462783) BOUND_VARIABLE_1462784))))))))) (let ((_let_2747 (forall ((BOUND_VARIABLE_1462758 tptp.int) (BOUND_VARIABLE_1462759 tptp.int) (BOUND_VARIABLE_1462760 tptp.int) (BOUND_VARIABLE_1462761 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8663 BOUND_VARIABLE_1462758) BOUND_VARIABLE_1462759) BOUND_VARIABLE_1462760) BOUND_VARIABLE_1462761) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462759) BOUND_VARIABLE_1462761)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462758) BOUND_VARIABLE_1462760)))))))))) (let ((_let_2748 (forall ((BOUND_VARIABLE_1462733 tptp.int) (BOUND_VARIABLE_1462734 tptp.int) (BOUND_VARIABLE_1462735 tptp.int) (BOUND_VARIABLE_1462736 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8664 BOUND_VARIABLE_1462733) BOUND_VARIABLE_1462734) BOUND_VARIABLE_1462735) BOUND_VARIABLE_1462736) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462734) BOUND_VARIABLE_1462736)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462733) BOUND_VARIABLE_1462735)))))))))) (let ((_let_2749 (forall ((BOUND_VARIABLE_1462686 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1462686) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 _let_7) _let_6)) (ho_7508 k_8665 BOUND_VARIABLE_1462686)))))))))))))) (let ((_let_2750 (forall ((BOUND_VARIABLE_1462639 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1462639) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 _let_7) _let_6)) (ho_7508 k_8666 BOUND_VARIABLE_1462639)))))))))))))) (let ((_let_2751 (forall ((BOUND_VARIABLE_1462614 tptp.int) (BOUND_VARIABLE_1462615 tptp.int) (BOUND_VARIABLE_1462616 tptp.int) (BOUND_VARIABLE_1462617 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8667 BOUND_VARIABLE_1462614) BOUND_VARIABLE_1462615) BOUND_VARIABLE_1462616) BOUND_VARIABLE_1462617) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462615) BOUND_VARIABLE_1462617)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462614) BOUND_VARIABLE_1462616)))))))))) (let ((_let_2752 (forall ((BOUND_VARIABLE_1462589 tptp.int) (BOUND_VARIABLE_1462590 tptp.int) (BOUND_VARIABLE_1462591 tptp.int) (BOUND_VARIABLE_1462592 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8668 BOUND_VARIABLE_1462589) BOUND_VARIABLE_1462590) BOUND_VARIABLE_1462591) BOUND_VARIABLE_1462592) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462590) BOUND_VARIABLE_1462592)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462589) BOUND_VARIABLE_1462591)))))))))) (let ((_let_2753 (forall ((BOUND_VARIABLE_1462564 tptp.int) (BOUND_VARIABLE_1462565 tptp.int) (BOUND_VARIABLE_1462566 tptp.int) (BOUND_VARIABLE_1462567 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8669 BOUND_VARIABLE_1462564) BOUND_VARIABLE_1462565) BOUND_VARIABLE_1462566) BOUND_VARIABLE_1462567) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462565) BOUND_VARIABLE_1462567)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462564) BOUND_VARIABLE_1462566)))))))))) (let ((_let_2754 (forall ((BOUND_VARIABLE_1462539 tptp.int) (BOUND_VARIABLE_1462540 tptp.int) (BOUND_VARIABLE_1462541 tptp.int) (BOUND_VARIABLE_1462542 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8670 BOUND_VARIABLE_1462539) BOUND_VARIABLE_1462540) BOUND_VARIABLE_1462541) BOUND_VARIABLE_1462542) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462540) BOUND_VARIABLE_1462542)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462539) BOUND_VARIABLE_1462541)))))))))) (let ((_let_2755 (forall ((BOUND_VARIABLE_1462514 tptp.int) (BOUND_VARIABLE_1462515 tptp.int) (BOUND_VARIABLE_1462516 tptp.int) (BOUND_VARIABLE_1462517 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8671 BOUND_VARIABLE_1462514) BOUND_VARIABLE_1462515) BOUND_VARIABLE_1462516) BOUND_VARIABLE_1462517) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462515) BOUND_VARIABLE_1462517)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462514) BOUND_VARIABLE_1462516)))))))))) (let ((_let_2756 (forall ((BOUND_VARIABLE_1462489 tptp.int) (BOUND_VARIABLE_1462490 tptp.int) (BOUND_VARIABLE_1462491 tptp.int) (BOUND_VARIABLE_1462492 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8672 BOUND_VARIABLE_1462489) BOUND_VARIABLE_1462490) BOUND_VARIABLE_1462491) BOUND_VARIABLE_1462492) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462490) BOUND_VARIABLE_1462492)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462489) BOUND_VARIABLE_1462491)))))))))) (let ((_let_2757 (forall ((BOUND_VARIABLE_1462464 tptp.int) (BOUND_VARIABLE_1462465 tptp.int) (BOUND_VARIABLE_1462466 tptp.int) (BOUND_VARIABLE_1462467 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8673 BOUND_VARIABLE_1462464) BOUND_VARIABLE_1462465) BOUND_VARIABLE_1462466) BOUND_VARIABLE_1462467) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462465) BOUND_VARIABLE_1462467)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462464) BOUND_VARIABLE_1462466)))))))))) (let ((_let_2758 (forall ((BOUND_VARIABLE_1462439 tptp.int) (BOUND_VARIABLE_1462440 tptp.int) (BOUND_VARIABLE_1462441 tptp.int) (BOUND_VARIABLE_1462442 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8674 BOUND_VARIABLE_1462439) BOUND_VARIABLE_1462440) BOUND_VARIABLE_1462441) BOUND_VARIABLE_1462442) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462440) BOUND_VARIABLE_1462442)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462439) BOUND_VARIABLE_1462441)))))))))) (let ((_let_2759 (forall ((BOUND_VARIABLE_1462414 tptp.int) (BOUND_VARIABLE_1462415 tptp.int) (BOUND_VARIABLE_1462416 tptp.int) (BOUND_VARIABLE_1462417 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8675 BOUND_VARIABLE_1462414) BOUND_VARIABLE_1462415) BOUND_VARIABLE_1462416) BOUND_VARIABLE_1462417) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462415) BOUND_VARIABLE_1462417)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462414) BOUND_VARIABLE_1462416)))))))))) (let ((_let_2760 (forall ((BOUND_VARIABLE_1462389 tptp.int) (BOUND_VARIABLE_1462390 tptp.int) (BOUND_VARIABLE_1462391 tptp.int) (BOUND_VARIABLE_1462392 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8676 BOUND_VARIABLE_1462389) BOUND_VARIABLE_1462390) BOUND_VARIABLE_1462391) BOUND_VARIABLE_1462392) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462390) BOUND_VARIABLE_1462392)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462389) BOUND_VARIABLE_1462391)))))))))) (let ((_let_2761 (forall ((BOUND_VARIABLE_1462364 tptp.int) (BOUND_VARIABLE_1462365 tptp.int) (BOUND_VARIABLE_1462366 tptp.int) (BOUND_VARIABLE_1462367 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8677 BOUND_VARIABLE_1462364) BOUND_VARIABLE_1462365) BOUND_VARIABLE_1462366) BOUND_VARIABLE_1462367) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462365) BOUND_VARIABLE_1462367)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462364) BOUND_VARIABLE_1462366)))))))))) (let ((_let_2762 (forall ((BOUND_VARIABLE_1462339 tptp.int) (BOUND_VARIABLE_1462340 tptp.int) (BOUND_VARIABLE_1462341 tptp.int) (BOUND_VARIABLE_1462342 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8678 BOUND_VARIABLE_1462339) BOUND_VARIABLE_1462340) BOUND_VARIABLE_1462341) BOUND_VARIABLE_1462342) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462340) BOUND_VARIABLE_1462342)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462339) BOUND_VARIABLE_1462341)))))))))) (let ((_let_2763 (forall ((BOUND_VARIABLE_1462314 tptp.int) (BOUND_VARIABLE_1462315 tptp.int) (BOUND_VARIABLE_1462316 tptp.int) (BOUND_VARIABLE_1462317 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8679 BOUND_VARIABLE_1462314) BOUND_VARIABLE_1462315) BOUND_VARIABLE_1462316) BOUND_VARIABLE_1462317) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462315) BOUND_VARIABLE_1462317)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462314) BOUND_VARIABLE_1462316)))))))))) (let ((_let_2764 (forall ((BOUND_VARIABLE_1462289 tptp.int) (BOUND_VARIABLE_1462290 tptp.int) (BOUND_VARIABLE_1462291 tptp.int) (BOUND_VARIABLE_1462292 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8680 BOUND_VARIABLE_1462289) BOUND_VARIABLE_1462290) BOUND_VARIABLE_1462291) BOUND_VARIABLE_1462292) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462290) BOUND_VARIABLE_1462292)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462289) BOUND_VARIABLE_1462291)))))))))) (let ((_let_2765 (forall ((BOUND_VARIABLE_1462264 tptp.int) (BOUND_VARIABLE_1462265 tptp.int) (BOUND_VARIABLE_1462266 tptp.int) (BOUND_VARIABLE_1462267 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8681 BOUND_VARIABLE_1462264) BOUND_VARIABLE_1462265) BOUND_VARIABLE_1462266) BOUND_VARIABLE_1462267) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462265) BOUND_VARIABLE_1462267)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462264) BOUND_VARIABLE_1462266)))))))))) (let ((_let_2766 (forall ((BOUND_VARIABLE_1462239 tptp.int) (BOUND_VARIABLE_1462240 tptp.int) (BOUND_VARIABLE_1462241 tptp.int) (BOUND_VARIABLE_1462242 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8682 BOUND_VARIABLE_1462239) BOUND_VARIABLE_1462240) BOUND_VARIABLE_1462241) BOUND_VARIABLE_1462242) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462240) BOUND_VARIABLE_1462242)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462239) BOUND_VARIABLE_1462241)))))))))) (let ((_let_2767 (forall ((BOUND_VARIABLE_1462214 tptp.int) (BOUND_VARIABLE_1462215 tptp.int) (BOUND_VARIABLE_1462216 tptp.int) (BOUND_VARIABLE_1462217 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8683 BOUND_VARIABLE_1462214) BOUND_VARIABLE_1462215) BOUND_VARIABLE_1462216) BOUND_VARIABLE_1462217) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462215) BOUND_VARIABLE_1462217)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462214) BOUND_VARIABLE_1462216)))))))))) (let ((_let_2768 (forall ((BOUND_VARIABLE_1462189 tptp.int) (BOUND_VARIABLE_1462190 tptp.int) (BOUND_VARIABLE_1462191 tptp.int) (BOUND_VARIABLE_1462192 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8684 BOUND_VARIABLE_1462189) BOUND_VARIABLE_1462190) BOUND_VARIABLE_1462191) BOUND_VARIABLE_1462192) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462190) BOUND_VARIABLE_1462192)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462189) BOUND_VARIABLE_1462191)))))))))) (let ((_let_2769 (forall ((BOUND_VARIABLE_1462164 tptp.int) (BOUND_VARIABLE_1462165 tptp.int) (BOUND_VARIABLE_1462166 tptp.int) (BOUND_VARIABLE_1462167 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8685 BOUND_VARIABLE_1462164) BOUND_VARIABLE_1462165) BOUND_VARIABLE_1462166) BOUND_VARIABLE_1462167) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462165) BOUND_VARIABLE_1462167)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462164) BOUND_VARIABLE_1462166)))))))))) (let ((_let_2770 (forall ((BOUND_VARIABLE_1462139 tptp.int) (BOUND_VARIABLE_1462140 tptp.int) (BOUND_VARIABLE_1462141 tptp.int) (BOUND_VARIABLE_1462142 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8686 BOUND_VARIABLE_1462139) BOUND_VARIABLE_1462140) BOUND_VARIABLE_1462141) BOUND_VARIABLE_1462142) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462140) BOUND_VARIABLE_1462142)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462139) BOUND_VARIABLE_1462141)))))))))) (let ((_let_2771 (forall ((BOUND_VARIABLE_1462114 tptp.int) (BOUND_VARIABLE_1462115 tptp.int) (BOUND_VARIABLE_1462116 tptp.int) (BOUND_VARIABLE_1462117 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8687 BOUND_VARIABLE_1462114) BOUND_VARIABLE_1462115) BOUND_VARIABLE_1462116) BOUND_VARIABLE_1462117) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462115) BOUND_VARIABLE_1462117)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462114) BOUND_VARIABLE_1462116)))))))))) (let ((_let_2772 (forall ((BOUND_VARIABLE_1462089 tptp.int) (BOUND_VARIABLE_1462090 tptp.int) (BOUND_VARIABLE_1462091 tptp.int) (BOUND_VARIABLE_1462092 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8688 BOUND_VARIABLE_1462089) BOUND_VARIABLE_1462090) BOUND_VARIABLE_1462091) BOUND_VARIABLE_1462092) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462090) BOUND_VARIABLE_1462092)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462089) BOUND_VARIABLE_1462091)))))))))) (let ((_let_2773 (forall ((BOUND_VARIABLE_1462064 tptp.int) (BOUND_VARIABLE_1462065 tptp.int) (BOUND_VARIABLE_1462066 tptp.int) (BOUND_VARIABLE_1462067 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8689 BOUND_VARIABLE_1462064) BOUND_VARIABLE_1462065) BOUND_VARIABLE_1462066) BOUND_VARIABLE_1462067) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462065) BOUND_VARIABLE_1462067)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462064) BOUND_VARIABLE_1462066)))))))))) (let ((_let_2774 (forall ((BOUND_VARIABLE_1462039 tptp.int) (BOUND_VARIABLE_1462040 tptp.int) (BOUND_VARIABLE_1462041 tptp.int) (BOUND_VARIABLE_1462042 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8690 BOUND_VARIABLE_1462039) BOUND_VARIABLE_1462040) BOUND_VARIABLE_1462041) BOUND_VARIABLE_1462042) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462040) BOUND_VARIABLE_1462042)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462039) BOUND_VARIABLE_1462041)))))))))) (let ((_let_2775 (forall ((BOUND_VARIABLE_1462014 tptp.int) (BOUND_VARIABLE_1462015 tptp.int) (BOUND_VARIABLE_1462016 tptp.int) (BOUND_VARIABLE_1462017 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8691 BOUND_VARIABLE_1462014) BOUND_VARIABLE_1462015) BOUND_VARIABLE_1462016) BOUND_VARIABLE_1462017) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462015) BOUND_VARIABLE_1462017)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1462014) BOUND_VARIABLE_1462016)))))))))) (let ((_let_2776 (forall ((BOUND_VARIABLE_1461989 tptp.int) (BOUND_VARIABLE_1461990 tptp.int) (BOUND_VARIABLE_1461991 tptp.int) (BOUND_VARIABLE_1461992 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8692 BOUND_VARIABLE_1461989) BOUND_VARIABLE_1461990) BOUND_VARIABLE_1461991) BOUND_VARIABLE_1461992) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461990) BOUND_VARIABLE_1461992)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461989) BOUND_VARIABLE_1461991)))))))))) (let ((_let_2777 (forall ((BOUND_VARIABLE_1461964 tptp.int) (BOUND_VARIABLE_1461965 tptp.int) (BOUND_VARIABLE_1461966 tptp.int) (BOUND_VARIABLE_1461967 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8693 BOUND_VARIABLE_1461964) BOUND_VARIABLE_1461965) BOUND_VARIABLE_1461966) BOUND_VARIABLE_1461967) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461965) BOUND_VARIABLE_1461967)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461964) BOUND_VARIABLE_1461966)))))))))) (let ((_let_2778 (forall ((BOUND_VARIABLE_1461939 tptp.int) (BOUND_VARIABLE_1461940 tptp.int) (BOUND_VARIABLE_1461941 tptp.int) (BOUND_VARIABLE_1461942 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8694 BOUND_VARIABLE_1461939) BOUND_VARIABLE_1461940) BOUND_VARIABLE_1461941) BOUND_VARIABLE_1461942) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461940) BOUND_VARIABLE_1461942)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461939) BOUND_VARIABLE_1461941)))))))))) (let ((_let_2779 (forall ((BOUND_VARIABLE_1461914 tptp.int) (BOUND_VARIABLE_1461915 tptp.int) (BOUND_VARIABLE_1461916 tptp.int) (BOUND_VARIABLE_1461917 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8695 BOUND_VARIABLE_1461914) BOUND_VARIABLE_1461915) BOUND_VARIABLE_1461916) BOUND_VARIABLE_1461917) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461915) BOUND_VARIABLE_1461917)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461914) BOUND_VARIABLE_1461916)))))))))) (let ((_let_2780 (forall ((BOUND_VARIABLE_1461889 tptp.int) (BOUND_VARIABLE_1461890 tptp.int) (BOUND_VARIABLE_1461891 tptp.int) (BOUND_VARIABLE_1461892 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8696 BOUND_VARIABLE_1461889) BOUND_VARIABLE_1461890) BOUND_VARIABLE_1461891) BOUND_VARIABLE_1461892) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461890) BOUND_VARIABLE_1461892)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461889) BOUND_VARIABLE_1461891)))))))))) (let ((_let_2781 (forall ((BOUND_VARIABLE_1461864 tptp.int) (BOUND_VARIABLE_1461865 tptp.int) (BOUND_VARIABLE_1461866 tptp.int) (BOUND_VARIABLE_1461867 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8697 BOUND_VARIABLE_1461864) BOUND_VARIABLE_1461865) BOUND_VARIABLE_1461866) BOUND_VARIABLE_1461867) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461865) BOUND_VARIABLE_1461867)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461864) BOUND_VARIABLE_1461866)))))))))) (let ((_let_2782 (forall ((BOUND_VARIABLE_1461839 tptp.int) (BOUND_VARIABLE_1461840 tptp.int) (BOUND_VARIABLE_1461841 tptp.int) (BOUND_VARIABLE_1461842 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8698 BOUND_VARIABLE_1461839) BOUND_VARIABLE_1461840) BOUND_VARIABLE_1461841) BOUND_VARIABLE_1461842) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461840) BOUND_VARIABLE_1461842)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461839) BOUND_VARIABLE_1461841)))))))))) (let ((_let_2783 (forall ((BOUND_VARIABLE_1461814 tptp.int) (BOUND_VARIABLE_1461815 tptp.int) (BOUND_VARIABLE_1461816 tptp.int) (BOUND_VARIABLE_1461817 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8699 BOUND_VARIABLE_1461814) BOUND_VARIABLE_1461815) BOUND_VARIABLE_1461816) BOUND_VARIABLE_1461817) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461815) BOUND_VARIABLE_1461817)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461814) BOUND_VARIABLE_1461816)))))))))) (let ((_let_2784 (forall ((BOUND_VARIABLE_1461789 tptp.int) (BOUND_VARIABLE_1461790 tptp.int) (BOUND_VARIABLE_1461791 tptp.int) (BOUND_VARIABLE_1461792 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8700 BOUND_VARIABLE_1461789) BOUND_VARIABLE_1461790) BOUND_VARIABLE_1461791) BOUND_VARIABLE_1461792) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461790) BOUND_VARIABLE_1461792)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461789) BOUND_VARIABLE_1461791)))))))))) (let ((_let_2785 (forall ((BOUND_VARIABLE_1461764 tptp.int) (BOUND_VARIABLE_1461765 tptp.int) (BOUND_VARIABLE_1461766 tptp.int) (BOUND_VARIABLE_1461767 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8701 BOUND_VARIABLE_1461764) BOUND_VARIABLE_1461765) BOUND_VARIABLE_1461766) BOUND_VARIABLE_1461767) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461765) BOUND_VARIABLE_1461767)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461764) BOUND_VARIABLE_1461766)))))))))) (let ((_let_2786 (forall ((BOUND_VARIABLE_1461739 tptp.int) (BOUND_VARIABLE_1461740 tptp.int) (BOUND_VARIABLE_1461741 tptp.int) (BOUND_VARIABLE_1461742 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8702 BOUND_VARIABLE_1461739) BOUND_VARIABLE_1461740) BOUND_VARIABLE_1461741) BOUND_VARIABLE_1461742) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461740) BOUND_VARIABLE_1461742)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461739) BOUND_VARIABLE_1461741)))))))))) (let ((_let_2787 (forall ((BOUND_VARIABLE_1461714 tptp.int) (BOUND_VARIABLE_1461715 tptp.int) (BOUND_VARIABLE_1461716 tptp.int) (BOUND_VARIABLE_1461717 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8703 BOUND_VARIABLE_1461714) BOUND_VARIABLE_1461715) BOUND_VARIABLE_1461716) BOUND_VARIABLE_1461717) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461715) BOUND_VARIABLE_1461717)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461714) BOUND_VARIABLE_1461716)))))))))) (let ((_let_2788 (forall ((BOUND_VARIABLE_1461689 tptp.int) (BOUND_VARIABLE_1461690 tptp.int) (BOUND_VARIABLE_1461691 tptp.int) (BOUND_VARIABLE_1461692 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8704 BOUND_VARIABLE_1461689) BOUND_VARIABLE_1461690) BOUND_VARIABLE_1461691) BOUND_VARIABLE_1461692) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461690) BOUND_VARIABLE_1461692)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461689) BOUND_VARIABLE_1461691)))))))))) (let ((_let_2789 (forall ((BOUND_VARIABLE_1461664 tptp.int) (BOUND_VARIABLE_1461665 tptp.int) (BOUND_VARIABLE_1461666 tptp.int) (BOUND_VARIABLE_1461667 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8705 BOUND_VARIABLE_1461664) BOUND_VARIABLE_1461665) BOUND_VARIABLE_1461666) BOUND_VARIABLE_1461667) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461665) BOUND_VARIABLE_1461667)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461664) BOUND_VARIABLE_1461666)))))))))) (let ((_let_2790 (forall ((BOUND_VARIABLE_1461639 tptp.int) (BOUND_VARIABLE_1461640 tptp.int) (BOUND_VARIABLE_1461641 tptp.int) (BOUND_VARIABLE_1461642 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8706 BOUND_VARIABLE_1461639) BOUND_VARIABLE_1461640) BOUND_VARIABLE_1461641) BOUND_VARIABLE_1461642) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461640) BOUND_VARIABLE_1461642)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461639) BOUND_VARIABLE_1461641)))))))))) (let ((_let_2791 (forall ((BOUND_VARIABLE_1461614 tptp.int) (BOUND_VARIABLE_1461615 tptp.int) (BOUND_VARIABLE_1461616 tptp.int) (BOUND_VARIABLE_1461617 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8707 BOUND_VARIABLE_1461614) BOUND_VARIABLE_1461615) BOUND_VARIABLE_1461616) BOUND_VARIABLE_1461617) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461615) BOUND_VARIABLE_1461617)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461614) BOUND_VARIABLE_1461616)))))))))) (let ((_let_2792 (forall ((BOUND_VARIABLE_1461589 tptp.int) (BOUND_VARIABLE_1461590 tptp.int) (BOUND_VARIABLE_1461591 tptp.int) (BOUND_VARIABLE_1461592 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8708 BOUND_VARIABLE_1461589) BOUND_VARIABLE_1461590) BOUND_VARIABLE_1461591) BOUND_VARIABLE_1461592) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461590) BOUND_VARIABLE_1461592)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461589) BOUND_VARIABLE_1461591)))))))))) (let ((_let_2793 (forall ((BOUND_VARIABLE_1461564 tptp.int) (BOUND_VARIABLE_1461565 tptp.int) (BOUND_VARIABLE_1461566 tptp.int) (BOUND_VARIABLE_1461567 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8709 BOUND_VARIABLE_1461564) BOUND_VARIABLE_1461565) BOUND_VARIABLE_1461566) BOUND_VARIABLE_1461567) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461565) BOUND_VARIABLE_1461567)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461564) BOUND_VARIABLE_1461566)))))))))) (let ((_let_2794 (forall ((BOUND_VARIABLE_1461539 tptp.int) (BOUND_VARIABLE_1461540 tptp.int) (BOUND_VARIABLE_1461541 tptp.int) (BOUND_VARIABLE_1461542 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8710 BOUND_VARIABLE_1461539) BOUND_VARIABLE_1461540) BOUND_VARIABLE_1461541) BOUND_VARIABLE_1461542) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461540) BOUND_VARIABLE_1461542)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461539) BOUND_VARIABLE_1461541)))))))))) (let ((_let_2795 (forall ((BOUND_VARIABLE_1461514 tptp.int) (BOUND_VARIABLE_1461515 tptp.int) (BOUND_VARIABLE_1461516 tptp.int) (BOUND_VARIABLE_1461517 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8711 BOUND_VARIABLE_1461514) BOUND_VARIABLE_1461515) BOUND_VARIABLE_1461516) BOUND_VARIABLE_1461517) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461515) BOUND_VARIABLE_1461517)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461514) BOUND_VARIABLE_1461516)))))))))) (let ((_let_2796 (forall ((BOUND_VARIABLE_1461489 tptp.int) (BOUND_VARIABLE_1461490 tptp.int) (BOUND_VARIABLE_1461491 tptp.int) (BOUND_VARIABLE_1461492 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8712 BOUND_VARIABLE_1461489) BOUND_VARIABLE_1461490) BOUND_VARIABLE_1461491) BOUND_VARIABLE_1461492) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461490) BOUND_VARIABLE_1461492)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461489) BOUND_VARIABLE_1461491)))))))))) (let ((_let_2797 (forall ((BOUND_VARIABLE_1461464 tptp.int) (BOUND_VARIABLE_1461465 tptp.int) (BOUND_VARIABLE_1461466 tptp.int) (BOUND_VARIABLE_1461467 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8713 BOUND_VARIABLE_1461464) BOUND_VARIABLE_1461465) BOUND_VARIABLE_1461466) BOUND_VARIABLE_1461467) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461465) BOUND_VARIABLE_1461467)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461464) BOUND_VARIABLE_1461466)))))))))) (let ((_let_2798 (forall ((BOUND_VARIABLE_1461439 tptp.int) (BOUND_VARIABLE_1461440 tptp.int) (BOUND_VARIABLE_1461441 tptp.int) (BOUND_VARIABLE_1461442 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8714 BOUND_VARIABLE_1461439) BOUND_VARIABLE_1461440) BOUND_VARIABLE_1461441) BOUND_VARIABLE_1461442) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461440) BOUND_VARIABLE_1461442)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461439) BOUND_VARIABLE_1461441)))))))))) (let ((_let_2799 (forall ((BOUND_VARIABLE_1461414 tptp.int) (BOUND_VARIABLE_1461415 tptp.int) (BOUND_VARIABLE_1461416 tptp.int) (BOUND_VARIABLE_1461417 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8715 BOUND_VARIABLE_1461414) BOUND_VARIABLE_1461415) BOUND_VARIABLE_1461416) BOUND_VARIABLE_1461417) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461415) BOUND_VARIABLE_1461417)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461414) BOUND_VARIABLE_1461416)))))))))) (let ((_let_2800 (forall ((BOUND_VARIABLE_1461389 tptp.int) (BOUND_VARIABLE_1461390 tptp.int) (BOUND_VARIABLE_1461391 tptp.int) (BOUND_VARIABLE_1461392 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8716 BOUND_VARIABLE_1461389) BOUND_VARIABLE_1461390) BOUND_VARIABLE_1461391) BOUND_VARIABLE_1461392) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461390) BOUND_VARIABLE_1461392)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461389) BOUND_VARIABLE_1461391)))))))))) (let ((_let_2801 (forall ((BOUND_VARIABLE_1461364 tptp.int) (BOUND_VARIABLE_1461365 tptp.int) (BOUND_VARIABLE_1461366 tptp.int) (BOUND_VARIABLE_1461367 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8717 BOUND_VARIABLE_1461364) BOUND_VARIABLE_1461365) BOUND_VARIABLE_1461366) BOUND_VARIABLE_1461367) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461365) BOUND_VARIABLE_1461367)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461364) BOUND_VARIABLE_1461366)))))))))) (let ((_let_2802 (forall ((BOUND_VARIABLE_1461339 tptp.int) (BOUND_VARIABLE_1461340 tptp.int) (BOUND_VARIABLE_1461341 tptp.int) (BOUND_VARIABLE_1461342 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8718 BOUND_VARIABLE_1461339) BOUND_VARIABLE_1461340) BOUND_VARIABLE_1461341) BOUND_VARIABLE_1461342) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461340) BOUND_VARIABLE_1461342)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461339) BOUND_VARIABLE_1461341)))))))))) (let ((_let_2803 (forall ((BOUND_VARIABLE_1461314 tptp.int) (BOUND_VARIABLE_1461315 tptp.int) (BOUND_VARIABLE_1461316 tptp.int) (BOUND_VARIABLE_1461317 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8719 BOUND_VARIABLE_1461314) BOUND_VARIABLE_1461315) BOUND_VARIABLE_1461316) BOUND_VARIABLE_1461317) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461315) BOUND_VARIABLE_1461317)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461314) BOUND_VARIABLE_1461316)))))))))) (let ((_let_2804 (forall ((BOUND_VARIABLE_1461289 tptp.int) (BOUND_VARIABLE_1461290 tptp.int) (BOUND_VARIABLE_1461291 tptp.int) (BOUND_VARIABLE_1461292 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8720 BOUND_VARIABLE_1461289) BOUND_VARIABLE_1461290) BOUND_VARIABLE_1461291) BOUND_VARIABLE_1461292) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461290) BOUND_VARIABLE_1461292)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461289) BOUND_VARIABLE_1461291)))))))))) (let ((_let_2805 (forall ((BOUND_VARIABLE_1461264 tptp.int) (BOUND_VARIABLE_1461265 tptp.int) (BOUND_VARIABLE_1461266 tptp.int) (BOUND_VARIABLE_1461267 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8721 BOUND_VARIABLE_1461264) BOUND_VARIABLE_1461265) BOUND_VARIABLE_1461266) BOUND_VARIABLE_1461267) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461265) BOUND_VARIABLE_1461267)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461264) BOUND_VARIABLE_1461266)))))))))) (let ((_let_2806 (forall ((BOUND_VARIABLE_1461239 tptp.int) (BOUND_VARIABLE_1461240 tptp.int) (BOUND_VARIABLE_1461241 tptp.int) (BOUND_VARIABLE_1461242 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8722 BOUND_VARIABLE_1461239) BOUND_VARIABLE_1461240) BOUND_VARIABLE_1461241) BOUND_VARIABLE_1461242) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461240) BOUND_VARIABLE_1461242)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461239) BOUND_VARIABLE_1461241)))))))))) (let ((_let_2807 (forall ((BOUND_VARIABLE_1461214 tptp.int) (BOUND_VARIABLE_1461215 tptp.int) (BOUND_VARIABLE_1461216 tptp.int) (BOUND_VARIABLE_1461217 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8723 BOUND_VARIABLE_1461214) BOUND_VARIABLE_1461215) BOUND_VARIABLE_1461216) BOUND_VARIABLE_1461217) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461215) BOUND_VARIABLE_1461217)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461214) BOUND_VARIABLE_1461216)))))))))) (let ((_let_2808 (forall ((BOUND_VARIABLE_1461189 tptp.int) (BOUND_VARIABLE_1461190 tptp.int) (BOUND_VARIABLE_1461191 tptp.int) (BOUND_VARIABLE_1461192 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8724 BOUND_VARIABLE_1461189) BOUND_VARIABLE_1461190) BOUND_VARIABLE_1461191) BOUND_VARIABLE_1461192) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461190) BOUND_VARIABLE_1461192)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461189) BOUND_VARIABLE_1461191)))))))))) (let ((_let_2809 (forall ((BOUND_VARIABLE_1461164 tptp.int) (BOUND_VARIABLE_1461165 tptp.int) (BOUND_VARIABLE_1461166 tptp.int) (BOUND_VARIABLE_1461167 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8725 BOUND_VARIABLE_1461164) BOUND_VARIABLE_1461165) BOUND_VARIABLE_1461166) BOUND_VARIABLE_1461167) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461165) BOUND_VARIABLE_1461167)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461164) BOUND_VARIABLE_1461166)))))))))) (let ((_let_2810 (forall ((BOUND_VARIABLE_1461139 tptp.int) (BOUND_VARIABLE_1461140 tptp.int) (BOUND_VARIABLE_1461141 tptp.int) (BOUND_VARIABLE_1461142 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8726 BOUND_VARIABLE_1461139) BOUND_VARIABLE_1461140) BOUND_VARIABLE_1461141) BOUND_VARIABLE_1461142) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461140) BOUND_VARIABLE_1461142)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461139) BOUND_VARIABLE_1461141)))))))))) (let ((_let_2811 (forall ((BOUND_VARIABLE_1461114 tptp.int) (BOUND_VARIABLE_1461115 tptp.int) (BOUND_VARIABLE_1461116 tptp.int) (BOUND_VARIABLE_1461117 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8727 BOUND_VARIABLE_1461114) BOUND_VARIABLE_1461115) BOUND_VARIABLE_1461116) BOUND_VARIABLE_1461117) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461115) BOUND_VARIABLE_1461117)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461114) BOUND_VARIABLE_1461116)))))))))) (let ((_let_2812 (forall ((BOUND_VARIABLE_1461089 tptp.int) (BOUND_VARIABLE_1461090 tptp.int) (BOUND_VARIABLE_1461091 tptp.int) (BOUND_VARIABLE_1461092 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8728 BOUND_VARIABLE_1461089) BOUND_VARIABLE_1461090) BOUND_VARIABLE_1461091) BOUND_VARIABLE_1461092) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461090) BOUND_VARIABLE_1461092)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461089) BOUND_VARIABLE_1461091)))))))))) (let ((_let_2813 (forall ((BOUND_VARIABLE_1461064 tptp.int) (BOUND_VARIABLE_1461065 tptp.int) (BOUND_VARIABLE_1461066 tptp.int) (BOUND_VARIABLE_1461067 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8729 BOUND_VARIABLE_1461064) BOUND_VARIABLE_1461065) BOUND_VARIABLE_1461066) BOUND_VARIABLE_1461067) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461065) BOUND_VARIABLE_1461067)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461064) BOUND_VARIABLE_1461066)))))))))) (let ((_let_2814 (forall ((BOUND_VARIABLE_1461039 tptp.int) (BOUND_VARIABLE_1461040 tptp.int) (BOUND_VARIABLE_1461041 tptp.int) (BOUND_VARIABLE_1461042 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8730 BOUND_VARIABLE_1461039) BOUND_VARIABLE_1461040) BOUND_VARIABLE_1461041) BOUND_VARIABLE_1461042) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461040) BOUND_VARIABLE_1461042)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461039) BOUND_VARIABLE_1461041)))))))))) (let ((_let_2815 (forall ((BOUND_VARIABLE_1461014 tptp.int) (BOUND_VARIABLE_1461015 tptp.int) (BOUND_VARIABLE_1461016 tptp.int) (BOUND_VARIABLE_1461017 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8731 BOUND_VARIABLE_1461014) BOUND_VARIABLE_1461015) BOUND_VARIABLE_1461016) BOUND_VARIABLE_1461017) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461015) BOUND_VARIABLE_1461017)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1461014) BOUND_VARIABLE_1461016)))))))))) (let ((_let_2816 (forall ((BOUND_VARIABLE_1460989 tptp.int) (BOUND_VARIABLE_1460990 tptp.int) (BOUND_VARIABLE_1460991 tptp.int) (BOUND_VARIABLE_1460992 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8732 BOUND_VARIABLE_1460989) BOUND_VARIABLE_1460990) BOUND_VARIABLE_1460991) BOUND_VARIABLE_1460992) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460990) BOUND_VARIABLE_1460992)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460989) BOUND_VARIABLE_1460991)))))))))) (let ((_let_2817 (forall ((BOUND_VARIABLE_1460964 tptp.int) (BOUND_VARIABLE_1460965 tptp.int) (BOUND_VARIABLE_1460966 tptp.int) (BOUND_VARIABLE_1460967 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8733 BOUND_VARIABLE_1460964) BOUND_VARIABLE_1460965) BOUND_VARIABLE_1460966) BOUND_VARIABLE_1460967) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460965) BOUND_VARIABLE_1460967)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460964) BOUND_VARIABLE_1460966)))))))))) (let ((_let_2818 (forall ((BOUND_VARIABLE_1460939 tptp.int) (BOUND_VARIABLE_1460940 tptp.int) (BOUND_VARIABLE_1460941 tptp.int) (BOUND_VARIABLE_1460942 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8734 BOUND_VARIABLE_1460939) BOUND_VARIABLE_1460940) BOUND_VARIABLE_1460941) BOUND_VARIABLE_1460942) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460940) BOUND_VARIABLE_1460942)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460939) BOUND_VARIABLE_1460941)))))))))) (let ((_let_2819 (forall ((BOUND_VARIABLE_1460914 tptp.int) (BOUND_VARIABLE_1460915 tptp.int) (BOUND_VARIABLE_1460916 tptp.int) (BOUND_VARIABLE_1460917 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8735 BOUND_VARIABLE_1460914) BOUND_VARIABLE_1460915) BOUND_VARIABLE_1460916) BOUND_VARIABLE_1460917) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460915) BOUND_VARIABLE_1460917)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460914) BOUND_VARIABLE_1460916)))))))))) (let ((_let_2820 (forall ((BOUND_VARIABLE_1460889 tptp.int) (BOUND_VARIABLE_1460890 tptp.int) (BOUND_VARIABLE_1460891 tptp.int) (BOUND_VARIABLE_1460892 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8736 BOUND_VARIABLE_1460889) BOUND_VARIABLE_1460890) BOUND_VARIABLE_1460891) BOUND_VARIABLE_1460892) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460890) BOUND_VARIABLE_1460892)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460889) BOUND_VARIABLE_1460891)))))))))) (let ((_let_2821 (forall ((BOUND_VARIABLE_1460864 tptp.int) (BOUND_VARIABLE_1460865 tptp.int) (BOUND_VARIABLE_1460866 tptp.int) (BOUND_VARIABLE_1460867 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8737 BOUND_VARIABLE_1460864) BOUND_VARIABLE_1460865) BOUND_VARIABLE_1460866) BOUND_VARIABLE_1460867) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460865) BOUND_VARIABLE_1460867)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460864) BOUND_VARIABLE_1460866)))))))))) (let ((_let_2822 (forall ((BOUND_VARIABLE_1460839 tptp.int) (BOUND_VARIABLE_1460840 tptp.int) (BOUND_VARIABLE_1460841 tptp.int) (BOUND_VARIABLE_1460842 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8738 BOUND_VARIABLE_1460839) BOUND_VARIABLE_1460840) BOUND_VARIABLE_1460841) BOUND_VARIABLE_1460842) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460840) BOUND_VARIABLE_1460842)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460839) BOUND_VARIABLE_1460841)))))))))) (let ((_let_2823 (forall ((BOUND_VARIABLE_1460814 tptp.int) (BOUND_VARIABLE_1460815 tptp.int) (BOUND_VARIABLE_1460816 tptp.int) (BOUND_VARIABLE_1460817 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8739 BOUND_VARIABLE_1460814) BOUND_VARIABLE_1460815) BOUND_VARIABLE_1460816) BOUND_VARIABLE_1460817) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460815) BOUND_VARIABLE_1460817)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460814) BOUND_VARIABLE_1460816)))))))))) (let ((_let_2824 (forall ((BOUND_VARIABLE_1460789 tptp.int) (BOUND_VARIABLE_1460790 tptp.int) (BOUND_VARIABLE_1460791 tptp.int) (BOUND_VARIABLE_1460792 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8740 BOUND_VARIABLE_1460789) BOUND_VARIABLE_1460790) BOUND_VARIABLE_1460791) BOUND_VARIABLE_1460792) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460790) BOUND_VARIABLE_1460792)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460789) BOUND_VARIABLE_1460791)))))))))) (let ((_let_2825 (forall ((BOUND_VARIABLE_1460764 tptp.int) (BOUND_VARIABLE_1460765 tptp.int) (BOUND_VARIABLE_1460766 tptp.int) (BOUND_VARIABLE_1460767 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8741 BOUND_VARIABLE_1460764) BOUND_VARIABLE_1460765) BOUND_VARIABLE_1460766) BOUND_VARIABLE_1460767) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460765) BOUND_VARIABLE_1460767)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460764) BOUND_VARIABLE_1460766)))))))))) (let ((_let_2826 (forall ((BOUND_VARIABLE_1460739 tptp.int) (BOUND_VARIABLE_1460740 tptp.int) (BOUND_VARIABLE_1460741 tptp.int) (BOUND_VARIABLE_1460742 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8742 BOUND_VARIABLE_1460739) BOUND_VARIABLE_1460740) BOUND_VARIABLE_1460741) BOUND_VARIABLE_1460742) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460740) BOUND_VARIABLE_1460742)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460739) BOUND_VARIABLE_1460741)))))))))) (let ((_let_2827 (forall ((BOUND_VARIABLE_1460714 tptp.int) (BOUND_VARIABLE_1460715 tptp.int) (BOUND_VARIABLE_1460716 tptp.int) (BOUND_VARIABLE_1460717 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8743 BOUND_VARIABLE_1460714) BOUND_VARIABLE_1460715) BOUND_VARIABLE_1460716) BOUND_VARIABLE_1460717) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460715) BOUND_VARIABLE_1460717)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460714) BOUND_VARIABLE_1460716)))))))))) (let ((_let_2828 (forall ((BOUND_VARIABLE_1460689 tptp.int) (BOUND_VARIABLE_1460690 tptp.int) (BOUND_VARIABLE_1460691 tptp.int) (BOUND_VARIABLE_1460692 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8744 BOUND_VARIABLE_1460689) BOUND_VARIABLE_1460690) BOUND_VARIABLE_1460691) BOUND_VARIABLE_1460692) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460690) BOUND_VARIABLE_1460692)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460689) BOUND_VARIABLE_1460691)))))))))) (let ((_let_2829 (forall ((BOUND_VARIABLE_1460664 tptp.int) (BOUND_VARIABLE_1460665 tptp.int) (BOUND_VARIABLE_1460666 tptp.int) (BOUND_VARIABLE_1460667 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8745 BOUND_VARIABLE_1460664) BOUND_VARIABLE_1460665) BOUND_VARIABLE_1460666) BOUND_VARIABLE_1460667) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460665) BOUND_VARIABLE_1460667)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460664) BOUND_VARIABLE_1460666)))))))))) (let ((_let_2830 (forall ((BOUND_VARIABLE_1460639 tptp.int) (BOUND_VARIABLE_1460640 tptp.int) (BOUND_VARIABLE_1460641 tptp.int) (BOUND_VARIABLE_1460642 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8746 BOUND_VARIABLE_1460639) BOUND_VARIABLE_1460640) BOUND_VARIABLE_1460641) BOUND_VARIABLE_1460642) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460640) BOUND_VARIABLE_1460642)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460639) BOUND_VARIABLE_1460641)))))))))) (let ((_let_2831 (forall ((BOUND_VARIABLE_1460614 tptp.int) (BOUND_VARIABLE_1460615 tptp.int) (BOUND_VARIABLE_1460616 tptp.int) (BOUND_VARIABLE_1460617 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8747 BOUND_VARIABLE_1460614) BOUND_VARIABLE_1460615) BOUND_VARIABLE_1460616) BOUND_VARIABLE_1460617) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460615) BOUND_VARIABLE_1460617)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460614) BOUND_VARIABLE_1460616)))))))))) (let ((_let_2832 (forall ((BOUND_VARIABLE_1460589 tptp.int) (BOUND_VARIABLE_1460590 tptp.int) (BOUND_VARIABLE_1460591 tptp.int) (BOUND_VARIABLE_1460592 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8748 BOUND_VARIABLE_1460589) BOUND_VARIABLE_1460590) BOUND_VARIABLE_1460591) BOUND_VARIABLE_1460592) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460590) BOUND_VARIABLE_1460592)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460589) BOUND_VARIABLE_1460591)))))))))) (let ((_let_2833 (forall ((BOUND_VARIABLE_1460564 tptp.int) (BOUND_VARIABLE_1460565 tptp.int) (BOUND_VARIABLE_1460566 tptp.int) (BOUND_VARIABLE_1460567 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8749 BOUND_VARIABLE_1460564) BOUND_VARIABLE_1460565) BOUND_VARIABLE_1460566) BOUND_VARIABLE_1460567) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460565) BOUND_VARIABLE_1460567)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460564) BOUND_VARIABLE_1460566)))))))))) (let ((_let_2834 (forall ((BOUND_VARIABLE_1460539 tptp.int) (BOUND_VARIABLE_1460540 tptp.int) (BOUND_VARIABLE_1460541 tptp.int) (BOUND_VARIABLE_1460542 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8750 BOUND_VARIABLE_1460539) BOUND_VARIABLE_1460540) BOUND_VARIABLE_1460541) BOUND_VARIABLE_1460542) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460540) BOUND_VARIABLE_1460542)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460539) BOUND_VARIABLE_1460541)))))))))) (let ((_let_2835 (forall ((BOUND_VARIABLE_1460514 tptp.int) (BOUND_VARIABLE_1460515 tptp.int) (BOUND_VARIABLE_1460516 tptp.int) (BOUND_VARIABLE_1460517 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8751 BOUND_VARIABLE_1460514) BOUND_VARIABLE_1460515) BOUND_VARIABLE_1460516) BOUND_VARIABLE_1460517) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460515) BOUND_VARIABLE_1460517)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460514) BOUND_VARIABLE_1460516)))))))))) (let ((_let_2836 (forall ((BOUND_VARIABLE_1460489 tptp.int) (BOUND_VARIABLE_1460490 tptp.int) (BOUND_VARIABLE_1460491 tptp.int) (BOUND_VARIABLE_1460492 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8752 BOUND_VARIABLE_1460489) BOUND_VARIABLE_1460490) BOUND_VARIABLE_1460491) BOUND_VARIABLE_1460492) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460490) BOUND_VARIABLE_1460492)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460489) BOUND_VARIABLE_1460491)))))))))) (let ((_let_2837 (forall ((BOUND_VARIABLE_1460464 tptp.int) (BOUND_VARIABLE_1460465 tptp.int) (BOUND_VARIABLE_1460466 tptp.int) (BOUND_VARIABLE_1460467 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8753 BOUND_VARIABLE_1460464) BOUND_VARIABLE_1460465) BOUND_VARIABLE_1460466) BOUND_VARIABLE_1460467) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460465) BOUND_VARIABLE_1460467)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460464) BOUND_VARIABLE_1460466)))))))))) (let ((_let_2838 (forall ((BOUND_VARIABLE_1460439 tptp.int) (BOUND_VARIABLE_1460440 tptp.int) (BOUND_VARIABLE_1460441 tptp.int) (BOUND_VARIABLE_1460442 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8754 BOUND_VARIABLE_1460439) BOUND_VARIABLE_1460440) BOUND_VARIABLE_1460441) BOUND_VARIABLE_1460442) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460440) BOUND_VARIABLE_1460442)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460439) BOUND_VARIABLE_1460441)))))))))) (let ((_let_2839 (forall ((BOUND_VARIABLE_1460414 tptp.int) (BOUND_VARIABLE_1460415 tptp.int) (BOUND_VARIABLE_1460416 tptp.int) (BOUND_VARIABLE_1460417 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8755 BOUND_VARIABLE_1460414) BOUND_VARIABLE_1460415) BOUND_VARIABLE_1460416) BOUND_VARIABLE_1460417) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460415) BOUND_VARIABLE_1460417)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460414) BOUND_VARIABLE_1460416)))))))))) (let ((_let_2840 (forall ((BOUND_VARIABLE_1460389 tptp.int) (BOUND_VARIABLE_1460390 tptp.int) (BOUND_VARIABLE_1460391 tptp.int) (BOUND_VARIABLE_1460392 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8756 BOUND_VARIABLE_1460389) BOUND_VARIABLE_1460390) BOUND_VARIABLE_1460391) BOUND_VARIABLE_1460392) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460390) BOUND_VARIABLE_1460392)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460389) BOUND_VARIABLE_1460391)))))))))) (let ((_let_2841 (forall ((BOUND_VARIABLE_1460364 tptp.int) (BOUND_VARIABLE_1460365 tptp.int) (BOUND_VARIABLE_1460366 tptp.int) (BOUND_VARIABLE_1460367 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8757 BOUND_VARIABLE_1460364) BOUND_VARIABLE_1460365) BOUND_VARIABLE_1460366) BOUND_VARIABLE_1460367) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460365) BOUND_VARIABLE_1460367)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460364) BOUND_VARIABLE_1460366)))))))))) (let ((_let_2842 (forall ((BOUND_VARIABLE_1460339 tptp.int) (BOUND_VARIABLE_1460340 tptp.int) (BOUND_VARIABLE_1460341 tptp.int) (BOUND_VARIABLE_1460342 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8758 BOUND_VARIABLE_1460339) BOUND_VARIABLE_1460340) BOUND_VARIABLE_1460341) BOUND_VARIABLE_1460342) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460340) BOUND_VARIABLE_1460342)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460339) BOUND_VARIABLE_1460341)))))))))) (let ((_let_2843 (forall ((BOUND_VARIABLE_1460314 tptp.int) (BOUND_VARIABLE_1460315 tptp.int) (BOUND_VARIABLE_1460316 tptp.int) (BOUND_VARIABLE_1460317 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8759 BOUND_VARIABLE_1460314) BOUND_VARIABLE_1460315) BOUND_VARIABLE_1460316) BOUND_VARIABLE_1460317) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460315) BOUND_VARIABLE_1460317)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460314) BOUND_VARIABLE_1460316)))))))))) (let ((_let_2844 (forall ((BOUND_VARIABLE_1460289 tptp.int) (BOUND_VARIABLE_1460290 tptp.int) (BOUND_VARIABLE_1460291 tptp.int) (BOUND_VARIABLE_1460292 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8760 BOUND_VARIABLE_1460289) BOUND_VARIABLE_1460290) BOUND_VARIABLE_1460291) BOUND_VARIABLE_1460292) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460290) BOUND_VARIABLE_1460292)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460289) BOUND_VARIABLE_1460291)))))))))) (let ((_let_2845 (forall ((BOUND_VARIABLE_1460264 tptp.int) (BOUND_VARIABLE_1460265 tptp.int) (BOUND_VARIABLE_1460266 tptp.int) (BOUND_VARIABLE_1460267 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8761 BOUND_VARIABLE_1460264) BOUND_VARIABLE_1460265) BOUND_VARIABLE_1460266) BOUND_VARIABLE_1460267) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460265) BOUND_VARIABLE_1460267)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460264) BOUND_VARIABLE_1460266)))))))))) (let ((_let_2846 (forall ((BOUND_VARIABLE_1460239 tptp.int) (BOUND_VARIABLE_1460240 tptp.int) (BOUND_VARIABLE_1460241 tptp.int) (BOUND_VARIABLE_1460242 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8762 BOUND_VARIABLE_1460239) BOUND_VARIABLE_1460240) BOUND_VARIABLE_1460241) BOUND_VARIABLE_1460242) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460240) BOUND_VARIABLE_1460242)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460239) BOUND_VARIABLE_1460241)))))))))) (let ((_let_2847 (forall ((BOUND_VARIABLE_1460214 tptp.int) (BOUND_VARIABLE_1460215 tptp.int) (BOUND_VARIABLE_1460216 tptp.int) (BOUND_VARIABLE_1460217 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8763 BOUND_VARIABLE_1460214) BOUND_VARIABLE_1460215) BOUND_VARIABLE_1460216) BOUND_VARIABLE_1460217) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460215) BOUND_VARIABLE_1460217)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460214) BOUND_VARIABLE_1460216)))))))))) (let ((_let_2848 (forall ((BOUND_VARIABLE_1460189 tptp.int) (BOUND_VARIABLE_1460190 tptp.int) (BOUND_VARIABLE_1460191 tptp.int) (BOUND_VARIABLE_1460192 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8764 BOUND_VARIABLE_1460189) BOUND_VARIABLE_1460190) BOUND_VARIABLE_1460191) BOUND_VARIABLE_1460192) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460190) BOUND_VARIABLE_1460192)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460189) BOUND_VARIABLE_1460191)))))))))) (let ((_let_2849 (forall ((BOUND_VARIABLE_1460164 tptp.int) (BOUND_VARIABLE_1460165 tptp.int) (BOUND_VARIABLE_1460166 tptp.int) (BOUND_VARIABLE_1460167 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8765 BOUND_VARIABLE_1460164) BOUND_VARIABLE_1460165) BOUND_VARIABLE_1460166) BOUND_VARIABLE_1460167) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460165) BOUND_VARIABLE_1460167)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460164) BOUND_VARIABLE_1460166)))))))))) (let ((_let_2850 (forall ((BOUND_VARIABLE_1460139 tptp.int) (BOUND_VARIABLE_1460140 tptp.int) (BOUND_VARIABLE_1460141 tptp.int) (BOUND_VARIABLE_1460142 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8766 BOUND_VARIABLE_1460139) BOUND_VARIABLE_1460140) BOUND_VARIABLE_1460141) BOUND_VARIABLE_1460142) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460140) BOUND_VARIABLE_1460142)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460139) BOUND_VARIABLE_1460141)))))))))) (let ((_let_2851 (forall ((BOUND_VARIABLE_1460114 tptp.int) (BOUND_VARIABLE_1460115 tptp.int) (BOUND_VARIABLE_1460116 tptp.int) (BOUND_VARIABLE_1460117 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8767 BOUND_VARIABLE_1460114) BOUND_VARIABLE_1460115) BOUND_VARIABLE_1460116) BOUND_VARIABLE_1460117) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460115) BOUND_VARIABLE_1460117)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460114) BOUND_VARIABLE_1460116)))))))))) (let ((_let_2852 (forall ((BOUND_VARIABLE_1460089 tptp.int) (BOUND_VARIABLE_1460090 tptp.int) (BOUND_VARIABLE_1460091 tptp.int) (BOUND_VARIABLE_1460092 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8768 BOUND_VARIABLE_1460089) BOUND_VARIABLE_1460090) BOUND_VARIABLE_1460091) BOUND_VARIABLE_1460092) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460090) BOUND_VARIABLE_1460092)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460089) BOUND_VARIABLE_1460091)))))))))) (let ((_let_2853 (forall ((BOUND_VARIABLE_1460064 tptp.int) (BOUND_VARIABLE_1460065 tptp.int) (BOUND_VARIABLE_1460066 tptp.int) (BOUND_VARIABLE_1460067 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8769 BOUND_VARIABLE_1460064) BOUND_VARIABLE_1460065) BOUND_VARIABLE_1460066) BOUND_VARIABLE_1460067) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460065) BOUND_VARIABLE_1460067)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460064) BOUND_VARIABLE_1460066)))))))))) (let ((_let_2854 (forall ((BOUND_VARIABLE_1460039 tptp.int) (BOUND_VARIABLE_1460040 tptp.int) (BOUND_VARIABLE_1460041 tptp.int) (BOUND_VARIABLE_1460042 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8770 BOUND_VARIABLE_1460039) BOUND_VARIABLE_1460040) BOUND_VARIABLE_1460041) BOUND_VARIABLE_1460042) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460040) BOUND_VARIABLE_1460042)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460039) BOUND_VARIABLE_1460041)))))))))) (let ((_let_2855 (forall ((BOUND_VARIABLE_1460014 tptp.int) (BOUND_VARIABLE_1460015 tptp.int) (BOUND_VARIABLE_1460016 tptp.int) (BOUND_VARIABLE_1460017 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8771 BOUND_VARIABLE_1460014) BOUND_VARIABLE_1460015) BOUND_VARIABLE_1460016) BOUND_VARIABLE_1460017) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460015) BOUND_VARIABLE_1460017)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1460014) BOUND_VARIABLE_1460016)))))))))) (let ((_let_2856 (forall ((BOUND_VARIABLE_1459989 tptp.int) (BOUND_VARIABLE_1459990 tptp.int) (BOUND_VARIABLE_1459991 tptp.int) (BOUND_VARIABLE_1459992 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8772 BOUND_VARIABLE_1459989) BOUND_VARIABLE_1459990) BOUND_VARIABLE_1459991) BOUND_VARIABLE_1459992) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459990) BOUND_VARIABLE_1459992)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459989) BOUND_VARIABLE_1459991)))))))))) (let ((_let_2857 (forall ((BOUND_VARIABLE_1459964 tptp.int) (BOUND_VARIABLE_1459965 tptp.int) (BOUND_VARIABLE_1459966 tptp.int) (BOUND_VARIABLE_1459967 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8773 BOUND_VARIABLE_1459964) BOUND_VARIABLE_1459965) BOUND_VARIABLE_1459966) BOUND_VARIABLE_1459967) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459965) BOUND_VARIABLE_1459967)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459964) BOUND_VARIABLE_1459966)))))))))) (let ((_let_2858 (forall ((BOUND_VARIABLE_1459939 tptp.int) (BOUND_VARIABLE_1459940 tptp.int) (BOUND_VARIABLE_1459941 tptp.int) (BOUND_VARIABLE_1459942 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8774 BOUND_VARIABLE_1459939) BOUND_VARIABLE_1459940) BOUND_VARIABLE_1459941) BOUND_VARIABLE_1459942) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459940) BOUND_VARIABLE_1459942)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459939) BOUND_VARIABLE_1459941)))))))))) (let ((_let_2859 (forall ((BOUND_VARIABLE_1459914 tptp.int) (BOUND_VARIABLE_1459915 tptp.int) (BOUND_VARIABLE_1459916 tptp.int) (BOUND_VARIABLE_1459917 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8775 BOUND_VARIABLE_1459914) BOUND_VARIABLE_1459915) BOUND_VARIABLE_1459916) BOUND_VARIABLE_1459917) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459915) BOUND_VARIABLE_1459917)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459914) BOUND_VARIABLE_1459916)))))))))) (let ((_let_2860 (forall ((BOUND_VARIABLE_1459889 tptp.int) (BOUND_VARIABLE_1459890 tptp.int) (BOUND_VARIABLE_1459891 tptp.int) (BOUND_VARIABLE_1459892 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8776 BOUND_VARIABLE_1459889) BOUND_VARIABLE_1459890) BOUND_VARIABLE_1459891) BOUND_VARIABLE_1459892) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459890) BOUND_VARIABLE_1459892)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459889) BOUND_VARIABLE_1459891)))))))))) (let ((_let_2861 (forall ((BOUND_VARIABLE_1459864 tptp.int) (BOUND_VARIABLE_1459865 tptp.int) (BOUND_VARIABLE_1459866 tptp.int) (BOUND_VARIABLE_1459867 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8777 BOUND_VARIABLE_1459864) BOUND_VARIABLE_1459865) BOUND_VARIABLE_1459866) BOUND_VARIABLE_1459867) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459865) BOUND_VARIABLE_1459867)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459864) BOUND_VARIABLE_1459866)))))))))) (let ((_let_2862 (forall ((BOUND_VARIABLE_1459839 tptp.int) (BOUND_VARIABLE_1459840 tptp.int) (BOUND_VARIABLE_1459841 tptp.int) (BOUND_VARIABLE_1459842 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8778 BOUND_VARIABLE_1459839) BOUND_VARIABLE_1459840) BOUND_VARIABLE_1459841) BOUND_VARIABLE_1459842) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459840) BOUND_VARIABLE_1459842)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459839) BOUND_VARIABLE_1459841)))))))))) (let ((_let_2863 (forall ((BOUND_VARIABLE_1459814 tptp.int) (BOUND_VARIABLE_1459815 tptp.int) (BOUND_VARIABLE_1459816 tptp.int) (BOUND_VARIABLE_1459817 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8779 BOUND_VARIABLE_1459814) BOUND_VARIABLE_1459815) BOUND_VARIABLE_1459816) BOUND_VARIABLE_1459817) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459815) BOUND_VARIABLE_1459817)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459814) BOUND_VARIABLE_1459816)))))))))) (let ((_let_2864 (forall ((BOUND_VARIABLE_1459789 tptp.int) (BOUND_VARIABLE_1459790 tptp.int) (BOUND_VARIABLE_1459791 tptp.int) (BOUND_VARIABLE_1459792 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8780 BOUND_VARIABLE_1459789) BOUND_VARIABLE_1459790) BOUND_VARIABLE_1459791) BOUND_VARIABLE_1459792) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459790) BOUND_VARIABLE_1459792)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459789) BOUND_VARIABLE_1459791)))))))))) (let ((_let_2865 (forall ((BOUND_VARIABLE_1459764 tptp.int) (BOUND_VARIABLE_1459765 tptp.int) (BOUND_VARIABLE_1459766 tptp.int) (BOUND_VARIABLE_1459767 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8781 BOUND_VARIABLE_1459764) BOUND_VARIABLE_1459765) BOUND_VARIABLE_1459766) BOUND_VARIABLE_1459767) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459765) BOUND_VARIABLE_1459767)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459764) BOUND_VARIABLE_1459766)))))))))) (let ((_let_2866 (forall ((BOUND_VARIABLE_1459739 tptp.int) (BOUND_VARIABLE_1459740 tptp.int) (BOUND_VARIABLE_1459741 tptp.int) (BOUND_VARIABLE_1459742 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8782 BOUND_VARIABLE_1459739) BOUND_VARIABLE_1459740) BOUND_VARIABLE_1459741) BOUND_VARIABLE_1459742) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459740) BOUND_VARIABLE_1459742)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459739) BOUND_VARIABLE_1459741)))))))))) (let ((_let_2867 (forall ((BOUND_VARIABLE_1459714 tptp.int) (BOUND_VARIABLE_1459715 tptp.int) (BOUND_VARIABLE_1459716 tptp.int) (BOUND_VARIABLE_1459717 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8783 BOUND_VARIABLE_1459714) BOUND_VARIABLE_1459715) BOUND_VARIABLE_1459716) BOUND_VARIABLE_1459717) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459715) BOUND_VARIABLE_1459717)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459714) BOUND_VARIABLE_1459716)))))))))) (let ((_let_2868 (forall ((BOUND_VARIABLE_1459689 tptp.int) (BOUND_VARIABLE_1459690 tptp.int) (BOUND_VARIABLE_1459691 tptp.int) (BOUND_VARIABLE_1459692 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8784 BOUND_VARIABLE_1459689) BOUND_VARIABLE_1459690) BOUND_VARIABLE_1459691) BOUND_VARIABLE_1459692) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459690) BOUND_VARIABLE_1459692)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459689) BOUND_VARIABLE_1459691)))))))))) (let ((_let_2869 (forall ((BOUND_VARIABLE_1459664 tptp.int) (BOUND_VARIABLE_1459665 tptp.int) (BOUND_VARIABLE_1459666 tptp.int) (BOUND_VARIABLE_1459667 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8785 BOUND_VARIABLE_1459664) BOUND_VARIABLE_1459665) BOUND_VARIABLE_1459666) BOUND_VARIABLE_1459667) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459665) BOUND_VARIABLE_1459667)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459664) BOUND_VARIABLE_1459666)))))))))) (let ((_let_2870 (forall ((BOUND_VARIABLE_1459639 tptp.int) (BOUND_VARIABLE_1459640 tptp.int) (BOUND_VARIABLE_1459641 tptp.int) (BOUND_VARIABLE_1459642 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8786 BOUND_VARIABLE_1459639) BOUND_VARIABLE_1459640) BOUND_VARIABLE_1459641) BOUND_VARIABLE_1459642) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459640) BOUND_VARIABLE_1459642)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459639) BOUND_VARIABLE_1459641)))))))))) (let ((_let_2871 (forall ((BOUND_VARIABLE_1459614 tptp.int) (BOUND_VARIABLE_1459615 tptp.int) (BOUND_VARIABLE_1459616 tptp.int) (BOUND_VARIABLE_1459617 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8787 BOUND_VARIABLE_1459614) BOUND_VARIABLE_1459615) BOUND_VARIABLE_1459616) BOUND_VARIABLE_1459617) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459615) BOUND_VARIABLE_1459617)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459614) BOUND_VARIABLE_1459616)))))))))) (let ((_let_2872 (forall ((BOUND_VARIABLE_1459589 tptp.int) (BOUND_VARIABLE_1459590 tptp.int) (BOUND_VARIABLE_1459591 tptp.int) (BOUND_VARIABLE_1459592 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8788 BOUND_VARIABLE_1459589) BOUND_VARIABLE_1459590) BOUND_VARIABLE_1459591) BOUND_VARIABLE_1459592) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459590) BOUND_VARIABLE_1459592)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459589) BOUND_VARIABLE_1459591)))))))))) (let ((_let_2873 (forall ((BOUND_VARIABLE_1459564 tptp.int) (BOUND_VARIABLE_1459565 tptp.int) (BOUND_VARIABLE_1459566 tptp.int) (BOUND_VARIABLE_1459567 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8789 BOUND_VARIABLE_1459564) BOUND_VARIABLE_1459565) BOUND_VARIABLE_1459566) BOUND_VARIABLE_1459567) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459565) BOUND_VARIABLE_1459567)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459564) BOUND_VARIABLE_1459566)))))))))) (let ((_let_2874 (forall ((BOUND_VARIABLE_1459539 tptp.int) (BOUND_VARIABLE_1459540 tptp.int) (BOUND_VARIABLE_1459541 tptp.int) (BOUND_VARIABLE_1459542 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8790 BOUND_VARIABLE_1459539) BOUND_VARIABLE_1459540) BOUND_VARIABLE_1459541) BOUND_VARIABLE_1459542) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459540) BOUND_VARIABLE_1459542)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459539) BOUND_VARIABLE_1459541)))))))))) (let ((_let_2875 (forall ((BOUND_VARIABLE_1459514 tptp.int) (BOUND_VARIABLE_1459515 tptp.int) (BOUND_VARIABLE_1459516 tptp.int) (BOUND_VARIABLE_1459517 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8791 BOUND_VARIABLE_1459514) BOUND_VARIABLE_1459515) BOUND_VARIABLE_1459516) BOUND_VARIABLE_1459517) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459515) BOUND_VARIABLE_1459517)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459514) BOUND_VARIABLE_1459516)))))))))) (let ((_let_2876 (forall ((BOUND_VARIABLE_1459489 tptp.int) (BOUND_VARIABLE_1459490 tptp.int) (BOUND_VARIABLE_1459491 tptp.int) (BOUND_VARIABLE_1459492 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8792 BOUND_VARIABLE_1459489) BOUND_VARIABLE_1459490) BOUND_VARIABLE_1459491) BOUND_VARIABLE_1459492) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459490) BOUND_VARIABLE_1459492)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459489) BOUND_VARIABLE_1459491)))))))))) (let ((_let_2877 (forall ((BOUND_VARIABLE_1459464 tptp.int) (BOUND_VARIABLE_1459465 tptp.int) (BOUND_VARIABLE_1459466 tptp.int) (BOUND_VARIABLE_1459467 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8793 BOUND_VARIABLE_1459464) BOUND_VARIABLE_1459465) BOUND_VARIABLE_1459466) BOUND_VARIABLE_1459467) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459465) BOUND_VARIABLE_1459467)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459464) BOUND_VARIABLE_1459466)))))))))) (let ((_let_2878 (forall ((BOUND_VARIABLE_1459439 tptp.int) (BOUND_VARIABLE_1459440 tptp.int) (BOUND_VARIABLE_1459441 tptp.int) (BOUND_VARIABLE_1459442 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8794 BOUND_VARIABLE_1459439) BOUND_VARIABLE_1459440) BOUND_VARIABLE_1459441) BOUND_VARIABLE_1459442) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459440) BOUND_VARIABLE_1459442)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459439) BOUND_VARIABLE_1459441)))))))))) (let ((_let_2879 (forall ((BOUND_VARIABLE_1459414 tptp.int) (BOUND_VARIABLE_1459415 tptp.int) (BOUND_VARIABLE_1459416 tptp.int) (BOUND_VARIABLE_1459417 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8795 BOUND_VARIABLE_1459414) BOUND_VARIABLE_1459415) BOUND_VARIABLE_1459416) BOUND_VARIABLE_1459417) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459415) BOUND_VARIABLE_1459417)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459414) BOUND_VARIABLE_1459416)))))))))) (let ((_let_2880 (forall ((BOUND_VARIABLE_1459389 tptp.int) (BOUND_VARIABLE_1459390 tptp.int) (BOUND_VARIABLE_1459391 tptp.int) (BOUND_VARIABLE_1459392 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8796 BOUND_VARIABLE_1459389) BOUND_VARIABLE_1459390) BOUND_VARIABLE_1459391) BOUND_VARIABLE_1459392) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459390) BOUND_VARIABLE_1459392)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459389) BOUND_VARIABLE_1459391)))))))))) (let ((_let_2881 (forall ((BOUND_VARIABLE_1459364 tptp.int) (BOUND_VARIABLE_1459365 tptp.int) (BOUND_VARIABLE_1459366 tptp.int) (BOUND_VARIABLE_1459367 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8797 BOUND_VARIABLE_1459364) BOUND_VARIABLE_1459365) BOUND_VARIABLE_1459366) BOUND_VARIABLE_1459367) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459365) BOUND_VARIABLE_1459367)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459364) BOUND_VARIABLE_1459366)))))))))) (let ((_let_2882 (forall ((BOUND_VARIABLE_1459339 tptp.int) (BOUND_VARIABLE_1459340 tptp.int) (BOUND_VARIABLE_1459341 tptp.int) (BOUND_VARIABLE_1459342 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8798 BOUND_VARIABLE_1459339) BOUND_VARIABLE_1459340) BOUND_VARIABLE_1459341) BOUND_VARIABLE_1459342) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459340) BOUND_VARIABLE_1459342)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459339) BOUND_VARIABLE_1459341)))))))))) (let ((_let_2883 (forall ((BOUND_VARIABLE_1459314 tptp.int) (BOUND_VARIABLE_1459315 tptp.int) (BOUND_VARIABLE_1459316 tptp.int) (BOUND_VARIABLE_1459317 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8799 BOUND_VARIABLE_1459314) BOUND_VARIABLE_1459315) BOUND_VARIABLE_1459316) BOUND_VARIABLE_1459317) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459315) BOUND_VARIABLE_1459317)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459314) BOUND_VARIABLE_1459316)))))))))) (let ((_let_2884 (forall ((BOUND_VARIABLE_1459289 tptp.int) (BOUND_VARIABLE_1459290 tptp.int) (BOUND_VARIABLE_1459291 tptp.int) (BOUND_VARIABLE_1459292 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8800 BOUND_VARIABLE_1459289) BOUND_VARIABLE_1459290) BOUND_VARIABLE_1459291) BOUND_VARIABLE_1459292) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459290) BOUND_VARIABLE_1459292)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459289) BOUND_VARIABLE_1459291)))))))))) (let ((_let_2885 (forall ((BOUND_VARIABLE_1459264 tptp.int) (BOUND_VARIABLE_1459265 tptp.int) (BOUND_VARIABLE_1459266 tptp.int) (BOUND_VARIABLE_1459267 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8801 BOUND_VARIABLE_1459264) BOUND_VARIABLE_1459265) BOUND_VARIABLE_1459266) BOUND_VARIABLE_1459267) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459265) BOUND_VARIABLE_1459267)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459264) BOUND_VARIABLE_1459266)))))))))) (let ((_let_2886 (forall ((BOUND_VARIABLE_1459239 tptp.int) (BOUND_VARIABLE_1459240 tptp.int) (BOUND_VARIABLE_1459241 tptp.int) (BOUND_VARIABLE_1459242 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8802 BOUND_VARIABLE_1459239) BOUND_VARIABLE_1459240) BOUND_VARIABLE_1459241) BOUND_VARIABLE_1459242) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459240) BOUND_VARIABLE_1459242)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459239) BOUND_VARIABLE_1459241)))))))))) (let ((_let_2887 (forall ((BOUND_VARIABLE_1459214 tptp.int) (BOUND_VARIABLE_1459215 tptp.int) (BOUND_VARIABLE_1459216 tptp.int) (BOUND_VARIABLE_1459217 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8803 BOUND_VARIABLE_1459214) BOUND_VARIABLE_1459215) BOUND_VARIABLE_1459216) BOUND_VARIABLE_1459217) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459215) BOUND_VARIABLE_1459217)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459214) BOUND_VARIABLE_1459216)))))))))) (let ((_let_2888 (forall ((BOUND_VARIABLE_1459189 tptp.int) (BOUND_VARIABLE_1459190 tptp.int) (BOUND_VARIABLE_1459191 tptp.int) (BOUND_VARIABLE_1459192 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8804 BOUND_VARIABLE_1459189) BOUND_VARIABLE_1459190) BOUND_VARIABLE_1459191) BOUND_VARIABLE_1459192) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459190) BOUND_VARIABLE_1459192)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459189) BOUND_VARIABLE_1459191)))))))))) (let ((_let_2889 (forall ((BOUND_VARIABLE_1459164 tptp.int) (BOUND_VARIABLE_1459165 tptp.int) (BOUND_VARIABLE_1459166 tptp.int) (BOUND_VARIABLE_1459167 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8805 BOUND_VARIABLE_1459164) BOUND_VARIABLE_1459165) BOUND_VARIABLE_1459166) BOUND_VARIABLE_1459167) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459165) BOUND_VARIABLE_1459167)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459164) BOUND_VARIABLE_1459166)))))))))) (let ((_let_2890 (forall ((BOUND_VARIABLE_1459139 tptp.int) (BOUND_VARIABLE_1459140 tptp.int) (BOUND_VARIABLE_1459141 tptp.int) (BOUND_VARIABLE_1459142 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8806 BOUND_VARIABLE_1459139) BOUND_VARIABLE_1459140) BOUND_VARIABLE_1459141) BOUND_VARIABLE_1459142) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459140) BOUND_VARIABLE_1459142)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459139) BOUND_VARIABLE_1459141)))))))))) (let ((_let_2891 (forall ((BOUND_VARIABLE_1459114 tptp.int) (BOUND_VARIABLE_1459115 tptp.int) (BOUND_VARIABLE_1459116 tptp.int) (BOUND_VARIABLE_1459117 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8807 BOUND_VARIABLE_1459114) BOUND_VARIABLE_1459115) BOUND_VARIABLE_1459116) BOUND_VARIABLE_1459117) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459115) BOUND_VARIABLE_1459117)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459114) BOUND_VARIABLE_1459116)))))))))) (let ((_let_2892 (forall ((BOUND_VARIABLE_1459089 tptp.int) (BOUND_VARIABLE_1459090 tptp.int) (BOUND_VARIABLE_1459091 tptp.int) (BOUND_VARIABLE_1459092 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8808 BOUND_VARIABLE_1459089) BOUND_VARIABLE_1459090) BOUND_VARIABLE_1459091) BOUND_VARIABLE_1459092) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459090) BOUND_VARIABLE_1459092)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459089) BOUND_VARIABLE_1459091)))))))))) (let ((_let_2893 (forall ((BOUND_VARIABLE_1459064 tptp.int) (BOUND_VARIABLE_1459065 tptp.int) (BOUND_VARIABLE_1459066 tptp.int) (BOUND_VARIABLE_1459067 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8809 BOUND_VARIABLE_1459064) BOUND_VARIABLE_1459065) BOUND_VARIABLE_1459066) BOUND_VARIABLE_1459067) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459065) BOUND_VARIABLE_1459067)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459064) BOUND_VARIABLE_1459066)))))))))) (let ((_let_2894 (forall ((BOUND_VARIABLE_1459039 tptp.int) (BOUND_VARIABLE_1459040 tptp.int) (BOUND_VARIABLE_1459041 tptp.int) (BOUND_VARIABLE_1459042 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8810 BOUND_VARIABLE_1459039) BOUND_VARIABLE_1459040) BOUND_VARIABLE_1459041) BOUND_VARIABLE_1459042) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459040) BOUND_VARIABLE_1459042)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459039) BOUND_VARIABLE_1459041)))))))))) (let ((_let_2895 (forall ((BOUND_VARIABLE_1459014 tptp.int) (BOUND_VARIABLE_1459015 tptp.int) (BOUND_VARIABLE_1459016 tptp.int) (BOUND_VARIABLE_1459017 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8811 BOUND_VARIABLE_1459014) BOUND_VARIABLE_1459015) BOUND_VARIABLE_1459016) BOUND_VARIABLE_1459017) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459015) BOUND_VARIABLE_1459017)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1459014) BOUND_VARIABLE_1459016)))))))))) (let ((_let_2896 (forall ((BOUND_VARIABLE_1458989 tptp.int) (BOUND_VARIABLE_1458990 tptp.int) (BOUND_VARIABLE_1458991 tptp.int) (BOUND_VARIABLE_1458992 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8812 BOUND_VARIABLE_1458989) BOUND_VARIABLE_1458990) BOUND_VARIABLE_1458991) BOUND_VARIABLE_1458992) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458990) BOUND_VARIABLE_1458992)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458989) BOUND_VARIABLE_1458991)))))))))) (let ((_let_2897 (forall ((BOUND_VARIABLE_1458964 tptp.int) (BOUND_VARIABLE_1458965 tptp.int) (BOUND_VARIABLE_1458966 tptp.int) (BOUND_VARIABLE_1458967 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8813 BOUND_VARIABLE_1458964) BOUND_VARIABLE_1458965) BOUND_VARIABLE_1458966) BOUND_VARIABLE_1458967) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458965) BOUND_VARIABLE_1458967)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458964) BOUND_VARIABLE_1458966)))))))))) (let ((_let_2898 (forall ((BOUND_VARIABLE_1458939 tptp.int) (BOUND_VARIABLE_1458940 tptp.int) (BOUND_VARIABLE_1458941 tptp.int) (BOUND_VARIABLE_1458942 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8814 BOUND_VARIABLE_1458939) BOUND_VARIABLE_1458940) BOUND_VARIABLE_1458941) BOUND_VARIABLE_1458942) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458940) BOUND_VARIABLE_1458942)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458939) BOUND_VARIABLE_1458941)))))))))) (let ((_let_2899 (forall ((BOUND_VARIABLE_1458914 tptp.int) (BOUND_VARIABLE_1458915 tptp.int) (BOUND_VARIABLE_1458916 tptp.int) (BOUND_VARIABLE_1458917 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8815 BOUND_VARIABLE_1458914) BOUND_VARIABLE_1458915) BOUND_VARIABLE_1458916) BOUND_VARIABLE_1458917) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458915) BOUND_VARIABLE_1458917)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458914) BOUND_VARIABLE_1458916)))))))))) (let ((_let_2900 (forall ((BOUND_VARIABLE_1458889 tptp.int) (BOUND_VARIABLE_1458890 tptp.int) (BOUND_VARIABLE_1458891 tptp.int) (BOUND_VARIABLE_1458892 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8816 BOUND_VARIABLE_1458889) BOUND_VARIABLE_1458890) BOUND_VARIABLE_1458891) BOUND_VARIABLE_1458892) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458890) BOUND_VARIABLE_1458892)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458889) BOUND_VARIABLE_1458891)))))))))) (let ((_let_2901 (forall ((BOUND_VARIABLE_1458864 tptp.int) (BOUND_VARIABLE_1458865 tptp.int) (BOUND_VARIABLE_1458866 tptp.int) (BOUND_VARIABLE_1458867 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8817 BOUND_VARIABLE_1458864) BOUND_VARIABLE_1458865) BOUND_VARIABLE_1458866) BOUND_VARIABLE_1458867) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458865) BOUND_VARIABLE_1458867)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458864) BOUND_VARIABLE_1458866)))))))))) (let ((_let_2902 (forall ((BOUND_VARIABLE_1458839 tptp.int) (BOUND_VARIABLE_1458840 tptp.int) (BOUND_VARIABLE_1458841 tptp.int) (BOUND_VARIABLE_1458842 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8818 BOUND_VARIABLE_1458839) BOUND_VARIABLE_1458840) BOUND_VARIABLE_1458841) BOUND_VARIABLE_1458842) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458840) BOUND_VARIABLE_1458842)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458839) BOUND_VARIABLE_1458841)))))))))) (let ((_let_2903 (forall ((BOUND_VARIABLE_1458814 tptp.int) (BOUND_VARIABLE_1458815 tptp.int) (BOUND_VARIABLE_1458816 tptp.int) (BOUND_VARIABLE_1458817 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8819 BOUND_VARIABLE_1458814) BOUND_VARIABLE_1458815) BOUND_VARIABLE_1458816) BOUND_VARIABLE_1458817) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458815) BOUND_VARIABLE_1458817)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458814) BOUND_VARIABLE_1458816)))))))))) (let ((_let_2904 (forall ((BOUND_VARIABLE_1458789 tptp.int) (BOUND_VARIABLE_1458790 tptp.int) (BOUND_VARIABLE_1458791 tptp.int) (BOUND_VARIABLE_1458792 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8820 BOUND_VARIABLE_1458789) BOUND_VARIABLE_1458790) BOUND_VARIABLE_1458791) BOUND_VARIABLE_1458792) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458790) BOUND_VARIABLE_1458792)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458789) BOUND_VARIABLE_1458791)))))))))) (let ((_let_2905 (forall ((BOUND_VARIABLE_1544270 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1458778 tptp.nat) (BOUND_VARIABLE_1544269 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1458780 tptp.nat)) (= (ho_7508 (ho_7761 (ho_8823 (ho_8822 k_8821 BOUND_VARIABLE_1544270) BOUND_VARIABLE_1458778) BOUND_VARIABLE_1544269) BOUND_VARIABLE_1458780) (ho_7516 (ho_7519 k_7522 (ho_7508 BOUND_VARIABLE_1544270 BOUND_VARIABLE_1458778)) (ho_7508 BOUND_VARIABLE_1544269 BOUND_VARIABLE_1458780)))))) (let ((_let_2906 (forall ((BOUND_VARIABLE_1544295 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1458752 tptp.nat) (BOUND_VARIABLE_1544291 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1458754 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7466 BOUND_VARIABLE_1544295 BOUND_VARIABLE_1458752)) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7466 BOUND_VARIABLE_1544291 BOUND_VARIABLE_1458754)) _let_2))) (ho_7466 (ho_8827 (ho_8826 (ho_8825 k_8824 BOUND_VARIABLE_1544295) BOUND_VARIABLE_1458752) BOUND_VARIABLE_1544291) BOUND_VARIABLE_1458754)))))))) (let ((_let_2907 (forall ((BOUND_VARIABLE_1544330 |u_(-> tptp.complex tptp.complex)|) (BOUND_VARIABLE_1458725 tptp.complex) (BOUND_VARIABLE_1544329 |u_(-> tptp.complex tptp.complex)|) (BOUND_VARIABLE_1458727 tptp.complex)) (let ((_let_1 (ho_7958 BOUND_VARIABLE_1544329 BOUND_VARIABLE_1458727))) (let ((_let_2 (ho_7730 k_7729 _let_1))) (let ((_let_3 (ho_7958 BOUND_VARIABLE_1544330 BOUND_VARIABLE_1458725))) (let ((_let_4 (ho_7519 k_7522 (ho_7730 k_7733 _let_3)))) (let ((_let_5 (ho_7730 k_7733 _let_1))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7729 _let_3)))) (= (ho_7958 (ho_8831 (ho_8830 (ho_8829 k_8828 BOUND_VARIABLE_1544330) BOUND_VARIABLE_1458725) BOUND_VARIABLE_1544329) BOUND_VARIABLE_1458727) (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_2)) (ho_7516 k_7521 (ho_7516 _let_4 _let_5)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_6 _let_5)) (ho_7516 _let_4 _let_2))))))))))))) (let ((_let_2908 (forall ((BOUND_VARIABLE_1544374 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1458713 tptp.int) (BOUND_VARIABLE_1544373 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1458715 tptp.int)) (= (ho_7459 (ho_8835 (ho_8834 (ho_8833 k_8832 BOUND_VARIABLE_1544374) BOUND_VARIABLE_1458713) BOUND_VARIABLE_1544373) BOUND_VARIABLE_1458715) (ho_7459 (ho_7461 k_7472 (ho_7459 BOUND_VARIABLE_1544374 BOUND_VARIABLE_1458713)) (ho_7459 BOUND_VARIABLE_1544373 BOUND_VARIABLE_1458715)))))) (let ((_let_2909 (forall ((BOUND_VARIABLE_1458687 tptp.int) (BOUND_VARIABLE_1458688 tptp.int) (BOUND_VARIABLE_1458689 tptp.int) (BOUND_VARIABLE_1458690 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8836 BOUND_VARIABLE_1458687) BOUND_VARIABLE_1458688) BOUND_VARIABLE_1458689) BOUND_VARIABLE_1458690) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458688) BOUND_VARIABLE_1458690)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458687) BOUND_VARIABLE_1458689)))))))))) (let ((_let_2910 (forall ((BOUND_VARIABLE_1458662 tptp.int) (BOUND_VARIABLE_1458663 tptp.int) (BOUND_VARIABLE_1458664 tptp.int) (BOUND_VARIABLE_1458665 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8837 BOUND_VARIABLE_1458662) BOUND_VARIABLE_1458663) BOUND_VARIABLE_1458664) BOUND_VARIABLE_1458665) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458663) BOUND_VARIABLE_1458665)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458662) BOUND_VARIABLE_1458664)))))))))) (let ((_let_2911 (forall ((BOUND_VARIABLE_1458637 tptp.int) (BOUND_VARIABLE_1458638 tptp.int) (BOUND_VARIABLE_1458639 tptp.int) (BOUND_VARIABLE_1458640 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8838 BOUND_VARIABLE_1458637) BOUND_VARIABLE_1458638) BOUND_VARIABLE_1458639) BOUND_VARIABLE_1458640) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458638) BOUND_VARIABLE_1458640)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458637) BOUND_VARIABLE_1458639)))))))))) (let ((_let_2912 (forall ((BOUND_VARIABLE_1458612 tptp.int) (BOUND_VARIABLE_1458613 tptp.int) (BOUND_VARIABLE_1458614 tptp.int) (BOUND_VARIABLE_1458615 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8839 BOUND_VARIABLE_1458612) BOUND_VARIABLE_1458613) BOUND_VARIABLE_1458614) BOUND_VARIABLE_1458615) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458613) BOUND_VARIABLE_1458615)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458612) BOUND_VARIABLE_1458614)))))))))) (let ((_let_2913 (forall ((BOUND_VARIABLE_1458587 tptp.int) (BOUND_VARIABLE_1458588 tptp.int) (BOUND_VARIABLE_1458589 tptp.int) (BOUND_VARIABLE_1458590 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8840 BOUND_VARIABLE_1458587) BOUND_VARIABLE_1458588) BOUND_VARIABLE_1458589) BOUND_VARIABLE_1458590) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458588) BOUND_VARIABLE_1458590)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458587) BOUND_VARIABLE_1458589)))))))))) (let ((_let_2914 (forall ((BOUND_VARIABLE_1458562 tptp.int) (BOUND_VARIABLE_1458563 tptp.int) (BOUND_VARIABLE_1458564 tptp.int) (BOUND_VARIABLE_1458565 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8841 BOUND_VARIABLE_1458562) BOUND_VARIABLE_1458563) BOUND_VARIABLE_1458564) BOUND_VARIABLE_1458565) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458563) BOUND_VARIABLE_1458565)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458562) BOUND_VARIABLE_1458564)))))))))) (let ((_let_2915 (forall ((BOUND_VARIABLE_1458537 tptp.int) (BOUND_VARIABLE_1458538 tptp.int) (BOUND_VARIABLE_1458539 tptp.int) (BOUND_VARIABLE_1458540 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8842 BOUND_VARIABLE_1458537) BOUND_VARIABLE_1458538) BOUND_VARIABLE_1458539) BOUND_VARIABLE_1458540) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458538) BOUND_VARIABLE_1458540)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458537) BOUND_VARIABLE_1458539)))))))))) (let ((_let_2916 (forall ((BOUND_VARIABLE_1458512 tptp.int) (BOUND_VARIABLE_1458513 tptp.int) (BOUND_VARIABLE_1458514 tptp.int) (BOUND_VARIABLE_1458515 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8843 BOUND_VARIABLE_1458512) BOUND_VARIABLE_1458513) BOUND_VARIABLE_1458514) BOUND_VARIABLE_1458515) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458513) BOUND_VARIABLE_1458515)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458512) BOUND_VARIABLE_1458514)))))))))) (let ((_let_2917 (forall ((BOUND_VARIABLE_1458487 tptp.int) (BOUND_VARIABLE_1458488 tptp.int) (BOUND_VARIABLE_1458489 tptp.int) (BOUND_VARIABLE_1458490 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8844 BOUND_VARIABLE_1458487) BOUND_VARIABLE_1458488) BOUND_VARIABLE_1458489) BOUND_VARIABLE_1458490) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458488) BOUND_VARIABLE_1458490)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458487) BOUND_VARIABLE_1458489)))))))))) (let ((_let_2918 (forall ((BOUND_VARIABLE_1458462 tptp.int) (BOUND_VARIABLE_1458463 tptp.int) (BOUND_VARIABLE_1458464 tptp.int) (BOUND_VARIABLE_1458465 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8845 BOUND_VARIABLE_1458462) BOUND_VARIABLE_1458463) BOUND_VARIABLE_1458464) BOUND_VARIABLE_1458465) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458463) BOUND_VARIABLE_1458465)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458462) BOUND_VARIABLE_1458464)))))))))) (let ((_let_2919 (forall ((BOUND_VARIABLE_1458437 tptp.int) (BOUND_VARIABLE_1458438 tptp.int) (BOUND_VARIABLE_1458439 tptp.int) (BOUND_VARIABLE_1458440 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8846 BOUND_VARIABLE_1458437) BOUND_VARIABLE_1458438) BOUND_VARIABLE_1458439) BOUND_VARIABLE_1458440) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458438) BOUND_VARIABLE_1458440)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458437) BOUND_VARIABLE_1458439)))))))))) (let ((_let_2920 (forall ((BOUND_VARIABLE_1458412 tptp.int) (BOUND_VARIABLE_1458413 tptp.int) (BOUND_VARIABLE_1458414 tptp.int) (BOUND_VARIABLE_1458415 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8847 BOUND_VARIABLE_1458412) BOUND_VARIABLE_1458413) BOUND_VARIABLE_1458414) BOUND_VARIABLE_1458415) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458413) BOUND_VARIABLE_1458415)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458412) BOUND_VARIABLE_1458414)))))))))) (let ((_let_2921 (forall ((BOUND_VARIABLE_1458387 tptp.int) (BOUND_VARIABLE_1458388 tptp.int) (BOUND_VARIABLE_1458389 tptp.int) (BOUND_VARIABLE_1458390 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8848 BOUND_VARIABLE_1458387) BOUND_VARIABLE_1458388) BOUND_VARIABLE_1458389) BOUND_VARIABLE_1458390) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458388) BOUND_VARIABLE_1458390)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458387) BOUND_VARIABLE_1458389)))))))))) (let ((_let_2922 (forall ((BOUND_VARIABLE_1458362 tptp.int) (BOUND_VARIABLE_1458363 tptp.int) (BOUND_VARIABLE_1458364 tptp.int) (BOUND_VARIABLE_1458365 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8849 BOUND_VARIABLE_1458362) BOUND_VARIABLE_1458363) BOUND_VARIABLE_1458364) BOUND_VARIABLE_1458365) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458363) BOUND_VARIABLE_1458365)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458362) BOUND_VARIABLE_1458364)))))))))) (let ((_let_2923 (forall ((BOUND_VARIABLE_1458337 tptp.int) (BOUND_VARIABLE_1458338 tptp.int) (BOUND_VARIABLE_1458339 tptp.int) (BOUND_VARIABLE_1458340 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8850 BOUND_VARIABLE_1458337) BOUND_VARIABLE_1458338) BOUND_VARIABLE_1458339) BOUND_VARIABLE_1458340) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458338) BOUND_VARIABLE_1458340)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458337) BOUND_VARIABLE_1458339)))))))))) (let ((_let_2924 (forall ((BOUND_VARIABLE_1458312 tptp.int) (BOUND_VARIABLE_1458313 tptp.int) (BOUND_VARIABLE_1458314 tptp.int) (BOUND_VARIABLE_1458315 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8851 BOUND_VARIABLE_1458312) BOUND_VARIABLE_1458313) BOUND_VARIABLE_1458314) BOUND_VARIABLE_1458315) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458313) BOUND_VARIABLE_1458315)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458312) BOUND_VARIABLE_1458314)))))))))) (let ((_let_2925 (forall ((BOUND_VARIABLE_1458287 tptp.int) (BOUND_VARIABLE_1458288 tptp.int) (BOUND_VARIABLE_1458289 tptp.int) (BOUND_VARIABLE_1458290 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8852 BOUND_VARIABLE_1458287) BOUND_VARIABLE_1458288) BOUND_VARIABLE_1458289) BOUND_VARIABLE_1458290) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458288) BOUND_VARIABLE_1458290)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458287) BOUND_VARIABLE_1458289)))))))))) (let ((_let_2926 (forall ((BOUND_VARIABLE_1458262 tptp.int) (BOUND_VARIABLE_1458263 tptp.int) (BOUND_VARIABLE_1458264 tptp.int) (BOUND_VARIABLE_1458265 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8853 BOUND_VARIABLE_1458262) BOUND_VARIABLE_1458263) BOUND_VARIABLE_1458264) BOUND_VARIABLE_1458265) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458263) BOUND_VARIABLE_1458265)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458262) BOUND_VARIABLE_1458264)))))))))) (let ((_let_2927 (forall ((BOUND_VARIABLE_1458237 tptp.int) (BOUND_VARIABLE_1458238 tptp.int) (BOUND_VARIABLE_1458239 tptp.int) (BOUND_VARIABLE_1458240 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8854 BOUND_VARIABLE_1458237) BOUND_VARIABLE_1458238) BOUND_VARIABLE_1458239) BOUND_VARIABLE_1458240) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458238) BOUND_VARIABLE_1458240)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458237) BOUND_VARIABLE_1458239)))))))))) (let ((_let_2928 (forall ((BOUND_VARIABLE_1458212 tptp.int) (BOUND_VARIABLE_1458213 tptp.int) (BOUND_VARIABLE_1458214 tptp.int) (BOUND_VARIABLE_1458215 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8855 BOUND_VARIABLE_1458212) BOUND_VARIABLE_1458213) BOUND_VARIABLE_1458214) BOUND_VARIABLE_1458215) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458213) BOUND_VARIABLE_1458215)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458212) BOUND_VARIABLE_1458214)))))))))) (let ((_let_2929 (forall ((BOUND_VARIABLE_1458187 tptp.int) (BOUND_VARIABLE_1458188 tptp.int) (BOUND_VARIABLE_1458189 tptp.int) (BOUND_VARIABLE_1458190 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8856 BOUND_VARIABLE_1458187) BOUND_VARIABLE_1458188) BOUND_VARIABLE_1458189) BOUND_VARIABLE_1458190) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458188) BOUND_VARIABLE_1458190)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458187) BOUND_VARIABLE_1458189)))))))))) (let ((_let_2930 (forall ((BOUND_VARIABLE_1458162 tptp.int) (BOUND_VARIABLE_1458163 tptp.int) (BOUND_VARIABLE_1458164 tptp.int) (BOUND_VARIABLE_1458165 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8857 BOUND_VARIABLE_1458162) BOUND_VARIABLE_1458163) BOUND_VARIABLE_1458164) BOUND_VARIABLE_1458165) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458163) BOUND_VARIABLE_1458165)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458162) BOUND_VARIABLE_1458164)))))))))) (let ((_let_2931 (forall ((BOUND_VARIABLE_1458137 tptp.int) (BOUND_VARIABLE_1458138 tptp.int) (BOUND_VARIABLE_1458139 tptp.int) (BOUND_VARIABLE_1458140 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8858 BOUND_VARIABLE_1458137) BOUND_VARIABLE_1458138) BOUND_VARIABLE_1458139) BOUND_VARIABLE_1458140) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458138) BOUND_VARIABLE_1458140)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458137) BOUND_VARIABLE_1458139)))))))))) (let ((_let_2932 (forall ((BOUND_VARIABLE_1458112 tptp.int) (BOUND_VARIABLE_1458113 tptp.int) (BOUND_VARIABLE_1458114 tptp.int) (BOUND_VARIABLE_1458115 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8859 BOUND_VARIABLE_1458112) BOUND_VARIABLE_1458113) BOUND_VARIABLE_1458114) BOUND_VARIABLE_1458115) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458113) BOUND_VARIABLE_1458115)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458112) BOUND_VARIABLE_1458114)))))))))) (let ((_let_2933 (forall ((BOUND_VARIABLE_1458087 tptp.int) (BOUND_VARIABLE_1458088 tptp.int) (BOUND_VARIABLE_1458089 tptp.int) (BOUND_VARIABLE_1458090 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8860 BOUND_VARIABLE_1458087) BOUND_VARIABLE_1458088) BOUND_VARIABLE_1458089) BOUND_VARIABLE_1458090) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458088) BOUND_VARIABLE_1458090)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458087) BOUND_VARIABLE_1458089)))))))))) (let ((_let_2934 (forall ((BOUND_VARIABLE_1458062 tptp.int) (BOUND_VARIABLE_1458063 tptp.int) (BOUND_VARIABLE_1458064 tptp.int) (BOUND_VARIABLE_1458065 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8861 BOUND_VARIABLE_1458062) BOUND_VARIABLE_1458063) BOUND_VARIABLE_1458064) BOUND_VARIABLE_1458065) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458063) BOUND_VARIABLE_1458065)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458062) BOUND_VARIABLE_1458064)))))))))) (let ((_let_2935 (forall ((BOUND_VARIABLE_1458037 tptp.int) (BOUND_VARIABLE_1458038 tptp.int) (BOUND_VARIABLE_1458039 tptp.int) (BOUND_VARIABLE_1458040 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8862 BOUND_VARIABLE_1458037) BOUND_VARIABLE_1458038) BOUND_VARIABLE_1458039) BOUND_VARIABLE_1458040) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458038) BOUND_VARIABLE_1458040)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458037) BOUND_VARIABLE_1458039)))))))))) (let ((_let_2936 (forall ((BOUND_VARIABLE_1458012 tptp.int) (BOUND_VARIABLE_1458013 tptp.int) (BOUND_VARIABLE_1458014 tptp.int) (BOUND_VARIABLE_1458015 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8863 BOUND_VARIABLE_1458012) BOUND_VARIABLE_1458013) BOUND_VARIABLE_1458014) BOUND_VARIABLE_1458015) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458013) BOUND_VARIABLE_1458015)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1458012) BOUND_VARIABLE_1458014)))))))))) (let ((_let_2937 (forall ((BOUND_VARIABLE_1457987 tptp.int) (BOUND_VARIABLE_1457988 tptp.int) (BOUND_VARIABLE_1457989 tptp.int) (BOUND_VARIABLE_1457990 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8864 BOUND_VARIABLE_1457987) BOUND_VARIABLE_1457988) BOUND_VARIABLE_1457989) BOUND_VARIABLE_1457990) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457988) BOUND_VARIABLE_1457990)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457987) BOUND_VARIABLE_1457989)))))))))) (let ((_let_2938 (forall ((BOUND_VARIABLE_1457962 tptp.int) (BOUND_VARIABLE_1457963 tptp.int) (BOUND_VARIABLE_1457964 tptp.int) (BOUND_VARIABLE_1457965 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8865 BOUND_VARIABLE_1457962) BOUND_VARIABLE_1457963) BOUND_VARIABLE_1457964) BOUND_VARIABLE_1457965) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457963) BOUND_VARIABLE_1457965)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457962) BOUND_VARIABLE_1457964)))))))))) (let ((_let_2939 (forall ((BOUND_VARIABLE_1457937 tptp.int) (BOUND_VARIABLE_1457938 tptp.int) (BOUND_VARIABLE_1457939 tptp.int) (BOUND_VARIABLE_1457940 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8866 BOUND_VARIABLE_1457937) BOUND_VARIABLE_1457938) BOUND_VARIABLE_1457939) BOUND_VARIABLE_1457940) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457938) BOUND_VARIABLE_1457940)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457937) BOUND_VARIABLE_1457939)))))))))) (let ((_let_2940 (forall ((BOUND_VARIABLE_1457912 tptp.int) (BOUND_VARIABLE_1457913 tptp.int) (BOUND_VARIABLE_1457914 tptp.int) (BOUND_VARIABLE_1457915 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8867 BOUND_VARIABLE_1457912) BOUND_VARIABLE_1457913) BOUND_VARIABLE_1457914) BOUND_VARIABLE_1457915) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457913) BOUND_VARIABLE_1457915)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457912) BOUND_VARIABLE_1457914)))))))))) (let ((_let_2941 (forall ((BOUND_VARIABLE_1457887 tptp.int) (BOUND_VARIABLE_1457888 tptp.int) (BOUND_VARIABLE_1457889 tptp.int) (BOUND_VARIABLE_1457890 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8868 BOUND_VARIABLE_1457887) BOUND_VARIABLE_1457888) BOUND_VARIABLE_1457889) BOUND_VARIABLE_1457890) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457888) BOUND_VARIABLE_1457890)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457887) BOUND_VARIABLE_1457889)))))))))) (let ((_let_2942 (forall ((BOUND_VARIABLE_1457862 tptp.int) (BOUND_VARIABLE_1457863 tptp.int) (BOUND_VARIABLE_1457864 tptp.int) (BOUND_VARIABLE_1457865 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8869 BOUND_VARIABLE_1457862) BOUND_VARIABLE_1457863) BOUND_VARIABLE_1457864) BOUND_VARIABLE_1457865) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457863) BOUND_VARIABLE_1457865)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457862) BOUND_VARIABLE_1457864)))))))))) (let ((_let_2943 (forall ((BOUND_VARIABLE_1457837 tptp.int) (BOUND_VARIABLE_1457838 tptp.int) (BOUND_VARIABLE_1457839 tptp.int) (BOUND_VARIABLE_1457840 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8870 BOUND_VARIABLE_1457837) BOUND_VARIABLE_1457838) BOUND_VARIABLE_1457839) BOUND_VARIABLE_1457840) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457838) BOUND_VARIABLE_1457840)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457837) BOUND_VARIABLE_1457839)))))))))) (let ((_let_2944 (forall ((BOUND_VARIABLE_1457812 tptp.int) (BOUND_VARIABLE_1457813 tptp.int) (BOUND_VARIABLE_1457814 tptp.int) (BOUND_VARIABLE_1457815 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8871 BOUND_VARIABLE_1457812) BOUND_VARIABLE_1457813) BOUND_VARIABLE_1457814) BOUND_VARIABLE_1457815) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457813) BOUND_VARIABLE_1457815)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457812) BOUND_VARIABLE_1457814)))))))))) (let ((_let_2945 (forall ((BOUND_VARIABLE_1457787 tptp.int) (BOUND_VARIABLE_1457788 tptp.int) (BOUND_VARIABLE_1457789 tptp.int) (BOUND_VARIABLE_1457790 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8872 BOUND_VARIABLE_1457787) BOUND_VARIABLE_1457788) BOUND_VARIABLE_1457789) BOUND_VARIABLE_1457790) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457788) BOUND_VARIABLE_1457790)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457787) BOUND_VARIABLE_1457789)))))))))) (let ((_let_2946 (forall ((BOUND_VARIABLE_1457762 tptp.int) (BOUND_VARIABLE_1457763 tptp.int) (BOUND_VARIABLE_1457764 tptp.int) (BOUND_VARIABLE_1457765 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8873 BOUND_VARIABLE_1457762) BOUND_VARIABLE_1457763) BOUND_VARIABLE_1457764) BOUND_VARIABLE_1457765) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457763) BOUND_VARIABLE_1457765)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457762) BOUND_VARIABLE_1457764)))))))))) (let ((_let_2947 (forall ((BOUND_VARIABLE_1457737 tptp.int) (BOUND_VARIABLE_1457738 tptp.int) (BOUND_VARIABLE_1457739 tptp.int) (BOUND_VARIABLE_1457740 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8874 BOUND_VARIABLE_1457737) BOUND_VARIABLE_1457738) BOUND_VARIABLE_1457739) BOUND_VARIABLE_1457740) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457738) BOUND_VARIABLE_1457740)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457737) BOUND_VARIABLE_1457739)))))))))) (let ((_let_2948 (forall ((BOUND_VARIABLE_1457712 tptp.int) (BOUND_VARIABLE_1457713 tptp.int) (BOUND_VARIABLE_1457714 tptp.int) (BOUND_VARIABLE_1457715 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8875 BOUND_VARIABLE_1457712) BOUND_VARIABLE_1457713) BOUND_VARIABLE_1457714) BOUND_VARIABLE_1457715) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457713) BOUND_VARIABLE_1457715)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457712) BOUND_VARIABLE_1457714)))))))))) (let ((_let_2949 (forall ((BOUND_VARIABLE_1457687 tptp.int) (BOUND_VARIABLE_1457688 tptp.int) (BOUND_VARIABLE_1457689 tptp.int) (BOUND_VARIABLE_1457690 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8876 BOUND_VARIABLE_1457687) BOUND_VARIABLE_1457688) BOUND_VARIABLE_1457689) BOUND_VARIABLE_1457690) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457688) BOUND_VARIABLE_1457690)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457687) BOUND_VARIABLE_1457689)))))))))) (let ((_let_2950 (forall ((BOUND_VARIABLE_1457662 tptp.int) (BOUND_VARIABLE_1457663 tptp.int) (BOUND_VARIABLE_1457664 tptp.int) (BOUND_VARIABLE_1457665 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8877 BOUND_VARIABLE_1457662) BOUND_VARIABLE_1457663) BOUND_VARIABLE_1457664) BOUND_VARIABLE_1457665) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457663) BOUND_VARIABLE_1457665)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457662) BOUND_VARIABLE_1457664)))))))))) (let ((_let_2951 (forall ((BOUND_VARIABLE_1457637 tptp.int) (BOUND_VARIABLE_1457638 tptp.int) (BOUND_VARIABLE_1457639 tptp.int) (BOUND_VARIABLE_1457640 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8878 BOUND_VARIABLE_1457637) BOUND_VARIABLE_1457638) BOUND_VARIABLE_1457639) BOUND_VARIABLE_1457640) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457638) BOUND_VARIABLE_1457640)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457637) BOUND_VARIABLE_1457639)))))))))) (let ((_let_2952 (forall ((BOUND_VARIABLE_1457612 tptp.int) (BOUND_VARIABLE_1457613 tptp.int) (BOUND_VARIABLE_1457614 tptp.int) (BOUND_VARIABLE_1457615 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8879 BOUND_VARIABLE_1457612) BOUND_VARIABLE_1457613) BOUND_VARIABLE_1457614) BOUND_VARIABLE_1457615) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457613) BOUND_VARIABLE_1457615)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457612) BOUND_VARIABLE_1457614)))))))))) (let ((_let_2953 (forall ((BOUND_VARIABLE_1457587 tptp.int) (BOUND_VARIABLE_1457588 tptp.int) (BOUND_VARIABLE_1457589 tptp.int) (BOUND_VARIABLE_1457590 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8880 BOUND_VARIABLE_1457587) BOUND_VARIABLE_1457588) BOUND_VARIABLE_1457589) BOUND_VARIABLE_1457590) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457588) BOUND_VARIABLE_1457590)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457587) BOUND_VARIABLE_1457589)))))))))) (let ((_let_2954 (forall ((BOUND_VARIABLE_1457562 tptp.int) (BOUND_VARIABLE_1457563 tptp.int) (BOUND_VARIABLE_1457564 tptp.int) (BOUND_VARIABLE_1457565 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8881 BOUND_VARIABLE_1457562) BOUND_VARIABLE_1457563) BOUND_VARIABLE_1457564) BOUND_VARIABLE_1457565) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457563) BOUND_VARIABLE_1457565)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457562) BOUND_VARIABLE_1457564)))))))))) (let ((_let_2955 (forall ((BOUND_VARIABLE_1457537 tptp.int) (BOUND_VARIABLE_1457538 tptp.int) (BOUND_VARIABLE_1457539 tptp.int) (BOUND_VARIABLE_1457540 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8882 BOUND_VARIABLE_1457537) BOUND_VARIABLE_1457538) BOUND_VARIABLE_1457539) BOUND_VARIABLE_1457540) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457538) BOUND_VARIABLE_1457540)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457537) BOUND_VARIABLE_1457539)))))))))) (let ((_let_2956 (forall ((BOUND_VARIABLE_1457512 tptp.int) (BOUND_VARIABLE_1457513 tptp.int) (BOUND_VARIABLE_1457514 tptp.int) (BOUND_VARIABLE_1457515 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8883 BOUND_VARIABLE_1457512) BOUND_VARIABLE_1457513) BOUND_VARIABLE_1457514) BOUND_VARIABLE_1457515) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457513) BOUND_VARIABLE_1457515)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457512) BOUND_VARIABLE_1457514)))))))))) (let ((_let_2957 (forall ((BOUND_VARIABLE_1457487 tptp.int) (BOUND_VARIABLE_1457488 tptp.int) (BOUND_VARIABLE_1457489 tptp.int) (BOUND_VARIABLE_1457490 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8884 BOUND_VARIABLE_1457487) BOUND_VARIABLE_1457488) BOUND_VARIABLE_1457489) BOUND_VARIABLE_1457490) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457488) BOUND_VARIABLE_1457490)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457487) BOUND_VARIABLE_1457489)))))))))) (let ((_let_2958 (forall ((BOUND_VARIABLE_1457462 tptp.int) (BOUND_VARIABLE_1457463 tptp.int) (BOUND_VARIABLE_1457464 tptp.int) (BOUND_VARIABLE_1457465 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8885 BOUND_VARIABLE_1457462) BOUND_VARIABLE_1457463) BOUND_VARIABLE_1457464) BOUND_VARIABLE_1457465) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457463) BOUND_VARIABLE_1457465)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457462) BOUND_VARIABLE_1457464)))))))))) (let ((_let_2959 (forall ((BOUND_VARIABLE_1457437 tptp.int) (BOUND_VARIABLE_1457438 tptp.int) (BOUND_VARIABLE_1457439 tptp.int) (BOUND_VARIABLE_1457440 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8886 BOUND_VARIABLE_1457437) BOUND_VARIABLE_1457438) BOUND_VARIABLE_1457439) BOUND_VARIABLE_1457440) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457438) BOUND_VARIABLE_1457440)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457437) BOUND_VARIABLE_1457439)))))))))) (let ((_let_2960 (forall ((BOUND_VARIABLE_1457412 tptp.int) (BOUND_VARIABLE_1457413 tptp.int) (BOUND_VARIABLE_1457414 tptp.int) (BOUND_VARIABLE_1457415 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8887 BOUND_VARIABLE_1457412) BOUND_VARIABLE_1457413) BOUND_VARIABLE_1457414) BOUND_VARIABLE_1457415) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457413) BOUND_VARIABLE_1457415)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457412) BOUND_VARIABLE_1457414)))))))))) (let ((_let_2961 (forall ((BOUND_VARIABLE_1457387 tptp.int) (BOUND_VARIABLE_1457388 tptp.int) (BOUND_VARIABLE_1457389 tptp.int) (BOUND_VARIABLE_1457390 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8888 BOUND_VARIABLE_1457387) BOUND_VARIABLE_1457388) BOUND_VARIABLE_1457389) BOUND_VARIABLE_1457390) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457388) BOUND_VARIABLE_1457390)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457387) BOUND_VARIABLE_1457389)))))))))) (let ((_let_2962 (forall ((BOUND_VARIABLE_1457362 tptp.int) (BOUND_VARIABLE_1457363 tptp.int) (BOUND_VARIABLE_1457364 tptp.int) (BOUND_VARIABLE_1457365 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8889 BOUND_VARIABLE_1457362) BOUND_VARIABLE_1457363) BOUND_VARIABLE_1457364) BOUND_VARIABLE_1457365) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457363) BOUND_VARIABLE_1457365)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457362) BOUND_VARIABLE_1457364)))))))))) (let ((_let_2963 (forall ((BOUND_VARIABLE_1457337 tptp.int) (BOUND_VARIABLE_1457338 tptp.int) (BOUND_VARIABLE_1457339 tptp.int) (BOUND_VARIABLE_1457340 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8890 BOUND_VARIABLE_1457337) BOUND_VARIABLE_1457338) BOUND_VARIABLE_1457339) BOUND_VARIABLE_1457340) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457338) BOUND_VARIABLE_1457340)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457337) BOUND_VARIABLE_1457339)))))))))) (let ((_let_2964 (forall ((BOUND_VARIABLE_1457312 tptp.int) (BOUND_VARIABLE_1457313 tptp.int) (BOUND_VARIABLE_1457314 tptp.int) (BOUND_VARIABLE_1457315 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8891 BOUND_VARIABLE_1457312) BOUND_VARIABLE_1457313) BOUND_VARIABLE_1457314) BOUND_VARIABLE_1457315) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457313) BOUND_VARIABLE_1457315)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457312) BOUND_VARIABLE_1457314)))))))))) (let ((_let_2965 (forall ((BOUND_VARIABLE_1457287 tptp.int) (BOUND_VARIABLE_1457288 tptp.int) (BOUND_VARIABLE_1457289 tptp.int) (BOUND_VARIABLE_1457290 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8892 BOUND_VARIABLE_1457287) BOUND_VARIABLE_1457288) BOUND_VARIABLE_1457289) BOUND_VARIABLE_1457290) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457288) BOUND_VARIABLE_1457290)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457287) BOUND_VARIABLE_1457289)))))))))) (let ((_let_2966 (forall ((BOUND_VARIABLE_1457262 tptp.int) (BOUND_VARIABLE_1457263 tptp.int) (BOUND_VARIABLE_1457264 tptp.int) (BOUND_VARIABLE_1457265 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8893 BOUND_VARIABLE_1457262) BOUND_VARIABLE_1457263) BOUND_VARIABLE_1457264) BOUND_VARIABLE_1457265) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457263) BOUND_VARIABLE_1457265)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457262) BOUND_VARIABLE_1457264)))))))))) (let ((_let_2967 (forall ((BOUND_VARIABLE_1457237 tptp.int) (BOUND_VARIABLE_1457238 tptp.int) (BOUND_VARIABLE_1457239 tptp.int) (BOUND_VARIABLE_1457240 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8894 BOUND_VARIABLE_1457237) BOUND_VARIABLE_1457238) BOUND_VARIABLE_1457239) BOUND_VARIABLE_1457240) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457238) BOUND_VARIABLE_1457240)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457237) BOUND_VARIABLE_1457239)))))))))) (let ((_let_2968 (forall ((BOUND_VARIABLE_1457212 tptp.int) (BOUND_VARIABLE_1457213 tptp.int) (BOUND_VARIABLE_1457214 tptp.int) (BOUND_VARIABLE_1457215 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8895 BOUND_VARIABLE_1457212) BOUND_VARIABLE_1457213) BOUND_VARIABLE_1457214) BOUND_VARIABLE_1457215) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457213) BOUND_VARIABLE_1457215)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457212) BOUND_VARIABLE_1457214)))))))))) (let ((_let_2969 (forall ((BOUND_VARIABLE_1457187 tptp.int) (BOUND_VARIABLE_1457188 tptp.int) (BOUND_VARIABLE_1457189 tptp.int) (BOUND_VARIABLE_1457190 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8896 BOUND_VARIABLE_1457187) BOUND_VARIABLE_1457188) BOUND_VARIABLE_1457189) BOUND_VARIABLE_1457190) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457188) BOUND_VARIABLE_1457190)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457187) BOUND_VARIABLE_1457189)))))))))) (let ((_let_2970 (forall ((BOUND_VARIABLE_1457162 tptp.int) (BOUND_VARIABLE_1457163 tptp.int) (BOUND_VARIABLE_1457164 tptp.int) (BOUND_VARIABLE_1457165 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8897 BOUND_VARIABLE_1457162) BOUND_VARIABLE_1457163) BOUND_VARIABLE_1457164) BOUND_VARIABLE_1457165) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457163) BOUND_VARIABLE_1457165)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457162) BOUND_VARIABLE_1457164)))))))))) (let ((_let_2971 (forall ((BOUND_VARIABLE_1457137 tptp.int) (BOUND_VARIABLE_1457138 tptp.int) (BOUND_VARIABLE_1457139 tptp.int) (BOUND_VARIABLE_1457140 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8898 BOUND_VARIABLE_1457137) BOUND_VARIABLE_1457138) BOUND_VARIABLE_1457139) BOUND_VARIABLE_1457140) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457138) BOUND_VARIABLE_1457140)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457137) BOUND_VARIABLE_1457139)))))))))) (let ((_let_2972 (forall ((BOUND_VARIABLE_1457112 tptp.int) (BOUND_VARIABLE_1457113 tptp.int) (BOUND_VARIABLE_1457114 tptp.int) (BOUND_VARIABLE_1457115 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8899 BOUND_VARIABLE_1457112) BOUND_VARIABLE_1457113) BOUND_VARIABLE_1457114) BOUND_VARIABLE_1457115) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457113) BOUND_VARIABLE_1457115)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457112) BOUND_VARIABLE_1457114)))))))))) (let ((_let_2973 (forall ((BOUND_VARIABLE_1457087 tptp.int) (BOUND_VARIABLE_1457088 tptp.int) (BOUND_VARIABLE_1457089 tptp.int) (BOUND_VARIABLE_1457090 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8900 BOUND_VARIABLE_1457087) BOUND_VARIABLE_1457088) BOUND_VARIABLE_1457089) BOUND_VARIABLE_1457090) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457088) BOUND_VARIABLE_1457090)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457087) BOUND_VARIABLE_1457089)))))))))) (let ((_let_2974 (forall ((BOUND_VARIABLE_1457062 tptp.int) (BOUND_VARIABLE_1457063 tptp.int) (BOUND_VARIABLE_1457064 tptp.int) (BOUND_VARIABLE_1457065 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8901 BOUND_VARIABLE_1457062) BOUND_VARIABLE_1457063) BOUND_VARIABLE_1457064) BOUND_VARIABLE_1457065) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457063) BOUND_VARIABLE_1457065)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457062) BOUND_VARIABLE_1457064)))))))))) (let ((_let_2975 (forall ((BOUND_VARIABLE_1457037 tptp.int) (BOUND_VARIABLE_1457038 tptp.int) (BOUND_VARIABLE_1457039 tptp.int) (BOUND_VARIABLE_1457040 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8902 BOUND_VARIABLE_1457037) BOUND_VARIABLE_1457038) BOUND_VARIABLE_1457039) BOUND_VARIABLE_1457040) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457038) BOUND_VARIABLE_1457040)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457037) BOUND_VARIABLE_1457039)))))))))) (let ((_let_2976 (forall ((BOUND_VARIABLE_1457012 tptp.int) (BOUND_VARIABLE_1457013 tptp.int) (BOUND_VARIABLE_1457014 tptp.int) (BOUND_VARIABLE_1457015 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8903 BOUND_VARIABLE_1457012) BOUND_VARIABLE_1457013) BOUND_VARIABLE_1457014) BOUND_VARIABLE_1457015) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457013) BOUND_VARIABLE_1457015)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1457012) BOUND_VARIABLE_1457014)))))))))) (let ((_let_2977 (forall ((BOUND_VARIABLE_1456987 tptp.int) (BOUND_VARIABLE_1456988 tptp.int) (BOUND_VARIABLE_1456989 tptp.int) (BOUND_VARIABLE_1456990 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8904 BOUND_VARIABLE_1456987) BOUND_VARIABLE_1456988) BOUND_VARIABLE_1456989) BOUND_VARIABLE_1456990) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456988) BOUND_VARIABLE_1456990)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456987) BOUND_VARIABLE_1456989)))))))))) (let ((_let_2978 (forall ((BOUND_VARIABLE_1456945 tptp.rat) (BOUND_VARIABLE_1456946 tptp.int) (BOUND_VARIABLE_1456947 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7594 BOUND_VARIABLE_1456947) BOUND_VARIABLE_1456946)) (ho_7630 k_7629 BOUND_VARIABLE_1456945)) (ho_7496 (ho_7495 (ho_7635 k_8905 BOUND_VARIABLE_1456945) BOUND_VARIABLE_1456946) BOUND_VARIABLE_1456947))))) (let ((_let_2979 (forall ((BOUND_VARIABLE_1456920 tptp.int) (BOUND_VARIABLE_1456921 tptp.int) (BOUND_VARIABLE_1456922 tptp.int) (BOUND_VARIABLE_1456923 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8906 BOUND_VARIABLE_1456920) BOUND_VARIABLE_1456921) BOUND_VARIABLE_1456922) BOUND_VARIABLE_1456923) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456921) BOUND_VARIABLE_1456923)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456920) BOUND_VARIABLE_1456922)))))))))) (let ((_let_2980 (forall ((BOUND_VARIABLE_1456895 tptp.int) (BOUND_VARIABLE_1456896 tptp.int) (BOUND_VARIABLE_1456897 tptp.int) (BOUND_VARIABLE_1456898 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8907 BOUND_VARIABLE_1456895) BOUND_VARIABLE_1456896) BOUND_VARIABLE_1456897) BOUND_VARIABLE_1456898) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456896) BOUND_VARIABLE_1456898)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456895) BOUND_VARIABLE_1456897)))))))))) (let ((_let_2981 (forall ((BOUND_VARIABLE_1456870 tptp.int) (BOUND_VARIABLE_1456871 tptp.int) (BOUND_VARIABLE_1456872 tptp.int) (BOUND_VARIABLE_1456873 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8908 BOUND_VARIABLE_1456870) BOUND_VARIABLE_1456871) BOUND_VARIABLE_1456872) BOUND_VARIABLE_1456873) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456871) BOUND_VARIABLE_1456873)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456870) BOUND_VARIABLE_1456872)))))))))) (let ((_let_2982 (forall ((BOUND_VARIABLE_1456828 tptp.rat) (BOUND_VARIABLE_1456829 tptp.int) (BOUND_VARIABLE_1456830 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7595 BOUND_VARIABLE_1456830) BOUND_VARIABLE_1456829)) (ho_7630 k_7629 BOUND_VARIABLE_1456828)) (ho_7496 (ho_7495 (ho_7635 k_8909 BOUND_VARIABLE_1456828) BOUND_VARIABLE_1456829) BOUND_VARIABLE_1456830))))) (let ((_let_2983 (forall ((BOUND_VARIABLE_1456803 tptp.int) (BOUND_VARIABLE_1456804 tptp.int) (BOUND_VARIABLE_1456805 tptp.int) (BOUND_VARIABLE_1456806 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8910 BOUND_VARIABLE_1456803) BOUND_VARIABLE_1456804) BOUND_VARIABLE_1456805) BOUND_VARIABLE_1456806) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456804) BOUND_VARIABLE_1456806)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456803) BOUND_VARIABLE_1456805)))))))))) (let ((_let_2984 (forall ((BOUND_VARIABLE_1456761 tptp.rat) (BOUND_VARIABLE_1456762 tptp.int) (BOUND_VARIABLE_1456763 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7596 BOUND_VARIABLE_1456763) BOUND_VARIABLE_1456762)) (ho_7630 k_7629 BOUND_VARIABLE_1456761)) (ho_7496 (ho_7495 (ho_7635 k_8911 BOUND_VARIABLE_1456761) BOUND_VARIABLE_1456762) BOUND_VARIABLE_1456763))))) (let ((_let_2985 (forall ((BOUND_VARIABLE_1456736 tptp.int) (BOUND_VARIABLE_1456737 tptp.int) (BOUND_VARIABLE_1456738 tptp.int) (BOUND_VARIABLE_1456739 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8912 BOUND_VARIABLE_1456736) BOUND_VARIABLE_1456737) BOUND_VARIABLE_1456738) BOUND_VARIABLE_1456739) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456737) BOUND_VARIABLE_1456739)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456736) BOUND_VARIABLE_1456738)))))))))) (let ((_let_2986 (forall ((BOUND_VARIABLE_1456711 tptp.int) (BOUND_VARIABLE_1456712 tptp.int) (BOUND_VARIABLE_1456713 tptp.int) (BOUND_VARIABLE_1456714 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8913 BOUND_VARIABLE_1456711) BOUND_VARIABLE_1456712) BOUND_VARIABLE_1456713) BOUND_VARIABLE_1456714) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456712) BOUND_VARIABLE_1456714)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456711) BOUND_VARIABLE_1456713)))))))))) (let ((_let_2987 (forall ((BOUND_VARIABLE_1456686 tptp.int) (BOUND_VARIABLE_1456687 tptp.int) (BOUND_VARIABLE_1456688 tptp.int) (BOUND_VARIABLE_1456689 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8914 BOUND_VARIABLE_1456686) BOUND_VARIABLE_1456687) BOUND_VARIABLE_1456688) BOUND_VARIABLE_1456689) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456687) BOUND_VARIABLE_1456689)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456686) BOUND_VARIABLE_1456688)))))))))) (let ((_let_2988 (forall ((BOUND_VARIABLE_1456661 tptp.int) (BOUND_VARIABLE_1456662 tptp.int) (BOUND_VARIABLE_1456663 tptp.int) (BOUND_VARIABLE_1456664 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8915 BOUND_VARIABLE_1456661) BOUND_VARIABLE_1456662) BOUND_VARIABLE_1456663) BOUND_VARIABLE_1456664) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456662) BOUND_VARIABLE_1456664)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456661) BOUND_VARIABLE_1456663)))))))))) (let ((_let_2989 (forall ((BOUND_VARIABLE_1456619 tptp.rat) (BOUND_VARIABLE_1456620 tptp.int) (BOUND_VARIABLE_1456621 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7597 BOUND_VARIABLE_1456621) BOUND_VARIABLE_1456620)) (ho_7630 k_7629 BOUND_VARIABLE_1456619)) (ho_7496 (ho_7495 (ho_7635 k_8916 BOUND_VARIABLE_1456619) BOUND_VARIABLE_1456620) BOUND_VARIABLE_1456621))))) (let ((_let_2990 (forall ((BOUND_VARIABLE_1456594 tptp.int) (BOUND_VARIABLE_1456595 tptp.int) (BOUND_VARIABLE_1456596 tptp.int) (BOUND_VARIABLE_1456597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8917 BOUND_VARIABLE_1456594) BOUND_VARIABLE_1456595) BOUND_VARIABLE_1456596) BOUND_VARIABLE_1456597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456595) BOUND_VARIABLE_1456597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456594) BOUND_VARIABLE_1456596)))))))))) (let ((_let_2991 (forall ((BOUND_VARIABLE_1456569 tptp.int) (BOUND_VARIABLE_1456570 tptp.int) (BOUND_VARIABLE_1456571 tptp.int) (BOUND_VARIABLE_1456572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8918 BOUND_VARIABLE_1456569) BOUND_VARIABLE_1456570) BOUND_VARIABLE_1456571) BOUND_VARIABLE_1456572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456570) BOUND_VARIABLE_1456572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456569) BOUND_VARIABLE_1456571)))))))))) (let ((_let_2992 (forall ((BOUND_VARIABLE_1456544 tptp.int) (BOUND_VARIABLE_1456545 tptp.int) (BOUND_VARIABLE_1456546 tptp.int) (BOUND_VARIABLE_1456547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8919 BOUND_VARIABLE_1456544) BOUND_VARIABLE_1456545) BOUND_VARIABLE_1456546) BOUND_VARIABLE_1456547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456545) BOUND_VARIABLE_1456547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456544) BOUND_VARIABLE_1456546)))))))))) (let ((_let_2993 (forall ((BOUND_VARIABLE_1456502 tptp.rat) (BOUND_VARIABLE_1456503 tptp.int) (BOUND_VARIABLE_1456504 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7598 BOUND_VARIABLE_1456504) BOUND_VARIABLE_1456503)) (ho_7630 k_7629 BOUND_VARIABLE_1456502)) (ho_7496 (ho_7495 (ho_7635 k_8920 BOUND_VARIABLE_1456502) BOUND_VARIABLE_1456503) BOUND_VARIABLE_1456504))))) (let ((_let_2994 (forall ((BOUND_VARIABLE_1456477 tptp.int) (BOUND_VARIABLE_1456478 tptp.int) (BOUND_VARIABLE_1456479 tptp.int) (BOUND_VARIABLE_1456480 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8921 BOUND_VARIABLE_1456477) BOUND_VARIABLE_1456478) BOUND_VARIABLE_1456479) BOUND_VARIABLE_1456480) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456478) BOUND_VARIABLE_1456480)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456477) BOUND_VARIABLE_1456479)))))))))) (let ((_let_2995 (forall ((BOUND_VARIABLE_1456452 tptp.int) (BOUND_VARIABLE_1456453 tptp.int) (BOUND_VARIABLE_1456454 tptp.int) (BOUND_VARIABLE_1456455 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8922 BOUND_VARIABLE_1456452) BOUND_VARIABLE_1456453) BOUND_VARIABLE_1456454) BOUND_VARIABLE_1456455) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456453) BOUND_VARIABLE_1456455)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456452) BOUND_VARIABLE_1456454)))))))))) (let ((_let_2996 (forall ((BOUND_VARIABLE_1456410 tptp.rat) (BOUND_VARIABLE_1456411 tptp.int) (BOUND_VARIABLE_1456412 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7599 BOUND_VARIABLE_1456412) BOUND_VARIABLE_1456411)) (ho_7630 k_7629 BOUND_VARIABLE_1456410)) (ho_7496 (ho_7495 (ho_7635 k_8923 BOUND_VARIABLE_1456410) BOUND_VARIABLE_1456411) BOUND_VARIABLE_1456412))))) (let ((_let_2997 (forall ((BOUND_VARIABLE_1456368 tptp.rat) (BOUND_VARIABLE_1456369 tptp.int) (BOUND_VARIABLE_1456370 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7600 BOUND_VARIABLE_1456370) BOUND_VARIABLE_1456369)) (ho_7630 k_7629 BOUND_VARIABLE_1456368)) (ho_7496 (ho_7495 (ho_7635 k_8924 BOUND_VARIABLE_1456368) BOUND_VARIABLE_1456369) BOUND_VARIABLE_1456370))))) (let ((_let_2998 (forall ((BOUND_VARIABLE_1456326 tptp.rat) (BOUND_VARIABLE_1456327 tptp.int) (BOUND_VARIABLE_1456328 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7601 BOUND_VARIABLE_1456328) BOUND_VARIABLE_1456327)) (ho_7630 k_7629 BOUND_VARIABLE_1456326)) (ho_7496 (ho_7495 (ho_7635 k_8925 BOUND_VARIABLE_1456326) BOUND_VARIABLE_1456327) BOUND_VARIABLE_1456328))))) (let ((_let_2999 (forall ((BOUND_VARIABLE_1456301 tptp.int) (BOUND_VARIABLE_1456302 tptp.int) (BOUND_VARIABLE_1456303 tptp.int) (BOUND_VARIABLE_1456304 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8926 BOUND_VARIABLE_1456301) BOUND_VARIABLE_1456302) BOUND_VARIABLE_1456303) BOUND_VARIABLE_1456304) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456302) BOUND_VARIABLE_1456304)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456301) BOUND_VARIABLE_1456303)))))))))) (let ((_let_3000 (forall ((BOUND_VARIABLE_1456276 tptp.int) (BOUND_VARIABLE_1456277 tptp.int) (BOUND_VARIABLE_1456278 tptp.int) (BOUND_VARIABLE_1456279 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8927 BOUND_VARIABLE_1456276) BOUND_VARIABLE_1456277) BOUND_VARIABLE_1456278) BOUND_VARIABLE_1456279) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456277) BOUND_VARIABLE_1456279)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456276) BOUND_VARIABLE_1456278)))))))))) (let ((_let_3001 (forall ((BOUND_VARIABLE_1456251 tptp.int) (BOUND_VARIABLE_1456252 tptp.int) (BOUND_VARIABLE_1456253 tptp.int) (BOUND_VARIABLE_1456254 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8928 BOUND_VARIABLE_1456251) BOUND_VARIABLE_1456252) BOUND_VARIABLE_1456253) BOUND_VARIABLE_1456254) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456252) BOUND_VARIABLE_1456254)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456251) BOUND_VARIABLE_1456253)))))))))) (let ((_let_3002 (forall ((BOUND_VARIABLE_1456209 tptp.rat) (BOUND_VARIABLE_1456210 tptp.int) (BOUND_VARIABLE_1456211 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7602 BOUND_VARIABLE_1456211) BOUND_VARIABLE_1456210)) (ho_7630 k_7629 BOUND_VARIABLE_1456209)) (ho_7496 (ho_7495 (ho_7635 k_8929 BOUND_VARIABLE_1456209) BOUND_VARIABLE_1456210) BOUND_VARIABLE_1456211))))) (let ((_let_3003 (forall ((BOUND_VARIABLE_1456184 tptp.int) (BOUND_VARIABLE_1456185 tptp.int) (BOUND_VARIABLE_1456186 tptp.int) (BOUND_VARIABLE_1456187 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8930 BOUND_VARIABLE_1456184) BOUND_VARIABLE_1456185) BOUND_VARIABLE_1456186) BOUND_VARIABLE_1456187) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456185) BOUND_VARIABLE_1456187)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456184) BOUND_VARIABLE_1456186)))))))))) (let ((_let_3004 (forall ((BOUND_VARIABLE_1456142 tptp.rat) (BOUND_VARIABLE_1456143 tptp.int) (BOUND_VARIABLE_1456144 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7603 BOUND_VARIABLE_1456144) BOUND_VARIABLE_1456143)) (ho_7630 k_7629 BOUND_VARIABLE_1456142)) (ho_7496 (ho_7495 (ho_7635 k_8931 BOUND_VARIABLE_1456142) BOUND_VARIABLE_1456143) BOUND_VARIABLE_1456144))))) (let ((_let_3005 (forall ((BOUND_VARIABLE_1456117 tptp.int) (BOUND_VARIABLE_1456118 tptp.int) (BOUND_VARIABLE_1456119 tptp.int) (BOUND_VARIABLE_1456120 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8932 BOUND_VARIABLE_1456117) BOUND_VARIABLE_1456118) BOUND_VARIABLE_1456119) BOUND_VARIABLE_1456120) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456118) BOUND_VARIABLE_1456120)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456117) BOUND_VARIABLE_1456119)))))))))) (let ((_let_3006 (forall ((BOUND_VARIABLE_1456075 tptp.rat) (BOUND_VARIABLE_1456076 tptp.int) (BOUND_VARIABLE_1456077 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7604 BOUND_VARIABLE_1456077) BOUND_VARIABLE_1456076)) (ho_7630 k_7629 BOUND_VARIABLE_1456075)) (ho_7496 (ho_7495 (ho_7635 k_8933 BOUND_VARIABLE_1456075) BOUND_VARIABLE_1456076) BOUND_VARIABLE_1456077))))) (let ((_let_3007 (forall ((BOUND_VARIABLE_1456033 tptp.rat) (BOUND_VARIABLE_1456034 tptp.int) (BOUND_VARIABLE_1456035 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7605 BOUND_VARIABLE_1456035) BOUND_VARIABLE_1456034)) (ho_7630 k_7629 BOUND_VARIABLE_1456033)) (ho_7496 (ho_7495 (ho_7635 k_8934 BOUND_VARIABLE_1456033) BOUND_VARIABLE_1456034) BOUND_VARIABLE_1456035))))) (let ((_let_3008 (forall ((BOUND_VARIABLE_1456008 tptp.int) (BOUND_VARIABLE_1456009 tptp.int) (BOUND_VARIABLE_1456010 tptp.int) (BOUND_VARIABLE_1456011 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8935 BOUND_VARIABLE_1456008) BOUND_VARIABLE_1456009) BOUND_VARIABLE_1456010) BOUND_VARIABLE_1456011) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456009) BOUND_VARIABLE_1456011)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1456008) BOUND_VARIABLE_1456010)))))))))) (let ((_let_3009 (forall ((BOUND_VARIABLE_1455983 tptp.int) (BOUND_VARIABLE_1455984 tptp.int) (BOUND_VARIABLE_1455985 tptp.int) (BOUND_VARIABLE_1455986 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8936 BOUND_VARIABLE_1455983) BOUND_VARIABLE_1455984) BOUND_VARIABLE_1455985) BOUND_VARIABLE_1455986) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455984) BOUND_VARIABLE_1455986)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455983) BOUND_VARIABLE_1455985)))))))))) (let ((_let_3010 (forall ((BOUND_VARIABLE_1455958 tptp.int) (BOUND_VARIABLE_1455959 tptp.int) (BOUND_VARIABLE_1455960 tptp.int) (BOUND_VARIABLE_1455961 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8937 BOUND_VARIABLE_1455958) BOUND_VARIABLE_1455959) BOUND_VARIABLE_1455960) BOUND_VARIABLE_1455961) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455959) BOUND_VARIABLE_1455961)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455958) BOUND_VARIABLE_1455960)))))))))) (let ((_let_3011 (forall ((BOUND_VARIABLE_1455933 tptp.int) (BOUND_VARIABLE_1455934 tptp.int) (BOUND_VARIABLE_1455935 tptp.int) (BOUND_VARIABLE_1455936 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8938 BOUND_VARIABLE_1455933) BOUND_VARIABLE_1455934) BOUND_VARIABLE_1455935) BOUND_VARIABLE_1455936) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455934) BOUND_VARIABLE_1455936)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455933) BOUND_VARIABLE_1455935)))))))))) (let ((_let_3012 (forall ((BOUND_VARIABLE_1455908 tptp.int) (BOUND_VARIABLE_1455909 tptp.int) (BOUND_VARIABLE_1455910 tptp.int) (BOUND_VARIABLE_1455911 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8939 BOUND_VARIABLE_1455908) BOUND_VARIABLE_1455909) BOUND_VARIABLE_1455910) BOUND_VARIABLE_1455911) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455909) BOUND_VARIABLE_1455911)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455908) BOUND_VARIABLE_1455910)))))))))) (let ((_let_3013 (forall ((BOUND_VARIABLE_1455883 tptp.int) (BOUND_VARIABLE_1455884 tptp.int) (BOUND_VARIABLE_1455885 tptp.int) (BOUND_VARIABLE_1455886 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8940 BOUND_VARIABLE_1455883) BOUND_VARIABLE_1455884) BOUND_VARIABLE_1455885) BOUND_VARIABLE_1455886) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455884) BOUND_VARIABLE_1455886)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455883) BOUND_VARIABLE_1455885)))))))))) (let ((_let_3014 (forall ((BOUND_VARIABLE_1455858 tptp.int) (BOUND_VARIABLE_1455859 tptp.int) (BOUND_VARIABLE_1455860 tptp.int) (BOUND_VARIABLE_1455861 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8941 BOUND_VARIABLE_1455858) BOUND_VARIABLE_1455859) BOUND_VARIABLE_1455860) BOUND_VARIABLE_1455861) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455859) BOUND_VARIABLE_1455861)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455858) BOUND_VARIABLE_1455860)))))))))) (let ((_let_3015 (forall ((BOUND_VARIABLE_1455833 tptp.int) (BOUND_VARIABLE_1455834 tptp.int) (BOUND_VARIABLE_1455835 tptp.int) (BOUND_VARIABLE_1455836 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8942 BOUND_VARIABLE_1455833) BOUND_VARIABLE_1455834) BOUND_VARIABLE_1455835) BOUND_VARIABLE_1455836) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455834) BOUND_VARIABLE_1455836)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455833) BOUND_VARIABLE_1455835)))))))))) (let ((_let_3016 (forall ((BOUND_VARIABLE_1455808 tptp.int) (BOUND_VARIABLE_1455809 tptp.int) (BOUND_VARIABLE_1455810 tptp.int) (BOUND_VARIABLE_1455811 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8943 BOUND_VARIABLE_1455808) BOUND_VARIABLE_1455809) BOUND_VARIABLE_1455810) BOUND_VARIABLE_1455811) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455809) BOUND_VARIABLE_1455811)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455808) BOUND_VARIABLE_1455810)))))))))) (let ((_let_3017 (forall ((BOUND_VARIABLE_1455783 tptp.int) (BOUND_VARIABLE_1455784 tptp.int) (BOUND_VARIABLE_1455785 tptp.int) (BOUND_VARIABLE_1455786 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8944 BOUND_VARIABLE_1455783) BOUND_VARIABLE_1455784) BOUND_VARIABLE_1455785) BOUND_VARIABLE_1455786) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455784) BOUND_VARIABLE_1455786)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455783) BOUND_VARIABLE_1455785)))))))))) (let ((_let_3018 (forall ((BOUND_VARIABLE_1455758 tptp.int) (BOUND_VARIABLE_1455759 tptp.int) (BOUND_VARIABLE_1455760 tptp.int) (BOUND_VARIABLE_1455761 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8945 BOUND_VARIABLE_1455758) BOUND_VARIABLE_1455759) BOUND_VARIABLE_1455760) BOUND_VARIABLE_1455761) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455759) BOUND_VARIABLE_1455761)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455758) BOUND_VARIABLE_1455760)))))))))) (let ((_let_3019 (forall ((BOUND_VARIABLE_1455716 tptp.rat) (BOUND_VARIABLE_1455717 tptp.int) (BOUND_VARIABLE_1455718 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7606 BOUND_VARIABLE_1455718) BOUND_VARIABLE_1455717)) (ho_7630 k_7629 BOUND_VARIABLE_1455716)) (ho_7496 (ho_7495 (ho_7635 k_8946 BOUND_VARIABLE_1455716) BOUND_VARIABLE_1455717) BOUND_VARIABLE_1455718))))) (let ((_let_3020 (forall ((BOUND_VARIABLE_1455691 tptp.int) (BOUND_VARIABLE_1455692 tptp.int) (BOUND_VARIABLE_1455693 tptp.int) (BOUND_VARIABLE_1455694 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8947 BOUND_VARIABLE_1455691) BOUND_VARIABLE_1455692) BOUND_VARIABLE_1455693) BOUND_VARIABLE_1455694) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455692) BOUND_VARIABLE_1455694)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455691) BOUND_VARIABLE_1455693)))))))))) (let ((_let_3021 (forall ((BOUND_VARIABLE_1455666 tptp.int) (BOUND_VARIABLE_1455667 tptp.int) (BOUND_VARIABLE_1455668 tptp.int) (BOUND_VARIABLE_1455669 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8948 BOUND_VARIABLE_1455666) BOUND_VARIABLE_1455667) BOUND_VARIABLE_1455668) BOUND_VARIABLE_1455669) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455667) BOUND_VARIABLE_1455669)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455666) BOUND_VARIABLE_1455668)))))))))) (let ((_let_3022 (forall ((BOUND_VARIABLE_1455641 tptp.int) (BOUND_VARIABLE_1455642 tptp.int) (BOUND_VARIABLE_1455643 tptp.int) (BOUND_VARIABLE_1455644 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8949 BOUND_VARIABLE_1455641) BOUND_VARIABLE_1455642) BOUND_VARIABLE_1455643) BOUND_VARIABLE_1455644) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455642) BOUND_VARIABLE_1455644)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455641) BOUND_VARIABLE_1455643)))))))))) (let ((_let_3023 (forall ((BOUND_VARIABLE_1455616 tptp.int) (BOUND_VARIABLE_1455617 tptp.int) (BOUND_VARIABLE_1455618 tptp.int) (BOUND_VARIABLE_1455619 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8950 BOUND_VARIABLE_1455616) BOUND_VARIABLE_1455617) BOUND_VARIABLE_1455618) BOUND_VARIABLE_1455619) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455617) BOUND_VARIABLE_1455619)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455616) BOUND_VARIABLE_1455618)))))))))) (let ((_let_3024 (forall ((BOUND_VARIABLE_1455591 tptp.int) (BOUND_VARIABLE_1455592 tptp.int) (BOUND_VARIABLE_1455593 tptp.int) (BOUND_VARIABLE_1455594 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8951 BOUND_VARIABLE_1455591) BOUND_VARIABLE_1455592) BOUND_VARIABLE_1455593) BOUND_VARIABLE_1455594) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455592) BOUND_VARIABLE_1455594)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455591) BOUND_VARIABLE_1455593)))))))))) (let ((_let_3025 (forall ((BOUND_VARIABLE_1455566 tptp.int) (BOUND_VARIABLE_1455567 tptp.int) (BOUND_VARIABLE_1455568 tptp.int) (BOUND_VARIABLE_1455569 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8952 BOUND_VARIABLE_1455566) BOUND_VARIABLE_1455567) BOUND_VARIABLE_1455568) BOUND_VARIABLE_1455569) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455567) BOUND_VARIABLE_1455569)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455566) BOUND_VARIABLE_1455568)))))))))) (let ((_let_3026 (forall ((BOUND_VARIABLE_1455541 tptp.int) (BOUND_VARIABLE_1455542 tptp.int) (BOUND_VARIABLE_1455543 tptp.int) (BOUND_VARIABLE_1455544 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8953 BOUND_VARIABLE_1455541) BOUND_VARIABLE_1455542) BOUND_VARIABLE_1455543) BOUND_VARIABLE_1455544) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455542) BOUND_VARIABLE_1455544)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455541) BOUND_VARIABLE_1455543)))))))))) (let ((_let_3027 (forall ((BOUND_VARIABLE_1455516 tptp.int) (BOUND_VARIABLE_1455517 tptp.int) (BOUND_VARIABLE_1455518 tptp.int) (BOUND_VARIABLE_1455519 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8954 BOUND_VARIABLE_1455516) BOUND_VARIABLE_1455517) BOUND_VARIABLE_1455518) BOUND_VARIABLE_1455519) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455517) BOUND_VARIABLE_1455519)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455516) BOUND_VARIABLE_1455518)))))))))) (let ((_let_3028 (forall ((BOUND_VARIABLE_1455491 tptp.int) (BOUND_VARIABLE_1455492 tptp.int) (BOUND_VARIABLE_1455493 tptp.int) (BOUND_VARIABLE_1455494 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8955 BOUND_VARIABLE_1455491) BOUND_VARIABLE_1455492) BOUND_VARIABLE_1455493) BOUND_VARIABLE_1455494) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455492) BOUND_VARIABLE_1455494)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455491) BOUND_VARIABLE_1455493)))))))))) (let ((_let_3029 (forall ((BOUND_VARIABLE_1455466 tptp.int) (BOUND_VARIABLE_1455467 tptp.int) (BOUND_VARIABLE_1455468 tptp.int) (BOUND_VARIABLE_1455469 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8956 BOUND_VARIABLE_1455466) BOUND_VARIABLE_1455467) BOUND_VARIABLE_1455468) BOUND_VARIABLE_1455469) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455467) BOUND_VARIABLE_1455469)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455466) BOUND_VARIABLE_1455468)))))))))) (let ((_let_3030 (forall ((BOUND_VARIABLE_1455441 tptp.int) (BOUND_VARIABLE_1455442 tptp.int) (BOUND_VARIABLE_1455443 tptp.int) (BOUND_VARIABLE_1455444 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8957 BOUND_VARIABLE_1455441) BOUND_VARIABLE_1455442) BOUND_VARIABLE_1455443) BOUND_VARIABLE_1455444) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455442) BOUND_VARIABLE_1455444)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455441) BOUND_VARIABLE_1455443)))))))))) (let ((_let_3031 (forall ((BOUND_VARIABLE_1455399 tptp.rat) (BOUND_VARIABLE_1455400 tptp.int) (BOUND_VARIABLE_1455401 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7607 BOUND_VARIABLE_1455401) BOUND_VARIABLE_1455400)) (ho_7630 k_7629 BOUND_VARIABLE_1455399)) (ho_7496 (ho_7495 (ho_7635 k_8958 BOUND_VARIABLE_1455399) BOUND_VARIABLE_1455400) BOUND_VARIABLE_1455401))))) (let ((_let_3032 (forall ((BOUND_VARIABLE_1455357 tptp.rat) (BOUND_VARIABLE_1455358 tptp.int) (BOUND_VARIABLE_1455359 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7608 BOUND_VARIABLE_1455359) BOUND_VARIABLE_1455358)) (ho_7630 k_7629 BOUND_VARIABLE_1455357)) (ho_7496 (ho_7495 (ho_7635 k_8959 BOUND_VARIABLE_1455357) BOUND_VARIABLE_1455358) BOUND_VARIABLE_1455359))))) (let ((_let_3033 (forall ((BOUND_VARIABLE_1455332 tptp.int) (BOUND_VARIABLE_1455333 tptp.int) (BOUND_VARIABLE_1455334 tptp.int) (BOUND_VARIABLE_1455335 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8960 BOUND_VARIABLE_1455332) BOUND_VARIABLE_1455333) BOUND_VARIABLE_1455334) BOUND_VARIABLE_1455335) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455333) BOUND_VARIABLE_1455335)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455332) BOUND_VARIABLE_1455334)))))))))) (let ((_let_3034 (forall ((BOUND_VARIABLE_1455307 tptp.int) (BOUND_VARIABLE_1455308 tptp.int) (BOUND_VARIABLE_1455309 tptp.int) (BOUND_VARIABLE_1455310 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8961 BOUND_VARIABLE_1455307) BOUND_VARIABLE_1455308) BOUND_VARIABLE_1455309) BOUND_VARIABLE_1455310) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455308) BOUND_VARIABLE_1455310)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455307) BOUND_VARIABLE_1455309)))))))))) (let ((_let_3035 (forall ((BOUND_VARIABLE_1455282 tptp.int) (BOUND_VARIABLE_1455283 tptp.int) (BOUND_VARIABLE_1455284 tptp.int) (BOUND_VARIABLE_1455285 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8962 BOUND_VARIABLE_1455282) BOUND_VARIABLE_1455283) BOUND_VARIABLE_1455284) BOUND_VARIABLE_1455285) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455283) BOUND_VARIABLE_1455285)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455282) BOUND_VARIABLE_1455284)))))))))) (let ((_let_3036 (forall ((BOUND_VARIABLE_1455257 tptp.int) (BOUND_VARIABLE_1455258 tptp.int) (BOUND_VARIABLE_1455259 tptp.int) (BOUND_VARIABLE_1455260 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8963 BOUND_VARIABLE_1455257) BOUND_VARIABLE_1455258) BOUND_VARIABLE_1455259) BOUND_VARIABLE_1455260) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455258) BOUND_VARIABLE_1455260)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455257) BOUND_VARIABLE_1455259)))))))))) (let ((_let_3037 (forall ((BOUND_VARIABLE_1455232 tptp.int) (BOUND_VARIABLE_1455233 tptp.int) (BOUND_VARIABLE_1455234 tptp.int) (BOUND_VARIABLE_1455235 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8964 BOUND_VARIABLE_1455232) BOUND_VARIABLE_1455233) BOUND_VARIABLE_1455234) BOUND_VARIABLE_1455235) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455233) BOUND_VARIABLE_1455235)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455232) BOUND_VARIABLE_1455234)))))))))) (let ((_let_3038 (forall ((BOUND_VARIABLE_1455207 tptp.int) (BOUND_VARIABLE_1455208 tptp.int) (BOUND_VARIABLE_1455209 tptp.int) (BOUND_VARIABLE_1455210 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8965 BOUND_VARIABLE_1455207) BOUND_VARIABLE_1455208) BOUND_VARIABLE_1455209) BOUND_VARIABLE_1455210) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455208) BOUND_VARIABLE_1455210)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455207) BOUND_VARIABLE_1455209)))))))))) (let ((_let_3039 (forall ((BOUND_VARIABLE_1455182 tptp.int) (BOUND_VARIABLE_1455183 tptp.int) (BOUND_VARIABLE_1455184 tptp.int) (BOUND_VARIABLE_1455185 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8966 BOUND_VARIABLE_1455182) BOUND_VARIABLE_1455183) BOUND_VARIABLE_1455184) BOUND_VARIABLE_1455185) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455183) BOUND_VARIABLE_1455185)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455182) BOUND_VARIABLE_1455184)))))))))) (let ((_let_3040 (forall ((BOUND_VARIABLE_1455157 tptp.int) (BOUND_VARIABLE_1455158 tptp.int) (BOUND_VARIABLE_1455159 tptp.int) (BOUND_VARIABLE_1455160 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8967 BOUND_VARIABLE_1455157) BOUND_VARIABLE_1455158) BOUND_VARIABLE_1455159) BOUND_VARIABLE_1455160) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455158) BOUND_VARIABLE_1455160)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455157) BOUND_VARIABLE_1455159)))))))))) (let ((_let_3041 (forall ((BOUND_VARIABLE_1455132 tptp.int) (BOUND_VARIABLE_1455133 tptp.int) (BOUND_VARIABLE_1455134 tptp.int) (BOUND_VARIABLE_1455135 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8968 BOUND_VARIABLE_1455132) BOUND_VARIABLE_1455133) BOUND_VARIABLE_1455134) BOUND_VARIABLE_1455135) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455133) BOUND_VARIABLE_1455135)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455132) BOUND_VARIABLE_1455134)))))))))) (let ((_let_3042 (forall ((BOUND_VARIABLE_1455107 tptp.int) (BOUND_VARIABLE_1455108 tptp.int) (BOUND_VARIABLE_1455109 tptp.int) (BOUND_VARIABLE_1455110 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8969 BOUND_VARIABLE_1455107) BOUND_VARIABLE_1455108) BOUND_VARIABLE_1455109) BOUND_VARIABLE_1455110) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455108) BOUND_VARIABLE_1455110)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455107) BOUND_VARIABLE_1455109)))))))))) (let ((_let_3043 (forall ((BOUND_VARIABLE_1455082 tptp.int) (BOUND_VARIABLE_1455083 tptp.int) (BOUND_VARIABLE_1455084 tptp.int) (BOUND_VARIABLE_1455085 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8970 BOUND_VARIABLE_1455082) BOUND_VARIABLE_1455083) BOUND_VARIABLE_1455084) BOUND_VARIABLE_1455085) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455083) BOUND_VARIABLE_1455085)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455082) BOUND_VARIABLE_1455084)))))))))) (let ((_let_3044 (forall ((BOUND_VARIABLE_1455057 tptp.int) (BOUND_VARIABLE_1455058 tptp.int) (BOUND_VARIABLE_1455059 tptp.int) (BOUND_VARIABLE_1455060 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8971 BOUND_VARIABLE_1455057) BOUND_VARIABLE_1455058) BOUND_VARIABLE_1455059) BOUND_VARIABLE_1455060) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455058) BOUND_VARIABLE_1455060)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455057) BOUND_VARIABLE_1455059)))))))))) (let ((_let_3045 (forall ((BOUND_VARIABLE_1455032 tptp.int) (BOUND_VARIABLE_1455033 tptp.int) (BOUND_VARIABLE_1455034 tptp.int) (BOUND_VARIABLE_1455035 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8972 BOUND_VARIABLE_1455032) BOUND_VARIABLE_1455033) BOUND_VARIABLE_1455034) BOUND_VARIABLE_1455035) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455033) BOUND_VARIABLE_1455035)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455032) BOUND_VARIABLE_1455034)))))))))) (let ((_let_3046 (forall ((BOUND_VARIABLE_1455007 tptp.int) (BOUND_VARIABLE_1455008 tptp.int) (BOUND_VARIABLE_1455009 tptp.int) (BOUND_VARIABLE_1455010 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8973 BOUND_VARIABLE_1455007) BOUND_VARIABLE_1455008) BOUND_VARIABLE_1455009) BOUND_VARIABLE_1455010) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455008) BOUND_VARIABLE_1455010)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1455007) BOUND_VARIABLE_1455009)))))))))) (let ((_let_3047 (forall ((BOUND_VARIABLE_1454982 tptp.int) (BOUND_VARIABLE_1454983 tptp.int) (BOUND_VARIABLE_1454984 tptp.int) (BOUND_VARIABLE_1454985 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8974 BOUND_VARIABLE_1454982) BOUND_VARIABLE_1454983) BOUND_VARIABLE_1454984) BOUND_VARIABLE_1454985) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454983) BOUND_VARIABLE_1454985)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454982) BOUND_VARIABLE_1454984)))))))))) (let ((_let_3048 (forall ((BOUND_VARIABLE_1454957 tptp.int) (BOUND_VARIABLE_1454958 tptp.int) (BOUND_VARIABLE_1454959 tptp.int) (BOUND_VARIABLE_1454960 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8975 BOUND_VARIABLE_1454957) BOUND_VARIABLE_1454958) BOUND_VARIABLE_1454959) BOUND_VARIABLE_1454960) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454958) BOUND_VARIABLE_1454960)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454957) BOUND_VARIABLE_1454959)))))))))) (let ((_let_3049 (forall ((BOUND_VARIABLE_1454932 tptp.int) (BOUND_VARIABLE_1454933 tptp.int) (BOUND_VARIABLE_1454934 tptp.int) (BOUND_VARIABLE_1454935 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8976 BOUND_VARIABLE_1454932) BOUND_VARIABLE_1454933) BOUND_VARIABLE_1454934) BOUND_VARIABLE_1454935) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454933) BOUND_VARIABLE_1454935)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454932) BOUND_VARIABLE_1454934)))))))))) (let ((_let_3050 (forall ((BOUND_VARIABLE_1454907 tptp.int) (BOUND_VARIABLE_1454908 tptp.int) (BOUND_VARIABLE_1454909 tptp.int) (BOUND_VARIABLE_1454910 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8977 BOUND_VARIABLE_1454907) BOUND_VARIABLE_1454908) BOUND_VARIABLE_1454909) BOUND_VARIABLE_1454910) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454908) BOUND_VARIABLE_1454910)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454907) BOUND_VARIABLE_1454909)))))))))) (let ((_let_3051 (forall ((BOUND_VARIABLE_1454882 tptp.int) (BOUND_VARIABLE_1454883 tptp.int) (BOUND_VARIABLE_1454884 tptp.int) (BOUND_VARIABLE_1454885 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8978 BOUND_VARIABLE_1454882) BOUND_VARIABLE_1454883) BOUND_VARIABLE_1454884) BOUND_VARIABLE_1454885) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454883) BOUND_VARIABLE_1454885)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454882) BOUND_VARIABLE_1454884)))))))))) (let ((_let_3052 (forall ((BOUND_VARIABLE_1454857 tptp.int) (BOUND_VARIABLE_1454858 tptp.int) (BOUND_VARIABLE_1454859 tptp.int) (BOUND_VARIABLE_1454860 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8979 BOUND_VARIABLE_1454857) BOUND_VARIABLE_1454858) BOUND_VARIABLE_1454859) BOUND_VARIABLE_1454860) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454858) BOUND_VARIABLE_1454860)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454857) BOUND_VARIABLE_1454859)))))))))) (let ((_let_3053 (forall ((BOUND_VARIABLE_1454840 tptp.list_nat) (BOUND_VARIABLE_1454841 tptp.nat)) (= (ho_7541 (ho_8981 k_8980 BOUND_VARIABLE_1454840) BOUND_VARIABLE_1454841) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454841 (ho_7466 (ho_7754 k_7753 BOUND_VARIABLE_1454840) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 BOUND_VARIABLE_1454840))))))))))) (let ((_let_3054 (forall ((BOUND_VARIABLE_1454823 tptp.list_int) (BOUND_VARIABLE_1454824 tptp.int)) (= (ho_7496 (ho_8983 k_8982 BOUND_VARIABLE_1454823) BOUND_VARIABLE_1454824) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454824 (ho_7927 (ho_7926 k_7925 BOUND_VARIABLE_1454823) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7924 k_7923 BOUND_VARIABLE_1454823))))))))))) (let ((_let_3055 (forall ((BOUND_VARIABLE_1454806 tptp.list_o) (BOUND_VARIABLE_1454807 Bool)) (= (ho_8986 (ho_8985 k_8984 BOUND_VARIABLE_1454806) BOUND_VARIABLE_1454807) (not (forall ((I4 tptp.nat)) (or (= (not BOUND_VARIABLE_1454807) (ho_7541 (ho_8990 k_8989 BOUND_VARIABLE_1454806) I4)) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_8988 k_8987 BOUND_VARIABLE_1454806))))))))))) (let ((_let_3056 (forall ((BOUND_VARIABLE_1454789 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1454790 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_8991 BOUND_VARIABLE_1454789) BOUND_VARIABLE_1454790) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454790 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1454789) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1454789))))))))))) (let ((_let_3057 (forall ((BOUND_VARIABLE_1454772 tptp.list_complex) (BOUND_VARIABLE_1454773 tptp.complex)) (= (ho_8994 (ho_8993 k_8992 BOUND_VARIABLE_1454772) BOUND_VARIABLE_1454773) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454773 (ho_7736 (ho_8998 k_8997 BOUND_VARIABLE_1454772) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_8996 k_8995 BOUND_VARIABLE_1454772))))))))))) (let ((_let_3058 (forall ((BOUND_VARIABLE_1454747 tptp.int) (BOUND_VARIABLE_1454748 tptp.int) (BOUND_VARIABLE_1454749 tptp.int) (BOUND_VARIABLE_1454750 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_8999 BOUND_VARIABLE_1454747) BOUND_VARIABLE_1454748) BOUND_VARIABLE_1454749) BOUND_VARIABLE_1454750) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454748) BOUND_VARIABLE_1454750)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454747) BOUND_VARIABLE_1454749)))))))))) (let ((_let_3059 (forall ((BOUND_VARIABLE_1454730 tptp.list_nat) (BOUND_VARIABLE_1454731 tptp.nat)) (= (ho_7541 (ho_8981 k_9000 BOUND_VARIABLE_1454730) BOUND_VARIABLE_1454731) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454731 (ho_7466 (ho_7754 k_7753 BOUND_VARIABLE_1454730) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 BOUND_VARIABLE_1454730))))))))))) (let ((_let_3060 (forall ((BOUND_VARIABLE_1454713 tptp.list_int) (BOUND_VARIABLE_1454714 tptp.int)) (= (ho_7496 (ho_8983 k_9001 BOUND_VARIABLE_1454713) BOUND_VARIABLE_1454714) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454714 (ho_7927 (ho_7926 k_7925 BOUND_VARIABLE_1454713) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7924 k_7923 BOUND_VARIABLE_1454713))))))))))) (let ((_let_3061 (forall ((BOUND_VARIABLE_1454696 tptp.list_o) (BOUND_VARIABLE_1454697 Bool)) (= (ho_8986 (ho_8985 k_9002 BOUND_VARIABLE_1454696) BOUND_VARIABLE_1454697) (not (forall ((I4 tptp.nat)) (or (= (not BOUND_VARIABLE_1454697) (ho_7541 (ho_8990 k_8989 BOUND_VARIABLE_1454696) I4)) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_8988 k_8987 BOUND_VARIABLE_1454696))))))))))) (let ((_let_3062 (forall ((BOUND_VARIABLE_1454679 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1454680 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_9003 BOUND_VARIABLE_1454679) BOUND_VARIABLE_1454680) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454680 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1454679) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1454679))))))))))) (let ((_let_3063 (forall ((BOUND_VARIABLE_1454662 tptp.list_complex) (BOUND_VARIABLE_1454663 tptp.complex)) (= (ho_8994 (ho_8993 k_9004 BOUND_VARIABLE_1454662) BOUND_VARIABLE_1454663) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1454663 (ho_7736 (ho_8998 k_8997 BOUND_VARIABLE_1454662) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_8996 k_8995 BOUND_VARIABLE_1454662))))))))))) (let ((_let_3064 (forall ((BOUND_VARIABLE_1454637 tptp.int) (BOUND_VARIABLE_1454638 tptp.int) (BOUND_VARIABLE_1454639 tptp.int) (BOUND_VARIABLE_1454640 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9005 BOUND_VARIABLE_1454637) BOUND_VARIABLE_1454638) BOUND_VARIABLE_1454639) BOUND_VARIABLE_1454640) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454638) BOUND_VARIABLE_1454640)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454637) BOUND_VARIABLE_1454639)))))))))) (let ((_let_3065 (forall ((BOUND_VARIABLE_1454612 tptp.int) (BOUND_VARIABLE_1454613 tptp.int) (BOUND_VARIABLE_1454614 tptp.int) (BOUND_VARIABLE_1454615 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9006 BOUND_VARIABLE_1454612) BOUND_VARIABLE_1454613) BOUND_VARIABLE_1454614) BOUND_VARIABLE_1454615) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454613) BOUND_VARIABLE_1454615)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454612) BOUND_VARIABLE_1454614)))))))))) (let ((_let_3066 (forall ((BOUND_VARIABLE_1454587 tptp.int) (BOUND_VARIABLE_1454588 tptp.int) (BOUND_VARIABLE_1454589 tptp.int) (BOUND_VARIABLE_1454590 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9007 BOUND_VARIABLE_1454587) BOUND_VARIABLE_1454588) BOUND_VARIABLE_1454589) BOUND_VARIABLE_1454590) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454588) BOUND_VARIABLE_1454590)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454587) BOUND_VARIABLE_1454589)))))))))) (let ((_let_3067 (forall ((BOUND_VARIABLE_1454562 tptp.int) (BOUND_VARIABLE_1454563 tptp.int) (BOUND_VARIABLE_1454564 tptp.int) (BOUND_VARIABLE_1454565 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9008 BOUND_VARIABLE_1454562) BOUND_VARIABLE_1454563) BOUND_VARIABLE_1454564) BOUND_VARIABLE_1454565) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454563) BOUND_VARIABLE_1454565)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454562) BOUND_VARIABLE_1454564)))))))))) (let ((_let_3068 (forall ((BOUND_VARIABLE_1454537 tptp.int) (BOUND_VARIABLE_1454538 tptp.int) (BOUND_VARIABLE_1454539 tptp.int) (BOUND_VARIABLE_1454540 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9009 BOUND_VARIABLE_1454537) BOUND_VARIABLE_1454538) BOUND_VARIABLE_1454539) BOUND_VARIABLE_1454540) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454538) BOUND_VARIABLE_1454540)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454537) BOUND_VARIABLE_1454539)))))))))) (let ((_let_3069 (forall ((BOUND_VARIABLE_1454512 tptp.int) (BOUND_VARIABLE_1454513 tptp.int) (BOUND_VARIABLE_1454514 tptp.int) (BOUND_VARIABLE_1454515 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9010 BOUND_VARIABLE_1454512) BOUND_VARIABLE_1454513) BOUND_VARIABLE_1454514) BOUND_VARIABLE_1454515) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454513) BOUND_VARIABLE_1454515)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454512) BOUND_VARIABLE_1454514)))))))))) (let ((_let_3070 (forall ((BOUND_VARIABLE_1454487 tptp.int) (BOUND_VARIABLE_1454488 tptp.int) (BOUND_VARIABLE_1454489 tptp.int) (BOUND_VARIABLE_1454490 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9011 BOUND_VARIABLE_1454487) BOUND_VARIABLE_1454488) BOUND_VARIABLE_1454489) BOUND_VARIABLE_1454490) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454488) BOUND_VARIABLE_1454490)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454487) BOUND_VARIABLE_1454489)))))))))) (let ((_let_3071 (forall ((BOUND_VARIABLE_1454462 tptp.int) (BOUND_VARIABLE_1454463 tptp.int) (BOUND_VARIABLE_1454464 tptp.int) (BOUND_VARIABLE_1454465 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9012 BOUND_VARIABLE_1454462) BOUND_VARIABLE_1454463) BOUND_VARIABLE_1454464) BOUND_VARIABLE_1454465) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454463) BOUND_VARIABLE_1454465)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454462) BOUND_VARIABLE_1454464)))))))))) (let ((_let_3072 (forall ((BOUND_VARIABLE_1454437 tptp.int) (BOUND_VARIABLE_1454438 tptp.int) (BOUND_VARIABLE_1454439 tptp.int) (BOUND_VARIABLE_1454440 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9013 BOUND_VARIABLE_1454437) BOUND_VARIABLE_1454438) BOUND_VARIABLE_1454439) BOUND_VARIABLE_1454440) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454438) BOUND_VARIABLE_1454440)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454437) BOUND_VARIABLE_1454439)))))))))) (let ((_let_3073 (forall ((BOUND_VARIABLE_1454412 tptp.int) (BOUND_VARIABLE_1454413 tptp.int) (BOUND_VARIABLE_1454414 tptp.int) (BOUND_VARIABLE_1454415 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9014 BOUND_VARIABLE_1454412) BOUND_VARIABLE_1454413) BOUND_VARIABLE_1454414) BOUND_VARIABLE_1454415) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454413) BOUND_VARIABLE_1454415)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454412) BOUND_VARIABLE_1454414)))))))))) (let ((_let_3074 (forall ((BOUND_VARIABLE_1454387 tptp.int) (BOUND_VARIABLE_1454388 tptp.int) (BOUND_VARIABLE_1454389 tptp.int) (BOUND_VARIABLE_1454390 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9015 BOUND_VARIABLE_1454387) BOUND_VARIABLE_1454388) BOUND_VARIABLE_1454389) BOUND_VARIABLE_1454390) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454388) BOUND_VARIABLE_1454390)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454387) BOUND_VARIABLE_1454389)))))))))) (let ((_let_3075 (forall ((BOUND_VARIABLE_1454362 tptp.int) (BOUND_VARIABLE_1454363 tptp.int) (BOUND_VARIABLE_1454364 tptp.int) (BOUND_VARIABLE_1454365 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9016 BOUND_VARIABLE_1454362) BOUND_VARIABLE_1454363) BOUND_VARIABLE_1454364) BOUND_VARIABLE_1454365) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454363) BOUND_VARIABLE_1454365)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454362) BOUND_VARIABLE_1454364)))))))))) (let ((_let_3076 (forall ((BOUND_VARIABLE_1454337 tptp.int) (BOUND_VARIABLE_1454338 tptp.int) (BOUND_VARIABLE_1454339 tptp.int) (BOUND_VARIABLE_1454340 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9017 BOUND_VARIABLE_1454337) BOUND_VARIABLE_1454338) BOUND_VARIABLE_1454339) BOUND_VARIABLE_1454340) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454338) BOUND_VARIABLE_1454340)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454337) BOUND_VARIABLE_1454339)))))))))) (let ((_let_3077 (forall ((BOUND_VARIABLE_1454312 tptp.int) (BOUND_VARIABLE_1454313 tptp.int) (BOUND_VARIABLE_1454314 tptp.int) (BOUND_VARIABLE_1454315 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9018 BOUND_VARIABLE_1454312) BOUND_VARIABLE_1454313) BOUND_VARIABLE_1454314) BOUND_VARIABLE_1454315) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454313) BOUND_VARIABLE_1454315)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454312) BOUND_VARIABLE_1454314)))))))))) (let ((_let_3078 (forall ((BOUND_VARIABLE_1454287 tptp.int) (BOUND_VARIABLE_1454288 tptp.int) (BOUND_VARIABLE_1454289 tptp.int) (BOUND_VARIABLE_1454290 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9019 BOUND_VARIABLE_1454287) BOUND_VARIABLE_1454288) BOUND_VARIABLE_1454289) BOUND_VARIABLE_1454290) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454288) BOUND_VARIABLE_1454290)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454287) BOUND_VARIABLE_1454289)))))))))) (let ((_let_3079 (forall ((BOUND_VARIABLE_1454262 tptp.int) (BOUND_VARIABLE_1454263 tptp.int) (BOUND_VARIABLE_1454264 tptp.int) (BOUND_VARIABLE_1454265 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9020 BOUND_VARIABLE_1454262) BOUND_VARIABLE_1454263) BOUND_VARIABLE_1454264) BOUND_VARIABLE_1454265) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454263) BOUND_VARIABLE_1454265)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454262) BOUND_VARIABLE_1454264)))))))))) (let ((_let_3080 (forall ((BOUND_VARIABLE_1454237 tptp.int) (BOUND_VARIABLE_1454238 tptp.int) (BOUND_VARIABLE_1454239 tptp.int) (BOUND_VARIABLE_1454240 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9021 BOUND_VARIABLE_1454237) BOUND_VARIABLE_1454238) BOUND_VARIABLE_1454239) BOUND_VARIABLE_1454240) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454238) BOUND_VARIABLE_1454240)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454237) BOUND_VARIABLE_1454239)))))))))) (let ((_let_3081 (forall ((BOUND_VARIABLE_1454212 tptp.int) (BOUND_VARIABLE_1454213 tptp.int) (BOUND_VARIABLE_1454214 tptp.int) (BOUND_VARIABLE_1454215 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9022 BOUND_VARIABLE_1454212) BOUND_VARIABLE_1454213) BOUND_VARIABLE_1454214) BOUND_VARIABLE_1454215) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454213) BOUND_VARIABLE_1454215)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454212) BOUND_VARIABLE_1454214)))))))))) (let ((_let_3082 (forall ((BOUND_VARIABLE_1454187 tptp.int) (BOUND_VARIABLE_1454188 tptp.int) (BOUND_VARIABLE_1454189 tptp.int) (BOUND_VARIABLE_1454190 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9023 BOUND_VARIABLE_1454187) BOUND_VARIABLE_1454188) BOUND_VARIABLE_1454189) BOUND_VARIABLE_1454190) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454188) BOUND_VARIABLE_1454190)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454187) BOUND_VARIABLE_1454189)))))))))) (let ((_let_3083 (forall ((BOUND_VARIABLE_1454162 tptp.int) (BOUND_VARIABLE_1454163 tptp.int) (BOUND_VARIABLE_1454164 tptp.int) (BOUND_VARIABLE_1454165 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9024 BOUND_VARIABLE_1454162) BOUND_VARIABLE_1454163) BOUND_VARIABLE_1454164) BOUND_VARIABLE_1454165) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454163) BOUND_VARIABLE_1454165)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454162) BOUND_VARIABLE_1454164)))))))))) (let ((_let_3084 (forall ((BOUND_VARIABLE_1454137 tptp.int) (BOUND_VARIABLE_1454138 tptp.int) (BOUND_VARIABLE_1454139 tptp.int) (BOUND_VARIABLE_1454140 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9025 BOUND_VARIABLE_1454137) BOUND_VARIABLE_1454138) BOUND_VARIABLE_1454139) BOUND_VARIABLE_1454140) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454138) BOUND_VARIABLE_1454140)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454137) BOUND_VARIABLE_1454139)))))))))) (let ((_let_3085 (forall ((BOUND_VARIABLE_1454112 tptp.int) (BOUND_VARIABLE_1454113 tptp.int) (BOUND_VARIABLE_1454114 tptp.int) (BOUND_VARIABLE_1454115 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9026 BOUND_VARIABLE_1454112) BOUND_VARIABLE_1454113) BOUND_VARIABLE_1454114) BOUND_VARIABLE_1454115) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454113) BOUND_VARIABLE_1454115)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454112) BOUND_VARIABLE_1454114)))))))))) (let ((_let_3086 (forall ((BOUND_VARIABLE_1454087 tptp.int) (BOUND_VARIABLE_1454088 tptp.int) (BOUND_VARIABLE_1454089 tptp.int) (BOUND_VARIABLE_1454090 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9027 BOUND_VARIABLE_1454087) BOUND_VARIABLE_1454088) BOUND_VARIABLE_1454089) BOUND_VARIABLE_1454090) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454088) BOUND_VARIABLE_1454090)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454087) BOUND_VARIABLE_1454089)))))))))) (let ((_let_3087 (forall ((BOUND_VARIABLE_1454062 tptp.int) (BOUND_VARIABLE_1454063 tptp.int) (BOUND_VARIABLE_1454064 tptp.int) (BOUND_VARIABLE_1454065 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9028 BOUND_VARIABLE_1454062) BOUND_VARIABLE_1454063) BOUND_VARIABLE_1454064) BOUND_VARIABLE_1454065) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454063) BOUND_VARIABLE_1454065)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454062) BOUND_VARIABLE_1454064)))))))))) (let ((_let_3088 (forall ((BOUND_VARIABLE_1454037 tptp.int) (BOUND_VARIABLE_1454038 tptp.int) (BOUND_VARIABLE_1454039 tptp.int) (BOUND_VARIABLE_1454040 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9029 BOUND_VARIABLE_1454037) BOUND_VARIABLE_1454038) BOUND_VARIABLE_1454039) BOUND_VARIABLE_1454040) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454038) BOUND_VARIABLE_1454040)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454037) BOUND_VARIABLE_1454039)))))))))) (let ((_let_3089 (forall ((BOUND_VARIABLE_1454012 tptp.int) (BOUND_VARIABLE_1454013 tptp.int) (BOUND_VARIABLE_1454014 tptp.int) (BOUND_VARIABLE_1454015 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9030 BOUND_VARIABLE_1454012) BOUND_VARIABLE_1454013) BOUND_VARIABLE_1454014) BOUND_VARIABLE_1454015) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454013) BOUND_VARIABLE_1454015)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1454012) BOUND_VARIABLE_1454014)))))))))) (let ((_let_3090 (forall ((BOUND_VARIABLE_1453987 tptp.int) (BOUND_VARIABLE_1453988 tptp.int) (BOUND_VARIABLE_1453989 tptp.int) (BOUND_VARIABLE_1453990 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9031 BOUND_VARIABLE_1453987) BOUND_VARIABLE_1453988) BOUND_VARIABLE_1453989) BOUND_VARIABLE_1453990) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453988) BOUND_VARIABLE_1453990)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453987) BOUND_VARIABLE_1453989)))))))))) (let ((_let_3091 (forall ((BOUND_VARIABLE_1453962 tptp.int) (BOUND_VARIABLE_1453963 tptp.int) (BOUND_VARIABLE_1453964 tptp.int) (BOUND_VARIABLE_1453965 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9032 BOUND_VARIABLE_1453962) BOUND_VARIABLE_1453963) BOUND_VARIABLE_1453964) BOUND_VARIABLE_1453965) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453963) BOUND_VARIABLE_1453965)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453962) BOUND_VARIABLE_1453964)))))))))) (let ((_let_3092 (forall ((BOUND_VARIABLE_1453937 tptp.int) (BOUND_VARIABLE_1453938 tptp.int) (BOUND_VARIABLE_1453939 tptp.int) (BOUND_VARIABLE_1453940 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9033 BOUND_VARIABLE_1453937) BOUND_VARIABLE_1453938) BOUND_VARIABLE_1453939) BOUND_VARIABLE_1453940) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453938) BOUND_VARIABLE_1453940)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453937) BOUND_VARIABLE_1453939)))))))))) (let ((_let_3093 (forall ((BOUND_VARIABLE_1453912 tptp.int) (BOUND_VARIABLE_1453913 tptp.int) (BOUND_VARIABLE_1453914 tptp.int) (BOUND_VARIABLE_1453915 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9034 BOUND_VARIABLE_1453912) BOUND_VARIABLE_1453913) BOUND_VARIABLE_1453914) BOUND_VARIABLE_1453915) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453913) BOUND_VARIABLE_1453915)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453912) BOUND_VARIABLE_1453914)))))))))) (let ((_let_3094 (forall ((BOUND_VARIABLE_1453887 tptp.int) (BOUND_VARIABLE_1453888 tptp.int) (BOUND_VARIABLE_1453889 tptp.int) (BOUND_VARIABLE_1453890 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9035 BOUND_VARIABLE_1453887) BOUND_VARIABLE_1453888) BOUND_VARIABLE_1453889) BOUND_VARIABLE_1453890) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453888) BOUND_VARIABLE_1453890)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453887) BOUND_VARIABLE_1453889)))))))))) (let ((_let_3095 (forall ((BOUND_VARIABLE_1453862 tptp.int) (BOUND_VARIABLE_1453863 tptp.int) (BOUND_VARIABLE_1453864 tptp.int) (BOUND_VARIABLE_1453865 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9036 BOUND_VARIABLE_1453862) BOUND_VARIABLE_1453863) BOUND_VARIABLE_1453864) BOUND_VARIABLE_1453865) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453863) BOUND_VARIABLE_1453865)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453862) BOUND_VARIABLE_1453864)))))))))) (let ((_let_3096 (forall ((BOUND_VARIABLE_1453837 tptp.int) (BOUND_VARIABLE_1453838 tptp.int) (BOUND_VARIABLE_1453839 tptp.int) (BOUND_VARIABLE_1453840 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9037 BOUND_VARIABLE_1453837) BOUND_VARIABLE_1453838) BOUND_VARIABLE_1453839) BOUND_VARIABLE_1453840) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453838) BOUND_VARIABLE_1453840)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453837) BOUND_VARIABLE_1453839)))))))))) (let ((_let_3097 (forall ((BOUND_VARIABLE_1453812 tptp.int) (BOUND_VARIABLE_1453813 tptp.int) (BOUND_VARIABLE_1453814 tptp.int) (BOUND_VARIABLE_1453815 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9038 BOUND_VARIABLE_1453812) BOUND_VARIABLE_1453813) BOUND_VARIABLE_1453814) BOUND_VARIABLE_1453815) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453813) BOUND_VARIABLE_1453815)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453812) BOUND_VARIABLE_1453814)))))))))) (let ((_let_3098 (forall ((BOUND_VARIABLE_1453787 tptp.int) (BOUND_VARIABLE_1453788 tptp.int) (BOUND_VARIABLE_1453789 tptp.int) (BOUND_VARIABLE_1453790 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9039 BOUND_VARIABLE_1453787) BOUND_VARIABLE_1453788) BOUND_VARIABLE_1453789) BOUND_VARIABLE_1453790) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453788) BOUND_VARIABLE_1453790)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453787) BOUND_VARIABLE_1453789)))))))))) (let ((_let_3099 (forall ((BOUND_VARIABLE_1453762 tptp.int) (BOUND_VARIABLE_1453763 tptp.int) (BOUND_VARIABLE_1453764 tptp.int) (BOUND_VARIABLE_1453765 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9040 BOUND_VARIABLE_1453762) BOUND_VARIABLE_1453763) BOUND_VARIABLE_1453764) BOUND_VARIABLE_1453765) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453763) BOUND_VARIABLE_1453765)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453762) BOUND_VARIABLE_1453764)))))))))) (let ((_let_3100 (forall ((BOUND_VARIABLE_1453737 tptp.int) (BOUND_VARIABLE_1453738 tptp.int) (BOUND_VARIABLE_1453739 tptp.int) (BOUND_VARIABLE_1453740 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9041 BOUND_VARIABLE_1453737) BOUND_VARIABLE_1453738) BOUND_VARIABLE_1453739) BOUND_VARIABLE_1453740) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453738) BOUND_VARIABLE_1453740)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453737) BOUND_VARIABLE_1453739)))))))))) (let ((_let_3101 (forall ((BOUND_VARIABLE_1453712 tptp.int) (BOUND_VARIABLE_1453713 tptp.int) (BOUND_VARIABLE_1453714 tptp.int) (BOUND_VARIABLE_1453715 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9042 BOUND_VARIABLE_1453712) BOUND_VARIABLE_1453713) BOUND_VARIABLE_1453714) BOUND_VARIABLE_1453715) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453713) BOUND_VARIABLE_1453715)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453712) BOUND_VARIABLE_1453714)))))))))) (let ((_let_3102 (forall ((BOUND_VARIABLE_1453687 tptp.int) (BOUND_VARIABLE_1453688 tptp.int) (BOUND_VARIABLE_1453689 tptp.int) (BOUND_VARIABLE_1453690 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9043 BOUND_VARIABLE_1453687) BOUND_VARIABLE_1453688) BOUND_VARIABLE_1453689) BOUND_VARIABLE_1453690) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453688) BOUND_VARIABLE_1453690)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453687) BOUND_VARIABLE_1453689)))))))))) (let ((_let_3103 (forall ((BOUND_VARIABLE_1453662 tptp.int) (BOUND_VARIABLE_1453663 tptp.int) (BOUND_VARIABLE_1453664 tptp.int) (BOUND_VARIABLE_1453665 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9044 BOUND_VARIABLE_1453662) BOUND_VARIABLE_1453663) BOUND_VARIABLE_1453664) BOUND_VARIABLE_1453665) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453663) BOUND_VARIABLE_1453665)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453662) BOUND_VARIABLE_1453664)))))))))) (let ((_let_3104 (forall ((BOUND_VARIABLE_1453637 tptp.int) (BOUND_VARIABLE_1453638 tptp.int) (BOUND_VARIABLE_1453639 tptp.int) (BOUND_VARIABLE_1453640 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9045 BOUND_VARIABLE_1453637) BOUND_VARIABLE_1453638) BOUND_VARIABLE_1453639) BOUND_VARIABLE_1453640) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453638) BOUND_VARIABLE_1453640)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453637) BOUND_VARIABLE_1453639)))))))))) (let ((_let_3105 (forall ((BOUND_VARIABLE_1453612 tptp.int) (BOUND_VARIABLE_1453613 tptp.int) (BOUND_VARIABLE_1453614 tptp.int) (BOUND_VARIABLE_1453615 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9046 BOUND_VARIABLE_1453612) BOUND_VARIABLE_1453613) BOUND_VARIABLE_1453614) BOUND_VARIABLE_1453615) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453613) BOUND_VARIABLE_1453615)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453612) BOUND_VARIABLE_1453614)))))))))) (let ((_let_3106 (forall ((BOUND_VARIABLE_1453587 tptp.int) (BOUND_VARIABLE_1453588 tptp.int) (BOUND_VARIABLE_1453589 tptp.int) (BOUND_VARIABLE_1453590 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9047 BOUND_VARIABLE_1453587) BOUND_VARIABLE_1453588) BOUND_VARIABLE_1453589) BOUND_VARIABLE_1453590) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453588) BOUND_VARIABLE_1453590)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453587) BOUND_VARIABLE_1453589)))))))))) (let ((_let_3107 (forall ((BOUND_VARIABLE_1453562 tptp.int) (BOUND_VARIABLE_1453563 tptp.int) (BOUND_VARIABLE_1453564 tptp.int) (BOUND_VARIABLE_1453565 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9048 BOUND_VARIABLE_1453562) BOUND_VARIABLE_1453563) BOUND_VARIABLE_1453564) BOUND_VARIABLE_1453565) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453563) BOUND_VARIABLE_1453565)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453562) BOUND_VARIABLE_1453564)))))))))) (let ((_let_3108 (forall ((BOUND_VARIABLE_1453537 tptp.int) (BOUND_VARIABLE_1453538 tptp.int) (BOUND_VARIABLE_1453539 tptp.int) (BOUND_VARIABLE_1453540 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9049 BOUND_VARIABLE_1453537) BOUND_VARIABLE_1453538) BOUND_VARIABLE_1453539) BOUND_VARIABLE_1453540) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453538) BOUND_VARIABLE_1453540)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453537) BOUND_VARIABLE_1453539)))))))))) (let ((_let_3109 (forall ((BOUND_VARIABLE_1453512 tptp.int) (BOUND_VARIABLE_1453513 tptp.int) (BOUND_VARIABLE_1453514 tptp.int) (BOUND_VARIABLE_1453515 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9050 BOUND_VARIABLE_1453512) BOUND_VARIABLE_1453513) BOUND_VARIABLE_1453514) BOUND_VARIABLE_1453515) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453513) BOUND_VARIABLE_1453515)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453512) BOUND_VARIABLE_1453514)))))))))) (let ((_let_3110 (forall ((BOUND_VARIABLE_1453495 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1453496 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_9051 BOUND_VARIABLE_1453495) BOUND_VARIABLE_1453496) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1453496 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1453495) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1453495))))))))))) (let ((_let_3111 (forall ((BOUND_VARIABLE_1453478 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1453479 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_9052 BOUND_VARIABLE_1453478) BOUND_VARIABLE_1453479) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1453479 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1453478) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1453478))))))))))) (let ((_let_3112 (forall ((BOUND_VARIABLE_1453461 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1453462 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_9053 BOUND_VARIABLE_1453461) BOUND_VARIABLE_1453462) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1453462 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1453461) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1453461))))))))))) (let ((_let_3113 (forall ((BOUND_VARIABLE_1453444 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1453445 tptp.vEBT_VEBT)) (= (ho_7817 (ho_7816 k_9054 BOUND_VARIABLE_1453444) BOUND_VARIABLE_1453445) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1453445 (ho_7822 (ho_7821 k_7820 BOUND_VARIABLE_1453444) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7819 k_7818 BOUND_VARIABLE_1453444))))))))))) (let ((_let_3114 (forall ((BOUND_VARIABLE_1453419 tptp.int) (BOUND_VARIABLE_1453420 tptp.int) (BOUND_VARIABLE_1453421 tptp.int) (BOUND_VARIABLE_1453422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9055 BOUND_VARIABLE_1453419) BOUND_VARIABLE_1453420) BOUND_VARIABLE_1453421) BOUND_VARIABLE_1453422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453420) BOUND_VARIABLE_1453422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453419) BOUND_VARIABLE_1453421)))))))))) (let ((_let_3115 (forall ((BOUND_VARIABLE_1453394 tptp.int) (BOUND_VARIABLE_1453395 tptp.int) (BOUND_VARIABLE_1453396 tptp.int) (BOUND_VARIABLE_1453397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9056 BOUND_VARIABLE_1453394) BOUND_VARIABLE_1453395) BOUND_VARIABLE_1453396) BOUND_VARIABLE_1453397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453395) BOUND_VARIABLE_1453397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453394) BOUND_VARIABLE_1453396)))))))))) (let ((_let_3116 (forall ((BOUND_VARIABLE_1453369 tptp.int) (BOUND_VARIABLE_1453370 tptp.int) (BOUND_VARIABLE_1453371 tptp.int) (BOUND_VARIABLE_1453372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9057 BOUND_VARIABLE_1453369) BOUND_VARIABLE_1453370) BOUND_VARIABLE_1453371) BOUND_VARIABLE_1453372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453370) BOUND_VARIABLE_1453372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453369) BOUND_VARIABLE_1453371)))))))))) (let ((_let_3117 (forall ((BOUND_VARIABLE_1453344 tptp.int) (BOUND_VARIABLE_1453345 tptp.int) (BOUND_VARIABLE_1453346 tptp.int) (BOUND_VARIABLE_1453347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9058 BOUND_VARIABLE_1453344) BOUND_VARIABLE_1453345) BOUND_VARIABLE_1453346) BOUND_VARIABLE_1453347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453345) BOUND_VARIABLE_1453347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453344) BOUND_VARIABLE_1453346)))))))))) (let ((_let_3118 (forall ((BOUND_VARIABLE_1453319 tptp.int) (BOUND_VARIABLE_1453320 tptp.int) (BOUND_VARIABLE_1453321 tptp.int) (BOUND_VARIABLE_1453322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9059 BOUND_VARIABLE_1453319) BOUND_VARIABLE_1453320) BOUND_VARIABLE_1453321) BOUND_VARIABLE_1453322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453320) BOUND_VARIABLE_1453322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453319) BOUND_VARIABLE_1453321)))))))))) (let ((_let_3119 (forall ((BOUND_VARIABLE_1453294 tptp.int) (BOUND_VARIABLE_1453295 tptp.int) (BOUND_VARIABLE_1453296 tptp.int) (BOUND_VARIABLE_1453297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9060 BOUND_VARIABLE_1453294) BOUND_VARIABLE_1453295) BOUND_VARIABLE_1453296) BOUND_VARIABLE_1453297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453295) BOUND_VARIABLE_1453297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453294) BOUND_VARIABLE_1453296)))))))))) (let ((_let_3120 (forall ((BOUND_VARIABLE_1453269 tptp.int) (BOUND_VARIABLE_1453270 tptp.int) (BOUND_VARIABLE_1453271 tptp.int) (BOUND_VARIABLE_1453272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9061 BOUND_VARIABLE_1453269) BOUND_VARIABLE_1453270) BOUND_VARIABLE_1453271) BOUND_VARIABLE_1453272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453270) BOUND_VARIABLE_1453272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453269) BOUND_VARIABLE_1453271)))))))))) (let ((_let_3121 (forall ((BOUND_VARIABLE_1453244 tptp.int) (BOUND_VARIABLE_1453245 tptp.int) (BOUND_VARIABLE_1453246 tptp.int) (BOUND_VARIABLE_1453247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9062 BOUND_VARIABLE_1453244) BOUND_VARIABLE_1453245) BOUND_VARIABLE_1453246) BOUND_VARIABLE_1453247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453245) BOUND_VARIABLE_1453247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453244) BOUND_VARIABLE_1453246)))))))))) (let ((_let_3122 (forall ((BOUND_VARIABLE_1453219 tptp.int) (BOUND_VARIABLE_1453220 tptp.int) (BOUND_VARIABLE_1453221 tptp.int) (BOUND_VARIABLE_1453222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9063 BOUND_VARIABLE_1453219) BOUND_VARIABLE_1453220) BOUND_VARIABLE_1453221) BOUND_VARIABLE_1453222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453220) BOUND_VARIABLE_1453222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453219) BOUND_VARIABLE_1453221)))))))))) (let ((_let_3123 (forall ((BOUND_VARIABLE_1453194 tptp.int) (BOUND_VARIABLE_1453195 tptp.int) (BOUND_VARIABLE_1453196 tptp.int) (BOUND_VARIABLE_1453197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9064 BOUND_VARIABLE_1453194) BOUND_VARIABLE_1453195) BOUND_VARIABLE_1453196) BOUND_VARIABLE_1453197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453195) BOUND_VARIABLE_1453197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453194) BOUND_VARIABLE_1453196)))))))))) (let ((_let_3124 (forall ((BOUND_VARIABLE_1453169 tptp.int) (BOUND_VARIABLE_1453170 tptp.int) (BOUND_VARIABLE_1453171 tptp.int) (BOUND_VARIABLE_1453172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9065 BOUND_VARIABLE_1453169) BOUND_VARIABLE_1453170) BOUND_VARIABLE_1453171) BOUND_VARIABLE_1453172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453170) BOUND_VARIABLE_1453172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453169) BOUND_VARIABLE_1453171)))))))))) (let ((_let_3125 (forall ((BOUND_VARIABLE_1453144 tptp.int) (BOUND_VARIABLE_1453145 tptp.int) (BOUND_VARIABLE_1453146 tptp.int) (BOUND_VARIABLE_1453147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9066 BOUND_VARIABLE_1453144) BOUND_VARIABLE_1453145) BOUND_VARIABLE_1453146) BOUND_VARIABLE_1453147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453145) BOUND_VARIABLE_1453147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453144) BOUND_VARIABLE_1453146)))))))))) (let ((_let_3126 (forall ((BOUND_VARIABLE_1453119 tptp.int) (BOUND_VARIABLE_1453120 tptp.int) (BOUND_VARIABLE_1453121 tptp.int) (BOUND_VARIABLE_1453122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9067 BOUND_VARIABLE_1453119) BOUND_VARIABLE_1453120) BOUND_VARIABLE_1453121) BOUND_VARIABLE_1453122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453120) BOUND_VARIABLE_1453122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453119) BOUND_VARIABLE_1453121)))))))))) (let ((_let_3127 (forall ((BOUND_VARIABLE_1453094 tptp.int) (BOUND_VARIABLE_1453095 tptp.int) (BOUND_VARIABLE_1453096 tptp.int) (BOUND_VARIABLE_1453097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9068 BOUND_VARIABLE_1453094) BOUND_VARIABLE_1453095) BOUND_VARIABLE_1453096) BOUND_VARIABLE_1453097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453095) BOUND_VARIABLE_1453097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453094) BOUND_VARIABLE_1453096)))))))))) (let ((_let_3128 (forall ((BOUND_VARIABLE_1453069 tptp.int) (BOUND_VARIABLE_1453070 tptp.int) (BOUND_VARIABLE_1453071 tptp.int) (BOUND_VARIABLE_1453072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9069 BOUND_VARIABLE_1453069) BOUND_VARIABLE_1453070) BOUND_VARIABLE_1453071) BOUND_VARIABLE_1453072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453070) BOUND_VARIABLE_1453072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453069) BOUND_VARIABLE_1453071)))))))))) (let ((_let_3129 (forall ((BOUND_VARIABLE_1453044 tptp.int) (BOUND_VARIABLE_1453045 tptp.int) (BOUND_VARIABLE_1453046 tptp.int) (BOUND_VARIABLE_1453047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9070 BOUND_VARIABLE_1453044) BOUND_VARIABLE_1453045) BOUND_VARIABLE_1453046) BOUND_VARIABLE_1453047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453045) BOUND_VARIABLE_1453047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453044) BOUND_VARIABLE_1453046)))))))))) (let ((_let_3130 (forall ((BOUND_VARIABLE_1453019 tptp.int) (BOUND_VARIABLE_1453020 tptp.int) (BOUND_VARIABLE_1453021 tptp.int) (BOUND_VARIABLE_1453022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9071 BOUND_VARIABLE_1453019) BOUND_VARIABLE_1453020) BOUND_VARIABLE_1453021) BOUND_VARIABLE_1453022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453020) BOUND_VARIABLE_1453022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1453019) BOUND_VARIABLE_1453021)))))))))) (let ((_let_3131 (forall ((BOUND_VARIABLE_1452994 tptp.int) (BOUND_VARIABLE_1452995 tptp.int) (BOUND_VARIABLE_1452996 tptp.int) (BOUND_VARIABLE_1452997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9072 BOUND_VARIABLE_1452994) BOUND_VARIABLE_1452995) BOUND_VARIABLE_1452996) BOUND_VARIABLE_1452997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452995) BOUND_VARIABLE_1452997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452994) BOUND_VARIABLE_1452996)))))))))) (let ((_let_3132 (forall ((BOUND_VARIABLE_1452969 tptp.int) (BOUND_VARIABLE_1452970 tptp.int) (BOUND_VARIABLE_1452971 tptp.int) (BOUND_VARIABLE_1452972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9073 BOUND_VARIABLE_1452969) BOUND_VARIABLE_1452970) BOUND_VARIABLE_1452971) BOUND_VARIABLE_1452972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452970) BOUND_VARIABLE_1452972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452969) BOUND_VARIABLE_1452971)))))))))) (let ((_let_3133 (forall ((BOUND_VARIABLE_1452944 tptp.int) (BOUND_VARIABLE_1452945 tptp.int) (BOUND_VARIABLE_1452946 tptp.int) (BOUND_VARIABLE_1452947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9074 BOUND_VARIABLE_1452944) BOUND_VARIABLE_1452945) BOUND_VARIABLE_1452946) BOUND_VARIABLE_1452947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452945) BOUND_VARIABLE_1452947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452944) BOUND_VARIABLE_1452946)))))))))) (let ((_let_3134 (forall ((BOUND_VARIABLE_1452919 tptp.int) (BOUND_VARIABLE_1452920 tptp.int) (BOUND_VARIABLE_1452921 tptp.int) (BOUND_VARIABLE_1452922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9075 BOUND_VARIABLE_1452919) BOUND_VARIABLE_1452920) BOUND_VARIABLE_1452921) BOUND_VARIABLE_1452922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452920) BOUND_VARIABLE_1452922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452919) BOUND_VARIABLE_1452921)))))))))) (let ((_let_3135 (forall ((BOUND_VARIABLE_1452894 tptp.int) (BOUND_VARIABLE_1452895 tptp.int) (BOUND_VARIABLE_1452896 tptp.int) (BOUND_VARIABLE_1452897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9076 BOUND_VARIABLE_1452894) BOUND_VARIABLE_1452895) BOUND_VARIABLE_1452896) BOUND_VARIABLE_1452897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452895) BOUND_VARIABLE_1452897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452894) BOUND_VARIABLE_1452896)))))))))) (let ((_let_3136 (forall ((BOUND_VARIABLE_1452869 tptp.int) (BOUND_VARIABLE_1452870 tptp.int) (BOUND_VARIABLE_1452871 tptp.int) (BOUND_VARIABLE_1452872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9077 BOUND_VARIABLE_1452869) BOUND_VARIABLE_1452870) BOUND_VARIABLE_1452871) BOUND_VARIABLE_1452872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452870) BOUND_VARIABLE_1452872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452869) BOUND_VARIABLE_1452871)))))))))) (let ((_let_3137 (forall ((BOUND_VARIABLE_1452844 tptp.int) (BOUND_VARIABLE_1452845 tptp.int) (BOUND_VARIABLE_1452846 tptp.int) (BOUND_VARIABLE_1452847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9078 BOUND_VARIABLE_1452844) BOUND_VARIABLE_1452845) BOUND_VARIABLE_1452846) BOUND_VARIABLE_1452847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452845) BOUND_VARIABLE_1452847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452844) BOUND_VARIABLE_1452846)))))))))) (let ((_let_3138 (forall ((BOUND_VARIABLE_1452819 tptp.int) (BOUND_VARIABLE_1452820 tptp.int) (BOUND_VARIABLE_1452821 tptp.int) (BOUND_VARIABLE_1452822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9079 BOUND_VARIABLE_1452819) BOUND_VARIABLE_1452820) BOUND_VARIABLE_1452821) BOUND_VARIABLE_1452822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452820) BOUND_VARIABLE_1452822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452819) BOUND_VARIABLE_1452821)))))))))) (let ((_let_3139 (forall ((BOUND_VARIABLE_1452794 tptp.int) (BOUND_VARIABLE_1452795 tptp.int) (BOUND_VARIABLE_1452796 tptp.int) (BOUND_VARIABLE_1452797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9080 BOUND_VARIABLE_1452794) BOUND_VARIABLE_1452795) BOUND_VARIABLE_1452796) BOUND_VARIABLE_1452797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452795) BOUND_VARIABLE_1452797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452794) BOUND_VARIABLE_1452796)))))))))) (let ((_let_3140 (forall ((BOUND_VARIABLE_1452769 tptp.int) (BOUND_VARIABLE_1452770 tptp.int) (BOUND_VARIABLE_1452771 tptp.int) (BOUND_VARIABLE_1452772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9081 BOUND_VARIABLE_1452769) BOUND_VARIABLE_1452770) BOUND_VARIABLE_1452771) BOUND_VARIABLE_1452772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452770) BOUND_VARIABLE_1452772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452769) BOUND_VARIABLE_1452771)))))))))) (let ((_let_3141 (forall ((BOUND_VARIABLE_1452744 tptp.int) (BOUND_VARIABLE_1452745 tptp.int) (BOUND_VARIABLE_1452746 tptp.int) (BOUND_VARIABLE_1452747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9082 BOUND_VARIABLE_1452744) BOUND_VARIABLE_1452745) BOUND_VARIABLE_1452746) BOUND_VARIABLE_1452747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452745) BOUND_VARIABLE_1452747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452744) BOUND_VARIABLE_1452746)))))))))) (let ((_let_3142 (forall ((BOUND_VARIABLE_1452719 tptp.int) (BOUND_VARIABLE_1452720 tptp.int) (BOUND_VARIABLE_1452721 tptp.int) (BOUND_VARIABLE_1452722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9083 BOUND_VARIABLE_1452719) BOUND_VARIABLE_1452720) BOUND_VARIABLE_1452721) BOUND_VARIABLE_1452722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452720) BOUND_VARIABLE_1452722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452719) BOUND_VARIABLE_1452721)))))))))) (let ((_let_3143 (forall ((BOUND_VARIABLE_1452694 tptp.int) (BOUND_VARIABLE_1452695 tptp.int) (BOUND_VARIABLE_1452696 tptp.int) (BOUND_VARIABLE_1452697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9084 BOUND_VARIABLE_1452694) BOUND_VARIABLE_1452695) BOUND_VARIABLE_1452696) BOUND_VARIABLE_1452697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452695) BOUND_VARIABLE_1452697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452694) BOUND_VARIABLE_1452696)))))))))) (let ((_let_3144 (forall ((BOUND_VARIABLE_1452669 tptp.int) (BOUND_VARIABLE_1452670 tptp.int) (BOUND_VARIABLE_1452671 tptp.int) (BOUND_VARIABLE_1452672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9085 BOUND_VARIABLE_1452669) BOUND_VARIABLE_1452670) BOUND_VARIABLE_1452671) BOUND_VARIABLE_1452672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452670) BOUND_VARIABLE_1452672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452669) BOUND_VARIABLE_1452671)))))))))) (let ((_let_3145 (forall ((BOUND_VARIABLE_1452644 tptp.int) (BOUND_VARIABLE_1452645 tptp.int) (BOUND_VARIABLE_1452646 tptp.int) (BOUND_VARIABLE_1452647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9086 BOUND_VARIABLE_1452644) BOUND_VARIABLE_1452645) BOUND_VARIABLE_1452646) BOUND_VARIABLE_1452647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452645) BOUND_VARIABLE_1452647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452644) BOUND_VARIABLE_1452646)))))))))) (let ((_let_3146 (forall ((BOUND_VARIABLE_1452619 tptp.int) (BOUND_VARIABLE_1452620 tptp.int) (BOUND_VARIABLE_1452621 tptp.int) (BOUND_VARIABLE_1452622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9087 BOUND_VARIABLE_1452619) BOUND_VARIABLE_1452620) BOUND_VARIABLE_1452621) BOUND_VARIABLE_1452622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452620) BOUND_VARIABLE_1452622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452619) BOUND_VARIABLE_1452621)))))))))) (let ((_let_3147 (forall ((BOUND_VARIABLE_1452594 tptp.int) (BOUND_VARIABLE_1452595 tptp.int) (BOUND_VARIABLE_1452596 tptp.int) (BOUND_VARIABLE_1452597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9088 BOUND_VARIABLE_1452594) BOUND_VARIABLE_1452595) BOUND_VARIABLE_1452596) BOUND_VARIABLE_1452597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452595) BOUND_VARIABLE_1452597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452594) BOUND_VARIABLE_1452596)))))))))) (let ((_let_3148 (forall ((BOUND_VARIABLE_1452569 tptp.int) (BOUND_VARIABLE_1452570 tptp.int) (BOUND_VARIABLE_1452571 tptp.int) (BOUND_VARIABLE_1452572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9089 BOUND_VARIABLE_1452569) BOUND_VARIABLE_1452570) BOUND_VARIABLE_1452571) BOUND_VARIABLE_1452572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452570) BOUND_VARIABLE_1452572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452569) BOUND_VARIABLE_1452571)))))))))) (let ((_let_3149 (forall ((BOUND_VARIABLE_1452544 tptp.int) (BOUND_VARIABLE_1452545 tptp.int) (BOUND_VARIABLE_1452546 tptp.int) (BOUND_VARIABLE_1452547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9090 BOUND_VARIABLE_1452544) BOUND_VARIABLE_1452545) BOUND_VARIABLE_1452546) BOUND_VARIABLE_1452547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452545) BOUND_VARIABLE_1452547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452544) BOUND_VARIABLE_1452546)))))))))) (let ((_let_3150 (forall ((BOUND_VARIABLE_1452519 tptp.int) (BOUND_VARIABLE_1452520 tptp.int) (BOUND_VARIABLE_1452521 tptp.int) (BOUND_VARIABLE_1452522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9091 BOUND_VARIABLE_1452519) BOUND_VARIABLE_1452520) BOUND_VARIABLE_1452521) BOUND_VARIABLE_1452522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452520) BOUND_VARIABLE_1452522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452519) BOUND_VARIABLE_1452521)))))))))) (let ((_let_3151 (forall ((BOUND_VARIABLE_1452494 tptp.int) (BOUND_VARIABLE_1452495 tptp.int) (BOUND_VARIABLE_1452496 tptp.int) (BOUND_VARIABLE_1452497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9092 BOUND_VARIABLE_1452494) BOUND_VARIABLE_1452495) BOUND_VARIABLE_1452496) BOUND_VARIABLE_1452497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452495) BOUND_VARIABLE_1452497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452494) BOUND_VARIABLE_1452496)))))))))) (let ((_let_3152 (forall ((BOUND_VARIABLE_1452469 tptp.int) (BOUND_VARIABLE_1452470 tptp.int) (BOUND_VARIABLE_1452471 tptp.int) (BOUND_VARIABLE_1452472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9093 BOUND_VARIABLE_1452469) BOUND_VARIABLE_1452470) BOUND_VARIABLE_1452471) BOUND_VARIABLE_1452472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452470) BOUND_VARIABLE_1452472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452469) BOUND_VARIABLE_1452471)))))))))) (let ((_let_3153 (forall ((BOUND_VARIABLE_1452444 tptp.int) (BOUND_VARIABLE_1452445 tptp.int) (BOUND_VARIABLE_1452446 tptp.int) (BOUND_VARIABLE_1452447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9094 BOUND_VARIABLE_1452444) BOUND_VARIABLE_1452445) BOUND_VARIABLE_1452446) BOUND_VARIABLE_1452447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452445) BOUND_VARIABLE_1452447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452444) BOUND_VARIABLE_1452446)))))))))) (let ((_let_3154 (forall ((BOUND_VARIABLE_1452419 tptp.int) (BOUND_VARIABLE_1452420 tptp.int) (BOUND_VARIABLE_1452421 tptp.int) (BOUND_VARIABLE_1452422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9095 BOUND_VARIABLE_1452419) BOUND_VARIABLE_1452420) BOUND_VARIABLE_1452421) BOUND_VARIABLE_1452422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452420) BOUND_VARIABLE_1452422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452419) BOUND_VARIABLE_1452421)))))))))) (let ((_let_3155 (forall ((BOUND_VARIABLE_1452394 tptp.int) (BOUND_VARIABLE_1452395 tptp.int) (BOUND_VARIABLE_1452396 tptp.int) (BOUND_VARIABLE_1452397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9096 BOUND_VARIABLE_1452394) BOUND_VARIABLE_1452395) BOUND_VARIABLE_1452396) BOUND_VARIABLE_1452397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452395) BOUND_VARIABLE_1452397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452394) BOUND_VARIABLE_1452396)))))))))) (let ((_let_3156 (forall ((BOUND_VARIABLE_1452369 tptp.int) (BOUND_VARIABLE_1452370 tptp.int) (BOUND_VARIABLE_1452371 tptp.int) (BOUND_VARIABLE_1452372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9097 BOUND_VARIABLE_1452369) BOUND_VARIABLE_1452370) BOUND_VARIABLE_1452371) BOUND_VARIABLE_1452372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452370) BOUND_VARIABLE_1452372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452369) BOUND_VARIABLE_1452371)))))))))) (let ((_let_3157 (forall ((BOUND_VARIABLE_1452344 tptp.int) (BOUND_VARIABLE_1452345 tptp.int) (BOUND_VARIABLE_1452346 tptp.int) (BOUND_VARIABLE_1452347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9098 BOUND_VARIABLE_1452344) BOUND_VARIABLE_1452345) BOUND_VARIABLE_1452346) BOUND_VARIABLE_1452347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452345) BOUND_VARIABLE_1452347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452344) BOUND_VARIABLE_1452346)))))))))) (let ((_let_3158 (forall ((BOUND_VARIABLE_1452319 tptp.int) (BOUND_VARIABLE_1452320 tptp.int) (BOUND_VARIABLE_1452321 tptp.int) (BOUND_VARIABLE_1452322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9099 BOUND_VARIABLE_1452319) BOUND_VARIABLE_1452320) BOUND_VARIABLE_1452321) BOUND_VARIABLE_1452322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452320) BOUND_VARIABLE_1452322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452319) BOUND_VARIABLE_1452321)))))))))) (let ((_let_3159 (forall ((BOUND_VARIABLE_1452294 tptp.int) (BOUND_VARIABLE_1452295 tptp.int) (BOUND_VARIABLE_1452296 tptp.int) (BOUND_VARIABLE_1452297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9100 BOUND_VARIABLE_1452294) BOUND_VARIABLE_1452295) BOUND_VARIABLE_1452296) BOUND_VARIABLE_1452297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452295) BOUND_VARIABLE_1452297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452294) BOUND_VARIABLE_1452296)))))))))) (let ((_let_3160 (forall ((BOUND_VARIABLE_1452269 tptp.int) (BOUND_VARIABLE_1452270 tptp.int) (BOUND_VARIABLE_1452271 tptp.int) (BOUND_VARIABLE_1452272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9101 BOUND_VARIABLE_1452269) BOUND_VARIABLE_1452270) BOUND_VARIABLE_1452271) BOUND_VARIABLE_1452272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452270) BOUND_VARIABLE_1452272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452269) BOUND_VARIABLE_1452271)))))))))) (let ((_let_3161 (forall ((BOUND_VARIABLE_1452244 tptp.int) (BOUND_VARIABLE_1452245 tptp.int) (BOUND_VARIABLE_1452246 tptp.int) (BOUND_VARIABLE_1452247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9102 BOUND_VARIABLE_1452244) BOUND_VARIABLE_1452245) BOUND_VARIABLE_1452246) BOUND_VARIABLE_1452247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452245) BOUND_VARIABLE_1452247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452244) BOUND_VARIABLE_1452246)))))))))) (let ((_let_3162 (forall ((BOUND_VARIABLE_1452219 tptp.int) (BOUND_VARIABLE_1452220 tptp.int) (BOUND_VARIABLE_1452221 tptp.int) (BOUND_VARIABLE_1452222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9103 BOUND_VARIABLE_1452219) BOUND_VARIABLE_1452220) BOUND_VARIABLE_1452221) BOUND_VARIABLE_1452222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452220) BOUND_VARIABLE_1452222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452219) BOUND_VARIABLE_1452221)))))))))) (let ((_let_3163 (forall ((BOUND_VARIABLE_1452194 tptp.int) (BOUND_VARIABLE_1452195 tptp.int) (BOUND_VARIABLE_1452196 tptp.int) (BOUND_VARIABLE_1452197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9104 BOUND_VARIABLE_1452194) BOUND_VARIABLE_1452195) BOUND_VARIABLE_1452196) BOUND_VARIABLE_1452197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452195) BOUND_VARIABLE_1452197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452194) BOUND_VARIABLE_1452196)))))))))) (let ((_let_3164 (forall ((BOUND_VARIABLE_1452169 tptp.int) (BOUND_VARIABLE_1452170 tptp.int) (BOUND_VARIABLE_1452171 tptp.int) (BOUND_VARIABLE_1452172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9105 BOUND_VARIABLE_1452169) BOUND_VARIABLE_1452170) BOUND_VARIABLE_1452171) BOUND_VARIABLE_1452172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452170) BOUND_VARIABLE_1452172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452169) BOUND_VARIABLE_1452171)))))))))) (let ((_let_3165 (forall ((BOUND_VARIABLE_1452144 tptp.int) (BOUND_VARIABLE_1452145 tptp.int) (BOUND_VARIABLE_1452146 tptp.int) (BOUND_VARIABLE_1452147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9106 BOUND_VARIABLE_1452144) BOUND_VARIABLE_1452145) BOUND_VARIABLE_1452146) BOUND_VARIABLE_1452147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452145) BOUND_VARIABLE_1452147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452144) BOUND_VARIABLE_1452146)))))))))) (let ((_let_3166 (forall ((BOUND_VARIABLE_1452119 tptp.int) (BOUND_VARIABLE_1452120 tptp.int) (BOUND_VARIABLE_1452121 tptp.int) (BOUND_VARIABLE_1452122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9107 BOUND_VARIABLE_1452119) BOUND_VARIABLE_1452120) BOUND_VARIABLE_1452121) BOUND_VARIABLE_1452122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452120) BOUND_VARIABLE_1452122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452119) BOUND_VARIABLE_1452121)))))))))) (let ((_let_3167 (forall ((BOUND_VARIABLE_1452094 tptp.int) (BOUND_VARIABLE_1452095 tptp.int) (BOUND_VARIABLE_1452096 tptp.int) (BOUND_VARIABLE_1452097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9108 BOUND_VARIABLE_1452094) BOUND_VARIABLE_1452095) BOUND_VARIABLE_1452096) BOUND_VARIABLE_1452097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452095) BOUND_VARIABLE_1452097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452094) BOUND_VARIABLE_1452096)))))))))) (let ((_let_3168 (forall ((BOUND_VARIABLE_1452069 tptp.int) (BOUND_VARIABLE_1452070 tptp.int) (BOUND_VARIABLE_1452071 tptp.int) (BOUND_VARIABLE_1452072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9109 BOUND_VARIABLE_1452069) BOUND_VARIABLE_1452070) BOUND_VARIABLE_1452071) BOUND_VARIABLE_1452072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452070) BOUND_VARIABLE_1452072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452069) BOUND_VARIABLE_1452071)))))))))) (let ((_let_3169 (forall ((BOUND_VARIABLE_1452044 tptp.int) (BOUND_VARIABLE_1452045 tptp.int) (BOUND_VARIABLE_1452046 tptp.int) (BOUND_VARIABLE_1452047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9110 BOUND_VARIABLE_1452044) BOUND_VARIABLE_1452045) BOUND_VARIABLE_1452046) BOUND_VARIABLE_1452047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452045) BOUND_VARIABLE_1452047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452044) BOUND_VARIABLE_1452046)))))))))) (let ((_let_3170 (forall ((BOUND_VARIABLE_1452019 tptp.int) (BOUND_VARIABLE_1452020 tptp.int) (BOUND_VARIABLE_1452021 tptp.int) (BOUND_VARIABLE_1452022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9111 BOUND_VARIABLE_1452019) BOUND_VARIABLE_1452020) BOUND_VARIABLE_1452021) BOUND_VARIABLE_1452022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452020) BOUND_VARIABLE_1452022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1452019) BOUND_VARIABLE_1452021)))))))))) (let ((_let_3171 (forall ((BOUND_VARIABLE_1451994 tptp.int) (BOUND_VARIABLE_1451995 tptp.int) (BOUND_VARIABLE_1451996 tptp.int) (BOUND_VARIABLE_1451997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9112 BOUND_VARIABLE_1451994) BOUND_VARIABLE_1451995) BOUND_VARIABLE_1451996) BOUND_VARIABLE_1451997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451995) BOUND_VARIABLE_1451997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451994) BOUND_VARIABLE_1451996)))))))))) (let ((_let_3172 (forall ((BOUND_VARIABLE_1451969 tptp.int) (BOUND_VARIABLE_1451970 tptp.int) (BOUND_VARIABLE_1451971 tptp.int) (BOUND_VARIABLE_1451972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9113 BOUND_VARIABLE_1451969) BOUND_VARIABLE_1451970) BOUND_VARIABLE_1451971) BOUND_VARIABLE_1451972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451970) BOUND_VARIABLE_1451972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451969) BOUND_VARIABLE_1451971)))))))))) (let ((_let_3173 (forall ((BOUND_VARIABLE_1451944 tptp.int) (BOUND_VARIABLE_1451945 tptp.int) (BOUND_VARIABLE_1451946 tptp.int) (BOUND_VARIABLE_1451947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9114 BOUND_VARIABLE_1451944) BOUND_VARIABLE_1451945) BOUND_VARIABLE_1451946) BOUND_VARIABLE_1451947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451945) BOUND_VARIABLE_1451947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451944) BOUND_VARIABLE_1451946)))))))))) (let ((_let_3174 (forall ((BOUND_VARIABLE_1451919 tptp.int) (BOUND_VARIABLE_1451920 tptp.int) (BOUND_VARIABLE_1451921 tptp.int) (BOUND_VARIABLE_1451922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9115 BOUND_VARIABLE_1451919) BOUND_VARIABLE_1451920) BOUND_VARIABLE_1451921) BOUND_VARIABLE_1451922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451920) BOUND_VARIABLE_1451922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451919) BOUND_VARIABLE_1451921)))))))))) (let ((_let_3175 (forall ((BOUND_VARIABLE_1451894 tptp.int) (BOUND_VARIABLE_1451895 tptp.int) (BOUND_VARIABLE_1451896 tptp.int) (BOUND_VARIABLE_1451897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9116 BOUND_VARIABLE_1451894) BOUND_VARIABLE_1451895) BOUND_VARIABLE_1451896) BOUND_VARIABLE_1451897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451895) BOUND_VARIABLE_1451897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451894) BOUND_VARIABLE_1451896)))))))))) (let ((_let_3176 (forall ((BOUND_VARIABLE_1451869 tptp.int) (BOUND_VARIABLE_1451870 tptp.int) (BOUND_VARIABLE_1451871 tptp.int) (BOUND_VARIABLE_1451872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9117 BOUND_VARIABLE_1451869) BOUND_VARIABLE_1451870) BOUND_VARIABLE_1451871) BOUND_VARIABLE_1451872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451870) BOUND_VARIABLE_1451872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451869) BOUND_VARIABLE_1451871)))))))))) (let ((_let_3177 (forall ((BOUND_VARIABLE_1451844 tptp.int) (BOUND_VARIABLE_1451845 tptp.int) (BOUND_VARIABLE_1451846 tptp.int) (BOUND_VARIABLE_1451847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9118 BOUND_VARIABLE_1451844) BOUND_VARIABLE_1451845) BOUND_VARIABLE_1451846) BOUND_VARIABLE_1451847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451845) BOUND_VARIABLE_1451847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451844) BOUND_VARIABLE_1451846)))))))))) (let ((_let_3178 (forall ((BOUND_VARIABLE_1451819 tptp.int) (BOUND_VARIABLE_1451820 tptp.int) (BOUND_VARIABLE_1451821 tptp.int) (BOUND_VARIABLE_1451822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9119 BOUND_VARIABLE_1451819) BOUND_VARIABLE_1451820) BOUND_VARIABLE_1451821) BOUND_VARIABLE_1451822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451820) BOUND_VARIABLE_1451822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451819) BOUND_VARIABLE_1451821)))))))))) (let ((_let_3179 (forall ((BOUND_VARIABLE_1451794 tptp.int) (BOUND_VARIABLE_1451795 tptp.int) (BOUND_VARIABLE_1451796 tptp.int) (BOUND_VARIABLE_1451797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9120 BOUND_VARIABLE_1451794) BOUND_VARIABLE_1451795) BOUND_VARIABLE_1451796) BOUND_VARIABLE_1451797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451795) BOUND_VARIABLE_1451797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451794) BOUND_VARIABLE_1451796)))))))))) (let ((_let_3180 (forall ((BOUND_VARIABLE_1451769 tptp.int) (BOUND_VARIABLE_1451770 tptp.int) (BOUND_VARIABLE_1451771 tptp.int) (BOUND_VARIABLE_1451772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9121 BOUND_VARIABLE_1451769) BOUND_VARIABLE_1451770) BOUND_VARIABLE_1451771) BOUND_VARIABLE_1451772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451770) BOUND_VARIABLE_1451772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451769) BOUND_VARIABLE_1451771)))))))))) (let ((_let_3181 (forall ((BOUND_VARIABLE_1451744 tptp.int) (BOUND_VARIABLE_1451745 tptp.int) (BOUND_VARIABLE_1451746 tptp.int) (BOUND_VARIABLE_1451747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9122 BOUND_VARIABLE_1451744) BOUND_VARIABLE_1451745) BOUND_VARIABLE_1451746) BOUND_VARIABLE_1451747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451745) BOUND_VARIABLE_1451747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451744) BOUND_VARIABLE_1451746)))))))))) (let ((_let_3182 (forall ((BOUND_VARIABLE_1451719 tptp.int) (BOUND_VARIABLE_1451720 tptp.int) (BOUND_VARIABLE_1451721 tptp.int) (BOUND_VARIABLE_1451722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9123 BOUND_VARIABLE_1451719) BOUND_VARIABLE_1451720) BOUND_VARIABLE_1451721) BOUND_VARIABLE_1451722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451720) BOUND_VARIABLE_1451722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451719) BOUND_VARIABLE_1451721)))))))))) (let ((_let_3183 (forall ((BOUND_VARIABLE_1451694 tptp.int) (BOUND_VARIABLE_1451695 tptp.int) (BOUND_VARIABLE_1451696 tptp.int) (BOUND_VARIABLE_1451697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9124 BOUND_VARIABLE_1451694) BOUND_VARIABLE_1451695) BOUND_VARIABLE_1451696) BOUND_VARIABLE_1451697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451695) BOUND_VARIABLE_1451697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451694) BOUND_VARIABLE_1451696)))))))))) (let ((_let_3184 (forall ((BOUND_VARIABLE_1451669 tptp.int) (BOUND_VARIABLE_1451670 tptp.int) (BOUND_VARIABLE_1451671 tptp.int) (BOUND_VARIABLE_1451672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9125 BOUND_VARIABLE_1451669) BOUND_VARIABLE_1451670) BOUND_VARIABLE_1451671) BOUND_VARIABLE_1451672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451670) BOUND_VARIABLE_1451672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451669) BOUND_VARIABLE_1451671)))))))))) (let ((_let_3185 (forall ((BOUND_VARIABLE_1451644 tptp.int) (BOUND_VARIABLE_1451645 tptp.int) (BOUND_VARIABLE_1451646 tptp.int) (BOUND_VARIABLE_1451647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9126 BOUND_VARIABLE_1451644) BOUND_VARIABLE_1451645) BOUND_VARIABLE_1451646) BOUND_VARIABLE_1451647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451645) BOUND_VARIABLE_1451647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451644) BOUND_VARIABLE_1451646)))))))))) (let ((_let_3186 (forall ((BOUND_VARIABLE_1451619 tptp.int) (BOUND_VARIABLE_1451620 tptp.int) (BOUND_VARIABLE_1451621 tptp.int) (BOUND_VARIABLE_1451622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9127 BOUND_VARIABLE_1451619) BOUND_VARIABLE_1451620) BOUND_VARIABLE_1451621) BOUND_VARIABLE_1451622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451620) BOUND_VARIABLE_1451622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451619) BOUND_VARIABLE_1451621)))))))))) (let ((_let_3187 (forall ((BOUND_VARIABLE_1451594 tptp.int) (BOUND_VARIABLE_1451595 tptp.int) (BOUND_VARIABLE_1451596 tptp.int) (BOUND_VARIABLE_1451597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9128 BOUND_VARIABLE_1451594) BOUND_VARIABLE_1451595) BOUND_VARIABLE_1451596) BOUND_VARIABLE_1451597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451595) BOUND_VARIABLE_1451597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451594) BOUND_VARIABLE_1451596)))))))))) (let ((_let_3188 (forall ((BOUND_VARIABLE_1451569 tptp.int) (BOUND_VARIABLE_1451570 tptp.int) (BOUND_VARIABLE_1451571 tptp.int) (BOUND_VARIABLE_1451572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9129 BOUND_VARIABLE_1451569) BOUND_VARIABLE_1451570) BOUND_VARIABLE_1451571) BOUND_VARIABLE_1451572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451570) BOUND_VARIABLE_1451572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451569) BOUND_VARIABLE_1451571)))))))))) (let ((_let_3189 (forall ((BOUND_VARIABLE_1451544 tptp.int) (BOUND_VARIABLE_1451545 tptp.int) (BOUND_VARIABLE_1451546 tptp.int) (BOUND_VARIABLE_1451547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9130 BOUND_VARIABLE_1451544) BOUND_VARIABLE_1451545) BOUND_VARIABLE_1451546) BOUND_VARIABLE_1451547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451545) BOUND_VARIABLE_1451547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451544) BOUND_VARIABLE_1451546)))))))))) (let ((_let_3190 (forall ((BOUND_VARIABLE_1451519 tptp.int) (BOUND_VARIABLE_1451520 tptp.int) (BOUND_VARIABLE_1451521 tptp.int) (BOUND_VARIABLE_1451522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9131 BOUND_VARIABLE_1451519) BOUND_VARIABLE_1451520) BOUND_VARIABLE_1451521) BOUND_VARIABLE_1451522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451520) BOUND_VARIABLE_1451522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451519) BOUND_VARIABLE_1451521)))))))))) (let ((_let_3191 (forall ((BOUND_VARIABLE_1451494 tptp.int) (BOUND_VARIABLE_1451495 tptp.int) (BOUND_VARIABLE_1451496 tptp.int) (BOUND_VARIABLE_1451497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9132 BOUND_VARIABLE_1451494) BOUND_VARIABLE_1451495) BOUND_VARIABLE_1451496) BOUND_VARIABLE_1451497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451495) BOUND_VARIABLE_1451497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451494) BOUND_VARIABLE_1451496)))))))))) (let ((_let_3192 (forall ((BOUND_VARIABLE_1451469 tptp.int) (BOUND_VARIABLE_1451470 tptp.int) (BOUND_VARIABLE_1451471 tptp.int) (BOUND_VARIABLE_1451472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9133 BOUND_VARIABLE_1451469) BOUND_VARIABLE_1451470) BOUND_VARIABLE_1451471) BOUND_VARIABLE_1451472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451470) BOUND_VARIABLE_1451472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451469) BOUND_VARIABLE_1451471)))))))))) (let ((_let_3193 (forall ((BOUND_VARIABLE_1451444 tptp.int) (BOUND_VARIABLE_1451445 tptp.int) (BOUND_VARIABLE_1451446 tptp.int) (BOUND_VARIABLE_1451447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9134 BOUND_VARIABLE_1451444) BOUND_VARIABLE_1451445) BOUND_VARIABLE_1451446) BOUND_VARIABLE_1451447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451445) BOUND_VARIABLE_1451447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451444) BOUND_VARIABLE_1451446)))))))))) (let ((_let_3194 (forall ((BOUND_VARIABLE_1451419 tptp.int) (BOUND_VARIABLE_1451420 tptp.int) (BOUND_VARIABLE_1451421 tptp.int) (BOUND_VARIABLE_1451422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9135 BOUND_VARIABLE_1451419) BOUND_VARIABLE_1451420) BOUND_VARIABLE_1451421) BOUND_VARIABLE_1451422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451420) BOUND_VARIABLE_1451422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451419) BOUND_VARIABLE_1451421)))))))))) (let ((_let_3195 (forall ((BOUND_VARIABLE_1451394 tptp.int) (BOUND_VARIABLE_1451395 tptp.int) (BOUND_VARIABLE_1451396 tptp.int) (BOUND_VARIABLE_1451397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9136 BOUND_VARIABLE_1451394) BOUND_VARIABLE_1451395) BOUND_VARIABLE_1451396) BOUND_VARIABLE_1451397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451395) BOUND_VARIABLE_1451397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451394) BOUND_VARIABLE_1451396)))))))))) (let ((_let_3196 (forall ((BOUND_VARIABLE_1451369 tptp.int) (BOUND_VARIABLE_1451370 tptp.int) (BOUND_VARIABLE_1451371 tptp.int) (BOUND_VARIABLE_1451372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9137 BOUND_VARIABLE_1451369) BOUND_VARIABLE_1451370) BOUND_VARIABLE_1451371) BOUND_VARIABLE_1451372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451370) BOUND_VARIABLE_1451372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451369) BOUND_VARIABLE_1451371)))))))))) (let ((_let_3197 (forall ((BOUND_VARIABLE_1451344 tptp.int) (BOUND_VARIABLE_1451345 tptp.int) (BOUND_VARIABLE_1451346 tptp.int) (BOUND_VARIABLE_1451347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9138 BOUND_VARIABLE_1451344) BOUND_VARIABLE_1451345) BOUND_VARIABLE_1451346) BOUND_VARIABLE_1451347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451345) BOUND_VARIABLE_1451347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451344) BOUND_VARIABLE_1451346)))))))))) (let ((_let_3198 (forall ((BOUND_VARIABLE_1451319 tptp.int) (BOUND_VARIABLE_1451320 tptp.int) (BOUND_VARIABLE_1451321 tptp.int) (BOUND_VARIABLE_1451322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9139 BOUND_VARIABLE_1451319) BOUND_VARIABLE_1451320) BOUND_VARIABLE_1451321) BOUND_VARIABLE_1451322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451320) BOUND_VARIABLE_1451322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451319) BOUND_VARIABLE_1451321)))))))))) (let ((_let_3199 (forall ((BOUND_VARIABLE_1451294 tptp.int) (BOUND_VARIABLE_1451295 tptp.int) (BOUND_VARIABLE_1451296 tptp.int) (BOUND_VARIABLE_1451297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9140 BOUND_VARIABLE_1451294) BOUND_VARIABLE_1451295) BOUND_VARIABLE_1451296) BOUND_VARIABLE_1451297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451295) BOUND_VARIABLE_1451297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451294) BOUND_VARIABLE_1451296)))))))))) (let ((_let_3200 (forall ((BOUND_VARIABLE_1451269 tptp.int) (BOUND_VARIABLE_1451270 tptp.int) (BOUND_VARIABLE_1451271 tptp.int) (BOUND_VARIABLE_1451272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9141 BOUND_VARIABLE_1451269) BOUND_VARIABLE_1451270) BOUND_VARIABLE_1451271) BOUND_VARIABLE_1451272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451270) BOUND_VARIABLE_1451272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451269) BOUND_VARIABLE_1451271)))))))))) (let ((_let_3201 (forall ((BOUND_VARIABLE_1451244 tptp.int) (BOUND_VARIABLE_1451245 tptp.int) (BOUND_VARIABLE_1451246 tptp.int) (BOUND_VARIABLE_1451247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9142 BOUND_VARIABLE_1451244) BOUND_VARIABLE_1451245) BOUND_VARIABLE_1451246) BOUND_VARIABLE_1451247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451245) BOUND_VARIABLE_1451247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451244) BOUND_VARIABLE_1451246)))))))))) (let ((_let_3202 (forall ((BOUND_VARIABLE_1451219 tptp.int) (BOUND_VARIABLE_1451220 tptp.int) (BOUND_VARIABLE_1451221 tptp.int) (BOUND_VARIABLE_1451222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9143 BOUND_VARIABLE_1451219) BOUND_VARIABLE_1451220) BOUND_VARIABLE_1451221) BOUND_VARIABLE_1451222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451220) BOUND_VARIABLE_1451222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451219) BOUND_VARIABLE_1451221)))))))))) (let ((_let_3203 (forall ((BOUND_VARIABLE_1451194 tptp.int) (BOUND_VARIABLE_1451195 tptp.int) (BOUND_VARIABLE_1451196 tptp.int) (BOUND_VARIABLE_1451197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9144 BOUND_VARIABLE_1451194) BOUND_VARIABLE_1451195) BOUND_VARIABLE_1451196) BOUND_VARIABLE_1451197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451195) BOUND_VARIABLE_1451197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451194) BOUND_VARIABLE_1451196)))))))))) (let ((_let_3204 (forall ((BOUND_VARIABLE_1451169 tptp.int) (BOUND_VARIABLE_1451170 tptp.int) (BOUND_VARIABLE_1451171 tptp.int) (BOUND_VARIABLE_1451172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9145 BOUND_VARIABLE_1451169) BOUND_VARIABLE_1451170) BOUND_VARIABLE_1451171) BOUND_VARIABLE_1451172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451170) BOUND_VARIABLE_1451172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451169) BOUND_VARIABLE_1451171)))))))))) (let ((_let_3205 (forall ((BOUND_VARIABLE_1451144 tptp.int) (BOUND_VARIABLE_1451145 tptp.int) (BOUND_VARIABLE_1451146 tptp.int) (BOUND_VARIABLE_1451147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9146 BOUND_VARIABLE_1451144) BOUND_VARIABLE_1451145) BOUND_VARIABLE_1451146) BOUND_VARIABLE_1451147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451145) BOUND_VARIABLE_1451147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451144) BOUND_VARIABLE_1451146)))))))))) (let ((_let_3206 (forall ((BOUND_VARIABLE_1451119 tptp.int) (BOUND_VARIABLE_1451120 tptp.int) (BOUND_VARIABLE_1451121 tptp.int) (BOUND_VARIABLE_1451122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9147 BOUND_VARIABLE_1451119) BOUND_VARIABLE_1451120) BOUND_VARIABLE_1451121) BOUND_VARIABLE_1451122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451120) BOUND_VARIABLE_1451122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451119) BOUND_VARIABLE_1451121)))))))))) (let ((_let_3207 (forall ((BOUND_VARIABLE_1451094 tptp.int) (BOUND_VARIABLE_1451095 tptp.int) (BOUND_VARIABLE_1451096 tptp.int) (BOUND_VARIABLE_1451097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9148 BOUND_VARIABLE_1451094) BOUND_VARIABLE_1451095) BOUND_VARIABLE_1451096) BOUND_VARIABLE_1451097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451095) BOUND_VARIABLE_1451097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451094) BOUND_VARIABLE_1451096)))))))))) (let ((_let_3208 (forall ((BOUND_VARIABLE_1451069 tptp.int) (BOUND_VARIABLE_1451070 tptp.int) (BOUND_VARIABLE_1451071 tptp.int) (BOUND_VARIABLE_1451072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9149 BOUND_VARIABLE_1451069) BOUND_VARIABLE_1451070) BOUND_VARIABLE_1451071) BOUND_VARIABLE_1451072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451070) BOUND_VARIABLE_1451072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451069) BOUND_VARIABLE_1451071)))))))))) (let ((_let_3209 (forall ((BOUND_VARIABLE_1451044 tptp.int) (BOUND_VARIABLE_1451045 tptp.int) (BOUND_VARIABLE_1451046 tptp.int) (BOUND_VARIABLE_1451047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9150 BOUND_VARIABLE_1451044) BOUND_VARIABLE_1451045) BOUND_VARIABLE_1451046) BOUND_VARIABLE_1451047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451045) BOUND_VARIABLE_1451047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451044) BOUND_VARIABLE_1451046)))))))))) (let ((_let_3210 (forall ((BOUND_VARIABLE_1451019 tptp.int) (BOUND_VARIABLE_1451020 tptp.int) (BOUND_VARIABLE_1451021 tptp.int) (BOUND_VARIABLE_1451022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9151 BOUND_VARIABLE_1451019) BOUND_VARIABLE_1451020) BOUND_VARIABLE_1451021) BOUND_VARIABLE_1451022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451020) BOUND_VARIABLE_1451022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1451019) BOUND_VARIABLE_1451021)))))))))) (let ((_let_3211 (forall ((BOUND_VARIABLE_1450994 tptp.int) (BOUND_VARIABLE_1450995 tptp.int) (BOUND_VARIABLE_1450996 tptp.int) (BOUND_VARIABLE_1450997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9152 BOUND_VARIABLE_1450994) BOUND_VARIABLE_1450995) BOUND_VARIABLE_1450996) BOUND_VARIABLE_1450997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450995) BOUND_VARIABLE_1450997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450994) BOUND_VARIABLE_1450996)))))))))) (let ((_let_3212 (forall ((BOUND_VARIABLE_1450969 tptp.int) (BOUND_VARIABLE_1450970 tptp.int) (BOUND_VARIABLE_1450971 tptp.int) (BOUND_VARIABLE_1450972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9153 BOUND_VARIABLE_1450969) BOUND_VARIABLE_1450970) BOUND_VARIABLE_1450971) BOUND_VARIABLE_1450972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450970) BOUND_VARIABLE_1450972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450969) BOUND_VARIABLE_1450971)))))))))) (let ((_let_3213 (forall ((BOUND_VARIABLE_1450944 tptp.int) (BOUND_VARIABLE_1450945 tptp.int) (BOUND_VARIABLE_1450946 tptp.int) (BOUND_VARIABLE_1450947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9154 BOUND_VARIABLE_1450944) BOUND_VARIABLE_1450945) BOUND_VARIABLE_1450946) BOUND_VARIABLE_1450947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450945) BOUND_VARIABLE_1450947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450944) BOUND_VARIABLE_1450946)))))))))) (let ((_let_3214 (forall ((BOUND_VARIABLE_1450919 tptp.int) (BOUND_VARIABLE_1450920 tptp.int) (BOUND_VARIABLE_1450921 tptp.int) (BOUND_VARIABLE_1450922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9155 BOUND_VARIABLE_1450919) BOUND_VARIABLE_1450920) BOUND_VARIABLE_1450921) BOUND_VARIABLE_1450922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450920) BOUND_VARIABLE_1450922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450919) BOUND_VARIABLE_1450921)))))))))) (let ((_let_3215 (forall ((BOUND_VARIABLE_1450894 tptp.int) (BOUND_VARIABLE_1450895 tptp.int) (BOUND_VARIABLE_1450896 tptp.int) (BOUND_VARIABLE_1450897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9156 BOUND_VARIABLE_1450894) BOUND_VARIABLE_1450895) BOUND_VARIABLE_1450896) BOUND_VARIABLE_1450897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450895) BOUND_VARIABLE_1450897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450894) BOUND_VARIABLE_1450896)))))))))) (let ((_let_3216 (forall ((BOUND_VARIABLE_1450869 tptp.int) (BOUND_VARIABLE_1450870 tptp.int) (BOUND_VARIABLE_1450871 tptp.int) (BOUND_VARIABLE_1450872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9157 BOUND_VARIABLE_1450869) BOUND_VARIABLE_1450870) BOUND_VARIABLE_1450871) BOUND_VARIABLE_1450872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450870) BOUND_VARIABLE_1450872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450869) BOUND_VARIABLE_1450871)))))))))) (let ((_let_3217 (forall ((BOUND_VARIABLE_1450844 tptp.int) (BOUND_VARIABLE_1450845 tptp.int) (BOUND_VARIABLE_1450846 tptp.int) (BOUND_VARIABLE_1450847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9158 BOUND_VARIABLE_1450844) BOUND_VARIABLE_1450845) BOUND_VARIABLE_1450846) BOUND_VARIABLE_1450847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450845) BOUND_VARIABLE_1450847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450844) BOUND_VARIABLE_1450846)))))))))) (let ((_let_3218 (forall ((BOUND_VARIABLE_1450819 tptp.int) (BOUND_VARIABLE_1450820 tptp.int) (BOUND_VARIABLE_1450821 tptp.int) (BOUND_VARIABLE_1450822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9159 BOUND_VARIABLE_1450819) BOUND_VARIABLE_1450820) BOUND_VARIABLE_1450821) BOUND_VARIABLE_1450822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450820) BOUND_VARIABLE_1450822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450819) BOUND_VARIABLE_1450821)))))))))) (let ((_let_3219 (forall ((BOUND_VARIABLE_1450794 tptp.int) (BOUND_VARIABLE_1450795 tptp.int) (BOUND_VARIABLE_1450796 tptp.int) (BOUND_VARIABLE_1450797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9160 BOUND_VARIABLE_1450794) BOUND_VARIABLE_1450795) BOUND_VARIABLE_1450796) BOUND_VARIABLE_1450797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450795) BOUND_VARIABLE_1450797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450794) BOUND_VARIABLE_1450796)))))))))) (let ((_let_3220 (forall ((BOUND_VARIABLE_1450769 tptp.int) (BOUND_VARIABLE_1450770 tptp.int) (BOUND_VARIABLE_1450771 tptp.int) (BOUND_VARIABLE_1450772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9161 BOUND_VARIABLE_1450769) BOUND_VARIABLE_1450770) BOUND_VARIABLE_1450771) BOUND_VARIABLE_1450772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450770) BOUND_VARIABLE_1450772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450769) BOUND_VARIABLE_1450771)))))))))) (let ((_let_3221 (forall ((BOUND_VARIABLE_1450744 tptp.int) (BOUND_VARIABLE_1450745 tptp.int) (BOUND_VARIABLE_1450746 tptp.int) (BOUND_VARIABLE_1450747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9162 BOUND_VARIABLE_1450744) BOUND_VARIABLE_1450745) BOUND_VARIABLE_1450746) BOUND_VARIABLE_1450747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450745) BOUND_VARIABLE_1450747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450744) BOUND_VARIABLE_1450746)))))))))) (let ((_let_3222 (forall ((BOUND_VARIABLE_1450719 tptp.int) (BOUND_VARIABLE_1450720 tptp.int) (BOUND_VARIABLE_1450721 tptp.int) (BOUND_VARIABLE_1450722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9163 BOUND_VARIABLE_1450719) BOUND_VARIABLE_1450720) BOUND_VARIABLE_1450721) BOUND_VARIABLE_1450722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450720) BOUND_VARIABLE_1450722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450719) BOUND_VARIABLE_1450721)))))))))) (let ((_let_3223 (forall ((BOUND_VARIABLE_1450694 tptp.int) (BOUND_VARIABLE_1450695 tptp.int) (BOUND_VARIABLE_1450696 tptp.int) (BOUND_VARIABLE_1450697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9164 BOUND_VARIABLE_1450694) BOUND_VARIABLE_1450695) BOUND_VARIABLE_1450696) BOUND_VARIABLE_1450697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450695) BOUND_VARIABLE_1450697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450694) BOUND_VARIABLE_1450696)))))))))) (let ((_let_3224 (forall ((BOUND_VARIABLE_1450669 tptp.int) (BOUND_VARIABLE_1450670 tptp.int) (BOUND_VARIABLE_1450671 tptp.int) (BOUND_VARIABLE_1450672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9165 BOUND_VARIABLE_1450669) BOUND_VARIABLE_1450670) BOUND_VARIABLE_1450671) BOUND_VARIABLE_1450672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450670) BOUND_VARIABLE_1450672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450669) BOUND_VARIABLE_1450671)))))))))) (let ((_let_3225 (forall ((BOUND_VARIABLE_1450644 tptp.int) (BOUND_VARIABLE_1450645 tptp.int) (BOUND_VARIABLE_1450646 tptp.int) (BOUND_VARIABLE_1450647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9166 BOUND_VARIABLE_1450644) BOUND_VARIABLE_1450645) BOUND_VARIABLE_1450646) BOUND_VARIABLE_1450647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450645) BOUND_VARIABLE_1450647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450644) BOUND_VARIABLE_1450646)))))))))) (let ((_let_3226 (forall ((BOUND_VARIABLE_1450619 tptp.int) (BOUND_VARIABLE_1450620 tptp.int) (BOUND_VARIABLE_1450621 tptp.int) (BOUND_VARIABLE_1450622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9167 BOUND_VARIABLE_1450619) BOUND_VARIABLE_1450620) BOUND_VARIABLE_1450621) BOUND_VARIABLE_1450622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450620) BOUND_VARIABLE_1450622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450619) BOUND_VARIABLE_1450621)))))))))) (let ((_let_3227 (forall ((BOUND_VARIABLE_1450594 tptp.int) (BOUND_VARIABLE_1450595 tptp.int) (BOUND_VARIABLE_1450596 tptp.int) (BOUND_VARIABLE_1450597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9168 BOUND_VARIABLE_1450594) BOUND_VARIABLE_1450595) BOUND_VARIABLE_1450596) BOUND_VARIABLE_1450597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450595) BOUND_VARIABLE_1450597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450594) BOUND_VARIABLE_1450596)))))))))) (let ((_let_3228 (forall ((BOUND_VARIABLE_1450569 tptp.int) (BOUND_VARIABLE_1450570 tptp.int) (BOUND_VARIABLE_1450571 tptp.int) (BOUND_VARIABLE_1450572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9169 BOUND_VARIABLE_1450569) BOUND_VARIABLE_1450570) BOUND_VARIABLE_1450571) BOUND_VARIABLE_1450572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450570) BOUND_VARIABLE_1450572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450569) BOUND_VARIABLE_1450571)))))))))) (let ((_let_3229 (forall ((BOUND_VARIABLE_1450544 tptp.int) (BOUND_VARIABLE_1450545 tptp.int) (BOUND_VARIABLE_1450546 tptp.int) (BOUND_VARIABLE_1450547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9170 BOUND_VARIABLE_1450544) BOUND_VARIABLE_1450545) BOUND_VARIABLE_1450546) BOUND_VARIABLE_1450547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450545) BOUND_VARIABLE_1450547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450544) BOUND_VARIABLE_1450546)))))))))) (let ((_let_3230 (forall ((BOUND_VARIABLE_1450519 tptp.int) (BOUND_VARIABLE_1450520 tptp.int) (BOUND_VARIABLE_1450521 tptp.int) (BOUND_VARIABLE_1450522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9171 BOUND_VARIABLE_1450519) BOUND_VARIABLE_1450520) BOUND_VARIABLE_1450521) BOUND_VARIABLE_1450522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450520) BOUND_VARIABLE_1450522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450519) BOUND_VARIABLE_1450521)))))))))) (let ((_let_3231 (forall ((BOUND_VARIABLE_1450494 tptp.int) (BOUND_VARIABLE_1450495 tptp.int) (BOUND_VARIABLE_1450496 tptp.int) (BOUND_VARIABLE_1450497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9172 BOUND_VARIABLE_1450494) BOUND_VARIABLE_1450495) BOUND_VARIABLE_1450496) BOUND_VARIABLE_1450497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450495) BOUND_VARIABLE_1450497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450494) BOUND_VARIABLE_1450496)))))))))) (let ((_let_3232 (forall ((BOUND_VARIABLE_1450469 tptp.int) (BOUND_VARIABLE_1450470 tptp.int) (BOUND_VARIABLE_1450471 tptp.int) (BOUND_VARIABLE_1450472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9173 BOUND_VARIABLE_1450469) BOUND_VARIABLE_1450470) BOUND_VARIABLE_1450471) BOUND_VARIABLE_1450472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450470) BOUND_VARIABLE_1450472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450469) BOUND_VARIABLE_1450471)))))))))) (let ((_let_3233 (forall ((BOUND_VARIABLE_1450444 tptp.int) (BOUND_VARIABLE_1450445 tptp.int) (BOUND_VARIABLE_1450446 tptp.int) (BOUND_VARIABLE_1450447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9174 BOUND_VARIABLE_1450444) BOUND_VARIABLE_1450445) BOUND_VARIABLE_1450446) BOUND_VARIABLE_1450447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450445) BOUND_VARIABLE_1450447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450444) BOUND_VARIABLE_1450446)))))))))) (let ((_let_3234 (forall ((BOUND_VARIABLE_1450419 tptp.int) (BOUND_VARIABLE_1450420 tptp.int) (BOUND_VARIABLE_1450421 tptp.int) (BOUND_VARIABLE_1450422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9175 BOUND_VARIABLE_1450419) BOUND_VARIABLE_1450420) BOUND_VARIABLE_1450421) BOUND_VARIABLE_1450422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450420) BOUND_VARIABLE_1450422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450419) BOUND_VARIABLE_1450421)))))))))) (let ((_let_3235 (forall ((BOUND_VARIABLE_1450394 tptp.int) (BOUND_VARIABLE_1450395 tptp.int) (BOUND_VARIABLE_1450396 tptp.int) (BOUND_VARIABLE_1450397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9176 BOUND_VARIABLE_1450394) BOUND_VARIABLE_1450395) BOUND_VARIABLE_1450396) BOUND_VARIABLE_1450397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450395) BOUND_VARIABLE_1450397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450394) BOUND_VARIABLE_1450396)))))))))) (let ((_let_3236 (forall ((BOUND_VARIABLE_1450369 tptp.int) (BOUND_VARIABLE_1450370 tptp.int) (BOUND_VARIABLE_1450371 tptp.int) (BOUND_VARIABLE_1450372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9177 BOUND_VARIABLE_1450369) BOUND_VARIABLE_1450370) BOUND_VARIABLE_1450371) BOUND_VARIABLE_1450372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450370) BOUND_VARIABLE_1450372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450369) BOUND_VARIABLE_1450371)))))))))) (let ((_let_3237 (forall ((BOUND_VARIABLE_1450344 tptp.int) (BOUND_VARIABLE_1450345 tptp.int) (BOUND_VARIABLE_1450346 tptp.int) (BOUND_VARIABLE_1450347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9178 BOUND_VARIABLE_1450344) BOUND_VARIABLE_1450345) BOUND_VARIABLE_1450346) BOUND_VARIABLE_1450347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450345) BOUND_VARIABLE_1450347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450344) BOUND_VARIABLE_1450346)))))))))) (let ((_let_3238 (forall ((BOUND_VARIABLE_1450319 tptp.int) (BOUND_VARIABLE_1450320 tptp.int) (BOUND_VARIABLE_1450321 tptp.int) (BOUND_VARIABLE_1450322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9179 BOUND_VARIABLE_1450319) BOUND_VARIABLE_1450320) BOUND_VARIABLE_1450321) BOUND_VARIABLE_1450322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450320) BOUND_VARIABLE_1450322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450319) BOUND_VARIABLE_1450321)))))))))) (let ((_let_3239 (forall ((BOUND_VARIABLE_1450294 tptp.int) (BOUND_VARIABLE_1450295 tptp.int) (BOUND_VARIABLE_1450296 tptp.int) (BOUND_VARIABLE_1450297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9180 BOUND_VARIABLE_1450294) BOUND_VARIABLE_1450295) BOUND_VARIABLE_1450296) BOUND_VARIABLE_1450297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450295) BOUND_VARIABLE_1450297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450294) BOUND_VARIABLE_1450296)))))))))) (let ((_let_3240 (forall ((BOUND_VARIABLE_1450269 tptp.int) (BOUND_VARIABLE_1450270 tptp.int) (BOUND_VARIABLE_1450271 tptp.int) (BOUND_VARIABLE_1450272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9181 BOUND_VARIABLE_1450269) BOUND_VARIABLE_1450270) BOUND_VARIABLE_1450271) BOUND_VARIABLE_1450272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450270) BOUND_VARIABLE_1450272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450269) BOUND_VARIABLE_1450271)))))))))) (let ((_let_3241 (forall ((BOUND_VARIABLE_1450244 tptp.int) (BOUND_VARIABLE_1450245 tptp.int) (BOUND_VARIABLE_1450246 tptp.int) (BOUND_VARIABLE_1450247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9182 BOUND_VARIABLE_1450244) BOUND_VARIABLE_1450245) BOUND_VARIABLE_1450246) BOUND_VARIABLE_1450247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450245) BOUND_VARIABLE_1450247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450244) BOUND_VARIABLE_1450246)))))))))) (let ((_let_3242 (forall ((BOUND_VARIABLE_1450219 tptp.int) (BOUND_VARIABLE_1450220 tptp.int) (BOUND_VARIABLE_1450221 tptp.int) (BOUND_VARIABLE_1450222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9183 BOUND_VARIABLE_1450219) BOUND_VARIABLE_1450220) BOUND_VARIABLE_1450221) BOUND_VARIABLE_1450222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450220) BOUND_VARIABLE_1450222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450219) BOUND_VARIABLE_1450221)))))))))) (let ((_let_3243 (forall ((BOUND_VARIABLE_1450194 tptp.int) (BOUND_VARIABLE_1450195 tptp.int) (BOUND_VARIABLE_1450196 tptp.int) (BOUND_VARIABLE_1450197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9184 BOUND_VARIABLE_1450194) BOUND_VARIABLE_1450195) BOUND_VARIABLE_1450196) BOUND_VARIABLE_1450197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450195) BOUND_VARIABLE_1450197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450194) BOUND_VARIABLE_1450196)))))))))) (let ((_let_3244 (forall ((BOUND_VARIABLE_1450169 tptp.int) (BOUND_VARIABLE_1450170 tptp.int) (BOUND_VARIABLE_1450171 tptp.int) (BOUND_VARIABLE_1450172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9185 BOUND_VARIABLE_1450169) BOUND_VARIABLE_1450170) BOUND_VARIABLE_1450171) BOUND_VARIABLE_1450172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450170) BOUND_VARIABLE_1450172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450169) BOUND_VARIABLE_1450171)))))))))) (let ((_let_3245 (forall ((BOUND_VARIABLE_1450144 tptp.int) (BOUND_VARIABLE_1450145 tptp.int) (BOUND_VARIABLE_1450146 tptp.int) (BOUND_VARIABLE_1450147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9186 BOUND_VARIABLE_1450144) BOUND_VARIABLE_1450145) BOUND_VARIABLE_1450146) BOUND_VARIABLE_1450147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450145) BOUND_VARIABLE_1450147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450144) BOUND_VARIABLE_1450146)))))))))) (let ((_let_3246 (forall ((BOUND_VARIABLE_1450119 tptp.int) (BOUND_VARIABLE_1450120 tptp.int) (BOUND_VARIABLE_1450121 tptp.int) (BOUND_VARIABLE_1450122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9187 BOUND_VARIABLE_1450119) BOUND_VARIABLE_1450120) BOUND_VARIABLE_1450121) BOUND_VARIABLE_1450122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450120) BOUND_VARIABLE_1450122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450119) BOUND_VARIABLE_1450121)))))))))) (let ((_let_3247 (forall ((BOUND_VARIABLE_1450094 tptp.int) (BOUND_VARIABLE_1450095 tptp.int) (BOUND_VARIABLE_1450096 tptp.int) (BOUND_VARIABLE_1450097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9188 BOUND_VARIABLE_1450094) BOUND_VARIABLE_1450095) BOUND_VARIABLE_1450096) BOUND_VARIABLE_1450097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450095) BOUND_VARIABLE_1450097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450094) BOUND_VARIABLE_1450096)))))))))) (let ((_let_3248 (forall ((BOUND_VARIABLE_1450069 tptp.int) (BOUND_VARIABLE_1450070 tptp.int) (BOUND_VARIABLE_1450071 tptp.int) (BOUND_VARIABLE_1450072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9189 BOUND_VARIABLE_1450069) BOUND_VARIABLE_1450070) BOUND_VARIABLE_1450071) BOUND_VARIABLE_1450072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450070) BOUND_VARIABLE_1450072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450069) BOUND_VARIABLE_1450071)))))))))) (let ((_let_3249 (forall ((BOUND_VARIABLE_1450044 tptp.int) (BOUND_VARIABLE_1450045 tptp.int) (BOUND_VARIABLE_1450046 tptp.int) (BOUND_VARIABLE_1450047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9190 BOUND_VARIABLE_1450044) BOUND_VARIABLE_1450045) BOUND_VARIABLE_1450046) BOUND_VARIABLE_1450047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450045) BOUND_VARIABLE_1450047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450044) BOUND_VARIABLE_1450046)))))))))) (let ((_let_3250 (forall ((BOUND_VARIABLE_1450019 tptp.int) (BOUND_VARIABLE_1450020 tptp.int) (BOUND_VARIABLE_1450021 tptp.int) (BOUND_VARIABLE_1450022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9191 BOUND_VARIABLE_1450019) BOUND_VARIABLE_1450020) BOUND_VARIABLE_1450021) BOUND_VARIABLE_1450022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450020) BOUND_VARIABLE_1450022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1450019) BOUND_VARIABLE_1450021)))))))))) (let ((_let_3251 (forall ((BOUND_VARIABLE_1449994 tptp.int) (BOUND_VARIABLE_1449995 tptp.int) (BOUND_VARIABLE_1449996 tptp.int) (BOUND_VARIABLE_1449997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9192 BOUND_VARIABLE_1449994) BOUND_VARIABLE_1449995) BOUND_VARIABLE_1449996) BOUND_VARIABLE_1449997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449995) BOUND_VARIABLE_1449997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449994) BOUND_VARIABLE_1449996)))))))))) (let ((_let_3252 (forall ((BOUND_VARIABLE_1449969 tptp.int) (BOUND_VARIABLE_1449970 tptp.int) (BOUND_VARIABLE_1449971 tptp.int) (BOUND_VARIABLE_1449972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9193 BOUND_VARIABLE_1449969) BOUND_VARIABLE_1449970) BOUND_VARIABLE_1449971) BOUND_VARIABLE_1449972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449970) BOUND_VARIABLE_1449972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449969) BOUND_VARIABLE_1449971)))))))))) (let ((_let_3253 (forall ((BOUND_VARIABLE_1449944 tptp.int) (BOUND_VARIABLE_1449945 tptp.int) (BOUND_VARIABLE_1449946 tptp.int) (BOUND_VARIABLE_1449947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9194 BOUND_VARIABLE_1449944) BOUND_VARIABLE_1449945) BOUND_VARIABLE_1449946) BOUND_VARIABLE_1449947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449945) BOUND_VARIABLE_1449947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449944) BOUND_VARIABLE_1449946)))))))))) (let ((_let_3254 (forall ((BOUND_VARIABLE_1449919 tptp.int) (BOUND_VARIABLE_1449920 tptp.int) (BOUND_VARIABLE_1449921 tptp.int) (BOUND_VARIABLE_1449922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9195 BOUND_VARIABLE_1449919) BOUND_VARIABLE_1449920) BOUND_VARIABLE_1449921) BOUND_VARIABLE_1449922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449920) BOUND_VARIABLE_1449922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449919) BOUND_VARIABLE_1449921)))))))))) (let ((_let_3255 (forall ((BOUND_VARIABLE_1449894 tptp.int) (BOUND_VARIABLE_1449895 tptp.int) (BOUND_VARIABLE_1449896 tptp.int) (BOUND_VARIABLE_1449897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9196 BOUND_VARIABLE_1449894) BOUND_VARIABLE_1449895) BOUND_VARIABLE_1449896) BOUND_VARIABLE_1449897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449895) BOUND_VARIABLE_1449897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449894) BOUND_VARIABLE_1449896)))))))))) (let ((_let_3256 (forall ((BOUND_VARIABLE_1449869 tptp.int) (BOUND_VARIABLE_1449870 tptp.int) (BOUND_VARIABLE_1449871 tptp.int) (BOUND_VARIABLE_1449872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9197 BOUND_VARIABLE_1449869) BOUND_VARIABLE_1449870) BOUND_VARIABLE_1449871) BOUND_VARIABLE_1449872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449870) BOUND_VARIABLE_1449872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449869) BOUND_VARIABLE_1449871)))))))))) (let ((_let_3257 (forall ((BOUND_VARIABLE_1449844 tptp.int) (BOUND_VARIABLE_1449845 tptp.int) (BOUND_VARIABLE_1449846 tptp.int) (BOUND_VARIABLE_1449847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9198 BOUND_VARIABLE_1449844) BOUND_VARIABLE_1449845) BOUND_VARIABLE_1449846) BOUND_VARIABLE_1449847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449845) BOUND_VARIABLE_1449847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449844) BOUND_VARIABLE_1449846)))))))))) (let ((_let_3258 (forall ((BOUND_VARIABLE_1449819 tptp.int) (BOUND_VARIABLE_1449820 tptp.int) (BOUND_VARIABLE_1449821 tptp.int) (BOUND_VARIABLE_1449822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9199 BOUND_VARIABLE_1449819) BOUND_VARIABLE_1449820) BOUND_VARIABLE_1449821) BOUND_VARIABLE_1449822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449820) BOUND_VARIABLE_1449822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449819) BOUND_VARIABLE_1449821)))))))))) (let ((_let_3259 (forall ((BOUND_VARIABLE_1449794 tptp.int) (BOUND_VARIABLE_1449795 tptp.int) (BOUND_VARIABLE_1449796 tptp.int) (BOUND_VARIABLE_1449797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9200 BOUND_VARIABLE_1449794) BOUND_VARIABLE_1449795) BOUND_VARIABLE_1449796) BOUND_VARIABLE_1449797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449795) BOUND_VARIABLE_1449797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449794) BOUND_VARIABLE_1449796)))))))))) (let ((_let_3260 (forall ((BOUND_VARIABLE_1449769 tptp.int) (BOUND_VARIABLE_1449770 tptp.int) (BOUND_VARIABLE_1449771 tptp.int) (BOUND_VARIABLE_1449772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9201 BOUND_VARIABLE_1449769) BOUND_VARIABLE_1449770) BOUND_VARIABLE_1449771) BOUND_VARIABLE_1449772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449770) BOUND_VARIABLE_1449772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449769) BOUND_VARIABLE_1449771)))))))))) (let ((_let_3261 (forall ((BOUND_VARIABLE_1449744 tptp.int) (BOUND_VARIABLE_1449745 tptp.int) (BOUND_VARIABLE_1449746 tptp.int) (BOUND_VARIABLE_1449747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9202 BOUND_VARIABLE_1449744) BOUND_VARIABLE_1449745) BOUND_VARIABLE_1449746) BOUND_VARIABLE_1449747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449745) BOUND_VARIABLE_1449747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449744) BOUND_VARIABLE_1449746)))))))))) (let ((_let_3262 (forall ((BOUND_VARIABLE_1449719 tptp.int) (BOUND_VARIABLE_1449720 tptp.int) (BOUND_VARIABLE_1449721 tptp.int) (BOUND_VARIABLE_1449722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9203 BOUND_VARIABLE_1449719) BOUND_VARIABLE_1449720) BOUND_VARIABLE_1449721) BOUND_VARIABLE_1449722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449720) BOUND_VARIABLE_1449722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449719) BOUND_VARIABLE_1449721)))))))))) (let ((_let_3263 (forall ((BOUND_VARIABLE_1449694 tptp.int) (BOUND_VARIABLE_1449695 tptp.int) (BOUND_VARIABLE_1449696 tptp.int) (BOUND_VARIABLE_1449697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9204 BOUND_VARIABLE_1449694) BOUND_VARIABLE_1449695) BOUND_VARIABLE_1449696) BOUND_VARIABLE_1449697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449695) BOUND_VARIABLE_1449697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449694) BOUND_VARIABLE_1449696)))))))))) (let ((_let_3264 (forall ((BOUND_VARIABLE_1449669 tptp.int) (BOUND_VARIABLE_1449670 tptp.int) (BOUND_VARIABLE_1449671 tptp.int) (BOUND_VARIABLE_1449672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9205 BOUND_VARIABLE_1449669) BOUND_VARIABLE_1449670) BOUND_VARIABLE_1449671) BOUND_VARIABLE_1449672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449670) BOUND_VARIABLE_1449672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449669) BOUND_VARIABLE_1449671)))))))))) (let ((_let_3265 (forall ((BOUND_VARIABLE_1449644 tptp.int) (BOUND_VARIABLE_1449645 tptp.int) (BOUND_VARIABLE_1449646 tptp.int) (BOUND_VARIABLE_1449647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9206 BOUND_VARIABLE_1449644) BOUND_VARIABLE_1449645) BOUND_VARIABLE_1449646) BOUND_VARIABLE_1449647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449645) BOUND_VARIABLE_1449647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449644) BOUND_VARIABLE_1449646)))))))))) (let ((_let_3266 (forall ((BOUND_VARIABLE_1449619 tptp.int) (BOUND_VARIABLE_1449620 tptp.int) (BOUND_VARIABLE_1449621 tptp.int) (BOUND_VARIABLE_1449622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9207 BOUND_VARIABLE_1449619) BOUND_VARIABLE_1449620) BOUND_VARIABLE_1449621) BOUND_VARIABLE_1449622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449620) BOUND_VARIABLE_1449622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449619) BOUND_VARIABLE_1449621)))))))))) (let ((_let_3267 (forall ((BOUND_VARIABLE_1449594 tptp.int) (BOUND_VARIABLE_1449595 tptp.int) (BOUND_VARIABLE_1449596 tptp.int) (BOUND_VARIABLE_1449597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9208 BOUND_VARIABLE_1449594) BOUND_VARIABLE_1449595) BOUND_VARIABLE_1449596) BOUND_VARIABLE_1449597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449595) BOUND_VARIABLE_1449597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449594) BOUND_VARIABLE_1449596)))))))))) (let ((_let_3268 (forall ((BOUND_VARIABLE_1449569 tptp.int) (BOUND_VARIABLE_1449570 tptp.int) (BOUND_VARIABLE_1449571 tptp.int) (BOUND_VARIABLE_1449572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9209 BOUND_VARIABLE_1449569) BOUND_VARIABLE_1449570) BOUND_VARIABLE_1449571) BOUND_VARIABLE_1449572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449570) BOUND_VARIABLE_1449572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449569) BOUND_VARIABLE_1449571)))))))))) (let ((_let_3269 (forall ((BOUND_VARIABLE_1449544 tptp.int) (BOUND_VARIABLE_1449545 tptp.int) (BOUND_VARIABLE_1449546 tptp.int) (BOUND_VARIABLE_1449547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9210 BOUND_VARIABLE_1449544) BOUND_VARIABLE_1449545) BOUND_VARIABLE_1449546) BOUND_VARIABLE_1449547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449545) BOUND_VARIABLE_1449547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449544) BOUND_VARIABLE_1449546)))))))))) (let ((_let_3270 (forall ((BOUND_VARIABLE_1449519 tptp.int) (BOUND_VARIABLE_1449520 tptp.int) (BOUND_VARIABLE_1449521 tptp.int) (BOUND_VARIABLE_1449522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9211 BOUND_VARIABLE_1449519) BOUND_VARIABLE_1449520) BOUND_VARIABLE_1449521) BOUND_VARIABLE_1449522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449520) BOUND_VARIABLE_1449522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449519) BOUND_VARIABLE_1449521)))))))))) (let ((_let_3271 (forall ((BOUND_VARIABLE_1449494 tptp.int) (BOUND_VARIABLE_1449495 tptp.int) (BOUND_VARIABLE_1449496 tptp.int) (BOUND_VARIABLE_1449497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9212 BOUND_VARIABLE_1449494) BOUND_VARIABLE_1449495) BOUND_VARIABLE_1449496) BOUND_VARIABLE_1449497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449495) BOUND_VARIABLE_1449497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449494) BOUND_VARIABLE_1449496)))))))))) (let ((_let_3272 (forall ((BOUND_VARIABLE_1449469 tptp.int) (BOUND_VARIABLE_1449470 tptp.int) (BOUND_VARIABLE_1449471 tptp.int) (BOUND_VARIABLE_1449472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9213 BOUND_VARIABLE_1449469) BOUND_VARIABLE_1449470) BOUND_VARIABLE_1449471) BOUND_VARIABLE_1449472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449470) BOUND_VARIABLE_1449472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449469) BOUND_VARIABLE_1449471)))))))))) (let ((_let_3273 (forall ((BOUND_VARIABLE_1449444 tptp.int) (BOUND_VARIABLE_1449445 tptp.int) (BOUND_VARIABLE_1449446 tptp.int) (BOUND_VARIABLE_1449447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9214 BOUND_VARIABLE_1449444) BOUND_VARIABLE_1449445) BOUND_VARIABLE_1449446) BOUND_VARIABLE_1449447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449445) BOUND_VARIABLE_1449447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449444) BOUND_VARIABLE_1449446)))))))))) (let ((_let_3274 (forall ((BOUND_VARIABLE_1449419 tptp.int) (BOUND_VARIABLE_1449420 tptp.int) (BOUND_VARIABLE_1449421 tptp.int) (BOUND_VARIABLE_1449422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9215 BOUND_VARIABLE_1449419) BOUND_VARIABLE_1449420) BOUND_VARIABLE_1449421) BOUND_VARIABLE_1449422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449420) BOUND_VARIABLE_1449422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449419) BOUND_VARIABLE_1449421)))))))))) (let ((_let_3275 (forall ((BOUND_VARIABLE_1449394 tptp.int) (BOUND_VARIABLE_1449395 tptp.int) (BOUND_VARIABLE_1449396 tptp.int) (BOUND_VARIABLE_1449397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9216 BOUND_VARIABLE_1449394) BOUND_VARIABLE_1449395) BOUND_VARIABLE_1449396) BOUND_VARIABLE_1449397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449395) BOUND_VARIABLE_1449397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449394) BOUND_VARIABLE_1449396)))))))))) (let ((_let_3276 (forall ((BOUND_VARIABLE_1449369 tptp.int) (BOUND_VARIABLE_1449370 tptp.int) (BOUND_VARIABLE_1449371 tptp.int) (BOUND_VARIABLE_1449372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9217 BOUND_VARIABLE_1449369) BOUND_VARIABLE_1449370) BOUND_VARIABLE_1449371) BOUND_VARIABLE_1449372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449370) BOUND_VARIABLE_1449372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449369) BOUND_VARIABLE_1449371)))))))))) (let ((_let_3277 (forall ((BOUND_VARIABLE_1449344 tptp.int) (BOUND_VARIABLE_1449345 tptp.int) (BOUND_VARIABLE_1449346 tptp.int) (BOUND_VARIABLE_1449347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9218 BOUND_VARIABLE_1449344) BOUND_VARIABLE_1449345) BOUND_VARIABLE_1449346) BOUND_VARIABLE_1449347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449345) BOUND_VARIABLE_1449347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449344) BOUND_VARIABLE_1449346)))))))))) (let ((_let_3278 (forall ((BOUND_VARIABLE_1449319 tptp.int) (BOUND_VARIABLE_1449320 tptp.int) (BOUND_VARIABLE_1449321 tptp.int) (BOUND_VARIABLE_1449322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9219 BOUND_VARIABLE_1449319) BOUND_VARIABLE_1449320) BOUND_VARIABLE_1449321) BOUND_VARIABLE_1449322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449320) BOUND_VARIABLE_1449322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449319) BOUND_VARIABLE_1449321)))))))))) (let ((_let_3279 (forall ((BOUND_VARIABLE_1449294 tptp.int) (BOUND_VARIABLE_1449295 tptp.int) (BOUND_VARIABLE_1449296 tptp.int) (BOUND_VARIABLE_1449297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9220 BOUND_VARIABLE_1449294) BOUND_VARIABLE_1449295) BOUND_VARIABLE_1449296) BOUND_VARIABLE_1449297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449295) BOUND_VARIABLE_1449297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449294) BOUND_VARIABLE_1449296)))))))))) (let ((_let_3280 (forall ((BOUND_VARIABLE_1449269 tptp.int) (BOUND_VARIABLE_1449270 tptp.int) (BOUND_VARIABLE_1449271 tptp.int) (BOUND_VARIABLE_1449272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9221 BOUND_VARIABLE_1449269) BOUND_VARIABLE_1449270) BOUND_VARIABLE_1449271) BOUND_VARIABLE_1449272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449270) BOUND_VARIABLE_1449272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449269) BOUND_VARIABLE_1449271)))))))))) (let ((_let_3281 (forall ((BOUND_VARIABLE_1449244 tptp.int) (BOUND_VARIABLE_1449245 tptp.int) (BOUND_VARIABLE_1449246 tptp.int) (BOUND_VARIABLE_1449247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9222 BOUND_VARIABLE_1449244) BOUND_VARIABLE_1449245) BOUND_VARIABLE_1449246) BOUND_VARIABLE_1449247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449245) BOUND_VARIABLE_1449247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449244) BOUND_VARIABLE_1449246)))))))))) (let ((_let_3282 (forall ((BOUND_VARIABLE_1449219 tptp.int) (BOUND_VARIABLE_1449220 tptp.int) (BOUND_VARIABLE_1449221 tptp.int) (BOUND_VARIABLE_1449222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9223 BOUND_VARIABLE_1449219) BOUND_VARIABLE_1449220) BOUND_VARIABLE_1449221) BOUND_VARIABLE_1449222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449220) BOUND_VARIABLE_1449222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449219) BOUND_VARIABLE_1449221)))))))))) (let ((_let_3283 (forall ((BOUND_VARIABLE_1449194 tptp.int) (BOUND_VARIABLE_1449195 tptp.int) (BOUND_VARIABLE_1449196 tptp.int) (BOUND_VARIABLE_1449197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9224 BOUND_VARIABLE_1449194) BOUND_VARIABLE_1449195) BOUND_VARIABLE_1449196) BOUND_VARIABLE_1449197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449195) BOUND_VARIABLE_1449197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449194) BOUND_VARIABLE_1449196)))))))))) (let ((_let_3284 (forall ((BOUND_VARIABLE_1449169 tptp.int) (BOUND_VARIABLE_1449170 tptp.int) (BOUND_VARIABLE_1449171 tptp.int) (BOUND_VARIABLE_1449172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9225 BOUND_VARIABLE_1449169) BOUND_VARIABLE_1449170) BOUND_VARIABLE_1449171) BOUND_VARIABLE_1449172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449170) BOUND_VARIABLE_1449172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449169) BOUND_VARIABLE_1449171)))))))))) (let ((_let_3285 (forall ((BOUND_VARIABLE_1449144 tptp.int) (BOUND_VARIABLE_1449145 tptp.int) (BOUND_VARIABLE_1449146 tptp.int) (BOUND_VARIABLE_1449147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9226 BOUND_VARIABLE_1449144) BOUND_VARIABLE_1449145) BOUND_VARIABLE_1449146) BOUND_VARIABLE_1449147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449145) BOUND_VARIABLE_1449147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449144) BOUND_VARIABLE_1449146)))))))))) (let ((_let_3286 (forall ((BOUND_VARIABLE_1449119 tptp.int) (BOUND_VARIABLE_1449120 tptp.int) (BOUND_VARIABLE_1449121 tptp.int) (BOUND_VARIABLE_1449122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9227 BOUND_VARIABLE_1449119) BOUND_VARIABLE_1449120) BOUND_VARIABLE_1449121) BOUND_VARIABLE_1449122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449120) BOUND_VARIABLE_1449122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449119) BOUND_VARIABLE_1449121)))))))))) (let ((_let_3287 (forall ((BOUND_VARIABLE_1449094 tptp.int) (BOUND_VARIABLE_1449095 tptp.int) (BOUND_VARIABLE_1449096 tptp.int) (BOUND_VARIABLE_1449097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9228 BOUND_VARIABLE_1449094) BOUND_VARIABLE_1449095) BOUND_VARIABLE_1449096) BOUND_VARIABLE_1449097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449095) BOUND_VARIABLE_1449097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449094) BOUND_VARIABLE_1449096)))))))))) (let ((_let_3288 (forall ((BOUND_VARIABLE_1449069 tptp.int) (BOUND_VARIABLE_1449070 tptp.int) (BOUND_VARIABLE_1449071 tptp.int) (BOUND_VARIABLE_1449072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9229 BOUND_VARIABLE_1449069) BOUND_VARIABLE_1449070) BOUND_VARIABLE_1449071) BOUND_VARIABLE_1449072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449070) BOUND_VARIABLE_1449072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449069) BOUND_VARIABLE_1449071)))))))))) (let ((_let_3289 (forall ((BOUND_VARIABLE_1449044 tptp.int) (BOUND_VARIABLE_1449045 tptp.int) (BOUND_VARIABLE_1449046 tptp.int) (BOUND_VARIABLE_1449047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9230 BOUND_VARIABLE_1449044) BOUND_VARIABLE_1449045) BOUND_VARIABLE_1449046) BOUND_VARIABLE_1449047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449045) BOUND_VARIABLE_1449047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449044) BOUND_VARIABLE_1449046)))))))))) (let ((_let_3290 (forall ((BOUND_VARIABLE_1449019 tptp.int) (BOUND_VARIABLE_1449020 tptp.int) (BOUND_VARIABLE_1449021 tptp.int) (BOUND_VARIABLE_1449022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9231 BOUND_VARIABLE_1449019) BOUND_VARIABLE_1449020) BOUND_VARIABLE_1449021) BOUND_VARIABLE_1449022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449020) BOUND_VARIABLE_1449022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1449019) BOUND_VARIABLE_1449021)))))))))) (let ((_let_3291 (forall ((BOUND_VARIABLE_1448994 tptp.int) (BOUND_VARIABLE_1448995 tptp.int) (BOUND_VARIABLE_1448996 tptp.int) (BOUND_VARIABLE_1448997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9232 BOUND_VARIABLE_1448994) BOUND_VARIABLE_1448995) BOUND_VARIABLE_1448996) BOUND_VARIABLE_1448997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448995) BOUND_VARIABLE_1448997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448994) BOUND_VARIABLE_1448996)))))))))) (let ((_let_3292 (forall ((BOUND_VARIABLE_1448969 tptp.int) (BOUND_VARIABLE_1448970 tptp.int) (BOUND_VARIABLE_1448971 tptp.int) (BOUND_VARIABLE_1448972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9233 BOUND_VARIABLE_1448969) BOUND_VARIABLE_1448970) BOUND_VARIABLE_1448971) BOUND_VARIABLE_1448972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448970) BOUND_VARIABLE_1448972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448969) BOUND_VARIABLE_1448971)))))))))) (let ((_let_3293 (forall ((BOUND_VARIABLE_1448944 tptp.int) (BOUND_VARIABLE_1448945 tptp.int) (BOUND_VARIABLE_1448946 tptp.int) (BOUND_VARIABLE_1448947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9234 BOUND_VARIABLE_1448944) BOUND_VARIABLE_1448945) BOUND_VARIABLE_1448946) BOUND_VARIABLE_1448947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448945) BOUND_VARIABLE_1448947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448944) BOUND_VARIABLE_1448946)))))))))) (let ((_let_3294 (forall ((BOUND_VARIABLE_1448919 tptp.int) (BOUND_VARIABLE_1448920 tptp.int) (BOUND_VARIABLE_1448921 tptp.int) (BOUND_VARIABLE_1448922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9235 BOUND_VARIABLE_1448919) BOUND_VARIABLE_1448920) BOUND_VARIABLE_1448921) BOUND_VARIABLE_1448922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448920) BOUND_VARIABLE_1448922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448919) BOUND_VARIABLE_1448921)))))))))) (let ((_let_3295 (forall ((BOUND_VARIABLE_1448894 tptp.int) (BOUND_VARIABLE_1448895 tptp.int) (BOUND_VARIABLE_1448896 tptp.int) (BOUND_VARIABLE_1448897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9236 BOUND_VARIABLE_1448894) BOUND_VARIABLE_1448895) BOUND_VARIABLE_1448896) BOUND_VARIABLE_1448897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448895) BOUND_VARIABLE_1448897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448894) BOUND_VARIABLE_1448896)))))))))) (let ((_let_3296 (forall ((BOUND_VARIABLE_1448869 tptp.int) (BOUND_VARIABLE_1448870 tptp.int) (BOUND_VARIABLE_1448871 tptp.int) (BOUND_VARIABLE_1448872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9237 BOUND_VARIABLE_1448869) BOUND_VARIABLE_1448870) BOUND_VARIABLE_1448871) BOUND_VARIABLE_1448872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448870) BOUND_VARIABLE_1448872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448869) BOUND_VARIABLE_1448871)))))))))) (let ((_let_3297 (forall ((BOUND_VARIABLE_1448844 tptp.int) (BOUND_VARIABLE_1448845 tptp.int) (BOUND_VARIABLE_1448846 tptp.int) (BOUND_VARIABLE_1448847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9238 BOUND_VARIABLE_1448844) BOUND_VARIABLE_1448845) BOUND_VARIABLE_1448846) BOUND_VARIABLE_1448847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448845) BOUND_VARIABLE_1448847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448844) BOUND_VARIABLE_1448846)))))))))) (let ((_let_3298 (forall ((BOUND_VARIABLE_1448819 tptp.int) (BOUND_VARIABLE_1448820 tptp.int) (BOUND_VARIABLE_1448821 tptp.int) (BOUND_VARIABLE_1448822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9239 BOUND_VARIABLE_1448819) BOUND_VARIABLE_1448820) BOUND_VARIABLE_1448821) BOUND_VARIABLE_1448822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448820) BOUND_VARIABLE_1448822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448819) BOUND_VARIABLE_1448821)))))))))) (let ((_let_3299 (forall ((BOUND_VARIABLE_1448794 tptp.int) (BOUND_VARIABLE_1448795 tptp.int) (BOUND_VARIABLE_1448796 tptp.int) (BOUND_VARIABLE_1448797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9240 BOUND_VARIABLE_1448794) BOUND_VARIABLE_1448795) BOUND_VARIABLE_1448796) BOUND_VARIABLE_1448797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448795) BOUND_VARIABLE_1448797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448794) BOUND_VARIABLE_1448796)))))))))) (let ((_let_3300 (forall ((BOUND_VARIABLE_1448769 tptp.int) (BOUND_VARIABLE_1448770 tptp.int) (BOUND_VARIABLE_1448771 tptp.int) (BOUND_VARIABLE_1448772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9241 BOUND_VARIABLE_1448769) BOUND_VARIABLE_1448770) BOUND_VARIABLE_1448771) BOUND_VARIABLE_1448772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448770) BOUND_VARIABLE_1448772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448769) BOUND_VARIABLE_1448771)))))))))) (let ((_let_3301 (forall ((BOUND_VARIABLE_1448744 tptp.int) (BOUND_VARIABLE_1448745 tptp.int) (BOUND_VARIABLE_1448746 tptp.int) (BOUND_VARIABLE_1448747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9242 BOUND_VARIABLE_1448744) BOUND_VARIABLE_1448745) BOUND_VARIABLE_1448746) BOUND_VARIABLE_1448747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448745) BOUND_VARIABLE_1448747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448744) BOUND_VARIABLE_1448746)))))))))) (let ((_let_3302 (forall ((BOUND_VARIABLE_1448719 tptp.int) (BOUND_VARIABLE_1448720 tptp.int) (BOUND_VARIABLE_1448721 tptp.int) (BOUND_VARIABLE_1448722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9243 BOUND_VARIABLE_1448719) BOUND_VARIABLE_1448720) BOUND_VARIABLE_1448721) BOUND_VARIABLE_1448722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448720) BOUND_VARIABLE_1448722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448719) BOUND_VARIABLE_1448721)))))))))) (let ((_let_3303 (forall ((BOUND_VARIABLE_1448694 tptp.int) (BOUND_VARIABLE_1448695 tptp.int) (BOUND_VARIABLE_1448696 tptp.int) (BOUND_VARIABLE_1448697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9244 BOUND_VARIABLE_1448694) BOUND_VARIABLE_1448695) BOUND_VARIABLE_1448696) BOUND_VARIABLE_1448697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448695) BOUND_VARIABLE_1448697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448694) BOUND_VARIABLE_1448696)))))))))) (let ((_let_3304 (forall ((BOUND_VARIABLE_1448669 tptp.int) (BOUND_VARIABLE_1448670 tptp.int) (BOUND_VARIABLE_1448671 tptp.int) (BOUND_VARIABLE_1448672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9245 BOUND_VARIABLE_1448669) BOUND_VARIABLE_1448670) BOUND_VARIABLE_1448671) BOUND_VARIABLE_1448672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448670) BOUND_VARIABLE_1448672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448669) BOUND_VARIABLE_1448671)))))))))) (let ((_let_3305 (forall ((BOUND_VARIABLE_1448644 tptp.int) (BOUND_VARIABLE_1448645 tptp.int) (BOUND_VARIABLE_1448646 tptp.int) (BOUND_VARIABLE_1448647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9246 BOUND_VARIABLE_1448644) BOUND_VARIABLE_1448645) BOUND_VARIABLE_1448646) BOUND_VARIABLE_1448647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448645) BOUND_VARIABLE_1448647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448644) BOUND_VARIABLE_1448646)))))))))) (let ((_let_3306 (forall ((BOUND_VARIABLE_1448619 tptp.int) (BOUND_VARIABLE_1448620 tptp.int) (BOUND_VARIABLE_1448621 tptp.int) (BOUND_VARIABLE_1448622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9247 BOUND_VARIABLE_1448619) BOUND_VARIABLE_1448620) BOUND_VARIABLE_1448621) BOUND_VARIABLE_1448622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448620) BOUND_VARIABLE_1448622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448619) BOUND_VARIABLE_1448621)))))))))) (let ((_let_3307 (forall ((BOUND_VARIABLE_1448594 tptp.int) (BOUND_VARIABLE_1448595 tptp.int) (BOUND_VARIABLE_1448596 tptp.int) (BOUND_VARIABLE_1448597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9248 BOUND_VARIABLE_1448594) BOUND_VARIABLE_1448595) BOUND_VARIABLE_1448596) BOUND_VARIABLE_1448597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448595) BOUND_VARIABLE_1448597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448594) BOUND_VARIABLE_1448596)))))))))) (let ((_let_3308 (forall ((BOUND_VARIABLE_1448569 tptp.int) (BOUND_VARIABLE_1448570 tptp.int) (BOUND_VARIABLE_1448571 tptp.int) (BOUND_VARIABLE_1448572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9249 BOUND_VARIABLE_1448569) BOUND_VARIABLE_1448570) BOUND_VARIABLE_1448571) BOUND_VARIABLE_1448572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448570) BOUND_VARIABLE_1448572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448569) BOUND_VARIABLE_1448571)))))))))) (let ((_let_3309 (forall ((BOUND_VARIABLE_1448544 tptp.int) (BOUND_VARIABLE_1448545 tptp.int) (BOUND_VARIABLE_1448546 tptp.int) (BOUND_VARIABLE_1448547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9250 BOUND_VARIABLE_1448544) BOUND_VARIABLE_1448545) BOUND_VARIABLE_1448546) BOUND_VARIABLE_1448547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448545) BOUND_VARIABLE_1448547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448544) BOUND_VARIABLE_1448546)))))))))) (let ((_let_3310 (forall ((BOUND_VARIABLE_1448519 tptp.int) (BOUND_VARIABLE_1448520 tptp.int) (BOUND_VARIABLE_1448521 tptp.int) (BOUND_VARIABLE_1448522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9251 BOUND_VARIABLE_1448519) BOUND_VARIABLE_1448520) BOUND_VARIABLE_1448521) BOUND_VARIABLE_1448522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448520) BOUND_VARIABLE_1448522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448519) BOUND_VARIABLE_1448521)))))))))) (let ((_let_3311 (forall ((BOUND_VARIABLE_1448494 tptp.int) (BOUND_VARIABLE_1448495 tptp.int) (BOUND_VARIABLE_1448496 tptp.int) (BOUND_VARIABLE_1448497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9252 BOUND_VARIABLE_1448494) BOUND_VARIABLE_1448495) BOUND_VARIABLE_1448496) BOUND_VARIABLE_1448497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448495) BOUND_VARIABLE_1448497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448494) BOUND_VARIABLE_1448496)))))))))) (let ((_let_3312 (forall ((BOUND_VARIABLE_1448469 tptp.int) (BOUND_VARIABLE_1448470 tptp.int) (BOUND_VARIABLE_1448471 tptp.int) (BOUND_VARIABLE_1448472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9253 BOUND_VARIABLE_1448469) BOUND_VARIABLE_1448470) BOUND_VARIABLE_1448471) BOUND_VARIABLE_1448472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448470) BOUND_VARIABLE_1448472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448469) BOUND_VARIABLE_1448471)))))))))) (let ((_let_3313 (forall ((BOUND_VARIABLE_1448444 tptp.int) (BOUND_VARIABLE_1448445 tptp.int) (BOUND_VARIABLE_1448446 tptp.int) (BOUND_VARIABLE_1448447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9254 BOUND_VARIABLE_1448444) BOUND_VARIABLE_1448445) BOUND_VARIABLE_1448446) BOUND_VARIABLE_1448447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448445) BOUND_VARIABLE_1448447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448444) BOUND_VARIABLE_1448446)))))))))) (let ((_let_3314 (forall ((BOUND_VARIABLE_1448419 tptp.int) (BOUND_VARIABLE_1448420 tptp.int) (BOUND_VARIABLE_1448421 tptp.int) (BOUND_VARIABLE_1448422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9255 BOUND_VARIABLE_1448419) BOUND_VARIABLE_1448420) BOUND_VARIABLE_1448421) BOUND_VARIABLE_1448422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448420) BOUND_VARIABLE_1448422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448419) BOUND_VARIABLE_1448421)))))))))) (let ((_let_3315 (forall ((BOUND_VARIABLE_1448394 tptp.int) (BOUND_VARIABLE_1448395 tptp.int) (BOUND_VARIABLE_1448396 tptp.int) (BOUND_VARIABLE_1448397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9256 BOUND_VARIABLE_1448394) BOUND_VARIABLE_1448395) BOUND_VARIABLE_1448396) BOUND_VARIABLE_1448397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448395) BOUND_VARIABLE_1448397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448394) BOUND_VARIABLE_1448396)))))))))) (let ((_let_3316 (forall ((BOUND_VARIABLE_1448369 tptp.int) (BOUND_VARIABLE_1448370 tptp.int) (BOUND_VARIABLE_1448371 tptp.int) (BOUND_VARIABLE_1448372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9257 BOUND_VARIABLE_1448369) BOUND_VARIABLE_1448370) BOUND_VARIABLE_1448371) BOUND_VARIABLE_1448372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448370) BOUND_VARIABLE_1448372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448369) BOUND_VARIABLE_1448371)))))))))) (let ((_let_3317 (forall ((BOUND_VARIABLE_1448344 tptp.int) (BOUND_VARIABLE_1448345 tptp.int) (BOUND_VARIABLE_1448346 tptp.int) (BOUND_VARIABLE_1448347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9258 BOUND_VARIABLE_1448344) BOUND_VARIABLE_1448345) BOUND_VARIABLE_1448346) BOUND_VARIABLE_1448347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448345) BOUND_VARIABLE_1448347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448344) BOUND_VARIABLE_1448346)))))))))) (let ((_let_3318 (forall ((BOUND_VARIABLE_1448319 tptp.int) (BOUND_VARIABLE_1448320 tptp.int) (BOUND_VARIABLE_1448321 tptp.int) (BOUND_VARIABLE_1448322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9259 BOUND_VARIABLE_1448319) BOUND_VARIABLE_1448320) BOUND_VARIABLE_1448321) BOUND_VARIABLE_1448322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448320) BOUND_VARIABLE_1448322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448319) BOUND_VARIABLE_1448321)))))))))) (let ((_let_3319 (forall ((BOUND_VARIABLE_1448294 tptp.int) (BOUND_VARIABLE_1448295 tptp.int) (BOUND_VARIABLE_1448296 tptp.int) (BOUND_VARIABLE_1448297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9260 BOUND_VARIABLE_1448294) BOUND_VARIABLE_1448295) BOUND_VARIABLE_1448296) BOUND_VARIABLE_1448297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448295) BOUND_VARIABLE_1448297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448294) BOUND_VARIABLE_1448296)))))))))) (let ((_let_3320 (forall ((BOUND_VARIABLE_1448269 tptp.int) (BOUND_VARIABLE_1448270 tptp.int) (BOUND_VARIABLE_1448271 tptp.int) (BOUND_VARIABLE_1448272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9261 BOUND_VARIABLE_1448269) BOUND_VARIABLE_1448270) BOUND_VARIABLE_1448271) BOUND_VARIABLE_1448272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448270) BOUND_VARIABLE_1448272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448269) BOUND_VARIABLE_1448271)))))))))) (let ((_let_3321 (forall ((BOUND_VARIABLE_1448244 tptp.int) (BOUND_VARIABLE_1448245 tptp.int) (BOUND_VARIABLE_1448246 tptp.int) (BOUND_VARIABLE_1448247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9262 BOUND_VARIABLE_1448244) BOUND_VARIABLE_1448245) BOUND_VARIABLE_1448246) BOUND_VARIABLE_1448247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448245) BOUND_VARIABLE_1448247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448244) BOUND_VARIABLE_1448246)))))))))) (let ((_let_3322 (forall ((BOUND_VARIABLE_1448219 tptp.int) (BOUND_VARIABLE_1448220 tptp.int) (BOUND_VARIABLE_1448221 tptp.int) (BOUND_VARIABLE_1448222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9263 BOUND_VARIABLE_1448219) BOUND_VARIABLE_1448220) BOUND_VARIABLE_1448221) BOUND_VARIABLE_1448222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448220) BOUND_VARIABLE_1448222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448219) BOUND_VARIABLE_1448221)))))))))) (let ((_let_3323 (forall ((BOUND_VARIABLE_1448194 tptp.int) (BOUND_VARIABLE_1448195 tptp.int) (BOUND_VARIABLE_1448196 tptp.int) (BOUND_VARIABLE_1448197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9264 BOUND_VARIABLE_1448194) BOUND_VARIABLE_1448195) BOUND_VARIABLE_1448196) BOUND_VARIABLE_1448197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448195) BOUND_VARIABLE_1448197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448194) BOUND_VARIABLE_1448196)))))))))) (let ((_let_3324 (forall ((BOUND_VARIABLE_1448169 tptp.int) (BOUND_VARIABLE_1448170 tptp.int) (BOUND_VARIABLE_1448171 tptp.int) (BOUND_VARIABLE_1448172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9265 BOUND_VARIABLE_1448169) BOUND_VARIABLE_1448170) BOUND_VARIABLE_1448171) BOUND_VARIABLE_1448172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448170) BOUND_VARIABLE_1448172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448169) BOUND_VARIABLE_1448171)))))))))) (let ((_let_3325 (forall ((BOUND_VARIABLE_1448144 tptp.int) (BOUND_VARIABLE_1448145 tptp.int) (BOUND_VARIABLE_1448146 tptp.int) (BOUND_VARIABLE_1448147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9266 BOUND_VARIABLE_1448144) BOUND_VARIABLE_1448145) BOUND_VARIABLE_1448146) BOUND_VARIABLE_1448147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448145) BOUND_VARIABLE_1448147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448144) BOUND_VARIABLE_1448146)))))))))) (let ((_let_3326 (forall ((BOUND_VARIABLE_1448119 tptp.int) (BOUND_VARIABLE_1448120 tptp.int) (BOUND_VARIABLE_1448121 tptp.int) (BOUND_VARIABLE_1448122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9267 BOUND_VARIABLE_1448119) BOUND_VARIABLE_1448120) BOUND_VARIABLE_1448121) BOUND_VARIABLE_1448122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448120) BOUND_VARIABLE_1448122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448119) BOUND_VARIABLE_1448121)))))))))) (let ((_let_3327 (forall ((BOUND_VARIABLE_1448094 tptp.int) (BOUND_VARIABLE_1448095 tptp.int) (BOUND_VARIABLE_1448096 tptp.int) (BOUND_VARIABLE_1448097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9268 BOUND_VARIABLE_1448094) BOUND_VARIABLE_1448095) BOUND_VARIABLE_1448096) BOUND_VARIABLE_1448097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448095) BOUND_VARIABLE_1448097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448094) BOUND_VARIABLE_1448096)))))))))) (let ((_let_3328 (forall ((BOUND_VARIABLE_1448069 tptp.int) (BOUND_VARIABLE_1448070 tptp.int) (BOUND_VARIABLE_1448071 tptp.int) (BOUND_VARIABLE_1448072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9269 BOUND_VARIABLE_1448069) BOUND_VARIABLE_1448070) BOUND_VARIABLE_1448071) BOUND_VARIABLE_1448072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448070) BOUND_VARIABLE_1448072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448069) BOUND_VARIABLE_1448071)))))))))) (let ((_let_3329 (forall ((BOUND_VARIABLE_1448044 tptp.int) (BOUND_VARIABLE_1448045 tptp.int) (BOUND_VARIABLE_1448046 tptp.int) (BOUND_VARIABLE_1448047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9270 BOUND_VARIABLE_1448044) BOUND_VARIABLE_1448045) BOUND_VARIABLE_1448046) BOUND_VARIABLE_1448047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448045) BOUND_VARIABLE_1448047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448044) BOUND_VARIABLE_1448046)))))))))) (let ((_let_3330 (forall ((BOUND_VARIABLE_1448019 tptp.int) (BOUND_VARIABLE_1448020 tptp.int) (BOUND_VARIABLE_1448021 tptp.int) (BOUND_VARIABLE_1448022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9271 BOUND_VARIABLE_1448019) BOUND_VARIABLE_1448020) BOUND_VARIABLE_1448021) BOUND_VARIABLE_1448022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448020) BOUND_VARIABLE_1448022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1448019) BOUND_VARIABLE_1448021)))))))))) (let ((_let_3331 (forall ((BOUND_VARIABLE_1447994 tptp.int) (BOUND_VARIABLE_1447995 tptp.int) (BOUND_VARIABLE_1447996 tptp.int) (BOUND_VARIABLE_1447997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9272 BOUND_VARIABLE_1447994) BOUND_VARIABLE_1447995) BOUND_VARIABLE_1447996) BOUND_VARIABLE_1447997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447995) BOUND_VARIABLE_1447997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447994) BOUND_VARIABLE_1447996)))))))))) (let ((_let_3332 (forall ((BOUND_VARIABLE_1447969 tptp.int) (BOUND_VARIABLE_1447970 tptp.int) (BOUND_VARIABLE_1447971 tptp.int) (BOUND_VARIABLE_1447972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9273 BOUND_VARIABLE_1447969) BOUND_VARIABLE_1447970) BOUND_VARIABLE_1447971) BOUND_VARIABLE_1447972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447970) BOUND_VARIABLE_1447972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447969) BOUND_VARIABLE_1447971)))))))))) (let ((_let_3333 (forall ((BOUND_VARIABLE_1447944 tptp.int) (BOUND_VARIABLE_1447945 tptp.int) (BOUND_VARIABLE_1447946 tptp.int) (BOUND_VARIABLE_1447947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9274 BOUND_VARIABLE_1447944) BOUND_VARIABLE_1447945) BOUND_VARIABLE_1447946) BOUND_VARIABLE_1447947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447945) BOUND_VARIABLE_1447947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447944) BOUND_VARIABLE_1447946)))))))))) (let ((_let_3334 (forall ((BOUND_VARIABLE_1447919 tptp.int) (BOUND_VARIABLE_1447920 tptp.int) (BOUND_VARIABLE_1447921 tptp.int) (BOUND_VARIABLE_1447922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9275 BOUND_VARIABLE_1447919) BOUND_VARIABLE_1447920) BOUND_VARIABLE_1447921) BOUND_VARIABLE_1447922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447920) BOUND_VARIABLE_1447922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447919) BOUND_VARIABLE_1447921)))))))))) (let ((_let_3335 (forall ((BOUND_VARIABLE_1447894 tptp.int) (BOUND_VARIABLE_1447895 tptp.int) (BOUND_VARIABLE_1447896 tptp.int) (BOUND_VARIABLE_1447897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9276 BOUND_VARIABLE_1447894) BOUND_VARIABLE_1447895) BOUND_VARIABLE_1447896) BOUND_VARIABLE_1447897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447895) BOUND_VARIABLE_1447897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447894) BOUND_VARIABLE_1447896)))))))))) (let ((_let_3336 (forall ((BOUND_VARIABLE_1447869 tptp.int) (BOUND_VARIABLE_1447870 tptp.int) (BOUND_VARIABLE_1447871 tptp.int) (BOUND_VARIABLE_1447872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9277 BOUND_VARIABLE_1447869) BOUND_VARIABLE_1447870) BOUND_VARIABLE_1447871) BOUND_VARIABLE_1447872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447870) BOUND_VARIABLE_1447872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447869) BOUND_VARIABLE_1447871)))))))))) (let ((_let_3337 (forall ((BOUND_VARIABLE_1447844 tptp.int) (BOUND_VARIABLE_1447845 tptp.int) (BOUND_VARIABLE_1447846 tptp.int) (BOUND_VARIABLE_1447847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9278 BOUND_VARIABLE_1447844) BOUND_VARIABLE_1447845) BOUND_VARIABLE_1447846) BOUND_VARIABLE_1447847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447845) BOUND_VARIABLE_1447847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447844) BOUND_VARIABLE_1447846)))))))))) (let ((_let_3338 (forall ((BOUND_VARIABLE_1447819 tptp.int) (BOUND_VARIABLE_1447820 tptp.int) (BOUND_VARIABLE_1447821 tptp.int) (BOUND_VARIABLE_1447822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9279 BOUND_VARIABLE_1447819) BOUND_VARIABLE_1447820) BOUND_VARIABLE_1447821) BOUND_VARIABLE_1447822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447820) BOUND_VARIABLE_1447822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447819) BOUND_VARIABLE_1447821)))))))))) (let ((_let_3339 (forall ((BOUND_VARIABLE_1447794 tptp.int) (BOUND_VARIABLE_1447795 tptp.int) (BOUND_VARIABLE_1447796 tptp.int) (BOUND_VARIABLE_1447797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9280 BOUND_VARIABLE_1447794) BOUND_VARIABLE_1447795) BOUND_VARIABLE_1447796) BOUND_VARIABLE_1447797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447795) BOUND_VARIABLE_1447797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447794) BOUND_VARIABLE_1447796)))))))))) (let ((_let_3340 (forall ((BOUND_VARIABLE_1447769 tptp.int) (BOUND_VARIABLE_1447770 tptp.int) (BOUND_VARIABLE_1447771 tptp.int) (BOUND_VARIABLE_1447772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9281 BOUND_VARIABLE_1447769) BOUND_VARIABLE_1447770) BOUND_VARIABLE_1447771) BOUND_VARIABLE_1447772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447770) BOUND_VARIABLE_1447772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447769) BOUND_VARIABLE_1447771)))))))))) (let ((_let_3341 (forall ((BOUND_VARIABLE_1447744 tptp.int) (BOUND_VARIABLE_1447745 tptp.int) (BOUND_VARIABLE_1447746 tptp.int) (BOUND_VARIABLE_1447747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9282 BOUND_VARIABLE_1447744) BOUND_VARIABLE_1447745) BOUND_VARIABLE_1447746) BOUND_VARIABLE_1447747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447745) BOUND_VARIABLE_1447747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447744) BOUND_VARIABLE_1447746)))))))))) (let ((_let_3342 (forall ((BOUND_VARIABLE_1447719 tptp.int) (BOUND_VARIABLE_1447720 tptp.int) (BOUND_VARIABLE_1447721 tptp.int) (BOUND_VARIABLE_1447722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9283 BOUND_VARIABLE_1447719) BOUND_VARIABLE_1447720) BOUND_VARIABLE_1447721) BOUND_VARIABLE_1447722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447720) BOUND_VARIABLE_1447722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447719) BOUND_VARIABLE_1447721)))))))))) (let ((_let_3343 (forall ((BOUND_VARIABLE_1447694 tptp.int) (BOUND_VARIABLE_1447695 tptp.int) (BOUND_VARIABLE_1447696 tptp.int) (BOUND_VARIABLE_1447697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9284 BOUND_VARIABLE_1447694) BOUND_VARIABLE_1447695) BOUND_VARIABLE_1447696) BOUND_VARIABLE_1447697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447695) BOUND_VARIABLE_1447697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447694) BOUND_VARIABLE_1447696)))))))))) (let ((_let_3344 (forall ((BOUND_VARIABLE_1447669 tptp.int) (BOUND_VARIABLE_1447670 tptp.int) (BOUND_VARIABLE_1447671 tptp.int) (BOUND_VARIABLE_1447672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9285 BOUND_VARIABLE_1447669) BOUND_VARIABLE_1447670) BOUND_VARIABLE_1447671) BOUND_VARIABLE_1447672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447670) BOUND_VARIABLE_1447672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447669) BOUND_VARIABLE_1447671)))))))))) (let ((_let_3345 (forall ((BOUND_VARIABLE_1447644 tptp.int) (BOUND_VARIABLE_1447645 tptp.int) (BOUND_VARIABLE_1447646 tptp.int) (BOUND_VARIABLE_1447647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9286 BOUND_VARIABLE_1447644) BOUND_VARIABLE_1447645) BOUND_VARIABLE_1447646) BOUND_VARIABLE_1447647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447645) BOUND_VARIABLE_1447647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447644) BOUND_VARIABLE_1447646)))))))))) (let ((_let_3346 (forall ((BOUND_VARIABLE_1447619 tptp.int) (BOUND_VARIABLE_1447620 tptp.int) (BOUND_VARIABLE_1447621 tptp.int) (BOUND_VARIABLE_1447622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9287 BOUND_VARIABLE_1447619) BOUND_VARIABLE_1447620) BOUND_VARIABLE_1447621) BOUND_VARIABLE_1447622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447620) BOUND_VARIABLE_1447622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447619) BOUND_VARIABLE_1447621)))))))))) (let ((_let_3347 (forall ((BOUND_VARIABLE_1447594 tptp.int) (BOUND_VARIABLE_1447595 tptp.int) (BOUND_VARIABLE_1447596 tptp.int) (BOUND_VARIABLE_1447597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9288 BOUND_VARIABLE_1447594) BOUND_VARIABLE_1447595) BOUND_VARIABLE_1447596) BOUND_VARIABLE_1447597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447595) BOUND_VARIABLE_1447597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447594) BOUND_VARIABLE_1447596)))))))))) (let ((_let_3348 (forall ((BOUND_VARIABLE_1447569 tptp.int) (BOUND_VARIABLE_1447570 tptp.int) (BOUND_VARIABLE_1447571 tptp.int) (BOUND_VARIABLE_1447572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9289 BOUND_VARIABLE_1447569) BOUND_VARIABLE_1447570) BOUND_VARIABLE_1447571) BOUND_VARIABLE_1447572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447570) BOUND_VARIABLE_1447572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447569) BOUND_VARIABLE_1447571)))))))))) (let ((_let_3349 (forall ((BOUND_VARIABLE_1447544 tptp.int) (BOUND_VARIABLE_1447545 tptp.int) (BOUND_VARIABLE_1447546 tptp.int) (BOUND_VARIABLE_1447547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9290 BOUND_VARIABLE_1447544) BOUND_VARIABLE_1447545) BOUND_VARIABLE_1447546) BOUND_VARIABLE_1447547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447545) BOUND_VARIABLE_1447547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447544) BOUND_VARIABLE_1447546)))))))))) (let ((_let_3350 (forall ((BOUND_VARIABLE_1447519 tptp.int) (BOUND_VARIABLE_1447520 tptp.int) (BOUND_VARIABLE_1447521 tptp.int) (BOUND_VARIABLE_1447522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9291 BOUND_VARIABLE_1447519) BOUND_VARIABLE_1447520) BOUND_VARIABLE_1447521) BOUND_VARIABLE_1447522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447520) BOUND_VARIABLE_1447522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447519) BOUND_VARIABLE_1447521)))))))))) (let ((_let_3351 (forall ((BOUND_VARIABLE_1447494 tptp.int) (BOUND_VARIABLE_1447495 tptp.int) (BOUND_VARIABLE_1447496 tptp.int) (BOUND_VARIABLE_1447497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9292 BOUND_VARIABLE_1447494) BOUND_VARIABLE_1447495) BOUND_VARIABLE_1447496) BOUND_VARIABLE_1447497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447495) BOUND_VARIABLE_1447497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447494) BOUND_VARIABLE_1447496)))))))))) (let ((_let_3352 (forall ((BOUND_VARIABLE_1447469 tptp.int) (BOUND_VARIABLE_1447470 tptp.int) (BOUND_VARIABLE_1447471 tptp.int) (BOUND_VARIABLE_1447472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9293 BOUND_VARIABLE_1447469) BOUND_VARIABLE_1447470) BOUND_VARIABLE_1447471) BOUND_VARIABLE_1447472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447470) BOUND_VARIABLE_1447472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447469) BOUND_VARIABLE_1447471)))))))))) (let ((_let_3353 (forall ((BOUND_VARIABLE_1447444 tptp.int) (BOUND_VARIABLE_1447445 tptp.int) (BOUND_VARIABLE_1447446 tptp.int) (BOUND_VARIABLE_1447447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9294 BOUND_VARIABLE_1447444) BOUND_VARIABLE_1447445) BOUND_VARIABLE_1447446) BOUND_VARIABLE_1447447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447445) BOUND_VARIABLE_1447447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447444) BOUND_VARIABLE_1447446)))))))))) (let ((_let_3354 (forall ((BOUND_VARIABLE_1447419 tptp.int) (BOUND_VARIABLE_1447420 tptp.int) (BOUND_VARIABLE_1447421 tptp.int) (BOUND_VARIABLE_1447422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9295 BOUND_VARIABLE_1447419) BOUND_VARIABLE_1447420) BOUND_VARIABLE_1447421) BOUND_VARIABLE_1447422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447420) BOUND_VARIABLE_1447422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447419) BOUND_VARIABLE_1447421)))))))))) (let ((_let_3355 (forall ((BOUND_VARIABLE_1447394 tptp.int) (BOUND_VARIABLE_1447395 tptp.int) (BOUND_VARIABLE_1447396 tptp.int) (BOUND_VARIABLE_1447397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9296 BOUND_VARIABLE_1447394) BOUND_VARIABLE_1447395) BOUND_VARIABLE_1447396) BOUND_VARIABLE_1447397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447395) BOUND_VARIABLE_1447397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447394) BOUND_VARIABLE_1447396)))))))))) (let ((_let_3356 (forall ((BOUND_VARIABLE_1447369 tptp.int) (BOUND_VARIABLE_1447370 tptp.int) (BOUND_VARIABLE_1447371 tptp.int) (BOUND_VARIABLE_1447372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9297 BOUND_VARIABLE_1447369) BOUND_VARIABLE_1447370) BOUND_VARIABLE_1447371) BOUND_VARIABLE_1447372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447370) BOUND_VARIABLE_1447372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447369) BOUND_VARIABLE_1447371)))))))))) (let ((_let_3357 (forall ((BOUND_VARIABLE_1447344 tptp.int) (BOUND_VARIABLE_1447345 tptp.int) (BOUND_VARIABLE_1447346 tptp.int) (BOUND_VARIABLE_1447347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9298 BOUND_VARIABLE_1447344) BOUND_VARIABLE_1447345) BOUND_VARIABLE_1447346) BOUND_VARIABLE_1447347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447345) BOUND_VARIABLE_1447347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447344) BOUND_VARIABLE_1447346)))))))))) (let ((_let_3358 (forall ((BOUND_VARIABLE_1447319 tptp.int) (BOUND_VARIABLE_1447320 tptp.int) (BOUND_VARIABLE_1447321 tptp.int) (BOUND_VARIABLE_1447322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9299 BOUND_VARIABLE_1447319) BOUND_VARIABLE_1447320) BOUND_VARIABLE_1447321) BOUND_VARIABLE_1447322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447320) BOUND_VARIABLE_1447322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447319) BOUND_VARIABLE_1447321)))))))))) (let ((_let_3359 (forall ((BOUND_VARIABLE_1447294 tptp.int) (BOUND_VARIABLE_1447295 tptp.int) (BOUND_VARIABLE_1447296 tptp.int) (BOUND_VARIABLE_1447297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9300 BOUND_VARIABLE_1447294) BOUND_VARIABLE_1447295) BOUND_VARIABLE_1447296) BOUND_VARIABLE_1447297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447295) BOUND_VARIABLE_1447297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447294) BOUND_VARIABLE_1447296)))))))))) (let ((_let_3360 (forall ((BOUND_VARIABLE_1447269 tptp.int) (BOUND_VARIABLE_1447270 tptp.int) (BOUND_VARIABLE_1447271 tptp.int) (BOUND_VARIABLE_1447272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9301 BOUND_VARIABLE_1447269) BOUND_VARIABLE_1447270) BOUND_VARIABLE_1447271) BOUND_VARIABLE_1447272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447270) BOUND_VARIABLE_1447272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447269) BOUND_VARIABLE_1447271)))))))))) (let ((_let_3361 (forall ((BOUND_VARIABLE_1447244 tptp.int) (BOUND_VARIABLE_1447245 tptp.int) (BOUND_VARIABLE_1447246 tptp.int) (BOUND_VARIABLE_1447247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9302 BOUND_VARIABLE_1447244) BOUND_VARIABLE_1447245) BOUND_VARIABLE_1447246) BOUND_VARIABLE_1447247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447245) BOUND_VARIABLE_1447247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447244) BOUND_VARIABLE_1447246)))))))))) (let ((_let_3362 (forall ((BOUND_VARIABLE_1447219 tptp.int) (BOUND_VARIABLE_1447220 tptp.int) (BOUND_VARIABLE_1447221 tptp.int) (BOUND_VARIABLE_1447222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9303 BOUND_VARIABLE_1447219) BOUND_VARIABLE_1447220) BOUND_VARIABLE_1447221) BOUND_VARIABLE_1447222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447220) BOUND_VARIABLE_1447222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447219) BOUND_VARIABLE_1447221)))))))))) (let ((_let_3363 (forall ((BOUND_VARIABLE_1447194 tptp.int) (BOUND_VARIABLE_1447195 tptp.int) (BOUND_VARIABLE_1447196 tptp.int) (BOUND_VARIABLE_1447197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9304 BOUND_VARIABLE_1447194) BOUND_VARIABLE_1447195) BOUND_VARIABLE_1447196) BOUND_VARIABLE_1447197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447195) BOUND_VARIABLE_1447197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447194) BOUND_VARIABLE_1447196)))))))))) (let ((_let_3364 (forall ((BOUND_VARIABLE_1447169 tptp.int) (BOUND_VARIABLE_1447170 tptp.int) (BOUND_VARIABLE_1447171 tptp.int) (BOUND_VARIABLE_1447172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9305 BOUND_VARIABLE_1447169) BOUND_VARIABLE_1447170) BOUND_VARIABLE_1447171) BOUND_VARIABLE_1447172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447170) BOUND_VARIABLE_1447172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447169) BOUND_VARIABLE_1447171)))))))))) (let ((_let_3365 (forall ((BOUND_VARIABLE_1447144 tptp.int) (BOUND_VARIABLE_1447145 tptp.int) (BOUND_VARIABLE_1447146 tptp.int) (BOUND_VARIABLE_1447147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9306 BOUND_VARIABLE_1447144) BOUND_VARIABLE_1447145) BOUND_VARIABLE_1447146) BOUND_VARIABLE_1447147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447145) BOUND_VARIABLE_1447147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447144) BOUND_VARIABLE_1447146)))))))))) (let ((_let_3366 (forall ((BOUND_VARIABLE_1447119 tptp.int) (BOUND_VARIABLE_1447120 tptp.int) (BOUND_VARIABLE_1447121 tptp.int) (BOUND_VARIABLE_1447122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9307 BOUND_VARIABLE_1447119) BOUND_VARIABLE_1447120) BOUND_VARIABLE_1447121) BOUND_VARIABLE_1447122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447120) BOUND_VARIABLE_1447122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447119) BOUND_VARIABLE_1447121)))))))))) (let ((_let_3367 (forall ((BOUND_VARIABLE_1447094 tptp.int) (BOUND_VARIABLE_1447095 tptp.int) (BOUND_VARIABLE_1447096 tptp.int) (BOUND_VARIABLE_1447097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9308 BOUND_VARIABLE_1447094) BOUND_VARIABLE_1447095) BOUND_VARIABLE_1447096) BOUND_VARIABLE_1447097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447095) BOUND_VARIABLE_1447097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447094) BOUND_VARIABLE_1447096)))))))))) (let ((_let_3368 (forall ((BOUND_VARIABLE_1447069 tptp.int) (BOUND_VARIABLE_1447070 tptp.int) (BOUND_VARIABLE_1447071 tptp.int) (BOUND_VARIABLE_1447072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9309 BOUND_VARIABLE_1447069) BOUND_VARIABLE_1447070) BOUND_VARIABLE_1447071) BOUND_VARIABLE_1447072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447070) BOUND_VARIABLE_1447072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447069) BOUND_VARIABLE_1447071)))))))))) (let ((_let_3369 (forall ((BOUND_VARIABLE_1447044 tptp.int) (BOUND_VARIABLE_1447045 tptp.int) (BOUND_VARIABLE_1447046 tptp.int) (BOUND_VARIABLE_1447047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9310 BOUND_VARIABLE_1447044) BOUND_VARIABLE_1447045) BOUND_VARIABLE_1447046) BOUND_VARIABLE_1447047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447045) BOUND_VARIABLE_1447047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447044) BOUND_VARIABLE_1447046)))))))))) (let ((_let_3370 (forall ((BOUND_VARIABLE_1447019 tptp.int) (BOUND_VARIABLE_1447020 tptp.int) (BOUND_VARIABLE_1447021 tptp.int) (BOUND_VARIABLE_1447022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9311 BOUND_VARIABLE_1447019) BOUND_VARIABLE_1447020) BOUND_VARIABLE_1447021) BOUND_VARIABLE_1447022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447020) BOUND_VARIABLE_1447022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1447019) BOUND_VARIABLE_1447021)))))))))) (let ((_let_3371 (forall ((BOUND_VARIABLE_1446994 tptp.int) (BOUND_VARIABLE_1446995 tptp.int) (BOUND_VARIABLE_1446996 tptp.int) (BOUND_VARIABLE_1446997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9312 BOUND_VARIABLE_1446994) BOUND_VARIABLE_1446995) BOUND_VARIABLE_1446996) BOUND_VARIABLE_1446997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446995) BOUND_VARIABLE_1446997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446994) BOUND_VARIABLE_1446996)))))))))) (let ((_let_3372 (forall ((BOUND_VARIABLE_1446969 tptp.int) (BOUND_VARIABLE_1446970 tptp.int) (BOUND_VARIABLE_1446971 tptp.int) (BOUND_VARIABLE_1446972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9313 BOUND_VARIABLE_1446969) BOUND_VARIABLE_1446970) BOUND_VARIABLE_1446971) BOUND_VARIABLE_1446972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446970) BOUND_VARIABLE_1446972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446969) BOUND_VARIABLE_1446971)))))))))) (let ((_let_3373 (forall ((BOUND_VARIABLE_1446944 tptp.int) (BOUND_VARIABLE_1446945 tptp.int) (BOUND_VARIABLE_1446946 tptp.int) (BOUND_VARIABLE_1446947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9314 BOUND_VARIABLE_1446944) BOUND_VARIABLE_1446945) BOUND_VARIABLE_1446946) BOUND_VARIABLE_1446947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446945) BOUND_VARIABLE_1446947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446944) BOUND_VARIABLE_1446946)))))))))) (let ((_let_3374 (forall ((BOUND_VARIABLE_1446919 tptp.int) (BOUND_VARIABLE_1446920 tptp.int) (BOUND_VARIABLE_1446921 tptp.int) (BOUND_VARIABLE_1446922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9315 BOUND_VARIABLE_1446919) BOUND_VARIABLE_1446920) BOUND_VARIABLE_1446921) BOUND_VARIABLE_1446922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446920) BOUND_VARIABLE_1446922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446919) BOUND_VARIABLE_1446921)))))))))) (let ((_let_3375 (forall ((BOUND_VARIABLE_1446894 tptp.int) (BOUND_VARIABLE_1446895 tptp.int) (BOUND_VARIABLE_1446896 tptp.int) (BOUND_VARIABLE_1446897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9316 BOUND_VARIABLE_1446894) BOUND_VARIABLE_1446895) BOUND_VARIABLE_1446896) BOUND_VARIABLE_1446897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446895) BOUND_VARIABLE_1446897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446894) BOUND_VARIABLE_1446896)))))))))) (let ((_let_3376 (forall ((BOUND_VARIABLE_1446869 tptp.int) (BOUND_VARIABLE_1446870 tptp.int) (BOUND_VARIABLE_1446871 tptp.int) (BOUND_VARIABLE_1446872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9317 BOUND_VARIABLE_1446869) BOUND_VARIABLE_1446870) BOUND_VARIABLE_1446871) BOUND_VARIABLE_1446872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446870) BOUND_VARIABLE_1446872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446869) BOUND_VARIABLE_1446871)))))))))) (let ((_let_3377 (forall ((BOUND_VARIABLE_1446844 tptp.int) (BOUND_VARIABLE_1446845 tptp.int) (BOUND_VARIABLE_1446846 tptp.int) (BOUND_VARIABLE_1446847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9318 BOUND_VARIABLE_1446844) BOUND_VARIABLE_1446845) BOUND_VARIABLE_1446846) BOUND_VARIABLE_1446847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446845) BOUND_VARIABLE_1446847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446844) BOUND_VARIABLE_1446846)))))))))) (let ((_let_3378 (forall ((BOUND_VARIABLE_1446819 tptp.int) (BOUND_VARIABLE_1446820 tptp.int) (BOUND_VARIABLE_1446821 tptp.int) (BOUND_VARIABLE_1446822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9319 BOUND_VARIABLE_1446819) BOUND_VARIABLE_1446820) BOUND_VARIABLE_1446821) BOUND_VARIABLE_1446822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446820) BOUND_VARIABLE_1446822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446819) BOUND_VARIABLE_1446821)))))))))) (let ((_let_3379 (forall ((BOUND_VARIABLE_1446794 tptp.int) (BOUND_VARIABLE_1446795 tptp.int) (BOUND_VARIABLE_1446796 tptp.int) (BOUND_VARIABLE_1446797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9320 BOUND_VARIABLE_1446794) BOUND_VARIABLE_1446795) BOUND_VARIABLE_1446796) BOUND_VARIABLE_1446797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446795) BOUND_VARIABLE_1446797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446794) BOUND_VARIABLE_1446796)))))))))) (let ((_let_3380 (forall ((BOUND_VARIABLE_1446769 tptp.int) (BOUND_VARIABLE_1446770 tptp.int) (BOUND_VARIABLE_1446771 tptp.int) (BOUND_VARIABLE_1446772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9321 BOUND_VARIABLE_1446769) BOUND_VARIABLE_1446770) BOUND_VARIABLE_1446771) BOUND_VARIABLE_1446772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446770) BOUND_VARIABLE_1446772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446769) BOUND_VARIABLE_1446771)))))))))) (let ((_let_3381 (forall ((BOUND_VARIABLE_1446744 tptp.int) (BOUND_VARIABLE_1446745 tptp.int) (BOUND_VARIABLE_1446746 tptp.int) (BOUND_VARIABLE_1446747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9322 BOUND_VARIABLE_1446744) BOUND_VARIABLE_1446745) BOUND_VARIABLE_1446746) BOUND_VARIABLE_1446747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446745) BOUND_VARIABLE_1446747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446744) BOUND_VARIABLE_1446746)))))))))) (let ((_let_3382 (forall ((BOUND_VARIABLE_1446719 tptp.int) (BOUND_VARIABLE_1446720 tptp.int) (BOUND_VARIABLE_1446721 tptp.int) (BOUND_VARIABLE_1446722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9323 BOUND_VARIABLE_1446719) BOUND_VARIABLE_1446720) BOUND_VARIABLE_1446721) BOUND_VARIABLE_1446722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446720) BOUND_VARIABLE_1446722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446719) BOUND_VARIABLE_1446721)))))))))) (let ((_let_3383 (forall ((BOUND_VARIABLE_1446694 tptp.int) (BOUND_VARIABLE_1446695 tptp.int) (BOUND_VARIABLE_1446696 tptp.int) (BOUND_VARIABLE_1446697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9324 BOUND_VARIABLE_1446694) BOUND_VARIABLE_1446695) BOUND_VARIABLE_1446696) BOUND_VARIABLE_1446697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446695) BOUND_VARIABLE_1446697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446694) BOUND_VARIABLE_1446696)))))))))) (let ((_let_3384 (forall ((BOUND_VARIABLE_1446669 tptp.int) (BOUND_VARIABLE_1446670 tptp.int) (BOUND_VARIABLE_1446671 tptp.int) (BOUND_VARIABLE_1446672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9325 BOUND_VARIABLE_1446669) BOUND_VARIABLE_1446670) BOUND_VARIABLE_1446671) BOUND_VARIABLE_1446672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446670) BOUND_VARIABLE_1446672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446669) BOUND_VARIABLE_1446671)))))))))) (let ((_let_3385 (forall ((BOUND_VARIABLE_1446644 tptp.int) (BOUND_VARIABLE_1446645 tptp.int) (BOUND_VARIABLE_1446646 tptp.int) (BOUND_VARIABLE_1446647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9326 BOUND_VARIABLE_1446644) BOUND_VARIABLE_1446645) BOUND_VARIABLE_1446646) BOUND_VARIABLE_1446647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446645) BOUND_VARIABLE_1446647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446644) BOUND_VARIABLE_1446646)))))))))) (let ((_let_3386 (forall ((BOUND_VARIABLE_1446619 tptp.int) (BOUND_VARIABLE_1446620 tptp.int) (BOUND_VARIABLE_1446621 tptp.int) (BOUND_VARIABLE_1446622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9327 BOUND_VARIABLE_1446619) BOUND_VARIABLE_1446620) BOUND_VARIABLE_1446621) BOUND_VARIABLE_1446622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446620) BOUND_VARIABLE_1446622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446619) BOUND_VARIABLE_1446621)))))))))) (let ((_let_3387 (forall ((BOUND_VARIABLE_1446594 tptp.int) (BOUND_VARIABLE_1446595 tptp.int) (BOUND_VARIABLE_1446596 tptp.int) (BOUND_VARIABLE_1446597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9328 BOUND_VARIABLE_1446594) BOUND_VARIABLE_1446595) BOUND_VARIABLE_1446596) BOUND_VARIABLE_1446597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446595) BOUND_VARIABLE_1446597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446594) BOUND_VARIABLE_1446596)))))))))) (let ((_let_3388 (forall ((BOUND_VARIABLE_1446569 tptp.int) (BOUND_VARIABLE_1446570 tptp.int) (BOUND_VARIABLE_1446571 tptp.int) (BOUND_VARIABLE_1446572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9329 BOUND_VARIABLE_1446569) BOUND_VARIABLE_1446570) BOUND_VARIABLE_1446571) BOUND_VARIABLE_1446572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446570) BOUND_VARIABLE_1446572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446569) BOUND_VARIABLE_1446571)))))))))) (let ((_let_3389 (forall ((BOUND_VARIABLE_1446544 tptp.int) (BOUND_VARIABLE_1446545 tptp.int) (BOUND_VARIABLE_1446546 tptp.int) (BOUND_VARIABLE_1446547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9330 BOUND_VARIABLE_1446544) BOUND_VARIABLE_1446545) BOUND_VARIABLE_1446546) BOUND_VARIABLE_1446547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446545) BOUND_VARIABLE_1446547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446544) BOUND_VARIABLE_1446546)))))))))) (let ((_let_3390 (forall ((BOUND_VARIABLE_1446519 tptp.int) (BOUND_VARIABLE_1446520 tptp.int) (BOUND_VARIABLE_1446521 tptp.int) (BOUND_VARIABLE_1446522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9331 BOUND_VARIABLE_1446519) BOUND_VARIABLE_1446520) BOUND_VARIABLE_1446521) BOUND_VARIABLE_1446522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446520) BOUND_VARIABLE_1446522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446519) BOUND_VARIABLE_1446521)))))))))) (let ((_let_3391 (forall ((BOUND_VARIABLE_1446494 tptp.int) (BOUND_VARIABLE_1446495 tptp.int) (BOUND_VARIABLE_1446496 tptp.int) (BOUND_VARIABLE_1446497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9332 BOUND_VARIABLE_1446494) BOUND_VARIABLE_1446495) BOUND_VARIABLE_1446496) BOUND_VARIABLE_1446497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446495) BOUND_VARIABLE_1446497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446494) BOUND_VARIABLE_1446496)))))))))) (let ((_let_3392 (forall ((BOUND_VARIABLE_1446469 tptp.int) (BOUND_VARIABLE_1446470 tptp.int) (BOUND_VARIABLE_1446471 tptp.int) (BOUND_VARIABLE_1446472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9333 BOUND_VARIABLE_1446469) BOUND_VARIABLE_1446470) BOUND_VARIABLE_1446471) BOUND_VARIABLE_1446472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446470) BOUND_VARIABLE_1446472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446469) BOUND_VARIABLE_1446471)))))))))) (let ((_let_3393 (forall ((BOUND_VARIABLE_1446444 tptp.int) (BOUND_VARIABLE_1446445 tptp.int) (BOUND_VARIABLE_1446446 tptp.int) (BOUND_VARIABLE_1446447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9334 BOUND_VARIABLE_1446444) BOUND_VARIABLE_1446445) BOUND_VARIABLE_1446446) BOUND_VARIABLE_1446447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446445) BOUND_VARIABLE_1446447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446444) BOUND_VARIABLE_1446446)))))))))) (let ((_let_3394 (forall ((BOUND_VARIABLE_1446419 tptp.int) (BOUND_VARIABLE_1446420 tptp.int) (BOUND_VARIABLE_1446421 tptp.int) (BOUND_VARIABLE_1446422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9335 BOUND_VARIABLE_1446419) BOUND_VARIABLE_1446420) BOUND_VARIABLE_1446421) BOUND_VARIABLE_1446422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446420) BOUND_VARIABLE_1446422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446419) BOUND_VARIABLE_1446421)))))))))) (let ((_let_3395 (forall ((BOUND_VARIABLE_1446394 tptp.int) (BOUND_VARIABLE_1446395 tptp.int) (BOUND_VARIABLE_1446396 tptp.int) (BOUND_VARIABLE_1446397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9336 BOUND_VARIABLE_1446394) BOUND_VARIABLE_1446395) BOUND_VARIABLE_1446396) BOUND_VARIABLE_1446397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446395) BOUND_VARIABLE_1446397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446394) BOUND_VARIABLE_1446396)))))))))) (let ((_let_3396 (forall ((BOUND_VARIABLE_1446369 tptp.int) (BOUND_VARIABLE_1446370 tptp.int) (BOUND_VARIABLE_1446371 tptp.int) (BOUND_VARIABLE_1446372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9337 BOUND_VARIABLE_1446369) BOUND_VARIABLE_1446370) BOUND_VARIABLE_1446371) BOUND_VARIABLE_1446372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446370) BOUND_VARIABLE_1446372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446369) BOUND_VARIABLE_1446371)))))))))) (let ((_let_3397 (forall ((BOUND_VARIABLE_1446344 tptp.int) (BOUND_VARIABLE_1446345 tptp.int) (BOUND_VARIABLE_1446346 tptp.int) (BOUND_VARIABLE_1446347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9338 BOUND_VARIABLE_1446344) BOUND_VARIABLE_1446345) BOUND_VARIABLE_1446346) BOUND_VARIABLE_1446347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446345) BOUND_VARIABLE_1446347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446344) BOUND_VARIABLE_1446346)))))))))) (let ((_let_3398 (forall ((BOUND_VARIABLE_1446319 tptp.int) (BOUND_VARIABLE_1446320 tptp.int) (BOUND_VARIABLE_1446321 tptp.int) (BOUND_VARIABLE_1446322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9339 BOUND_VARIABLE_1446319) BOUND_VARIABLE_1446320) BOUND_VARIABLE_1446321) BOUND_VARIABLE_1446322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446320) BOUND_VARIABLE_1446322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446319) BOUND_VARIABLE_1446321)))))))))) (let ((_let_3399 (forall ((BOUND_VARIABLE_1446294 tptp.int) (BOUND_VARIABLE_1446295 tptp.int) (BOUND_VARIABLE_1446296 tptp.int) (BOUND_VARIABLE_1446297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9340 BOUND_VARIABLE_1446294) BOUND_VARIABLE_1446295) BOUND_VARIABLE_1446296) BOUND_VARIABLE_1446297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446295) BOUND_VARIABLE_1446297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446294) BOUND_VARIABLE_1446296)))))))))) (let ((_let_3400 (forall ((BOUND_VARIABLE_1446269 tptp.int) (BOUND_VARIABLE_1446270 tptp.int) (BOUND_VARIABLE_1446271 tptp.int) (BOUND_VARIABLE_1446272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9341 BOUND_VARIABLE_1446269) BOUND_VARIABLE_1446270) BOUND_VARIABLE_1446271) BOUND_VARIABLE_1446272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446270) BOUND_VARIABLE_1446272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446269) BOUND_VARIABLE_1446271)))))))))) (let ((_let_3401 (forall ((BOUND_VARIABLE_1446244 tptp.int) (BOUND_VARIABLE_1446245 tptp.int) (BOUND_VARIABLE_1446246 tptp.int) (BOUND_VARIABLE_1446247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9342 BOUND_VARIABLE_1446244) BOUND_VARIABLE_1446245) BOUND_VARIABLE_1446246) BOUND_VARIABLE_1446247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446245) BOUND_VARIABLE_1446247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446244) BOUND_VARIABLE_1446246)))))))))) (let ((_let_3402 (forall ((BOUND_VARIABLE_1446219 tptp.int) (BOUND_VARIABLE_1446220 tptp.int) (BOUND_VARIABLE_1446221 tptp.int) (BOUND_VARIABLE_1446222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9343 BOUND_VARIABLE_1446219) BOUND_VARIABLE_1446220) BOUND_VARIABLE_1446221) BOUND_VARIABLE_1446222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446220) BOUND_VARIABLE_1446222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446219) BOUND_VARIABLE_1446221)))))))))) (let ((_let_3403 (forall ((BOUND_VARIABLE_1446194 tptp.int) (BOUND_VARIABLE_1446195 tptp.int) (BOUND_VARIABLE_1446196 tptp.int) (BOUND_VARIABLE_1446197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9344 BOUND_VARIABLE_1446194) BOUND_VARIABLE_1446195) BOUND_VARIABLE_1446196) BOUND_VARIABLE_1446197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446195) BOUND_VARIABLE_1446197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446194) BOUND_VARIABLE_1446196)))))))))) (let ((_let_3404 (forall ((BOUND_VARIABLE_1446169 tptp.int) (BOUND_VARIABLE_1446170 tptp.int) (BOUND_VARIABLE_1446171 tptp.int) (BOUND_VARIABLE_1446172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9345 BOUND_VARIABLE_1446169) BOUND_VARIABLE_1446170) BOUND_VARIABLE_1446171) BOUND_VARIABLE_1446172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446170) BOUND_VARIABLE_1446172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446169) BOUND_VARIABLE_1446171)))))))))) (let ((_let_3405 (forall ((BOUND_VARIABLE_1446144 tptp.int) (BOUND_VARIABLE_1446145 tptp.int) (BOUND_VARIABLE_1446146 tptp.int) (BOUND_VARIABLE_1446147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9346 BOUND_VARIABLE_1446144) BOUND_VARIABLE_1446145) BOUND_VARIABLE_1446146) BOUND_VARIABLE_1446147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446145) BOUND_VARIABLE_1446147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446144) BOUND_VARIABLE_1446146)))))))))) (let ((_let_3406 (forall ((BOUND_VARIABLE_1446119 tptp.int) (BOUND_VARIABLE_1446120 tptp.int) (BOUND_VARIABLE_1446121 tptp.int) (BOUND_VARIABLE_1446122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9347 BOUND_VARIABLE_1446119) BOUND_VARIABLE_1446120) BOUND_VARIABLE_1446121) BOUND_VARIABLE_1446122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446120) BOUND_VARIABLE_1446122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446119) BOUND_VARIABLE_1446121)))))))))) (let ((_let_3407 (forall ((BOUND_VARIABLE_1446094 tptp.int) (BOUND_VARIABLE_1446095 tptp.int) (BOUND_VARIABLE_1446096 tptp.int) (BOUND_VARIABLE_1446097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9348 BOUND_VARIABLE_1446094) BOUND_VARIABLE_1446095) BOUND_VARIABLE_1446096) BOUND_VARIABLE_1446097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446095) BOUND_VARIABLE_1446097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446094) BOUND_VARIABLE_1446096)))))))))) (let ((_let_3408 (forall ((BOUND_VARIABLE_1446069 tptp.int) (BOUND_VARIABLE_1446070 tptp.int) (BOUND_VARIABLE_1446071 tptp.int) (BOUND_VARIABLE_1446072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9349 BOUND_VARIABLE_1446069) BOUND_VARIABLE_1446070) BOUND_VARIABLE_1446071) BOUND_VARIABLE_1446072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446070) BOUND_VARIABLE_1446072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446069) BOUND_VARIABLE_1446071)))))))))) (let ((_let_3409 (forall ((BOUND_VARIABLE_1446044 tptp.int) (BOUND_VARIABLE_1446045 tptp.int) (BOUND_VARIABLE_1446046 tptp.int) (BOUND_VARIABLE_1446047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9350 BOUND_VARIABLE_1446044) BOUND_VARIABLE_1446045) BOUND_VARIABLE_1446046) BOUND_VARIABLE_1446047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446045) BOUND_VARIABLE_1446047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446044) BOUND_VARIABLE_1446046)))))))))) (let ((_let_3410 (forall ((BOUND_VARIABLE_1446019 tptp.int) (BOUND_VARIABLE_1446020 tptp.int) (BOUND_VARIABLE_1446021 tptp.int) (BOUND_VARIABLE_1446022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9351 BOUND_VARIABLE_1446019) BOUND_VARIABLE_1446020) BOUND_VARIABLE_1446021) BOUND_VARIABLE_1446022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446020) BOUND_VARIABLE_1446022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1446019) BOUND_VARIABLE_1446021)))))))))) (let ((_let_3411 (forall ((BOUND_VARIABLE_1445994 tptp.int) (BOUND_VARIABLE_1445995 tptp.int) (BOUND_VARIABLE_1445996 tptp.int) (BOUND_VARIABLE_1445997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9352 BOUND_VARIABLE_1445994) BOUND_VARIABLE_1445995) BOUND_VARIABLE_1445996) BOUND_VARIABLE_1445997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445995) BOUND_VARIABLE_1445997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445994) BOUND_VARIABLE_1445996)))))))))) (let ((_let_3412 (forall ((BOUND_VARIABLE_1445969 tptp.int) (BOUND_VARIABLE_1445970 tptp.int) (BOUND_VARIABLE_1445971 tptp.int) (BOUND_VARIABLE_1445972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9353 BOUND_VARIABLE_1445969) BOUND_VARIABLE_1445970) BOUND_VARIABLE_1445971) BOUND_VARIABLE_1445972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445970) BOUND_VARIABLE_1445972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445969) BOUND_VARIABLE_1445971)))))))))) (let ((_let_3413 (forall ((BOUND_VARIABLE_1445944 tptp.int) (BOUND_VARIABLE_1445945 tptp.int) (BOUND_VARIABLE_1445946 tptp.int) (BOUND_VARIABLE_1445947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9354 BOUND_VARIABLE_1445944) BOUND_VARIABLE_1445945) BOUND_VARIABLE_1445946) BOUND_VARIABLE_1445947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445945) BOUND_VARIABLE_1445947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445944) BOUND_VARIABLE_1445946)))))))))) (let ((_let_3414 (forall ((BOUND_VARIABLE_1445919 tptp.int) (BOUND_VARIABLE_1445920 tptp.int) (BOUND_VARIABLE_1445921 tptp.int) (BOUND_VARIABLE_1445922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9355 BOUND_VARIABLE_1445919) BOUND_VARIABLE_1445920) BOUND_VARIABLE_1445921) BOUND_VARIABLE_1445922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445920) BOUND_VARIABLE_1445922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445919) BOUND_VARIABLE_1445921)))))))))) (let ((_let_3415 (forall ((BOUND_VARIABLE_1445894 tptp.int) (BOUND_VARIABLE_1445895 tptp.int) (BOUND_VARIABLE_1445896 tptp.int) (BOUND_VARIABLE_1445897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9356 BOUND_VARIABLE_1445894) BOUND_VARIABLE_1445895) BOUND_VARIABLE_1445896) BOUND_VARIABLE_1445897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445895) BOUND_VARIABLE_1445897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445894) BOUND_VARIABLE_1445896)))))))))) (let ((_let_3416 (forall ((BOUND_VARIABLE_1445869 tptp.int) (BOUND_VARIABLE_1445870 tptp.int) (BOUND_VARIABLE_1445871 tptp.int) (BOUND_VARIABLE_1445872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9357 BOUND_VARIABLE_1445869) BOUND_VARIABLE_1445870) BOUND_VARIABLE_1445871) BOUND_VARIABLE_1445872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445870) BOUND_VARIABLE_1445872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445869) BOUND_VARIABLE_1445871)))))))))) (let ((_let_3417 (forall ((BOUND_VARIABLE_1445844 tptp.int) (BOUND_VARIABLE_1445845 tptp.int) (BOUND_VARIABLE_1445846 tptp.int) (BOUND_VARIABLE_1445847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9358 BOUND_VARIABLE_1445844) BOUND_VARIABLE_1445845) BOUND_VARIABLE_1445846) BOUND_VARIABLE_1445847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445845) BOUND_VARIABLE_1445847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445844) BOUND_VARIABLE_1445846)))))))))) (let ((_let_3418 (forall ((BOUND_VARIABLE_1445819 tptp.int) (BOUND_VARIABLE_1445820 tptp.int) (BOUND_VARIABLE_1445821 tptp.int) (BOUND_VARIABLE_1445822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9359 BOUND_VARIABLE_1445819) BOUND_VARIABLE_1445820) BOUND_VARIABLE_1445821) BOUND_VARIABLE_1445822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445820) BOUND_VARIABLE_1445822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445819) BOUND_VARIABLE_1445821)))))))))) (let ((_let_3419 (forall ((BOUND_VARIABLE_1445794 tptp.int) (BOUND_VARIABLE_1445795 tptp.int) (BOUND_VARIABLE_1445796 tptp.int) (BOUND_VARIABLE_1445797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9360 BOUND_VARIABLE_1445794) BOUND_VARIABLE_1445795) BOUND_VARIABLE_1445796) BOUND_VARIABLE_1445797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445795) BOUND_VARIABLE_1445797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445794) BOUND_VARIABLE_1445796)))))))))) (let ((_let_3420 (forall ((BOUND_VARIABLE_1445769 tptp.int) (BOUND_VARIABLE_1445770 tptp.int) (BOUND_VARIABLE_1445771 tptp.int) (BOUND_VARIABLE_1445772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9361 BOUND_VARIABLE_1445769) BOUND_VARIABLE_1445770) BOUND_VARIABLE_1445771) BOUND_VARIABLE_1445772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445770) BOUND_VARIABLE_1445772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445769) BOUND_VARIABLE_1445771)))))))))) (let ((_let_3421 (forall ((BOUND_VARIABLE_1445744 tptp.int) (BOUND_VARIABLE_1445745 tptp.int) (BOUND_VARIABLE_1445746 tptp.int) (BOUND_VARIABLE_1445747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9362 BOUND_VARIABLE_1445744) BOUND_VARIABLE_1445745) BOUND_VARIABLE_1445746) BOUND_VARIABLE_1445747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445745) BOUND_VARIABLE_1445747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445744) BOUND_VARIABLE_1445746)))))))))) (let ((_let_3422 (forall ((BOUND_VARIABLE_1445719 tptp.int) (BOUND_VARIABLE_1445720 tptp.int) (BOUND_VARIABLE_1445721 tptp.int) (BOUND_VARIABLE_1445722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9363 BOUND_VARIABLE_1445719) BOUND_VARIABLE_1445720) BOUND_VARIABLE_1445721) BOUND_VARIABLE_1445722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445720) BOUND_VARIABLE_1445722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445719) BOUND_VARIABLE_1445721)))))))))) (let ((_let_3423 (forall ((BOUND_VARIABLE_1445694 tptp.int) (BOUND_VARIABLE_1445695 tptp.int) (BOUND_VARIABLE_1445696 tptp.int) (BOUND_VARIABLE_1445697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9364 BOUND_VARIABLE_1445694) BOUND_VARIABLE_1445695) BOUND_VARIABLE_1445696) BOUND_VARIABLE_1445697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445695) BOUND_VARIABLE_1445697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445694) BOUND_VARIABLE_1445696)))))))))) (let ((_let_3424 (forall ((BOUND_VARIABLE_1445669 tptp.int) (BOUND_VARIABLE_1445670 tptp.int) (BOUND_VARIABLE_1445671 tptp.int) (BOUND_VARIABLE_1445672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9365 BOUND_VARIABLE_1445669) BOUND_VARIABLE_1445670) BOUND_VARIABLE_1445671) BOUND_VARIABLE_1445672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445670) BOUND_VARIABLE_1445672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445669) BOUND_VARIABLE_1445671)))))))))) (let ((_let_3425 (forall ((BOUND_VARIABLE_1445644 tptp.int) (BOUND_VARIABLE_1445645 tptp.int) (BOUND_VARIABLE_1445646 tptp.int) (BOUND_VARIABLE_1445647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9366 BOUND_VARIABLE_1445644) BOUND_VARIABLE_1445645) BOUND_VARIABLE_1445646) BOUND_VARIABLE_1445647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445645) BOUND_VARIABLE_1445647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445644) BOUND_VARIABLE_1445646)))))))))) (let ((_let_3426 (forall ((BOUND_VARIABLE_1445619 tptp.int) (BOUND_VARIABLE_1445620 tptp.int) (BOUND_VARIABLE_1445621 tptp.int) (BOUND_VARIABLE_1445622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9367 BOUND_VARIABLE_1445619) BOUND_VARIABLE_1445620) BOUND_VARIABLE_1445621) BOUND_VARIABLE_1445622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445620) BOUND_VARIABLE_1445622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445619) BOUND_VARIABLE_1445621)))))))))) (let ((_let_3427 (forall ((BOUND_VARIABLE_1445594 tptp.int) (BOUND_VARIABLE_1445595 tptp.int) (BOUND_VARIABLE_1445596 tptp.int) (BOUND_VARIABLE_1445597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9368 BOUND_VARIABLE_1445594) BOUND_VARIABLE_1445595) BOUND_VARIABLE_1445596) BOUND_VARIABLE_1445597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445595) BOUND_VARIABLE_1445597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445594) BOUND_VARIABLE_1445596)))))))))) (let ((_let_3428 (forall ((BOUND_VARIABLE_1445569 tptp.int) (BOUND_VARIABLE_1445570 tptp.int) (BOUND_VARIABLE_1445571 tptp.int) (BOUND_VARIABLE_1445572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9369 BOUND_VARIABLE_1445569) BOUND_VARIABLE_1445570) BOUND_VARIABLE_1445571) BOUND_VARIABLE_1445572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445570) BOUND_VARIABLE_1445572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445569) BOUND_VARIABLE_1445571)))))))))) (let ((_let_3429 (forall ((BOUND_VARIABLE_1445544 tptp.int) (BOUND_VARIABLE_1445545 tptp.int) (BOUND_VARIABLE_1445546 tptp.int) (BOUND_VARIABLE_1445547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9370 BOUND_VARIABLE_1445544) BOUND_VARIABLE_1445545) BOUND_VARIABLE_1445546) BOUND_VARIABLE_1445547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445545) BOUND_VARIABLE_1445547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445544) BOUND_VARIABLE_1445546)))))))))) (let ((_let_3430 (forall ((BOUND_VARIABLE_1445519 tptp.int) (BOUND_VARIABLE_1445520 tptp.int) (BOUND_VARIABLE_1445521 tptp.int) (BOUND_VARIABLE_1445522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9371 BOUND_VARIABLE_1445519) BOUND_VARIABLE_1445520) BOUND_VARIABLE_1445521) BOUND_VARIABLE_1445522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445520) BOUND_VARIABLE_1445522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445519) BOUND_VARIABLE_1445521)))))))))) (let ((_let_3431 (forall ((BOUND_VARIABLE_1445494 tptp.int) (BOUND_VARIABLE_1445495 tptp.int) (BOUND_VARIABLE_1445496 tptp.int) (BOUND_VARIABLE_1445497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9372 BOUND_VARIABLE_1445494) BOUND_VARIABLE_1445495) BOUND_VARIABLE_1445496) BOUND_VARIABLE_1445497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445495) BOUND_VARIABLE_1445497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445494) BOUND_VARIABLE_1445496)))))))))) (let ((_let_3432 (forall ((BOUND_VARIABLE_1445469 tptp.int) (BOUND_VARIABLE_1445470 tptp.int) (BOUND_VARIABLE_1445471 tptp.int) (BOUND_VARIABLE_1445472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9373 BOUND_VARIABLE_1445469) BOUND_VARIABLE_1445470) BOUND_VARIABLE_1445471) BOUND_VARIABLE_1445472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445470) BOUND_VARIABLE_1445472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445469) BOUND_VARIABLE_1445471)))))))))) (let ((_let_3433 (forall ((BOUND_VARIABLE_1445444 tptp.int) (BOUND_VARIABLE_1445445 tptp.int) (BOUND_VARIABLE_1445446 tptp.int) (BOUND_VARIABLE_1445447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9374 BOUND_VARIABLE_1445444) BOUND_VARIABLE_1445445) BOUND_VARIABLE_1445446) BOUND_VARIABLE_1445447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445445) BOUND_VARIABLE_1445447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445444) BOUND_VARIABLE_1445446)))))))))) (let ((_let_3434 (forall ((BOUND_VARIABLE_1445419 tptp.int) (BOUND_VARIABLE_1445420 tptp.int) (BOUND_VARIABLE_1445421 tptp.int) (BOUND_VARIABLE_1445422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9375 BOUND_VARIABLE_1445419) BOUND_VARIABLE_1445420) BOUND_VARIABLE_1445421) BOUND_VARIABLE_1445422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445420) BOUND_VARIABLE_1445422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445419) BOUND_VARIABLE_1445421)))))))))) (let ((_let_3435 (forall ((BOUND_VARIABLE_1445394 tptp.int) (BOUND_VARIABLE_1445395 tptp.int) (BOUND_VARIABLE_1445396 tptp.int) (BOUND_VARIABLE_1445397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9376 BOUND_VARIABLE_1445394) BOUND_VARIABLE_1445395) BOUND_VARIABLE_1445396) BOUND_VARIABLE_1445397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445395) BOUND_VARIABLE_1445397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445394) BOUND_VARIABLE_1445396)))))))))) (let ((_let_3436 (forall ((BOUND_VARIABLE_1445369 tptp.int) (BOUND_VARIABLE_1445370 tptp.int) (BOUND_VARIABLE_1445371 tptp.int) (BOUND_VARIABLE_1445372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9377 BOUND_VARIABLE_1445369) BOUND_VARIABLE_1445370) BOUND_VARIABLE_1445371) BOUND_VARIABLE_1445372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445370) BOUND_VARIABLE_1445372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445369) BOUND_VARIABLE_1445371)))))))))) (let ((_let_3437 (forall ((BOUND_VARIABLE_1445344 tptp.int) (BOUND_VARIABLE_1445345 tptp.int) (BOUND_VARIABLE_1445346 tptp.int) (BOUND_VARIABLE_1445347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9378 BOUND_VARIABLE_1445344) BOUND_VARIABLE_1445345) BOUND_VARIABLE_1445346) BOUND_VARIABLE_1445347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445345) BOUND_VARIABLE_1445347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445344) BOUND_VARIABLE_1445346)))))))))) (let ((_let_3438 (forall ((BOUND_VARIABLE_1445319 tptp.int) (BOUND_VARIABLE_1445320 tptp.int) (BOUND_VARIABLE_1445321 tptp.int) (BOUND_VARIABLE_1445322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9379 BOUND_VARIABLE_1445319) BOUND_VARIABLE_1445320) BOUND_VARIABLE_1445321) BOUND_VARIABLE_1445322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445320) BOUND_VARIABLE_1445322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445319) BOUND_VARIABLE_1445321)))))))))) (let ((_let_3439 (forall ((BOUND_VARIABLE_1445294 tptp.int) (BOUND_VARIABLE_1445295 tptp.int) (BOUND_VARIABLE_1445296 tptp.int) (BOUND_VARIABLE_1445297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9380 BOUND_VARIABLE_1445294) BOUND_VARIABLE_1445295) BOUND_VARIABLE_1445296) BOUND_VARIABLE_1445297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445295) BOUND_VARIABLE_1445297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445294) BOUND_VARIABLE_1445296)))))))))) (let ((_let_3440 (forall ((BOUND_VARIABLE_1445269 tptp.int) (BOUND_VARIABLE_1445270 tptp.int) (BOUND_VARIABLE_1445271 tptp.int) (BOUND_VARIABLE_1445272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9381 BOUND_VARIABLE_1445269) BOUND_VARIABLE_1445270) BOUND_VARIABLE_1445271) BOUND_VARIABLE_1445272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445270) BOUND_VARIABLE_1445272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445269) BOUND_VARIABLE_1445271)))))))))) (let ((_let_3441 (forall ((BOUND_VARIABLE_1445244 tptp.int) (BOUND_VARIABLE_1445245 tptp.int) (BOUND_VARIABLE_1445246 tptp.int) (BOUND_VARIABLE_1445247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9382 BOUND_VARIABLE_1445244) BOUND_VARIABLE_1445245) BOUND_VARIABLE_1445246) BOUND_VARIABLE_1445247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445245) BOUND_VARIABLE_1445247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445244) BOUND_VARIABLE_1445246)))))))))) (let ((_let_3442 (forall ((BOUND_VARIABLE_1445219 tptp.int) (BOUND_VARIABLE_1445220 tptp.int) (BOUND_VARIABLE_1445221 tptp.int) (BOUND_VARIABLE_1445222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9383 BOUND_VARIABLE_1445219) BOUND_VARIABLE_1445220) BOUND_VARIABLE_1445221) BOUND_VARIABLE_1445222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445220) BOUND_VARIABLE_1445222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445219) BOUND_VARIABLE_1445221)))))))))) (let ((_let_3443 (forall ((BOUND_VARIABLE_1445194 tptp.int) (BOUND_VARIABLE_1445195 tptp.int) (BOUND_VARIABLE_1445196 tptp.int) (BOUND_VARIABLE_1445197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9384 BOUND_VARIABLE_1445194) BOUND_VARIABLE_1445195) BOUND_VARIABLE_1445196) BOUND_VARIABLE_1445197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445195) BOUND_VARIABLE_1445197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445194) BOUND_VARIABLE_1445196)))))))))) (let ((_let_3444 (forall ((BOUND_VARIABLE_1445169 tptp.int) (BOUND_VARIABLE_1445170 tptp.int) (BOUND_VARIABLE_1445171 tptp.int) (BOUND_VARIABLE_1445172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9385 BOUND_VARIABLE_1445169) BOUND_VARIABLE_1445170) BOUND_VARIABLE_1445171) BOUND_VARIABLE_1445172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445170) BOUND_VARIABLE_1445172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445169) BOUND_VARIABLE_1445171)))))))))) (let ((_let_3445 (forall ((BOUND_VARIABLE_1445144 tptp.int) (BOUND_VARIABLE_1445145 tptp.int) (BOUND_VARIABLE_1445146 tptp.int) (BOUND_VARIABLE_1445147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9386 BOUND_VARIABLE_1445144) BOUND_VARIABLE_1445145) BOUND_VARIABLE_1445146) BOUND_VARIABLE_1445147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445145) BOUND_VARIABLE_1445147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445144) BOUND_VARIABLE_1445146)))))))))) (let ((_let_3446 (forall ((BOUND_VARIABLE_1445119 tptp.int) (BOUND_VARIABLE_1445120 tptp.int) (BOUND_VARIABLE_1445121 tptp.int) (BOUND_VARIABLE_1445122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9387 BOUND_VARIABLE_1445119) BOUND_VARIABLE_1445120) BOUND_VARIABLE_1445121) BOUND_VARIABLE_1445122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445120) BOUND_VARIABLE_1445122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445119) BOUND_VARIABLE_1445121)))))))))) (let ((_let_3447 (forall ((BOUND_VARIABLE_1445094 tptp.int) (BOUND_VARIABLE_1445095 tptp.int) (BOUND_VARIABLE_1445096 tptp.int) (BOUND_VARIABLE_1445097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9388 BOUND_VARIABLE_1445094) BOUND_VARIABLE_1445095) BOUND_VARIABLE_1445096) BOUND_VARIABLE_1445097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445095) BOUND_VARIABLE_1445097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445094) BOUND_VARIABLE_1445096)))))))))) (let ((_let_3448 (forall ((BOUND_VARIABLE_1445069 tptp.int) (BOUND_VARIABLE_1445070 tptp.int) (BOUND_VARIABLE_1445071 tptp.int) (BOUND_VARIABLE_1445072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9389 BOUND_VARIABLE_1445069) BOUND_VARIABLE_1445070) BOUND_VARIABLE_1445071) BOUND_VARIABLE_1445072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445070) BOUND_VARIABLE_1445072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445069) BOUND_VARIABLE_1445071)))))))))) (let ((_let_3449 (forall ((BOUND_VARIABLE_1445044 tptp.int) (BOUND_VARIABLE_1445045 tptp.int) (BOUND_VARIABLE_1445046 tptp.int) (BOUND_VARIABLE_1445047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9390 BOUND_VARIABLE_1445044) BOUND_VARIABLE_1445045) BOUND_VARIABLE_1445046) BOUND_VARIABLE_1445047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445045) BOUND_VARIABLE_1445047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445044) BOUND_VARIABLE_1445046)))))))))) (let ((_let_3450 (forall ((BOUND_VARIABLE_1445019 tptp.int) (BOUND_VARIABLE_1445020 tptp.int) (BOUND_VARIABLE_1445021 tptp.int) (BOUND_VARIABLE_1445022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9391 BOUND_VARIABLE_1445019) BOUND_VARIABLE_1445020) BOUND_VARIABLE_1445021) BOUND_VARIABLE_1445022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445020) BOUND_VARIABLE_1445022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1445019) BOUND_VARIABLE_1445021)))))))))) (let ((_let_3451 (forall ((BOUND_VARIABLE_1444994 tptp.int) (BOUND_VARIABLE_1444995 tptp.int) (BOUND_VARIABLE_1444996 tptp.int) (BOUND_VARIABLE_1444997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9392 BOUND_VARIABLE_1444994) BOUND_VARIABLE_1444995) BOUND_VARIABLE_1444996) BOUND_VARIABLE_1444997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444995) BOUND_VARIABLE_1444997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444994) BOUND_VARIABLE_1444996)))))))))) (let ((_let_3452 (forall ((BOUND_VARIABLE_1444969 tptp.int) (BOUND_VARIABLE_1444970 tptp.int) (BOUND_VARIABLE_1444971 tptp.int) (BOUND_VARIABLE_1444972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9393 BOUND_VARIABLE_1444969) BOUND_VARIABLE_1444970) BOUND_VARIABLE_1444971) BOUND_VARIABLE_1444972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444970) BOUND_VARIABLE_1444972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444969) BOUND_VARIABLE_1444971)))))))))) (let ((_let_3453 (forall ((BOUND_VARIABLE_1444944 tptp.int) (BOUND_VARIABLE_1444945 tptp.int) (BOUND_VARIABLE_1444946 tptp.int) (BOUND_VARIABLE_1444947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9394 BOUND_VARIABLE_1444944) BOUND_VARIABLE_1444945) BOUND_VARIABLE_1444946) BOUND_VARIABLE_1444947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444945) BOUND_VARIABLE_1444947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444944) BOUND_VARIABLE_1444946)))))))))) (let ((_let_3454 (forall ((BOUND_VARIABLE_1444919 tptp.int) (BOUND_VARIABLE_1444920 tptp.int) (BOUND_VARIABLE_1444921 tptp.int) (BOUND_VARIABLE_1444922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9395 BOUND_VARIABLE_1444919) BOUND_VARIABLE_1444920) BOUND_VARIABLE_1444921) BOUND_VARIABLE_1444922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444920) BOUND_VARIABLE_1444922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444919) BOUND_VARIABLE_1444921)))))))))) (let ((_let_3455 (forall ((BOUND_VARIABLE_1444894 tptp.int) (BOUND_VARIABLE_1444895 tptp.int) (BOUND_VARIABLE_1444896 tptp.int) (BOUND_VARIABLE_1444897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9396 BOUND_VARIABLE_1444894) BOUND_VARIABLE_1444895) BOUND_VARIABLE_1444896) BOUND_VARIABLE_1444897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444895) BOUND_VARIABLE_1444897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444894) BOUND_VARIABLE_1444896)))))))))) (let ((_let_3456 (forall ((BOUND_VARIABLE_1444869 tptp.int) (BOUND_VARIABLE_1444870 tptp.int) (BOUND_VARIABLE_1444871 tptp.int) (BOUND_VARIABLE_1444872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9397 BOUND_VARIABLE_1444869) BOUND_VARIABLE_1444870) BOUND_VARIABLE_1444871) BOUND_VARIABLE_1444872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444870) BOUND_VARIABLE_1444872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444869) BOUND_VARIABLE_1444871)))))))))) (let ((_let_3457 (forall ((BOUND_VARIABLE_1444844 tptp.int) (BOUND_VARIABLE_1444845 tptp.int) (BOUND_VARIABLE_1444846 tptp.int) (BOUND_VARIABLE_1444847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9398 BOUND_VARIABLE_1444844) BOUND_VARIABLE_1444845) BOUND_VARIABLE_1444846) BOUND_VARIABLE_1444847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444845) BOUND_VARIABLE_1444847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444844) BOUND_VARIABLE_1444846)))))))))) (let ((_let_3458 (forall ((BOUND_VARIABLE_1444819 tptp.int) (BOUND_VARIABLE_1444820 tptp.int) (BOUND_VARIABLE_1444821 tptp.int) (BOUND_VARIABLE_1444822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9399 BOUND_VARIABLE_1444819) BOUND_VARIABLE_1444820) BOUND_VARIABLE_1444821) BOUND_VARIABLE_1444822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444820) BOUND_VARIABLE_1444822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444819) BOUND_VARIABLE_1444821)))))))))) (let ((_let_3459 (forall ((BOUND_VARIABLE_1444794 tptp.int) (BOUND_VARIABLE_1444795 tptp.int) (BOUND_VARIABLE_1444796 tptp.int) (BOUND_VARIABLE_1444797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9400 BOUND_VARIABLE_1444794) BOUND_VARIABLE_1444795) BOUND_VARIABLE_1444796) BOUND_VARIABLE_1444797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444795) BOUND_VARIABLE_1444797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444794) BOUND_VARIABLE_1444796)))))))))) (let ((_let_3460 (forall ((BOUND_VARIABLE_1444769 tptp.int) (BOUND_VARIABLE_1444770 tptp.int) (BOUND_VARIABLE_1444771 tptp.int) (BOUND_VARIABLE_1444772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9401 BOUND_VARIABLE_1444769) BOUND_VARIABLE_1444770) BOUND_VARIABLE_1444771) BOUND_VARIABLE_1444772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444770) BOUND_VARIABLE_1444772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444769) BOUND_VARIABLE_1444771)))))))))) (let ((_let_3461 (forall ((BOUND_VARIABLE_1444744 tptp.int) (BOUND_VARIABLE_1444745 tptp.int) (BOUND_VARIABLE_1444746 tptp.int) (BOUND_VARIABLE_1444747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9402 BOUND_VARIABLE_1444744) BOUND_VARIABLE_1444745) BOUND_VARIABLE_1444746) BOUND_VARIABLE_1444747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444745) BOUND_VARIABLE_1444747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444744) BOUND_VARIABLE_1444746)))))))))) (let ((_let_3462 (forall ((BOUND_VARIABLE_1444719 tptp.int) (BOUND_VARIABLE_1444720 tptp.int) (BOUND_VARIABLE_1444721 tptp.int) (BOUND_VARIABLE_1444722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9403 BOUND_VARIABLE_1444719) BOUND_VARIABLE_1444720) BOUND_VARIABLE_1444721) BOUND_VARIABLE_1444722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444720) BOUND_VARIABLE_1444722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444719) BOUND_VARIABLE_1444721)))))))))) (let ((_let_3463 (forall ((BOUND_VARIABLE_1444694 tptp.int) (BOUND_VARIABLE_1444695 tptp.int) (BOUND_VARIABLE_1444696 tptp.int) (BOUND_VARIABLE_1444697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9404 BOUND_VARIABLE_1444694) BOUND_VARIABLE_1444695) BOUND_VARIABLE_1444696) BOUND_VARIABLE_1444697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444695) BOUND_VARIABLE_1444697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444694) BOUND_VARIABLE_1444696)))))))))) (let ((_let_3464 (forall ((BOUND_VARIABLE_1444669 tptp.int) (BOUND_VARIABLE_1444670 tptp.int) (BOUND_VARIABLE_1444671 tptp.int) (BOUND_VARIABLE_1444672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9405 BOUND_VARIABLE_1444669) BOUND_VARIABLE_1444670) BOUND_VARIABLE_1444671) BOUND_VARIABLE_1444672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444670) BOUND_VARIABLE_1444672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444669) BOUND_VARIABLE_1444671)))))))))) (let ((_let_3465 (forall ((BOUND_VARIABLE_1444644 tptp.int) (BOUND_VARIABLE_1444645 tptp.int) (BOUND_VARIABLE_1444646 tptp.int) (BOUND_VARIABLE_1444647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9406 BOUND_VARIABLE_1444644) BOUND_VARIABLE_1444645) BOUND_VARIABLE_1444646) BOUND_VARIABLE_1444647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444645) BOUND_VARIABLE_1444647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444644) BOUND_VARIABLE_1444646)))))))))) (let ((_let_3466 (forall ((BOUND_VARIABLE_1444619 tptp.int) (BOUND_VARIABLE_1444620 tptp.int) (BOUND_VARIABLE_1444621 tptp.int) (BOUND_VARIABLE_1444622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9407 BOUND_VARIABLE_1444619) BOUND_VARIABLE_1444620) BOUND_VARIABLE_1444621) BOUND_VARIABLE_1444622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444620) BOUND_VARIABLE_1444622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444619) BOUND_VARIABLE_1444621)))))))))) (let ((_let_3467 (forall ((BOUND_VARIABLE_1444594 tptp.int) (BOUND_VARIABLE_1444595 tptp.int) (BOUND_VARIABLE_1444596 tptp.int) (BOUND_VARIABLE_1444597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9408 BOUND_VARIABLE_1444594) BOUND_VARIABLE_1444595) BOUND_VARIABLE_1444596) BOUND_VARIABLE_1444597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444595) BOUND_VARIABLE_1444597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444594) BOUND_VARIABLE_1444596)))))))))) (let ((_let_3468 (forall ((BOUND_VARIABLE_1444569 tptp.int) (BOUND_VARIABLE_1444570 tptp.int) (BOUND_VARIABLE_1444571 tptp.int) (BOUND_VARIABLE_1444572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9409 BOUND_VARIABLE_1444569) BOUND_VARIABLE_1444570) BOUND_VARIABLE_1444571) BOUND_VARIABLE_1444572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444570) BOUND_VARIABLE_1444572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444569) BOUND_VARIABLE_1444571)))))))))) (let ((_let_3469 (forall ((BOUND_VARIABLE_1444544 tptp.int) (BOUND_VARIABLE_1444545 tptp.int) (BOUND_VARIABLE_1444546 tptp.int) (BOUND_VARIABLE_1444547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9410 BOUND_VARIABLE_1444544) BOUND_VARIABLE_1444545) BOUND_VARIABLE_1444546) BOUND_VARIABLE_1444547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444545) BOUND_VARIABLE_1444547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444544) BOUND_VARIABLE_1444546)))))))))) (let ((_let_3470 (forall ((BOUND_VARIABLE_1444519 tptp.int) (BOUND_VARIABLE_1444520 tptp.int) (BOUND_VARIABLE_1444521 tptp.int) (BOUND_VARIABLE_1444522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9411 BOUND_VARIABLE_1444519) BOUND_VARIABLE_1444520) BOUND_VARIABLE_1444521) BOUND_VARIABLE_1444522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444520) BOUND_VARIABLE_1444522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444519) BOUND_VARIABLE_1444521)))))))))) (let ((_let_3471 (forall ((BOUND_VARIABLE_1444494 tptp.int) (BOUND_VARIABLE_1444495 tptp.int) (BOUND_VARIABLE_1444496 tptp.int) (BOUND_VARIABLE_1444497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9412 BOUND_VARIABLE_1444494) BOUND_VARIABLE_1444495) BOUND_VARIABLE_1444496) BOUND_VARIABLE_1444497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444495) BOUND_VARIABLE_1444497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444494) BOUND_VARIABLE_1444496)))))))))) (let ((_let_3472 (forall ((BOUND_VARIABLE_1444469 tptp.int) (BOUND_VARIABLE_1444470 tptp.int) (BOUND_VARIABLE_1444471 tptp.int) (BOUND_VARIABLE_1444472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9413 BOUND_VARIABLE_1444469) BOUND_VARIABLE_1444470) BOUND_VARIABLE_1444471) BOUND_VARIABLE_1444472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444470) BOUND_VARIABLE_1444472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444469) BOUND_VARIABLE_1444471)))))))))) (let ((_let_3473 (forall ((BOUND_VARIABLE_1444444 tptp.int) (BOUND_VARIABLE_1444445 tptp.int) (BOUND_VARIABLE_1444446 tptp.int) (BOUND_VARIABLE_1444447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9414 BOUND_VARIABLE_1444444) BOUND_VARIABLE_1444445) BOUND_VARIABLE_1444446) BOUND_VARIABLE_1444447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444445) BOUND_VARIABLE_1444447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444444) BOUND_VARIABLE_1444446)))))))))) (let ((_let_3474 (forall ((BOUND_VARIABLE_1444419 tptp.int) (BOUND_VARIABLE_1444420 tptp.int) (BOUND_VARIABLE_1444421 tptp.int) (BOUND_VARIABLE_1444422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9415 BOUND_VARIABLE_1444419) BOUND_VARIABLE_1444420) BOUND_VARIABLE_1444421) BOUND_VARIABLE_1444422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444420) BOUND_VARIABLE_1444422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444419) BOUND_VARIABLE_1444421)))))))))) (let ((_let_3475 (forall ((BOUND_VARIABLE_1444394 tptp.int) (BOUND_VARIABLE_1444395 tptp.int) (BOUND_VARIABLE_1444396 tptp.int) (BOUND_VARIABLE_1444397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9416 BOUND_VARIABLE_1444394) BOUND_VARIABLE_1444395) BOUND_VARIABLE_1444396) BOUND_VARIABLE_1444397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444395) BOUND_VARIABLE_1444397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444394) BOUND_VARIABLE_1444396)))))))))) (let ((_let_3476 (forall ((BOUND_VARIABLE_1444369 tptp.int) (BOUND_VARIABLE_1444370 tptp.int) (BOUND_VARIABLE_1444371 tptp.int) (BOUND_VARIABLE_1444372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9417 BOUND_VARIABLE_1444369) BOUND_VARIABLE_1444370) BOUND_VARIABLE_1444371) BOUND_VARIABLE_1444372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444370) BOUND_VARIABLE_1444372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444369) BOUND_VARIABLE_1444371)))))))))) (let ((_let_3477 (forall ((BOUND_VARIABLE_1444344 tptp.int) (BOUND_VARIABLE_1444345 tptp.int) (BOUND_VARIABLE_1444346 tptp.int) (BOUND_VARIABLE_1444347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9418 BOUND_VARIABLE_1444344) BOUND_VARIABLE_1444345) BOUND_VARIABLE_1444346) BOUND_VARIABLE_1444347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444345) BOUND_VARIABLE_1444347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444344) BOUND_VARIABLE_1444346)))))))))) (let ((_let_3478 (forall ((BOUND_VARIABLE_1444319 tptp.int) (BOUND_VARIABLE_1444320 tptp.int) (BOUND_VARIABLE_1444321 tptp.int) (BOUND_VARIABLE_1444322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9419 BOUND_VARIABLE_1444319) BOUND_VARIABLE_1444320) BOUND_VARIABLE_1444321) BOUND_VARIABLE_1444322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444320) BOUND_VARIABLE_1444322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444319) BOUND_VARIABLE_1444321)))))))))) (let ((_let_3479 (forall ((BOUND_VARIABLE_1444294 tptp.int) (BOUND_VARIABLE_1444295 tptp.int) (BOUND_VARIABLE_1444296 tptp.int) (BOUND_VARIABLE_1444297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9420 BOUND_VARIABLE_1444294) BOUND_VARIABLE_1444295) BOUND_VARIABLE_1444296) BOUND_VARIABLE_1444297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444295) BOUND_VARIABLE_1444297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444294) BOUND_VARIABLE_1444296)))))))))) (let ((_let_3480 (forall ((BOUND_VARIABLE_1444269 tptp.int) (BOUND_VARIABLE_1444270 tptp.int) (BOUND_VARIABLE_1444271 tptp.int) (BOUND_VARIABLE_1444272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9421 BOUND_VARIABLE_1444269) BOUND_VARIABLE_1444270) BOUND_VARIABLE_1444271) BOUND_VARIABLE_1444272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444270) BOUND_VARIABLE_1444272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444269) BOUND_VARIABLE_1444271)))))))))) (let ((_let_3481 (forall ((BOUND_VARIABLE_1444244 tptp.int) (BOUND_VARIABLE_1444245 tptp.int) (BOUND_VARIABLE_1444246 tptp.int) (BOUND_VARIABLE_1444247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9422 BOUND_VARIABLE_1444244) BOUND_VARIABLE_1444245) BOUND_VARIABLE_1444246) BOUND_VARIABLE_1444247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444245) BOUND_VARIABLE_1444247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444244) BOUND_VARIABLE_1444246)))))))))) (let ((_let_3482 (forall ((BOUND_VARIABLE_1444219 tptp.int) (BOUND_VARIABLE_1444220 tptp.int) (BOUND_VARIABLE_1444221 tptp.int) (BOUND_VARIABLE_1444222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9423 BOUND_VARIABLE_1444219) BOUND_VARIABLE_1444220) BOUND_VARIABLE_1444221) BOUND_VARIABLE_1444222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444220) BOUND_VARIABLE_1444222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444219) BOUND_VARIABLE_1444221)))))))))) (let ((_let_3483 (forall ((BOUND_VARIABLE_1444194 tptp.int) (BOUND_VARIABLE_1444195 tptp.int) (BOUND_VARIABLE_1444196 tptp.int) (BOUND_VARIABLE_1444197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9424 BOUND_VARIABLE_1444194) BOUND_VARIABLE_1444195) BOUND_VARIABLE_1444196) BOUND_VARIABLE_1444197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444195) BOUND_VARIABLE_1444197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444194) BOUND_VARIABLE_1444196)))))))))) (let ((_let_3484 (forall ((BOUND_VARIABLE_1444169 tptp.int) (BOUND_VARIABLE_1444170 tptp.int) (BOUND_VARIABLE_1444171 tptp.int) (BOUND_VARIABLE_1444172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9425 BOUND_VARIABLE_1444169) BOUND_VARIABLE_1444170) BOUND_VARIABLE_1444171) BOUND_VARIABLE_1444172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444170) BOUND_VARIABLE_1444172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444169) BOUND_VARIABLE_1444171)))))))))) (let ((_let_3485 (forall ((BOUND_VARIABLE_1444144 tptp.int) (BOUND_VARIABLE_1444145 tptp.int) (BOUND_VARIABLE_1444146 tptp.int) (BOUND_VARIABLE_1444147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9426 BOUND_VARIABLE_1444144) BOUND_VARIABLE_1444145) BOUND_VARIABLE_1444146) BOUND_VARIABLE_1444147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444145) BOUND_VARIABLE_1444147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444144) BOUND_VARIABLE_1444146)))))))))) (let ((_let_3486 (forall ((BOUND_VARIABLE_1444119 tptp.int) (BOUND_VARIABLE_1444120 tptp.int) (BOUND_VARIABLE_1444121 tptp.int) (BOUND_VARIABLE_1444122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9427 BOUND_VARIABLE_1444119) BOUND_VARIABLE_1444120) BOUND_VARIABLE_1444121) BOUND_VARIABLE_1444122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444120) BOUND_VARIABLE_1444122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444119) BOUND_VARIABLE_1444121)))))))))) (let ((_let_3487 (forall ((BOUND_VARIABLE_1444094 tptp.int) (BOUND_VARIABLE_1444095 tptp.int) (BOUND_VARIABLE_1444096 tptp.int) (BOUND_VARIABLE_1444097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9428 BOUND_VARIABLE_1444094) BOUND_VARIABLE_1444095) BOUND_VARIABLE_1444096) BOUND_VARIABLE_1444097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444095) BOUND_VARIABLE_1444097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444094) BOUND_VARIABLE_1444096)))))))))) (let ((_let_3488 (forall ((BOUND_VARIABLE_1444069 tptp.int) (BOUND_VARIABLE_1444070 tptp.int) (BOUND_VARIABLE_1444071 tptp.int) (BOUND_VARIABLE_1444072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9429 BOUND_VARIABLE_1444069) BOUND_VARIABLE_1444070) BOUND_VARIABLE_1444071) BOUND_VARIABLE_1444072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444070) BOUND_VARIABLE_1444072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444069) BOUND_VARIABLE_1444071)))))))))) (let ((_let_3489 (forall ((BOUND_VARIABLE_1444044 tptp.int) (BOUND_VARIABLE_1444045 tptp.int) (BOUND_VARIABLE_1444046 tptp.int) (BOUND_VARIABLE_1444047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9430 BOUND_VARIABLE_1444044) BOUND_VARIABLE_1444045) BOUND_VARIABLE_1444046) BOUND_VARIABLE_1444047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444045) BOUND_VARIABLE_1444047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444044) BOUND_VARIABLE_1444046)))))))))) (let ((_let_3490 (forall ((BOUND_VARIABLE_1444019 tptp.int) (BOUND_VARIABLE_1444020 tptp.int) (BOUND_VARIABLE_1444021 tptp.int) (BOUND_VARIABLE_1444022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9431 BOUND_VARIABLE_1444019) BOUND_VARIABLE_1444020) BOUND_VARIABLE_1444021) BOUND_VARIABLE_1444022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444020) BOUND_VARIABLE_1444022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1444019) BOUND_VARIABLE_1444021)))))))))) (let ((_let_3491 (forall ((BOUND_VARIABLE_1443994 tptp.int) (BOUND_VARIABLE_1443995 tptp.int) (BOUND_VARIABLE_1443996 tptp.int) (BOUND_VARIABLE_1443997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9432 BOUND_VARIABLE_1443994) BOUND_VARIABLE_1443995) BOUND_VARIABLE_1443996) BOUND_VARIABLE_1443997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443995) BOUND_VARIABLE_1443997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443994) BOUND_VARIABLE_1443996)))))))))) (let ((_let_3492 (forall ((BOUND_VARIABLE_1443969 tptp.int) (BOUND_VARIABLE_1443970 tptp.int) (BOUND_VARIABLE_1443971 tptp.int) (BOUND_VARIABLE_1443972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9433 BOUND_VARIABLE_1443969) BOUND_VARIABLE_1443970) BOUND_VARIABLE_1443971) BOUND_VARIABLE_1443972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443970) BOUND_VARIABLE_1443972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443969) BOUND_VARIABLE_1443971)))))))))) (let ((_let_3493 (forall ((BOUND_VARIABLE_1443944 tptp.int) (BOUND_VARIABLE_1443945 tptp.int) (BOUND_VARIABLE_1443946 tptp.int) (BOUND_VARIABLE_1443947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9434 BOUND_VARIABLE_1443944) BOUND_VARIABLE_1443945) BOUND_VARIABLE_1443946) BOUND_VARIABLE_1443947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443945) BOUND_VARIABLE_1443947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443944) BOUND_VARIABLE_1443946)))))))))) (let ((_let_3494 (forall ((BOUND_VARIABLE_1443919 tptp.int) (BOUND_VARIABLE_1443920 tptp.int) (BOUND_VARIABLE_1443921 tptp.int) (BOUND_VARIABLE_1443922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9435 BOUND_VARIABLE_1443919) BOUND_VARIABLE_1443920) BOUND_VARIABLE_1443921) BOUND_VARIABLE_1443922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443920) BOUND_VARIABLE_1443922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443919) BOUND_VARIABLE_1443921)))))))))) (let ((_let_3495 (forall ((BOUND_VARIABLE_1443894 tptp.int) (BOUND_VARIABLE_1443895 tptp.int) (BOUND_VARIABLE_1443896 tptp.int) (BOUND_VARIABLE_1443897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9436 BOUND_VARIABLE_1443894) BOUND_VARIABLE_1443895) BOUND_VARIABLE_1443896) BOUND_VARIABLE_1443897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443895) BOUND_VARIABLE_1443897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443894) BOUND_VARIABLE_1443896)))))))))) (let ((_let_3496 (forall ((BOUND_VARIABLE_1443869 tptp.int) (BOUND_VARIABLE_1443870 tptp.int) (BOUND_VARIABLE_1443871 tptp.int) (BOUND_VARIABLE_1443872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9437 BOUND_VARIABLE_1443869) BOUND_VARIABLE_1443870) BOUND_VARIABLE_1443871) BOUND_VARIABLE_1443872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443870) BOUND_VARIABLE_1443872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443869) BOUND_VARIABLE_1443871)))))))))) (let ((_let_3497 (forall ((BOUND_VARIABLE_1443844 tptp.int) (BOUND_VARIABLE_1443845 tptp.int) (BOUND_VARIABLE_1443846 tptp.int) (BOUND_VARIABLE_1443847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9438 BOUND_VARIABLE_1443844) BOUND_VARIABLE_1443845) BOUND_VARIABLE_1443846) BOUND_VARIABLE_1443847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443845) BOUND_VARIABLE_1443847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443844) BOUND_VARIABLE_1443846)))))))))) (let ((_let_3498 (forall ((BOUND_VARIABLE_1443819 tptp.int) (BOUND_VARIABLE_1443820 tptp.int) (BOUND_VARIABLE_1443821 tptp.int) (BOUND_VARIABLE_1443822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9439 BOUND_VARIABLE_1443819) BOUND_VARIABLE_1443820) BOUND_VARIABLE_1443821) BOUND_VARIABLE_1443822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443820) BOUND_VARIABLE_1443822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443819) BOUND_VARIABLE_1443821)))))))))) (let ((_let_3499 (forall ((BOUND_VARIABLE_1443794 tptp.int) (BOUND_VARIABLE_1443795 tptp.int) (BOUND_VARIABLE_1443796 tptp.int) (BOUND_VARIABLE_1443797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9440 BOUND_VARIABLE_1443794) BOUND_VARIABLE_1443795) BOUND_VARIABLE_1443796) BOUND_VARIABLE_1443797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443795) BOUND_VARIABLE_1443797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443794) BOUND_VARIABLE_1443796)))))))))) (let ((_let_3500 (forall ((BOUND_VARIABLE_1443769 tptp.int) (BOUND_VARIABLE_1443770 tptp.int) (BOUND_VARIABLE_1443771 tptp.int) (BOUND_VARIABLE_1443772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9441 BOUND_VARIABLE_1443769) BOUND_VARIABLE_1443770) BOUND_VARIABLE_1443771) BOUND_VARIABLE_1443772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443770) BOUND_VARIABLE_1443772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443769) BOUND_VARIABLE_1443771)))))))))) (let ((_let_3501 (forall ((BOUND_VARIABLE_1443744 tptp.int) (BOUND_VARIABLE_1443745 tptp.int) (BOUND_VARIABLE_1443746 tptp.int) (BOUND_VARIABLE_1443747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9442 BOUND_VARIABLE_1443744) BOUND_VARIABLE_1443745) BOUND_VARIABLE_1443746) BOUND_VARIABLE_1443747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443745) BOUND_VARIABLE_1443747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443744) BOUND_VARIABLE_1443746)))))))))) (let ((_let_3502 (forall ((BOUND_VARIABLE_1443719 tptp.int) (BOUND_VARIABLE_1443720 tptp.int) (BOUND_VARIABLE_1443721 tptp.int) (BOUND_VARIABLE_1443722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9443 BOUND_VARIABLE_1443719) BOUND_VARIABLE_1443720) BOUND_VARIABLE_1443721) BOUND_VARIABLE_1443722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443720) BOUND_VARIABLE_1443722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443719) BOUND_VARIABLE_1443721)))))))))) (let ((_let_3503 (forall ((BOUND_VARIABLE_1443694 tptp.int) (BOUND_VARIABLE_1443695 tptp.int) (BOUND_VARIABLE_1443696 tptp.int) (BOUND_VARIABLE_1443697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9444 BOUND_VARIABLE_1443694) BOUND_VARIABLE_1443695) BOUND_VARIABLE_1443696) BOUND_VARIABLE_1443697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443695) BOUND_VARIABLE_1443697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443694) BOUND_VARIABLE_1443696)))))))))) (let ((_let_3504 (forall ((BOUND_VARIABLE_1443669 tptp.int) (BOUND_VARIABLE_1443670 tptp.int) (BOUND_VARIABLE_1443671 tptp.int) (BOUND_VARIABLE_1443672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9445 BOUND_VARIABLE_1443669) BOUND_VARIABLE_1443670) BOUND_VARIABLE_1443671) BOUND_VARIABLE_1443672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443670) BOUND_VARIABLE_1443672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443669) BOUND_VARIABLE_1443671)))))))))) (let ((_let_3505 (forall ((BOUND_VARIABLE_1443644 tptp.int) (BOUND_VARIABLE_1443645 tptp.int) (BOUND_VARIABLE_1443646 tptp.int) (BOUND_VARIABLE_1443647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9446 BOUND_VARIABLE_1443644) BOUND_VARIABLE_1443645) BOUND_VARIABLE_1443646) BOUND_VARIABLE_1443647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443645) BOUND_VARIABLE_1443647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443644) BOUND_VARIABLE_1443646)))))))))) (let ((_let_3506 (forall ((BOUND_VARIABLE_1443619 tptp.int) (BOUND_VARIABLE_1443620 tptp.int) (BOUND_VARIABLE_1443621 tptp.int) (BOUND_VARIABLE_1443622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9447 BOUND_VARIABLE_1443619) BOUND_VARIABLE_1443620) BOUND_VARIABLE_1443621) BOUND_VARIABLE_1443622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443620) BOUND_VARIABLE_1443622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443619) BOUND_VARIABLE_1443621)))))))))) (let ((_let_3507 (forall ((BOUND_VARIABLE_1443594 tptp.int) (BOUND_VARIABLE_1443595 tptp.int) (BOUND_VARIABLE_1443596 tptp.int) (BOUND_VARIABLE_1443597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9448 BOUND_VARIABLE_1443594) BOUND_VARIABLE_1443595) BOUND_VARIABLE_1443596) BOUND_VARIABLE_1443597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443595) BOUND_VARIABLE_1443597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443594) BOUND_VARIABLE_1443596)))))))))) (let ((_let_3508 (forall ((BOUND_VARIABLE_1443569 tptp.int) (BOUND_VARIABLE_1443570 tptp.int) (BOUND_VARIABLE_1443571 tptp.int) (BOUND_VARIABLE_1443572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9449 BOUND_VARIABLE_1443569) BOUND_VARIABLE_1443570) BOUND_VARIABLE_1443571) BOUND_VARIABLE_1443572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443570) BOUND_VARIABLE_1443572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443569) BOUND_VARIABLE_1443571)))))))))) (let ((_let_3509 (forall ((BOUND_VARIABLE_1443544 tptp.int) (BOUND_VARIABLE_1443545 tptp.int) (BOUND_VARIABLE_1443546 tptp.int) (BOUND_VARIABLE_1443547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9450 BOUND_VARIABLE_1443544) BOUND_VARIABLE_1443545) BOUND_VARIABLE_1443546) BOUND_VARIABLE_1443547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443545) BOUND_VARIABLE_1443547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443544) BOUND_VARIABLE_1443546)))))))))) (let ((_let_3510 (forall ((BOUND_VARIABLE_1443519 tptp.int) (BOUND_VARIABLE_1443520 tptp.int) (BOUND_VARIABLE_1443521 tptp.int) (BOUND_VARIABLE_1443522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9451 BOUND_VARIABLE_1443519) BOUND_VARIABLE_1443520) BOUND_VARIABLE_1443521) BOUND_VARIABLE_1443522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443520) BOUND_VARIABLE_1443522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443519) BOUND_VARIABLE_1443521)))))))))) (let ((_let_3511 (forall ((BOUND_VARIABLE_1443494 tptp.int) (BOUND_VARIABLE_1443495 tptp.int) (BOUND_VARIABLE_1443496 tptp.int) (BOUND_VARIABLE_1443497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9452 BOUND_VARIABLE_1443494) BOUND_VARIABLE_1443495) BOUND_VARIABLE_1443496) BOUND_VARIABLE_1443497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443495) BOUND_VARIABLE_1443497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443494) BOUND_VARIABLE_1443496)))))))))) (let ((_let_3512 (forall ((BOUND_VARIABLE_1443469 tptp.int) (BOUND_VARIABLE_1443470 tptp.int) (BOUND_VARIABLE_1443471 tptp.int) (BOUND_VARIABLE_1443472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9453 BOUND_VARIABLE_1443469) BOUND_VARIABLE_1443470) BOUND_VARIABLE_1443471) BOUND_VARIABLE_1443472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443470) BOUND_VARIABLE_1443472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443469) BOUND_VARIABLE_1443471)))))))))) (let ((_let_3513 (forall ((BOUND_VARIABLE_1443444 tptp.int) (BOUND_VARIABLE_1443445 tptp.int) (BOUND_VARIABLE_1443446 tptp.int) (BOUND_VARIABLE_1443447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9454 BOUND_VARIABLE_1443444) BOUND_VARIABLE_1443445) BOUND_VARIABLE_1443446) BOUND_VARIABLE_1443447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443445) BOUND_VARIABLE_1443447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443444) BOUND_VARIABLE_1443446)))))))))) (let ((_let_3514 (forall ((BOUND_VARIABLE_1443419 tptp.int) (BOUND_VARIABLE_1443420 tptp.int) (BOUND_VARIABLE_1443421 tptp.int) (BOUND_VARIABLE_1443422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9455 BOUND_VARIABLE_1443419) BOUND_VARIABLE_1443420) BOUND_VARIABLE_1443421) BOUND_VARIABLE_1443422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443420) BOUND_VARIABLE_1443422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443419) BOUND_VARIABLE_1443421)))))))))) (let ((_let_3515 (forall ((BOUND_VARIABLE_1443394 tptp.int) (BOUND_VARIABLE_1443395 tptp.int) (BOUND_VARIABLE_1443396 tptp.int) (BOUND_VARIABLE_1443397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9456 BOUND_VARIABLE_1443394) BOUND_VARIABLE_1443395) BOUND_VARIABLE_1443396) BOUND_VARIABLE_1443397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443395) BOUND_VARIABLE_1443397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443394) BOUND_VARIABLE_1443396)))))))))) (let ((_let_3516 (forall ((BOUND_VARIABLE_1443369 tptp.int) (BOUND_VARIABLE_1443370 tptp.int) (BOUND_VARIABLE_1443371 tptp.int) (BOUND_VARIABLE_1443372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9457 BOUND_VARIABLE_1443369) BOUND_VARIABLE_1443370) BOUND_VARIABLE_1443371) BOUND_VARIABLE_1443372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443370) BOUND_VARIABLE_1443372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443369) BOUND_VARIABLE_1443371)))))))))) (let ((_let_3517 (forall ((BOUND_VARIABLE_1443344 tptp.int) (BOUND_VARIABLE_1443345 tptp.int) (BOUND_VARIABLE_1443346 tptp.int) (BOUND_VARIABLE_1443347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9458 BOUND_VARIABLE_1443344) BOUND_VARIABLE_1443345) BOUND_VARIABLE_1443346) BOUND_VARIABLE_1443347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443345) BOUND_VARIABLE_1443347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443344) BOUND_VARIABLE_1443346)))))))))) (let ((_let_3518 (forall ((BOUND_VARIABLE_1443319 tptp.int) (BOUND_VARIABLE_1443320 tptp.int) (BOUND_VARIABLE_1443321 tptp.int) (BOUND_VARIABLE_1443322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9459 BOUND_VARIABLE_1443319) BOUND_VARIABLE_1443320) BOUND_VARIABLE_1443321) BOUND_VARIABLE_1443322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443320) BOUND_VARIABLE_1443322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443319) BOUND_VARIABLE_1443321)))))))))) (let ((_let_3519 (forall ((BOUND_VARIABLE_1443294 tptp.int) (BOUND_VARIABLE_1443295 tptp.int) (BOUND_VARIABLE_1443296 tptp.int) (BOUND_VARIABLE_1443297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9460 BOUND_VARIABLE_1443294) BOUND_VARIABLE_1443295) BOUND_VARIABLE_1443296) BOUND_VARIABLE_1443297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443295) BOUND_VARIABLE_1443297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443294) BOUND_VARIABLE_1443296)))))))))) (let ((_let_3520 (forall ((BOUND_VARIABLE_1443269 tptp.int) (BOUND_VARIABLE_1443270 tptp.int) (BOUND_VARIABLE_1443271 tptp.int) (BOUND_VARIABLE_1443272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9461 BOUND_VARIABLE_1443269) BOUND_VARIABLE_1443270) BOUND_VARIABLE_1443271) BOUND_VARIABLE_1443272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443270) BOUND_VARIABLE_1443272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443269) BOUND_VARIABLE_1443271)))))))))) (let ((_let_3521 (forall ((BOUND_VARIABLE_1443244 tptp.int) (BOUND_VARIABLE_1443245 tptp.int) (BOUND_VARIABLE_1443246 tptp.int) (BOUND_VARIABLE_1443247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9462 BOUND_VARIABLE_1443244) BOUND_VARIABLE_1443245) BOUND_VARIABLE_1443246) BOUND_VARIABLE_1443247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443245) BOUND_VARIABLE_1443247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443244) BOUND_VARIABLE_1443246)))))))))) (let ((_let_3522 (forall ((BOUND_VARIABLE_1443219 tptp.int) (BOUND_VARIABLE_1443220 tptp.int) (BOUND_VARIABLE_1443221 tptp.int) (BOUND_VARIABLE_1443222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9463 BOUND_VARIABLE_1443219) BOUND_VARIABLE_1443220) BOUND_VARIABLE_1443221) BOUND_VARIABLE_1443222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443220) BOUND_VARIABLE_1443222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443219) BOUND_VARIABLE_1443221)))))))))) (let ((_let_3523 (forall ((BOUND_VARIABLE_1443194 tptp.int) (BOUND_VARIABLE_1443195 tptp.int) (BOUND_VARIABLE_1443196 tptp.int) (BOUND_VARIABLE_1443197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9464 BOUND_VARIABLE_1443194) BOUND_VARIABLE_1443195) BOUND_VARIABLE_1443196) BOUND_VARIABLE_1443197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443195) BOUND_VARIABLE_1443197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443194) BOUND_VARIABLE_1443196)))))))))) (let ((_let_3524 (forall ((BOUND_VARIABLE_1443169 tptp.int) (BOUND_VARIABLE_1443170 tptp.int) (BOUND_VARIABLE_1443171 tptp.int) (BOUND_VARIABLE_1443172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9465 BOUND_VARIABLE_1443169) BOUND_VARIABLE_1443170) BOUND_VARIABLE_1443171) BOUND_VARIABLE_1443172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443170) BOUND_VARIABLE_1443172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443169) BOUND_VARIABLE_1443171)))))))))) (let ((_let_3525 (forall ((BOUND_VARIABLE_1443144 tptp.int) (BOUND_VARIABLE_1443145 tptp.int) (BOUND_VARIABLE_1443146 tptp.int) (BOUND_VARIABLE_1443147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9466 BOUND_VARIABLE_1443144) BOUND_VARIABLE_1443145) BOUND_VARIABLE_1443146) BOUND_VARIABLE_1443147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443145) BOUND_VARIABLE_1443147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443144) BOUND_VARIABLE_1443146)))))))))) (let ((_let_3526 (forall ((BOUND_VARIABLE_1443119 tptp.int) (BOUND_VARIABLE_1443120 tptp.int) (BOUND_VARIABLE_1443121 tptp.int) (BOUND_VARIABLE_1443122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9467 BOUND_VARIABLE_1443119) BOUND_VARIABLE_1443120) BOUND_VARIABLE_1443121) BOUND_VARIABLE_1443122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443120) BOUND_VARIABLE_1443122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443119) BOUND_VARIABLE_1443121)))))))))) (let ((_let_3527 (forall ((BOUND_VARIABLE_1443094 tptp.int) (BOUND_VARIABLE_1443095 tptp.int) (BOUND_VARIABLE_1443096 tptp.int) (BOUND_VARIABLE_1443097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9468 BOUND_VARIABLE_1443094) BOUND_VARIABLE_1443095) BOUND_VARIABLE_1443096) BOUND_VARIABLE_1443097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443095) BOUND_VARIABLE_1443097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443094) BOUND_VARIABLE_1443096)))))))))) (let ((_let_3528 (forall ((BOUND_VARIABLE_1443069 tptp.int) (BOUND_VARIABLE_1443070 tptp.int) (BOUND_VARIABLE_1443071 tptp.int) (BOUND_VARIABLE_1443072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9469 BOUND_VARIABLE_1443069) BOUND_VARIABLE_1443070) BOUND_VARIABLE_1443071) BOUND_VARIABLE_1443072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443070) BOUND_VARIABLE_1443072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443069) BOUND_VARIABLE_1443071)))))))))) (let ((_let_3529 (forall ((BOUND_VARIABLE_1443044 tptp.int) (BOUND_VARIABLE_1443045 tptp.int) (BOUND_VARIABLE_1443046 tptp.int) (BOUND_VARIABLE_1443047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9470 BOUND_VARIABLE_1443044) BOUND_VARIABLE_1443045) BOUND_VARIABLE_1443046) BOUND_VARIABLE_1443047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443045) BOUND_VARIABLE_1443047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443044) BOUND_VARIABLE_1443046)))))))))) (let ((_let_3530 (forall ((BOUND_VARIABLE_1443019 tptp.int) (BOUND_VARIABLE_1443020 tptp.int) (BOUND_VARIABLE_1443021 tptp.int) (BOUND_VARIABLE_1443022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9471 BOUND_VARIABLE_1443019) BOUND_VARIABLE_1443020) BOUND_VARIABLE_1443021) BOUND_VARIABLE_1443022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443020) BOUND_VARIABLE_1443022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1443019) BOUND_VARIABLE_1443021)))))))))) (let ((_let_3531 (forall ((BOUND_VARIABLE_1442994 tptp.int) (BOUND_VARIABLE_1442995 tptp.int) (BOUND_VARIABLE_1442996 tptp.int) (BOUND_VARIABLE_1442997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9472 BOUND_VARIABLE_1442994) BOUND_VARIABLE_1442995) BOUND_VARIABLE_1442996) BOUND_VARIABLE_1442997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442995) BOUND_VARIABLE_1442997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442994) BOUND_VARIABLE_1442996)))))))))) (let ((_let_3532 (forall ((BOUND_VARIABLE_1442969 tptp.int) (BOUND_VARIABLE_1442970 tptp.int) (BOUND_VARIABLE_1442971 tptp.int) (BOUND_VARIABLE_1442972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9473 BOUND_VARIABLE_1442969) BOUND_VARIABLE_1442970) BOUND_VARIABLE_1442971) BOUND_VARIABLE_1442972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442970) BOUND_VARIABLE_1442972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442969) BOUND_VARIABLE_1442971)))))))))) (let ((_let_3533 (forall ((BOUND_VARIABLE_1442944 tptp.int) (BOUND_VARIABLE_1442945 tptp.int) (BOUND_VARIABLE_1442946 tptp.int) (BOUND_VARIABLE_1442947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9474 BOUND_VARIABLE_1442944) BOUND_VARIABLE_1442945) BOUND_VARIABLE_1442946) BOUND_VARIABLE_1442947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442945) BOUND_VARIABLE_1442947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442944) BOUND_VARIABLE_1442946)))))))))) (let ((_let_3534 (forall ((BOUND_VARIABLE_1442919 tptp.int) (BOUND_VARIABLE_1442920 tptp.int) (BOUND_VARIABLE_1442921 tptp.int) (BOUND_VARIABLE_1442922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9475 BOUND_VARIABLE_1442919) BOUND_VARIABLE_1442920) BOUND_VARIABLE_1442921) BOUND_VARIABLE_1442922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442920) BOUND_VARIABLE_1442922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442919) BOUND_VARIABLE_1442921)))))))))) (let ((_let_3535 (forall ((BOUND_VARIABLE_1442894 tptp.int) (BOUND_VARIABLE_1442895 tptp.int) (BOUND_VARIABLE_1442896 tptp.int) (BOUND_VARIABLE_1442897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9476 BOUND_VARIABLE_1442894) BOUND_VARIABLE_1442895) BOUND_VARIABLE_1442896) BOUND_VARIABLE_1442897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442895) BOUND_VARIABLE_1442897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442894) BOUND_VARIABLE_1442896)))))))))) (let ((_let_3536 (forall ((BOUND_VARIABLE_1442869 tptp.int) (BOUND_VARIABLE_1442870 tptp.int) (BOUND_VARIABLE_1442871 tptp.int) (BOUND_VARIABLE_1442872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9477 BOUND_VARIABLE_1442869) BOUND_VARIABLE_1442870) BOUND_VARIABLE_1442871) BOUND_VARIABLE_1442872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442870) BOUND_VARIABLE_1442872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442869) BOUND_VARIABLE_1442871)))))))))) (let ((_let_3537 (forall ((BOUND_VARIABLE_1442844 tptp.int) (BOUND_VARIABLE_1442845 tptp.int) (BOUND_VARIABLE_1442846 tptp.int) (BOUND_VARIABLE_1442847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9478 BOUND_VARIABLE_1442844) BOUND_VARIABLE_1442845) BOUND_VARIABLE_1442846) BOUND_VARIABLE_1442847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442845) BOUND_VARIABLE_1442847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442844) BOUND_VARIABLE_1442846)))))))))) (let ((_let_3538 (forall ((BOUND_VARIABLE_1442819 tptp.int) (BOUND_VARIABLE_1442820 tptp.int) (BOUND_VARIABLE_1442821 tptp.int) (BOUND_VARIABLE_1442822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9479 BOUND_VARIABLE_1442819) BOUND_VARIABLE_1442820) BOUND_VARIABLE_1442821) BOUND_VARIABLE_1442822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442820) BOUND_VARIABLE_1442822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442819) BOUND_VARIABLE_1442821)))))))))) (let ((_let_3539 (forall ((BOUND_VARIABLE_1442794 tptp.int) (BOUND_VARIABLE_1442795 tptp.int) (BOUND_VARIABLE_1442796 tptp.int) (BOUND_VARIABLE_1442797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9480 BOUND_VARIABLE_1442794) BOUND_VARIABLE_1442795) BOUND_VARIABLE_1442796) BOUND_VARIABLE_1442797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442795) BOUND_VARIABLE_1442797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442794) BOUND_VARIABLE_1442796)))))))))) (let ((_let_3540 (forall ((BOUND_VARIABLE_1442769 tptp.int) (BOUND_VARIABLE_1442770 tptp.int) (BOUND_VARIABLE_1442771 tptp.int) (BOUND_VARIABLE_1442772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9481 BOUND_VARIABLE_1442769) BOUND_VARIABLE_1442770) BOUND_VARIABLE_1442771) BOUND_VARIABLE_1442772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442770) BOUND_VARIABLE_1442772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442769) BOUND_VARIABLE_1442771)))))))))) (let ((_let_3541 (forall ((BOUND_VARIABLE_1442744 tptp.int) (BOUND_VARIABLE_1442745 tptp.int) (BOUND_VARIABLE_1442746 tptp.int) (BOUND_VARIABLE_1442747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9482 BOUND_VARIABLE_1442744) BOUND_VARIABLE_1442745) BOUND_VARIABLE_1442746) BOUND_VARIABLE_1442747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442745) BOUND_VARIABLE_1442747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442744) BOUND_VARIABLE_1442746)))))))))) (let ((_let_3542 (forall ((BOUND_VARIABLE_1442719 tptp.int) (BOUND_VARIABLE_1442720 tptp.int) (BOUND_VARIABLE_1442721 tptp.int) (BOUND_VARIABLE_1442722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9483 BOUND_VARIABLE_1442719) BOUND_VARIABLE_1442720) BOUND_VARIABLE_1442721) BOUND_VARIABLE_1442722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442720) BOUND_VARIABLE_1442722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442719) BOUND_VARIABLE_1442721)))))))))) (let ((_let_3543 (forall ((BOUND_VARIABLE_1442694 tptp.int) (BOUND_VARIABLE_1442695 tptp.int) (BOUND_VARIABLE_1442696 tptp.int) (BOUND_VARIABLE_1442697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9484 BOUND_VARIABLE_1442694) BOUND_VARIABLE_1442695) BOUND_VARIABLE_1442696) BOUND_VARIABLE_1442697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442695) BOUND_VARIABLE_1442697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442694) BOUND_VARIABLE_1442696)))))))))) (let ((_let_3544 (forall ((BOUND_VARIABLE_1442669 tptp.int) (BOUND_VARIABLE_1442670 tptp.int) (BOUND_VARIABLE_1442671 tptp.int) (BOUND_VARIABLE_1442672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9485 BOUND_VARIABLE_1442669) BOUND_VARIABLE_1442670) BOUND_VARIABLE_1442671) BOUND_VARIABLE_1442672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442670) BOUND_VARIABLE_1442672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442669) BOUND_VARIABLE_1442671)))))))))) (let ((_let_3545 (forall ((BOUND_VARIABLE_1442644 tptp.int) (BOUND_VARIABLE_1442645 tptp.int) (BOUND_VARIABLE_1442646 tptp.int) (BOUND_VARIABLE_1442647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9486 BOUND_VARIABLE_1442644) BOUND_VARIABLE_1442645) BOUND_VARIABLE_1442646) BOUND_VARIABLE_1442647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442645) BOUND_VARIABLE_1442647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442644) BOUND_VARIABLE_1442646)))))))))) (let ((_let_3546 (forall ((BOUND_VARIABLE_1442619 tptp.int) (BOUND_VARIABLE_1442620 tptp.int) (BOUND_VARIABLE_1442621 tptp.int) (BOUND_VARIABLE_1442622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9487 BOUND_VARIABLE_1442619) BOUND_VARIABLE_1442620) BOUND_VARIABLE_1442621) BOUND_VARIABLE_1442622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442620) BOUND_VARIABLE_1442622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442619) BOUND_VARIABLE_1442621)))))))))) (let ((_let_3547 (forall ((BOUND_VARIABLE_1442594 tptp.int) (BOUND_VARIABLE_1442595 tptp.int) (BOUND_VARIABLE_1442596 tptp.int) (BOUND_VARIABLE_1442597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9488 BOUND_VARIABLE_1442594) BOUND_VARIABLE_1442595) BOUND_VARIABLE_1442596) BOUND_VARIABLE_1442597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442595) BOUND_VARIABLE_1442597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442594) BOUND_VARIABLE_1442596)))))))))) (let ((_let_3548 (forall ((BOUND_VARIABLE_1442569 tptp.int) (BOUND_VARIABLE_1442570 tptp.int) (BOUND_VARIABLE_1442571 tptp.int) (BOUND_VARIABLE_1442572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9489 BOUND_VARIABLE_1442569) BOUND_VARIABLE_1442570) BOUND_VARIABLE_1442571) BOUND_VARIABLE_1442572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442570) BOUND_VARIABLE_1442572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442569) BOUND_VARIABLE_1442571)))))))))) (let ((_let_3549 (forall ((BOUND_VARIABLE_1442544 tptp.int) (BOUND_VARIABLE_1442545 tptp.int) (BOUND_VARIABLE_1442546 tptp.int) (BOUND_VARIABLE_1442547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9490 BOUND_VARIABLE_1442544) BOUND_VARIABLE_1442545) BOUND_VARIABLE_1442546) BOUND_VARIABLE_1442547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442545) BOUND_VARIABLE_1442547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442544) BOUND_VARIABLE_1442546)))))))))) (let ((_let_3550 (forall ((BOUND_VARIABLE_1442519 tptp.int) (BOUND_VARIABLE_1442520 tptp.int) (BOUND_VARIABLE_1442521 tptp.int) (BOUND_VARIABLE_1442522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9491 BOUND_VARIABLE_1442519) BOUND_VARIABLE_1442520) BOUND_VARIABLE_1442521) BOUND_VARIABLE_1442522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442520) BOUND_VARIABLE_1442522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442519) BOUND_VARIABLE_1442521)))))))))) (let ((_let_3551 (forall ((BOUND_VARIABLE_1442494 tptp.int) (BOUND_VARIABLE_1442495 tptp.int) (BOUND_VARIABLE_1442496 tptp.int) (BOUND_VARIABLE_1442497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9492 BOUND_VARIABLE_1442494) BOUND_VARIABLE_1442495) BOUND_VARIABLE_1442496) BOUND_VARIABLE_1442497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442495) BOUND_VARIABLE_1442497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442494) BOUND_VARIABLE_1442496)))))))))) (let ((_let_3552 (forall ((BOUND_VARIABLE_1442469 tptp.int) (BOUND_VARIABLE_1442470 tptp.int) (BOUND_VARIABLE_1442471 tptp.int) (BOUND_VARIABLE_1442472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9493 BOUND_VARIABLE_1442469) BOUND_VARIABLE_1442470) BOUND_VARIABLE_1442471) BOUND_VARIABLE_1442472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442470) BOUND_VARIABLE_1442472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442469) BOUND_VARIABLE_1442471)))))))))) (let ((_let_3553 (forall ((BOUND_VARIABLE_1442444 tptp.int) (BOUND_VARIABLE_1442445 tptp.int) (BOUND_VARIABLE_1442446 tptp.int) (BOUND_VARIABLE_1442447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9494 BOUND_VARIABLE_1442444) BOUND_VARIABLE_1442445) BOUND_VARIABLE_1442446) BOUND_VARIABLE_1442447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442445) BOUND_VARIABLE_1442447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442444) BOUND_VARIABLE_1442446)))))))))) (let ((_let_3554 (forall ((BOUND_VARIABLE_1442419 tptp.int) (BOUND_VARIABLE_1442420 tptp.int) (BOUND_VARIABLE_1442421 tptp.int) (BOUND_VARIABLE_1442422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9495 BOUND_VARIABLE_1442419) BOUND_VARIABLE_1442420) BOUND_VARIABLE_1442421) BOUND_VARIABLE_1442422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442420) BOUND_VARIABLE_1442422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442419) BOUND_VARIABLE_1442421)))))))))) (let ((_let_3555 (forall ((BOUND_VARIABLE_1442394 tptp.int) (BOUND_VARIABLE_1442395 tptp.int) (BOUND_VARIABLE_1442396 tptp.int) (BOUND_VARIABLE_1442397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9496 BOUND_VARIABLE_1442394) BOUND_VARIABLE_1442395) BOUND_VARIABLE_1442396) BOUND_VARIABLE_1442397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442395) BOUND_VARIABLE_1442397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442394) BOUND_VARIABLE_1442396)))))))))) (let ((_let_3556 (forall ((BOUND_VARIABLE_1442369 tptp.int) (BOUND_VARIABLE_1442370 tptp.int) (BOUND_VARIABLE_1442371 tptp.int) (BOUND_VARIABLE_1442372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9497 BOUND_VARIABLE_1442369) BOUND_VARIABLE_1442370) BOUND_VARIABLE_1442371) BOUND_VARIABLE_1442372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442370) BOUND_VARIABLE_1442372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442369) BOUND_VARIABLE_1442371)))))))))) (let ((_let_3557 (forall ((BOUND_VARIABLE_1442344 tptp.int) (BOUND_VARIABLE_1442345 tptp.int) (BOUND_VARIABLE_1442346 tptp.int) (BOUND_VARIABLE_1442347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9498 BOUND_VARIABLE_1442344) BOUND_VARIABLE_1442345) BOUND_VARIABLE_1442346) BOUND_VARIABLE_1442347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442345) BOUND_VARIABLE_1442347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442344) BOUND_VARIABLE_1442346)))))))))) (let ((_let_3558 (forall ((BOUND_VARIABLE_1442319 tptp.int) (BOUND_VARIABLE_1442320 tptp.int) (BOUND_VARIABLE_1442321 tptp.int) (BOUND_VARIABLE_1442322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9499 BOUND_VARIABLE_1442319) BOUND_VARIABLE_1442320) BOUND_VARIABLE_1442321) BOUND_VARIABLE_1442322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442320) BOUND_VARIABLE_1442322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442319) BOUND_VARIABLE_1442321)))))))))) (let ((_let_3559 (forall ((BOUND_VARIABLE_1442294 tptp.int) (BOUND_VARIABLE_1442295 tptp.int) (BOUND_VARIABLE_1442296 tptp.int) (BOUND_VARIABLE_1442297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9500 BOUND_VARIABLE_1442294) BOUND_VARIABLE_1442295) BOUND_VARIABLE_1442296) BOUND_VARIABLE_1442297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442295) BOUND_VARIABLE_1442297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442294) BOUND_VARIABLE_1442296)))))))))) (let ((_let_3560 (forall ((BOUND_VARIABLE_1442269 tptp.int) (BOUND_VARIABLE_1442270 tptp.int) (BOUND_VARIABLE_1442271 tptp.int) (BOUND_VARIABLE_1442272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9501 BOUND_VARIABLE_1442269) BOUND_VARIABLE_1442270) BOUND_VARIABLE_1442271) BOUND_VARIABLE_1442272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442270) BOUND_VARIABLE_1442272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442269) BOUND_VARIABLE_1442271)))))))))) (let ((_let_3561 (forall ((BOUND_VARIABLE_1442244 tptp.int) (BOUND_VARIABLE_1442245 tptp.int) (BOUND_VARIABLE_1442246 tptp.int) (BOUND_VARIABLE_1442247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9502 BOUND_VARIABLE_1442244) BOUND_VARIABLE_1442245) BOUND_VARIABLE_1442246) BOUND_VARIABLE_1442247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442245) BOUND_VARIABLE_1442247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442244) BOUND_VARIABLE_1442246)))))))))) (let ((_let_3562 (forall ((BOUND_VARIABLE_1442219 tptp.int) (BOUND_VARIABLE_1442220 tptp.int) (BOUND_VARIABLE_1442221 tptp.int) (BOUND_VARIABLE_1442222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9503 BOUND_VARIABLE_1442219) BOUND_VARIABLE_1442220) BOUND_VARIABLE_1442221) BOUND_VARIABLE_1442222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442220) BOUND_VARIABLE_1442222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442219) BOUND_VARIABLE_1442221)))))))))) (let ((_let_3563 (forall ((BOUND_VARIABLE_1442194 tptp.int) (BOUND_VARIABLE_1442195 tptp.int) (BOUND_VARIABLE_1442196 tptp.int) (BOUND_VARIABLE_1442197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9504 BOUND_VARIABLE_1442194) BOUND_VARIABLE_1442195) BOUND_VARIABLE_1442196) BOUND_VARIABLE_1442197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442195) BOUND_VARIABLE_1442197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442194) BOUND_VARIABLE_1442196)))))))))) (let ((_let_3564 (forall ((BOUND_VARIABLE_1442169 tptp.int) (BOUND_VARIABLE_1442170 tptp.int) (BOUND_VARIABLE_1442171 tptp.int) (BOUND_VARIABLE_1442172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9505 BOUND_VARIABLE_1442169) BOUND_VARIABLE_1442170) BOUND_VARIABLE_1442171) BOUND_VARIABLE_1442172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442170) BOUND_VARIABLE_1442172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442169) BOUND_VARIABLE_1442171)))))))))) (let ((_let_3565 (forall ((BOUND_VARIABLE_1442144 tptp.int) (BOUND_VARIABLE_1442145 tptp.int) (BOUND_VARIABLE_1442146 tptp.int) (BOUND_VARIABLE_1442147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9506 BOUND_VARIABLE_1442144) BOUND_VARIABLE_1442145) BOUND_VARIABLE_1442146) BOUND_VARIABLE_1442147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442145) BOUND_VARIABLE_1442147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442144) BOUND_VARIABLE_1442146)))))))))) (let ((_let_3566 (forall ((BOUND_VARIABLE_1442119 tptp.int) (BOUND_VARIABLE_1442120 tptp.int) (BOUND_VARIABLE_1442121 tptp.int) (BOUND_VARIABLE_1442122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9507 BOUND_VARIABLE_1442119) BOUND_VARIABLE_1442120) BOUND_VARIABLE_1442121) BOUND_VARIABLE_1442122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442120) BOUND_VARIABLE_1442122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442119) BOUND_VARIABLE_1442121)))))))))) (let ((_let_3567 (forall ((BOUND_VARIABLE_1442094 tptp.int) (BOUND_VARIABLE_1442095 tptp.int) (BOUND_VARIABLE_1442096 tptp.int) (BOUND_VARIABLE_1442097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9508 BOUND_VARIABLE_1442094) BOUND_VARIABLE_1442095) BOUND_VARIABLE_1442096) BOUND_VARIABLE_1442097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442095) BOUND_VARIABLE_1442097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442094) BOUND_VARIABLE_1442096)))))))))) (let ((_let_3568 (forall ((BOUND_VARIABLE_1442069 tptp.int) (BOUND_VARIABLE_1442070 tptp.int) (BOUND_VARIABLE_1442071 tptp.int) (BOUND_VARIABLE_1442072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9509 BOUND_VARIABLE_1442069) BOUND_VARIABLE_1442070) BOUND_VARIABLE_1442071) BOUND_VARIABLE_1442072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442070) BOUND_VARIABLE_1442072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442069) BOUND_VARIABLE_1442071)))))))))) (let ((_let_3569 (forall ((BOUND_VARIABLE_1442044 tptp.int) (BOUND_VARIABLE_1442045 tptp.int) (BOUND_VARIABLE_1442046 tptp.int) (BOUND_VARIABLE_1442047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9510 BOUND_VARIABLE_1442044) BOUND_VARIABLE_1442045) BOUND_VARIABLE_1442046) BOUND_VARIABLE_1442047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442045) BOUND_VARIABLE_1442047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442044) BOUND_VARIABLE_1442046)))))))))) (let ((_let_3570 (forall ((BOUND_VARIABLE_1442019 tptp.int) (BOUND_VARIABLE_1442020 tptp.int) (BOUND_VARIABLE_1442021 tptp.int) (BOUND_VARIABLE_1442022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9511 BOUND_VARIABLE_1442019) BOUND_VARIABLE_1442020) BOUND_VARIABLE_1442021) BOUND_VARIABLE_1442022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442020) BOUND_VARIABLE_1442022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1442019) BOUND_VARIABLE_1442021)))))))))) (let ((_let_3571 (forall ((BOUND_VARIABLE_1441994 tptp.int) (BOUND_VARIABLE_1441995 tptp.int) (BOUND_VARIABLE_1441996 tptp.int) (BOUND_VARIABLE_1441997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9512 BOUND_VARIABLE_1441994) BOUND_VARIABLE_1441995) BOUND_VARIABLE_1441996) BOUND_VARIABLE_1441997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441995) BOUND_VARIABLE_1441997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441994) BOUND_VARIABLE_1441996)))))))))) (let ((_let_3572 (forall ((BOUND_VARIABLE_1441969 tptp.int) (BOUND_VARIABLE_1441970 tptp.int) (BOUND_VARIABLE_1441971 tptp.int) (BOUND_VARIABLE_1441972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9513 BOUND_VARIABLE_1441969) BOUND_VARIABLE_1441970) BOUND_VARIABLE_1441971) BOUND_VARIABLE_1441972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441970) BOUND_VARIABLE_1441972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441969) BOUND_VARIABLE_1441971)))))))))) (let ((_let_3573 (forall ((BOUND_VARIABLE_1441944 tptp.int) (BOUND_VARIABLE_1441945 tptp.int) (BOUND_VARIABLE_1441946 tptp.int) (BOUND_VARIABLE_1441947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9514 BOUND_VARIABLE_1441944) BOUND_VARIABLE_1441945) BOUND_VARIABLE_1441946) BOUND_VARIABLE_1441947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441945) BOUND_VARIABLE_1441947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441944) BOUND_VARIABLE_1441946)))))))))) (let ((_let_3574 (forall ((BOUND_VARIABLE_1441919 tptp.int) (BOUND_VARIABLE_1441920 tptp.int) (BOUND_VARIABLE_1441921 tptp.int) (BOUND_VARIABLE_1441922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9515 BOUND_VARIABLE_1441919) BOUND_VARIABLE_1441920) BOUND_VARIABLE_1441921) BOUND_VARIABLE_1441922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441920) BOUND_VARIABLE_1441922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441919) BOUND_VARIABLE_1441921)))))))))) (let ((_let_3575 (forall ((BOUND_VARIABLE_1441894 tptp.int) (BOUND_VARIABLE_1441895 tptp.int) (BOUND_VARIABLE_1441896 tptp.int) (BOUND_VARIABLE_1441897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9516 BOUND_VARIABLE_1441894) BOUND_VARIABLE_1441895) BOUND_VARIABLE_1441896) BOUND_VARIABLE_1441897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441895) BOUND_VARIABLE_1441897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441894) BOUND_VARIABLE_1441896)))))))))) (let ((_let_3576 (forall ((BOUND_VARIABLE_1441869 tptp.int) (BOUND_VARIABLE_1441870 tptp.int) (BOUND_VARIABLE_1441871 tptp.int) (BOUND_VARIABLE_1441872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9517 BOUND_VARIABLE_1441869) BOUND_VARIABLE_1441870) BOUND_VARIABLE_1441871) BOUND_VARIABLE_1441872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441870) BOUND_VARIABLE_1441872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441869) BOUND_VARIABLE_1441871)))))))))) (let ((_let_3577 (forall ((BOUND_VARIABLE_1441844 tptp.int) (BOUND_VARIABLE_1441845 tptp.int) (BOUND_VARIABLE_1441846 tptp.int) (BOUND_VARIABLE_1441847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9518 BOUND_VARIABLE_1441844) BOUND_VARIABLE_1441845) BOUND_VARIABLE_1441846) BOUND_VARIABLE_1441847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441845) BOUND_VARIABLE_1441847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441844) BOUND_VARIABLE_1441846)))))))))) (let ((_let_3578 (forall ((BOUND_VARIABLE_1441819 tptp.int) (BOUND_VARIABLE_1441820 tptp.int) (BOUND_VARIABLE_1441821 tptp.int) (BOUND_VARIABLE_1441822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9519 BOUND_VARIABLE_1441819) BOUND_VARIABLE_1441820) BOUND_VARIABLE_1441821) BOUND_VARIABLE_1441822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441820) BOUND_VARIABLE_1441822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441819) BOUND_VARIABLE_1441821)))))))))) (let ((_let_3579 (forall ((BOUND_VARIABLE_1441794 tptp.int) (BOUND_VARIABLE_1441795 tptp.int) (BOUND_VARIABLE_1441796 tptp.int) (BOUND_VARIABLE_1441797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9520 BOUND_VARIABLE_1441794) BOUND_VARIABLE_1441795) BOUND_VARIABLE_1441796) BOUND_VARIABLE_1441797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441795) BOUND_VARIABLE_1441797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441794) BOUND_VARIABLE_1441796)))))))))) (let ((_let_3580 (forall ((BOUND_VARIABLE_1441769 tptp.int) (BOUND_VARIABLE_1441770 tptp.int) (BOUND_VARIABLE_1441771 tptp.int) (BOUND_VARIABLE_1441772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9521 BOUND_VARIABLE_1441769) BOUND_VARIABLE_1441770) BOUND_VARIABLE_1441771) BOUND_VARIABLE_1441772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441770) BOUND_VARIABLE_1441772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441769) BOUND_VARIABLE_1441771)))))))))) (let ((_let_3581 (forall ((BOUND_VARIABLE_1441744 tptp.int) (BOUND_VARIABLE_1441745 tptp.int) (BOUND_VARIABLE_1441746 tptp.int) (BOUND_VARIABLE_1441747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9522 BOUND_VARIABLE_1441744) BOUND_VARIABLE_1441745) BOUND_VARIABLE_1441746) BOUND_VARIABLE_1441747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441745) BOUND_VARIABLE_1441747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441744) BOUND_VARIABLE_1441746)))))))))) (let ((_let_3582 (forall ((BOUND_VARIABLE_1441719 tptp.int) (BOUND_VARIABLE_1441720 tptp.int) (BOUND_VARIABLE_1441721 tptp.int) (BOUND_VARIABLE_1441722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9523 BOUND_VARIABLE_1441719) BOUND_VARIABLE_1441720) BOUND_VARIABLE_1441721) BOUND_VARIABLE_1441722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441720) BOUND_VARIABLE_1441722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441719) BOUND_VARIABLE_1441721)))))))))) (let ((_let_3583 (forall ((BOUND_VARIABLE_1441694 tptp.int) (BOUND_VARIABLE_1441695 tptp.int) (BOUND_VARIABLE_1441696 tptp.int) (BOUND_VARIABLE_1441697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9524 BOUND_VARIABLE_1441694) BOUND_VARIABLE_1441695) BOUND_VARIABLE_1441696) BOUND_VARIABLE_1441697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441695) BOUND_VARIABLE_1441697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441694) BOUND_VARIABLE_1441696)))))))))) (let ((_let_3584 (forall ((BOUND_VARIABLE_1441669 tptp.int) (BOUND_VARIABLE_1441670 tptp.int) (BOUND_VARIABLE_1441671 tptp.int) (BOUND_VARIABLE_1441672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9525 BOUND_VARIABLE_1441669) BOUND_VARIABLE_1441670) BOUND_VARIABLE_1441671) BOUND_VARIABLE_1441672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441670) BOUND_VARIABLE_1441672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441669) BOUND_VARIABLE_1441671)))))))))) (let ((_let_3585 (forall ((BOUND_VARIABLE_1441644 tptp.int) (BOUND_VARIABLE_1441645 tptp.int) (BOUND_VARIABLE_1441646 tptp.int) (BOUND_VARIABLE_1441647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9526 BOUND_VARIABLE_1441644) BOUND_VARIABLE_1441645) BOUND_VARIABLE_1441646) BOUND_VARIABLE_1441647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441645) BOUND_VARIABLE_1441647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441644) BOUND_VARIABLE_1441646)))))))))) (let ((_let_3586 (forall ((BOUND_VARIABLE_1441619 tptp.int) (BOUND_VARIABLE_1441620 tptp.int) (BOUND_VARIABLE_1441621 tptp.int) (BOUND_VARIABLE_1441622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9527 BOUND_VARIABLE_1441619) BOUND_VARIABLE_1441620) BOUND_VARIABLE_1441621) BOUND_VARIABLE_1441622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441620) BOUND_VARIABLE_1441622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441619) BOUND_VARIABLE_1441621)))))))))) (let ((_let_3587 (forall ((BOUND_VARIABLE_1441594 tptp.int) (BOUND_VARIABLE_1441595 tptp.int) (BOUND_VARIABLE_1441596 tptp.int) (BOUND_VARIABLE_1441597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9528 BOUND_VARIABLE_1441594) BOUND_VARIABLE_1441595) BOUND_VARIABLE_1441596) BOUND_VARIABLE_1441597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441595) BOUND_VARIABLE_1441597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441594) BOUND_VARIABLE_1441596)))))))))) (let ((_let_3588 (forall ((BOUND_VARIABLE_1441569 tptp.int) (BOUND_VARIABLE_1441570 tptp.int) (BOUND_VARIABLE_1441571 tptp.int) (BOUND_VARIABLE_1441572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9529 BOUND_VARIABLE_1441569) BOUND_VARIABLE_1441570) BOUND_VARIABLE_1441571) BOUND_VARIABLE_1441572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441570) BOUND_VARIABLE_1441572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441569) BOUND_VARIABLE_1441571)))))))))) (let ((_let_3589 (forall ((BOUND_VARIABLE_1441544 tptp.int) (BOUND_VARIABLE_1441545 tptp.int) (BOUND_VARIABLE_1441546 tptp.int) (BOUND_VARIABLE_1441547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9530 BOUND_VARIABLE_1441544) BOUND_VARIABLE_1441545) BOUND_VARIABLE_1441546) BOUND_VARIABLE_1441547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441545) BOUND_VARIABLE_1441547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441544) BOUND_VARIABLE_1441546)))))))))) (let ((_let_3590 (forall ((BOUND_VARIABLE_1441519 tptp.int) (BOUND_VARIABLE_1441520 tptp.int) (BOUND_VARIABLE_1441521 tptp.int) (BOUND_VARIABLE_1441522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9531 BOUND_VARIABLE_1441519) BOUND_VARIABLE_1441520) BOUND_VARIABLE_1441521) BOUND_VARIABLE_1441522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441520) BOUND_VARIABLE_1441522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441519) BOUND_VARIABLE_1441521)))))))))) (let ((_let_3591 (forall ((BOUND_VARIABLE_1441494 tptp.int) (BOUND_VARIABLE_1441495 tptp.int) (BOUND_VARIABLE_1441496 tptp.int) (BOUND_VARIABLE_1441497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9532 BOUND_VARIABLE_1441494) BOUND_VARIABLE_1441495) BOUND_VARIABLE_1441496) BOUND_VARIABLE_1441497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441495) BOUND_VARIABLE_1441497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441494) BOUND_VARIABLE_1441496)))))))))) (let ((_let_3592 (forall ((BOUND_VARIABLE_1441469 tptp.int) (BOUND_VARIABLE_1441470 tptp.int) (BOUND_VARIABLE_1441471 tptp.int) (BOUND_VARIABLE_1441472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9533 BOUND_VARIABLE_1441469) BOUND_VARIABLE_1441470) BOUND_VARIABLE_1441471) BOUND_VARIABLE_1441472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441470) BOUND_VARIABLE_1441472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441469) BOUND_VARIABLE_1441471)))))))))) (let ((_let_3593 (forall ((BOUND_VARIABLE_1441444 tptp.int) (BOUND_VARIABLE_1441445 tptp.int) (BOUND_VARIABLE_1441446 tptp.int) (BOUND_VARIABLE_1441447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9534 BOUND_VARIABLE_1441444) BOUND_VARIABLE_1441445) BOUND_VARIABLE_1441446) BOUND_VARIABLE_1441447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441445) BOUND_VARIABLE_1441447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441444) BOUND_VARIABLE_1441446)))))))))) (let ((_let_3594 (forall ((BOUND_VARIABLE_1441419 tptp.int) (BOUND_VARIABLE_1441420 tptp.int) (BOUND_VARIABLE_1441421 tptp.int) (BOUND_VARIABLE_1441422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9535 BOUND_VARIABLE_1441419) BOUND_VARIABLE_1441420) BOUND_VARIABLE_1441421) BOUND_VARIABLE_1441422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441420) BOUND_VARIABLE_1441422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441419) BOUND_VARIABLE_1441421)))))))))) (let ((_let_3595 (forall ((BOUND_VARIABLE_1441394 tptp.int) (BOUND_VARIABLE_1441395 tptp.int) (BOUND_VARIABLE_1441396 tptp.int) (BOUND_VARIABLE_1441397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9536 BOUND_VARIABLE_1441394) BOUND_VARIABLE_1441395) BOUND_VARIABLE_1441396) BOUND_VARIABLE_1441397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441395) BOUND_VARIABLE_1441397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441394) BOUND_VARIABLE_1441396)))))))))) (let ((_let_3596 (forall ((BOUND_VARIABLE_1441369 tptp.int) (BOUND_VARIABLE_1441370 tptp.int) (BOUND_VARIABLE_1441371 tptp.int) (BOUND_VARIABLE_1441372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9537 BOUND_VARIABLE_1441369) BOUND_VARIABLE_1441370) BOUND_VARIABLE_1441371) BOUND_VARIABLE_1441372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441370) BOUND_VARIABLE_1441372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441369) BOUND_VARIABLE_1441371)))))))))) (let ((_let_3597 (forall ((BOUND_VARIABLE_1441344 tptp.int) (BOUND_VARIABLE_1441345 tptp.int) (BOUND_VARIABLE_1441346 tptp.int) (BOUND_VARIABLE_1441347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9538 BOUND_VARIABLE_1441344) BOUND_VARIABLE_1441345) BOUND_VARIABLE_1441346) BOUND_VARIABLE_1441347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441345) BOUND_VARIABLE_1441347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441344) BOUND_VARIABLE_1441346)))))))))) (let ((_let_3598 (forall ((BOUND_VARIABLE_1441319 tptp.int) (BOUND_VARIABLE_1441320 tptp.int) (BOUND_VARIABLE_1441321 tptp.int) (BOUND_VARIABLE_1441322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9539 BOUND_VARIABLE_1441319) BOUND_VARIABLE_1441320) BOUND_VARIABLE_1441321) BOUND_VARIABLE_1441322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441320) BOUND_VARIABLE_1441322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441319) BOUND_VARIABLE_1441321)))))))))) (let ((_let_3599 (forall ((BOUND_VARIABLE_1441294 tptp.int) (BOUND_VARIABLE_1441295 tptp.int) (BOUND_VARIABLE_1441296 tptp.int) (BOUND_VARIABLE_1441297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9540 BOUND_VARIABLE_1441294) BOUND_VARIABLE_1441295) BOUND_VARIABLE_1441296) BOUND_VARIABLE_1441297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441295) BOUND_VARIABLE_1441297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441294) BOUND_VARIABLE_1441296)))))))))) (let ((_let_3600 (forall ((BOUND_VARIABLE_1441269 tptp.int) (BOUND_VARIABLE_1441270 tptp.int) (BOUND_VARIABLE_1441271 tptp.int) (BOUND_VARIABLE_1441272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9541 BOUND_VARIABLE_1441269) BOUND_VARIABLE_1441270) BOUND_VARIABLE_1441271) BOUND_VARIABLE_1441272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441270) BOUND_VARIABLE_1441272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441269) BOUND_VARIABLE_1441271)))))))))) (let ((_let_3601 (forall ((BOUND_VARIABLE_1441244 tptp.int) (BOUND_VARIABLE_1441245 tptp.int) (BOUND_VARIABLE_1441246 tptp.int) (BOUND_VARIABLE_1441247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9542 BOUND_VARIABLE_1441244) BOUND_VARIABLE_1441245) BOUND_VARIABLE_1441246) BOUND_VARIABLE_1441247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441245) BOUND_VARIABLE_1441247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441244) BOUND_VARIABLE_1441246)))))))))) (let ((_let_3602 (forall ((BOUND_VARIABLE_1441219 tptp.int) (BOUND_VARIABLE_1441220 tptp.int) (BOUND_VARIABLE_1441221 tptp.int) (BOUND_VARIABLE_1441222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9543 BOUND_VARIABLE_1441219) BOUND_VARIABLE_1441220) BOUND_VARIABLE_1441221) BOUND_VARIABLE_1441222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441220) BOUND_VARIABLE_1441222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441219) BOUND_VARIABLE_1441221)))))))))) (let ((_let_3603 (forall ((BOUND_VARIABLE_1441194 tptp.int) (BOUND_VARIABLE_1441195 tptp.int) (BOUND_VARIABLE_1441196 tptp.int) (BOUND_VARIABLE_1441197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9544 BOUND_VARIABLE_1441194) BOUND_VARIABLE_1441195) BOUND_VARIABLE_1441196) BOUND_VARIABLE_1441197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441195) BOUND_VARIABLE_1441197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441194) BOUND_VARIABLE_1441196)))))))))) (let ((_let_3604 (forall ((BOUND_VARIABLE_1441169 tptp.int) (BOUND_VARIABLE_1441170 tptp.int) (BOUND_VARIABLE_1441171 tptp.int) (BOUND_VARIABLE_1441172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9545 BOUND_VARIABLE_1441169) BOUND_VARIABLE_1441170) BOUND_VARIABLE_1441171) BOUND_VARIABLE_1441172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441170) BOUND_VARIABLE_1441172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441169) BOUND_VARIABLE_1441171)))))))))) (let ((_let_3605 (forall ((BOUND_VARIABLE_1441144 tptp.int) (BOUND_VARIABLE_1441145 tptp.int) (BOUND_VARIABLE_1441146 tptp.int) (BOUND_VARIABLE_1441147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9546 BOUND_VARIABLE_1441144) BOUND_VARIABLE_1441145) BOUND_VARIABLE_1441146) BOUND_VARIABLE_1441147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441145) BOUND_VARIABLE_1441147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441144) BOUND_VARIABLE_1441146)))))))))) (let ((_let_3606 (forall ((BOUND_VARIABLE_1441119 tptp.int) (BOUND_VARIABLE_1441120 tptp.int) (BOUND_VARIABLE_1441121 tptp.int) (BOUND_VARIABLE_1441122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9547 BOUND_VARIABLE_1441119) BOUND_VARIABLE_1441120) BOUND_VARIABLE_1441121) BOUND_VARIABLE_1441122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441120) BOUND_VARIABLE_1441122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441119) BOUND_VARIABLE_1441121)))))))))) (let ((_let_3607 (forall ((BOUND_VARIABLE_1441094 tptp.int) (BOUND_VARIABLE_1441095 tptp.int) (BOUND_VARIABLE_1441096 tptp.int) (BOUND_VARIABLE_1441097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9548 BOUND_VARIABLE_1441094) BOUND_VARIABLE_1441095) BOUND_VARIABLE_1441096) BOUND_VARIABLE_1441097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441095) BOUND_VARIABLE_1441097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441094) BOUND_VARIABLE_1441096)))))))))) (let ((_let_3608 (forall ((BOUND_VARIABLE_1441069 tptp.int) (BOUND_VARIABLE_1441070 tptp.int) (BOUND_VARIABLE_1441071 tptp.int) (BOUND_VARIABLE_1441072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9549 BOUND_VARIABLE_1441069) BOUND_VARIABLE_1441070) BOUND_VARIABLE_1441071) BOUND_VARIABLE_1441072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441070) BOUND_VARIABLE_1441072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441069) BOUND_VARIABLE_1441071)))))))))) (let ((_let_3609 (forall ((BOUND_VARIABLE_1441044 tptp.int) (BOUND_VARIABLE_1441045 tptp.int) (BOUND_VARIABLE_1441046 tptp.int) (BOUND_VARIABLE_1441047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9550 BOUND_VARIABLE_1441044) BOUND_VARIABLE_1441045) BOUND_VARIABLE_1441046) BOUND_VARIABLE_1441047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441045) BOUND_VARIABLE_1441047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441044) BOUND_VARIABLE_1441046)))))))))) (let ((_let_3610 (forall ((BOUND_VARIABLE_1441019 tptp.int) (BOUND_VARIABLE_1441020 tptp.int) (BOUND_VARIABLE_1441021 tptp.int) (BOUND_VARIABLE_1441022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9551 BOUND_VARIABLE_1441019) BOUND_VARIABLE_1441020) BOUND_VARIABLE_1441021) BOUND_VARIABLE_1441022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441020) BOUND_VARIABLE_1441022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1441019) BOUND_VARIABLE_1441021)))))))))) (let ((_let_3611 (forall ((BOUND_VARIABLE_1440994 tptp.int) (BOUND_VARIABLE_1440995 tptp.int) (BOUND_VARIABLE_1440996 tptp.int) (BOUND_VARIABLE_1440997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9552 BOUND_VARIABLE_1440994) BOUND_VARIABLE_1440995) BOUND_VARIABLE_1440996) BOUND_VARIABLE_1440997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440995) BOUND_VARIABLE_1440997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440994) BOUND_VARIABLE_1440996)))))))))) (let ((_let_3612 (forall ((BOUND_VARIABLE_1440969 tptp.int) (BOUND_VARIABLE_1440970 tptp.int) (BOUND_VARIABLE_1440971 tptp.int) (BOUND_VARIABLE_1440972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9553 BOUND_VARIABLE_1440969) BOUND_VARIABLE_1440970) BOUND_VARIABLE_1440971) BOUND_VARIABLE_1440972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440970) BOUND_VARIABLE_1440972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440969) BOUND_VARIABLE_1440971)))))))))) (let ((_let_3613 (forall ((BOUND_VARIABLE_1440944 tptp.int) (BOUND_VARIABLE_1440945 tptp.int) (BOUND_VARIABLE_1440946 tptp.int) (BOUND_VARIABLE_1440947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9554 BOUND_VARIABLE_1440944) BOUND_VARIABLE_1440945) BOUND_VARIABLE_1440946) BOUND_VARIABLE_1440947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440945) BOUND_VARIABLE_1440947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440944) BOUND_VARIABLE_1440946)))))))))) (let ((_let_3614 (forall ((BOUND_VARIABLE_1440919 tptp.int) (BOUND_VARIABLE_1440920 tptp.int) (BOUND_VARIABLE_1440921 tptp.int) (BOUND_VARIABLE_1440922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9555 BOUND_VARIABLE_1440919) BOUND_VARIABLE_1440920) BOUND_VARIABLE_1440921) BOUND_VARIABLE_1440922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440920) BOUND_VARIABLE_1440922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440919) BOUND_VARIABLE_1440921)))))))))) (let ((_let_3615 (forall ((BOUND_VARIABLE_1440894 tptp.int) (BOUND_VARIABLE_1440895 tptp.int) (BOUND_VARIABLE_1440896 tptp.int) (BOUND_VARIABLE_1440897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9556 BOUND_VARIABLE_1440894) BOUND_VARIABLE_1440895) BOUND_VARIABLE_1440896) BOUND_VARIABLE_1440897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440895) BOUND_VARIABLE_1440897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440894) BOUND_VARIABLE_1440896)))))))))) (let ((_let_3616 (forall ((BOUND_VARIABLE_1440869 tptp.int) (BOUND_VARIABLE_1440870 tptp.int) (BOUND_VARIABLE_1440871 tptp.int) (BOUND_VARIABLE_1440872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9557 BOUND_VARIABLE_1440869) BOUND_VARIABLE_1440870) BOUND_VARIABLE_1440871) BOUND_VARIABLE_1440872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440870) BOUND_VARIABLE_1440872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440869) BOUND_VARIABLE_1440871)))))))))) (let ((_let_3617 (forall ((BOUND_VARIABLE_1440844 tptp.int) (BOUND_VARIABLE_1440845 tptp.int) (BOUND_VARIABLE_1440846 tptp.int) (BOUND_VARIABLE_1440847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9558 BOUND_VARIABLE_1440844) BOUND_VARIABLE_1440845) BOUND_VARIABLE_1440846) BOUND_VARIABLE_1440847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440845) BOUND_VARIABLE_1440847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440844) BOUND_VARIABLE_1440846)))))))))) (let ((_let_3618 (forall ((BOUND_VARIABLE_1440819 tptp.int) (BOUND_VARIABLE_1440820 tptp.int) (BOUND_VARIABLE_1440821 tptp.int) (BOUND_VARIABLE_1440822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9559 BOUND_VARIABLE_1440819) BOUND_VARIABLE_1440820) BOUND_VARIABLE_1440821) BOUND_VARIABLE_1440822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440820) BOUND_VARIABLE_1440822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440819) BOUND_VARIABLE_1440821)))))))))) (let ((_let_3619 (forall ((BOUND_VARIABLE_1440794 tptp.int) (BOUND_VARIABLE_1440795 tptp.int) (BOUND_VARIABLE_1440796 tptp.int) (BOUND_VARIABLE_1440797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9560 BOUND_VARIABLE_1440794) BOUND_VARIABLE_1440795) BOUND_VARIABLE_1440796) BOUND_VARIABLE_1440797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440795) BOUND_VARIABLE_1440797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440794) BOUND_VARIABLE_1440796)))))))))) (let ((_let_3620 (forall ((BOUND_VARIABLE_1440769 tptp.int) (BOUND_VARIABLE_1440770 tptp.int) (BOUND_VARIABLE_1440771 tptp.int) (BOUND_VARIABLE_1440772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9561 BOUND_VARIABLE_1440769) BOUND_VARIABLE_1440770) BOUND_VARIABLE_1440771) BOUND_VARIABLE_1440772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440770) BOUND_VARIABLE_1440772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440769) BOUND_VARIABLE_1440771)))))))))) (let ((_let_3621 (forall ((BOUND_VARIABLE_1440744 tptp.int) (BOUND_VARIABLE_1440745 tptp.int) (BOUND_VARIABLE_1440746 tptp.int) (BOUND_VARIABLE_1440747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9562 BOUND_VARIABLE_1440744) BOUND_VARIABLE_1440745) BOUND_VARIABLE_1440746) BOUND_VARIABLE_1440747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440745) BOUND_VARIABLE_1440747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440744) BOUND_VARIABLE_1440746)))))))))) (let ((_let_3622 (forall ((BOUND_VARIABLE_1440719 tptp.int) (BOUND_VARIABLE_1440720 tptp.int) (BOUND_VARIABLE_1440721 tptp.int) (BOUND_VARIABLE_1440722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9563 BOUND_VARIABLE_1440719) BOUND_VARIABLE_1440720) BOUND_VARIABLE_1440721) BOUND_VARIABLE_1440722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440720) BOUND_VARIABLE_1440722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440719) BOUND_VARIABLE_1440721)))))))))) (let ((_let_3623 (forall ((BOUND_VARIABLE_1440694 tptp.int) (BOUND_VARIABLE_1440695 tptp.int) (BOUND_VARIABLE_1440696 tptp.int) (BOUND_VARIABLE_1440697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9564 BOUND_VARIABLE_1440694) BOUND_VARIABLE_1440695) BOUND_VARIABLE_1440696) BOUND_VARIABLE_1440697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440695) BOUND_VARIABLE_1440697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440694) BOUND_VARIABLE_1440696)))))))))) (let ((_let_3624 (forall ((BOUND_VARIABLE_1440669 tptp.int) (BOUND_VARIABLE_1440670 tptp.int) (BOUND_VARIABLE_1440671 tptp.int) (BOUND_VARIABLE_1440672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9565 BOUND_VARIABLE_1440669) BOUND_VARIABLE_1440670) BOUND_VARIABLE_1440671) BOUND_VARIABLE_1440672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440670) BOUND_VARIABLE_1440672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440669) BOUND_VARIABLE_1440671)))))))))) (let ((_let_3625 (forall ((BOUND_VARIABLE_1440644 tptp.int) (BOUND_VARIABLE_1440645 tptp.int) (BOUND_VARIABLE_1440646 tptp.int) (BOUND_VARIABLE_1440647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9566 BOUND_VARIABLE_1440644) BOUND_VARIABLE_1440645) BOUND_VARIABLE_1440646) BOUND_VARIABLE_1440647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440645) BOUND_VARIABLE_1440647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440644) BOUND_VARIABLE_1440646)))))))))) (let ((_let_3626 (forall ((BOUND_VARIABLE_1440619 tptp.int) (BOUND_VARIABLE_1440620 tptp.int) (BOUND_VARIABLE_1440621 tptp.int) (BOUND_VARIABLE_1440622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9567 BOUND_VARIABLE_1440619) BOUND_VARIABLE_1440620) BOUND_VARIABLE_1440621) BOUND_VARIABLE_1440622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440620) BOUND_VARIABLE_1440622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440619) BOUND_VARIABLE_1440621)))))))))) (let ((_let_3627 (forall ((BOUND_VARIABLE_1440594 tptp.int) (BOUND_VARIABLE_1440595 tptp.int) (BOUND_VARIABLE_1440596 tptp.int) (BOUND_VARIABLE_1440597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9568 BOUND_VARIABLE_1440594) BOUND_VARIABLE_1440595) BOUND_VARIABLE_1440596) BOUND_VARIABLE_1440597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440595) BOUND_VARIABLE_1440597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440594) BOUND_VARIABLE_1440596)))))))))) (let ((_let_3628 (forall ((BOUND_VARIABLE_1440569 tptp.int) (BOUND_VARIABLE_1440570 tptp.int) (BOUND_VARIABLE_1440571 tptp.int) (BOUND_VARIABLE_1440572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9569 BOUND_VARIABLE_1440569) BOUND_VARIABLE_1440570) BOUND_VARIABLE_1440571) BOUND_VARIABLE_1440572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440570) BOUND_VARIABLE_1440572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440569) BOUND_VARIABLE_1440571)))))))))) (let ((_let_3629 (forall ((BOUND_VARIABLE_1440544 tptp.int) (BOUND_VARIABLE_1440545 tptp.int) (BOUND_VARIABLE_1440546 tptp.int) (BOUND_VARIABLE_1440547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9570 BOUND_VARIABLE_1440544) BOUND_VARIABLE_1440545) BOUND_VARIABLE_1440546) BOUND_VARIABLE_1440547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440545) BOUND_VARIABLE_1440547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440544) BOUND_VARIABLE_1440546)))))))))) (let ((_let_3630 (forall ((BOUND_VARIABLE_1440519 tptp.int) (BOUND_VARIABLE_1440520 tptp.int) (BOUND_VARIABLE_1440521 tptp.int) (BOUND_VARIABLE_1440522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9571 BOUND_VARIABLE_1440519) BOUND_VARIABLE_1440520) BOUND_VARIABLE_1440521) BOUND_VARIABLE_1440522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440520) BOUND_VARIABLE_1440522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440519) BOUND_VARIABLE_1440521)))))))))) (let ((_let_3631 (forall ((BOUND_VARIABLE_1440494 tptp.int) (BOUND_VARIABLE_1440495 tptp.int) (BOUND_VARIABLE_1440496 tptp.int) (BOUND_VARIABLE_1440497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9572 BOUND_VARIABLE_1440494) BOUND_VARIABLE_1440495) BOUND_VARIABLE_1440496) BOUND_VARIABLE_1440497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440495) BOUND_VARIABLE_1440497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440494) BOUND_VARIABLE_1440496)))))))))) (let ((_let_3632 (forall ((BOUND_VARIABLE_1440469 tptp.int) (BOUND_VARIABLE_1440470 tptp.int) (BOUND_VARIABLE_1440471 tptp.int) (BOUND_VARIABLE_1440472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9573 BOUND_VARIABLE_1440469) BOUND_VARIABLE_1440470) BOUND_VARIABLE_1440471) BOUND_VARIABLE_1440472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440470) BOUND_VARIABLE_1440472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440469) BOUND_VARIABLE_1440471)))))))))) (let ((_let_3633 (forall ((BOUND_VARIABLE_1440444 tptp.int) (BOUND_VARIABLE_1440445 tptp.int) (BOUND_VARIABLE_1440446 tptp.int) (BOUND_VARIABLE_1440447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9574 BOUND_VARIABLE_1440444) BOUND_VARIABLE_1440445) BOUND_VARIABLE_1440446) BOUND_VARIABLE_1440447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440445) BOUND_VARIABLE_1440447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440444) BOUND_VARIABLE_1440446)))))))))) (let ((_let_3634 (forall ((BOUND_VARIABLE_1440419 tptp.int) (BOUND_VARIABLE_1440420 tptp.int) (BOUND_VARIABLE_1440421 tptp.int) (BOUND_VARIABLE_1440422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9575 BOUND_VARIABLE_1440419) BOUND_VARIABLE_1440420) BOUND_VARIABLE_1440421) BOUND_VARIABLE_1440422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440420) BOUND_VARIABLE_1440422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440419) BOUND_VARIABLE_1440421)))))))))) (let ((_let_3635 (forall ((BOUND_VARIABLE_1440394 tptp.int) (BOUND_VARIABLE_1440395 tptp.int) (BOUND_VARIABLE_1440396 tptp.int) (BOUND_VARIABLE_1440397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9576 BOUND_VARIABLE_1440394) BOUND_VARIABLE_1440395) BOUND_VARIABLE_1440396) BOUND_VARIABLE_1440397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440395) BOUND_VARIABLE_1440397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440394) BOUND_VARIABLE_1440396)))))))))) (let ((_let_3636 (forall ((BOUND_VARIABLE_1440369 tptp.int) (BOUND_VARIABLE_1440370 tptp.int) (BOUND_VARIABLE_1440371 tptp.int) (BOUND_VARIABLE_1440372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9577 BOUND_VARIABLE_1440369) BOUND_VARIABLE_1440370) BOUND_VARIABLE_1440371) BOUND_VARIABLE_1440372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440370) BOUND_VARIABLE_1440372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440369) BOUND_VARIABLE_1440371)))))))))) (let ((_let_3637 (forall ((BOUND_VARIABLE_1440344 tptp.int) (BOUND_VARIABLE_1440345 tptp.int) (BOUND_VARIABLE_1440346 tptp.int) (BOUND_VARIABLE_1440347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9578 BOUND_VARIABLE_1440344) BOUND_VARIABLE_1440345) BOUND_VARIABLE_1440346) BOUND_VARIABLE_1440347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440345) BOUND_VARIABLE_1440347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440344) BOUND_VARIABLE_1440346)))))))))) (let ((_let_3638 (forall ((BOUND_VARIABLE_1440319 tptp.int) (BOUND_VARIABLE_1440320 tptp.int) (BOUND_VARIABLE_1440321 tptp.int) (BOUND_VARIABLE_1440322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9579 BOUND_VARIABLE_1440319) BOUND_VARIABLE_1440320) BOUND_VARIABLE_1440321) BOUND_VARIABLE_1440322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440320) BOUND_VARIABLE_1440322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440319) BOUND_VARIABLE_1440321)))))))))) (let ((_let_3639 (forall ((BOUND_VARIABLE_1440294 tptp.int) (BOUND_VARIABLE_1440295 tptp.int) (BOUND_VARIABLE_1440296 tptp.int) (BOUND_VARIABLE_1440297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9580 BOUND_VARIABLE_1440294) BOUND_VARIABLE_1440295) BOUND_VARIABLE_1440296) BOUND_VARIABLE_1440297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440295) BOUND_VARIABLE_1440297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440294) BOUND_VARIABLE_1440296)))))))))) (let ((_let_3640 (forall ((BOUND_VARIABLE_1440269 tptp.int) (BOUND_VARIABLE_1440270 tptp.int) (BOUND_VARIABLE_1440271 tptp.int) (BOUND_VARIABLE_1440272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9581 BOUND_VARIABLE_1440269) BOUND_VARIABLE_1440270) BOUND_VARIABLE_1440271) BOUND_VARIABLE_1440272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440270) BOUND_VARIABLE_1440272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440269) BOUND_VARIABLE_1440271)))))))))) (let ((_let_3641 (forall ((BOUND_VARIABLE_1440244 tptp.int) (BOUND_VARIABLE_1440245 tptp.int) (BOUND_VARIABLE_1440246 tptp.int) (BOUND_VARIABLE_1440247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9582 BOUND_VARIABLE_1440244) BOUND_VARIABLE_1440245) BOUND_VARIABLE_1440246) BOUND_VARIABLE_1440247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440245) BOUND_VARIABLE_1440247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440244) BOUND_VARIABLE_1440246)))))))))) (let ((_let_3642 (forall ((BOUND_VARIABLE_1440219 tptp.int) (BOUND_VARIABLE_1440220 tptp.int) (BOUND_VARIABLE_1440221 tptp.int) (BOUND_VARIABLE_1440222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9583 BOUND_VARIABLE_1440219) BOUND_VARIABLE_1440220) BOUND_VARIABLE_1440221) BOUND_VARIABLE_1440222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440220) BOUND_VARIABLE_1440222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440219) BOUND_VARIABLE_1440221)))))))))) (let ((_let_3643 (forall ((BOUND_VARIABLE_1440194 tptp.int) (BOUND_VARIABLE_1440195 tptp.int) (BOUND_VARIABLE_1440196 tptp.int) (BOUND_VARIABLE_1440197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9584 BOUND_VARIABLE_1440194) BOUND_VARIABLE_1440195) BOUND_VARIABLE_1440196) BOUND_VARIABLE_1440197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440195) BOUND_VARIABLE_1440197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440194) BOUND_VARIABLE_1440196)))))))))) (let ((_let_3644 (forall ((BOUND_VARIABLE_1440169 tptp.int) (BOUND_VARIABLE_1440170 tptp.int) (BOUND_VARIABLE_1440171 tptp.int) (BOUND_VARIABLE_1440172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9585 BOUND_VARIABLE_1440169) BOUND_VARIABLE_1440170) BOUND_VARIABLE_1440171) BOUND_VARIABLE_1440172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440170) BOUND_VARIABLE_1440172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440169) BOUND_VARIABLE_1440171)))))))))) (let ((_let_3645 (forall ((BOUND_VARIABLE_1440144 tptp.int) (BOUND_VARIABLE_1440145 tptp.int) (BOUND_VARIABLE_1440146 tptp.int) (BOUND_VARIABLE_1440147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9586 BOUND_VARIABLE_1440144) BOUND_VARIABLE_1440145) BOUND_VARIABLE_1440146) BOUND_VARIABLE_1440147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440145) BOUND_VARIABLE_1440147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440144) BOUND_VARIABLE_1440146)))))))))) (let ((_let_3646 (forall ((BOUND_VARIABLE_1440119 tptp.int) (BOUND_VARIABLE_1440120 tptp.int) (BOUND_VARIABLE_1440121 tptp.int) (BOUND_VARIABLE_1440122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9587 BOUND_VARIABLE_1440119) BOUND_VARIABLE_1440120) BOUND_VARIABLE_1440121) BOUND_VARIABLE_1440122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440120) BOUND_VARIABLE_1440122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440119) BOUND_VARIABLE_1440121)))))))))) (let ((_let_3647 (forall ((BOUND_VARIABLE_1440094 tptp.int) (BOUND_VARIABLE_1440095 tptp.int) (BOUND_VARIABLE_1440096 tptp.int) (BOUND_VARIABLE_1440097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9588 BOUND_VARIABLE_1440094) BOUND_VARIABLE_1440095) BOUND_VARIABLE_1440096) BOUND_VARIABLE_1440097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440095) BOUND_VARIABLE_1440097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440094) BOUND_VARIABLE_1440096)))))))))) (let ((_let_3648 (forall ((BOUND_VARIABLE_1440069 tptp.int) (BOUND_VARIABLE_1440070 tptp.int) (BOUND_VARIABLE_1440071 tptp.int) (BOUND_VARIABLE_1440072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9589 BOUND_VARIABLE_1440069) BOUND_VARIABLE_1440070) BOUND_VARIABLE_1440071) BOUND_VARIABLE_1440072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440070) BOUND_VARIABLE_1440072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440069) BOUND_VARIABLE_1440071)))))))))) (let ((_let_3649 (forall ((BOUND_VARIABLE_1440044 tptp.int) (BOUND_VARIABLE_1440045 tptp.int) (BOUND_VARIABLE_1440046 tptp.int) (BOUND_VARIABLE_1440047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9590 BOUND_VARIABLE_1440044) BOUND_VARIABLE_1440045) BOUND_VARIABLE_1440046) BOUND_VARIABLE_1440047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440045) BOUND_VARIABLE_1440047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440044) BOUND_VARIABLE_1440046)))))))))) (let ((_let_3650 (forall ((BOUND_VARIABLE_1440019 tptp.int) (BOUND_VARIABLE_1440020 tptp.int) (BOUND_VARIABLE_1440021 tptp.int) (BOUND_VARIABLE_1440022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9591 BOUND_VARIABLE_1440019) BOUND_VARIABLE_1440020) BOUND_VARIABLE_1440021) BOUND_VARIABLE_1440022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440020) BOUND_VARIABLE_1440022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1440019) BOUND_VARIABLE_1440021)))))))))) (let ((_let_3651 (forall ((BOUND_VARIABLE_1439994 tptp.int) (BOUND_VARIABLE_1439995 tptp.int) (BOUND_VARIABLE_1439996 tptp.int) (BOUND_VARIABLE_1439997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9592 BOUND_VARIABLE_1439994) BOUND_VARIABLE_1439995) BOUND_VARIABLE_1439996) BOUND_VARIABLE_1439997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439995) BOUND_VARIABLE_1439997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439994) BOUND_VARIABLE_1439996)))))))))) (let ((_let_3652 (forall ((BOUND_VARIABLE_1439969 tptp.int) (BOUND_VARIABLE_1439970 tptp.int) (BOUND_VARIABLE_1439971 tptp.int) (BOUND_VARIABLE_1439972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9593 BOUND_VARIABLE_1439969) BOUND_VARIABLE_1439970) BOUND_VARIABLE_1439971) BOUND_VARIABLE_1439972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439970) BOUND_VARIABLE_1439972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439969) BOUND_VARIABLE_1439971)))))))))) (let ((_let_3653 (forall ((BOUND_VARIABLE_1439944 tptp.int) (BOUND_VARIABLE_1439945 tptp.int) (BOUND_VARIABLE_1439946 tptp.int) (BOUND_VARIABLE_1439947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9594 BOUND_VARIABLE_1439944) BOUND_VARIABLE_1439945) BOUND_VARIABLE_1439946) BOUND_VARIABLE_1439947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439945) BOUND_VARIABLE_1439947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439944) BOUND_VARIABLE_1439946)))))))))) (let ((_let_3654 (forall ((BOUND_VARIABLE_1439919 tptp.int) (BOUND_VARIABLE_1439920 tptp.int) (BOUND_VARIABLE_1439921 tptp.int) (BOUND_VARIABLE_1439922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9595 BOUND_VARIABLE_1439919) BOUND_VARIABLE_1439920) BOUND_VARIABLE_1439921) BOUND_VARIABLE_1439922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439920) BOUND_VARIABLE_1439922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439919) BOUND_VARIABLE_1439921)))))))))) (let ((_let_3655 (forall ((BOUND_VARIABLE_1439894 tptp.int) (BOUND_VARIABLE_1439895 tptp.int) (BOUND_VARIABLE_1439896 tptp.int) (BOUND_VARIABLE_1439897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9596 BOUND_VARIABLE_1439894) BOUND_VARIABLE_1439895) BOUND_VARIABLE_1439896) BOUND_VARIABLE_1439897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439895) BOUND_VARIABLE_1439897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439894) BOUND_VARIABLE_1439896)))))))))) (let ((_let_3656 (forall ((BOUND_VARIABLE_1439869 tptp.int) (BOUND_VARIABLE_1439870 tptp.int) (BOUND_VARIABLE_1439871 tptp.int) (BOUND_VARIABLE_1439872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9597 BOUND_VARIABLE_1439869) BOUND_VARIABLE_1439870) BOUND_VARIABLE_1439871) BOUND_VARIABLE_1439872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439870) BOUND_VARIABLE_1439872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439869) BOUND_VARIABLE_1439871)))))))))) (let ((_let_3657 (forall ((BOUND_VARIABLE_1439844 tptp.int) (BOUND_VARIABLE_1439845 tptp.int) (BOUND_VARIABLE_1439846 tptp.int) (BOUND_VARIABLE_1439847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9598 BOUND_VARIABLE_1439844) BOUND_VARIABLE_1439845) BOUND_VARIABLE_1439846) BOUND_VARIABLE_1439847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439845) BOUND_VARIABLE_1439847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439844) BOUND_VARIABLE_1439846)))))))))) (let ((_let_3658 (forall ((BOUND_VARIABLE_1439819 tptp.int) (BOUND_VARIABLE_1439820 tptp.int) (BOUND_VARIABLE_1439821 tptp.int) (BOUND_VARIABLE_1439822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9599 BOUND_VARIABLE_1439819) BOUND_VARIABLE_1439820) BOUND_VARIABLE_1439821) BOUND_VARIABLE_1439822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439820) BOUND_VARIABLE_1439822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439819) BOUND_VARIABLE_1439821)))))))))) (let ((_let_3659 (forall ((BOUND_VARIABLE_1439794 tptp.int) (BOUND_VARIABLE_1439795 tptp.int) (BOUND_VARIABLE_1439796 tptp.int) (BOUND_VARIABLE_1439797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9600 BOUND_VARIABLE_1439794) BOUND_VARIABLE_1439795) BOUND_VARIABLE_1439796) BOUND_VARIABLE_1439797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439795) BOUND_VARIABLE_1439797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439794) BOUND_VARIABLE_1439796)))))))))) (let ((_let_3660 (forall ((BOUND_VARIABLE_1439769 tptp.int) (BOUND_VARIABLE_1439770 tptp.int) (BOUND_VARIABLE_1439771 tptp.int) (BOUND_VARIABLE_1439772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9601 BOUND_VARIABLE_1439769) BOUND_VARIABLE_1439770) BOUND_VARIABLE_1439771) BOUND_VARIABLE_1439772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439770) BOUND_VARIABLE_1439772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439769) BOUND_VARIABLE_1439771)))))))))) (let ((_let_3661 (forall ((BOUND_VARIABLE_1439744 tptp.int) (BOUND_VARIABLE_1439745 tptp.int) (BOUND_VARIABLE_1439746 tptp.int) (BOUND_VARIABLE_1439747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9602 BOUND_VARIABLE_1439744) BOUND_VARIABLE_1439745) BOUND_VARIABLE_1439746) BOUND_VARIABLE_1439747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439745) BOUND_VARIABLE_1439747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439744) BOUND_VARIABLE_1439746)))))))))) (let ((_let_3662 (forall ((BOUND_VARIABLE_1439719 tptp.int) (BOUND_VARIABLE_1439720 tptp.int) (BOUND_VARIABLE_1439721 tptp.int) (BOUND_VARIABLE_1439722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9603 BOUND_VARIABLE_1439719) BOUND_VARIABLE_1439720) BOUND_VARIABLE_1439721) BOUND_VARIABLE_1439722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439720) BOUND_VARIABLE_1439722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439719) BOUND_VARIABLE_1439721)))))))))) (let ((_let_3663 (forall ((BOUND_VARIABLE_1439694 tptp.int) (BOUND_VARIABLE_1439695 tptp.int) (BOUND_VARIABLE_1439696 tptp.int) (BOUND_VARIABLE_1439697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9604 BOUND_VARIABLE_1439694) BOUND_VARIABLE_1439695) BOUND_VARIABLE_1439696) BOUND_VARIABLE_1439697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439695) BOUND_VARIABLE_1439697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439694) BOUND_VARIABLE_1439696)))))))))) (let ((_let_3664 (forall ((BOUND_VARIABLE_1439669 tptp.int) (BOUND_VARIABLE_1439670 tptp.int) (BOUND_VARIABLE_1439671 tptp.int) (BOUND_VARIABLE_1439672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9605 BOUND_VARIABLE_1439669) BOUND_VARIABLE_1439670) BOUND_VARIABLE_1439671) BOUND_VARIABLE_1439672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439670) BOUND_VARIABLE_1439672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439669) BOUND_VARIABLE_1439671)))))))))) (let ((_let_3665 (forall ((BOUND_VARIABLE_1439644 tptp.int) (BOUND_VARIABLE_1439645 tptp.int) (BOUND_VARIABLE_1439646 tptp.int) (BOUND_VARIABLE_1439647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9606 BOUND_VARIABLE_1439644) BOUND_VARIABLE_1439645) BOUND_VARIABLE_1439646) BOUND_VARIABLE_1439647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439645) BOUND_VARIABLE_1439647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439644) BOUND_VARIABLE_1439646)))))))))) (let ((_let_3666 (forall ((BOUND_VARIABLE_1439619 tptp.int) (BOUND_VARIABLE_1439620 tptp.int) (BOUND_VARIABLE_1439621 tptp.int) (BOUND_VARIABLE_1439622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9607 BOUND_VARIABLE_1439619) BOUND_VARIABLE_1439620) BOUND_VARIABLE_1439621) BOUND_VARIABLE_1439622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439620) BOUND_VARIABLE_1439622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439619) BOUND_VARIABLE_1439621)))))))))) (let ((_let_3667 (forall ((BOUND_VARIABLE_1439594 tptp.int) (BOUND_VARIABLE_1439595 tptp.int) (BOUND_VARIABLE_1439596 tptp.int) (BOUND_VARIABLE_1439597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9608 BOUND_VARIABLE_1439594) BOUND_VARIABLE_1439595) BOUND_VARIABLE_1439596) BOUND_VARIABLE_1439597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439595) BOUND_VARIABLE_1439597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439594) BOUND_VARIABLE_1439596)))))))))) (let ((_let_3668 (forall ((BOUND_VARIABLE_1439569 tptp.int) (BOUND_VARIABLE_1439570 tptp.int) (BOUND_VARIABLE_1439571 tptp.int) (BOUND_VARIABLE_1439572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9609 BOUND_VARIABLE_1439569) BOUND_VARIABLE_1439570) BOUND_VARIABLE_1439571) BOUND_VARIABLE_1439572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439570) BOUND_VARIABLE_1439572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439569) BOUND_VARIABLE_1439571)))))))))) (let ((_let_3669 (forall ((BOUND_VARIABLE_1439544 tptp.int) (BOUND_VARIABLE_1439545 tptp.int) (BOUND_VARIABLE_1439546 tptp.int) (BOUND_VARIABLE_1439547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9610 BOUND_VARIABLE_1439544) BOUND_VARIABLE_1439545) BOUND_VARIABLE_1439546) BOUND_VARIABLE_1439547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439545) BOUND_VARIABLE_1439547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439544) BOUND_VARIABLE_1439546)))))))))) (let ((_let_3670 (forall ((BOUND_VARIABLE_1439519 tptp.int) (BOUND_VARIABLE_1439520 tptp.int) (BOUND_VARIABLE_1439521 tptp.int) (BOUND_VARIABLE_1439522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9611 BOUND_VARIABLE_1439519) BOUND_VARIABLE_1439520) BOUND_VARIABLE_1439521) BOUND_VARIABLE_1439522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439520) BOUND_VARIABLE_1439522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439519) BOUND_VARIABLE_1439521)))))))))) (let ((_let_3671 (forall ((BOUND_VARIABLE_1439494 tptp.int) (BOUND_VARIABLE_1439495 tptp.int) (BOUND_VARIABLE_1439496 tptp.int) (BOUND_VARIABLE_1439497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9612 BOUND_VARIABLE_1439494) BOUND_VARIABLE_1439495) BOUND_VARIABLE_1439496) BOUND_VARIABLE_1439497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439495) BOUND_VARIABLE_1439497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439494) BOUND_VARIABLE_1439496)))))))))) (let ((_let_3672 (forall ((BOUND_VARIABLE_1439469 tptp.int) (BOUND_VARIABLE_1439470 tptp.int) (BOUND_VARIABLE_1439471 tptp.int) (BOUND_VARIABLE_1439472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9613 BOUND_VARIABLE_1439469) BOUND_VARIABLE_1439470) BOUND_VARIABLE_1439471) BOUND_VARIABLE_1439472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439470) BOUND_VARIABLE_1439472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439469) BOUND_VARIABLE_1439471)))))))))) (let ((_let_3673 (forall ((BOUND_VARIABLE_1439444 tptp.int) (BOUND_VARIABLE_1439445 tptp.int) (BOUND_VARIABLE_1439446 tptp.int) (BOUND_VARIABLE_1439447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9614 BOUND_VARIABLE_1439444) BOUND_VARIABLE_1439445) BOUND_VARIABLE_1439446) BOUND_VARIABLE_1439447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439445) BOUND_VARIABLE_1439447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439444) BOUND_VARIABLE_1439446)))))))))) (let ((_let_3674 (forall ((BOUND_VARIABLE_1439419 tptp.int) (BOUND_VARIABLE_1439420 tptp.int) (BOUND_VARIABLE_1439421 tptp.int) (BOUND_VARIABLE_1439422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9615 BOUND_VARIABLE_1439419) BOUND_VARIABLE_1439420) BOUND_VARIABLE_1439421) BOUND_VARIABLE_1439422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439420) BOUND_VARIABLE_1439422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439419) BOUND_VARIABLE_1439421)))))))))) (let ((_let_3675 (forall ((BOUND_VARIABLE_1439394 tptp.int) (BOUND_VARIABLE_1439395 tptp.int) (BOUND_VARIABLE_1439396 tptp.int) (BOUND_VARIABLE_1439397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9616 BOUND_VARIABLE_1439394) BOUND_VARIABLE_1439395) BOUND_VARIABLE_1439396) BOUND_VARIABLE_1439397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439395) BOUND_VARIABLE_1439397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439394) BOUND_VARIABLE_1439396)))))))))) (let ((_let_3676 (forall ((BOUND_VARIABLE_1439369 tptp.int) (BOUND_VARIABLE_1439370 tptp.int) (BOUND_VARIABLE_1439371 tptp.int) (BOUND_VARIABLE_1439372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9617 BOUND_VARIABLE_1439369) BOUND_VARIABLE_1439370) BOUND_VARIABLE_1439371) BOUND_VARIABLE_1439372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439370) BOUND_VARIABLE_1439372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439369) BOUND_VARIABLE_1439371)))))))))) (let ((_let_3677 (forall ((BOUND_VARIABLE_1439344 tptp.int) (BOUND_VARIABLE_1439345 tptp.int) (BOUND_VARIABLE_1439346 tptp.int) (BOUND_VARIABLE_1439347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9618 BOUND_VARIABLE_1439344) BOUND_VARIABLE_1439345) BOUND_VARIABLE_1439346) BOUND_VARIABLE_1439347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439345) BOUND_VARIABLE_1439347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439344) BOUND_VARIABLE_1439346)))))))))) (let ((_let_3678 (forall ((BOUND_VARIABLE_1439319 tptp.int) (BOUND_VARIABLE_1439320 tptp.int) (BOUND_VARIABLE_1439321 tptp.int) (BOUND_VARIABLE_1439322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9619 BOUND_VARIABLE_1439319) BOUND_VARIABLE_1439320) BOUND_VARIABLE_1439321) BOUND_VARIABLE_1439322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439320) BOUND_VARIABLE_1439322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439319) BOUND_VARIABLE_1439321)))))))))) (let ((_let_3679 (forall ((BOUND_VARIABLE_1439294 tptp.int) (BOUND_VARIABLE_1439295 tptp.int) (BOUND_VARIABLE_1439296 tptp.int) (BOUND_VARIABLE_1439297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9620 BOUND_VARIABLE_1439294) BOUND_VARIABLE_1439295) BOUND_VARIABLE_1439296) BOUND_VARIABLE_1439297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439295) BOUND_VARIABLE_1439297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439294) BOUND_VARIABLE_1439296)))))))))) (let ((_let_3680 (forall ((BOUND_VARIABLE_1439269 tptp.int) (BOUND_VARIABLE_1439270 tptp.int) (BOUND_VARIABLE_1439271 tptp.int) (BOUND_VARIABLE_1439272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9621 BOUND_VARIABLE_1439269) BOUND_VARIABLE_1439270) BOUND_VARIABLE_1439271) BOUND_VARIABLE_1439272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439270) BOUND_VARIABLE_1439272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439269) BOUND_VARIABLE_1439271)))))))))) (let ((_let_3681 (forall ((BOUND_VARIABLE_1439244 tptp.int) (BOUND_VARIABLE_1439245 tptp.int) (BOUND_VARIABLE_1439246 tptp.int) (BOUND_VARIABLE_1439247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9622 BOUND_VARIABLE_1439244) BOUND_VARIABLE_1439245) BOUND_VARIABLE_1439246) BOUND_VARIABLE_1439247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439245) BOUND_VARIABLE_1439247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439244) BOUND_VARIABLE_1439246)))))))))) (let ((_let_3682 (forall ((BOUND_VARIABLE_1439219 tptp.int) (BOUND_VARIABLE_1439220 tptp.int) (BOUND_VARIABLE_1439221 tptp.int) (BOUND_VARIABLE_1439222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9623 BOUND_VARIABLE_1439219) BOUND_VARIABLE_1439220) BOUND_VARIABLE_1439221) BOUND_VARIABLE_1439222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439220) BOUND_VARIABLE_1439222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439219) BOUND_VARIABLE_1439221)))))))))) (let ((_let_3683 (forall ((BOUND_VARIABLE_1439194 tptp.int) (BOUND_VARIABLE_1439195 tptp.int) (BOUND_VARIABLE_1439196 tptp.int) (BOUND_VARIABLE_1439197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9624 BOUND_VARIABLE_1439194) BOUND_VARIABLE_1439195) BOUND_VARIABLE_1439196) BOUND_VARIABLE_1439197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439195) BOUND_VARIABLE_1439197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439194) BOUND_VARIABLE_1439196)))))))))) (let ((_let_3684 (forall ((BOUND_VARIABLE_1439169 tptp.int) (BOUND_VARIABLE_1439170 tptp.int) (BOUND_VARIABLE_1439171 tptp.int) (BOUND_VARIABLE_1439172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9625 BOUND_VARIABLE_1439169) BOUND_VARIABLE_1439170) BOUND_VARIABLE_1439171) BOUND_VARIABLE_1439172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439170) BOUND_VARIABLE_1439172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439169) BOUND_VARIABLE_1439171)))))))))) (let ((_let_3685 (forall ((BOUND_VARIABLE_1439144 tptp.int) (BOUND_VARIABLE_1439145 tptp.int) (BOUND_VARIABLE_1439146 tptp.int) (BOUND_VARIABLE_1439147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9626 BOUND_VARIABLE_1439144) BOUND_VARIABLE_1439145) BOUND_VARIABLE_1439146) BOUND_VARIABLE_1439147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439145) BOUND_VARIABLE_1439147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439144) BOUND_VARIABLE_1439146)))))))))) (let ((_let_3686 (forall ((BOUND_VARIABLE_1439119 tptp.int) (BOUND_VARIABLE_1439120 tptp.int) (BOUND_VARIABLE_1439121 tptp.int) (BOUND_VARIABLE_1439122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9627 BOUND_VARIABLE_1439119) BOUND_VARIABLE_1439120) BOUND_VARIABLE_1439121) BOUND_VARIABLE_1439122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439120) BOUND_VARIABLE_1439122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439119) BOUND_VARIABLE_1439121)))))))))) (let ((_let_3687 (forall ((BOUND_VARIABLE_1439094 tptp.int) (BOUND_VARIABLE_1439095 tptp.int) (BOUND_VARIABLE_1439096 tptp.int) (BOUND_VARIABLE_1439097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9628 BOUND_VARIABLE_1439094) BOUND_VARIABLE_1439095) BOUND_VARIABLE_1439096) BOUND_VARIABLE_1439097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439095) BOUND_VARIABLE_1439097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439094) BOUND_VARIABLE_1439096)))))))))) (let ((_let_3688 (forall ((BOUND_VARIABLE_1439069 tptp.int) (BOUND_VARIABLE_1439070 tptp.int) (BOUND_VARIABLE_1439071 tptp.int) (BOUND_VARIABLE_1439072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9629 BOUND_VARIABLE_1439069) BOUND_VARIABLE_1439070) BOUND_VARIABLE_1439071) BOUND_VARIABLE_1439072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439070) BOUND_VARIABLE_1439072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439069) BOUND_VARIABLE_1439071)))))))))) (let ((_let_3689 (forall ((BOUND_VARIABLE_1439044 tptp.int) (BOUND_VARIABLE_1439045 tptp.int) (BOUND_VARIABLE_1439046 tptp.int) (BOUND_VARIABLE_1439047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9630 BOUND_VARIABLE_1439044) BOUND_VARIABLE_1439045) BOUND_VARIABLE_1439046) BOUND_VARIABLE_1439047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439045) BOUND_VARIABLE_1439047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439044) BOUND_VARIABLE_1439046)))))))))) (let ((_let_3690 (forall ((BOUND_VARIABLE_1439019 tptp.int) (BOUND_VARIABLE_1439020 tptp.int) (BOUND_VARIABLE_1439021 tptp.int) (BOUND_VARIABLE_1439022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9631 BOUND_VARIABLE_1439019) BOUND_VARIABLE_1439020) BOUND_VARIABLE_1439021) BOUND_VARIABLE_1439022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439020) BOUND_VARIABLE_1439022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1439019) BOUND_VARIABLE_1439021)))))))))) (let ((_let_3691 (forall ((BOUND_VARIABLE_1438994 tptp.int) (BOUND_VARIABLE_1438995 tptp.int) (BOUND_VARIABLE_1438996 tptp.int) (BOUND_VARIABLE_1438997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9632 BOUND_VARIABLE_1438994) BOUND_VARIABLE_1438995) BOUND_VARIABLE_1438996) BOUND_VARIABLE_1438997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438995) BOUND_VARIABLE_1438997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438994) BOUND_VARIABLE_1438996)))))))))) (let ((_let_3692 (forall ((BOUND_VARIABLE_1438969 tptp.int) (BOUND_VARIABLE_1438970 tptp.int) (BOUND_VARIABLE_1438971 tptp.int) (BOUND_VARIABLE_1438972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9633 BOUND_VARIABLE_1438969) BOUND_VARIABLE_1438970) BOUND_VARIABLE_1438971) BOUND_VARIABLE_1438972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438970) BOUND_VARIABLE_1438972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438969) BOUND_VARIABLE_1438971)))))))))) (let ((_let_3693 (forall ((BOUND_VARIABLE_1438944 tptp.int) (BOUND_VARIABLE_1438945 tptp.int) (BOUND_VARIABLE_1438946 tptp.int) (BOUND_VARIABLE_1438947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9634 BOUND_VARIABLE_1438944) BOUND_VARIABLE_1438945) BOUND_VARIABLE_1438946) BOUND_VARIABLE_1438947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438945) BOUND_VARIABLE_1438947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438944) BOUND_VARIABLE_1438946)))))))))) (let ((_let_3694 (forall ((BOUND_VARIABLE_1438919 tptp.int) (BOUND_VARIABLE_1438920 tptp.int) (BOUND_VARIABLE_1438921 tptp.int) (BOUND_VARIABLE_1438922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9635 BOUND_VARIABLE_1438919) BOUND_VARIABLE_1438920) BOUND_VARIABLE_1438921) BOUND_VARIABLE_1438922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438920) BOUND_VARIABLE_1438922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438919) BOUND_VARIABLE_1438921)))))))))) (let ((_let_3695 (forall ((BOUND_VARIABLE_1438894 tptp.int) (BOUND_VARIABLE_1438895 tptp.int) (BOUND_VARIABLE_1438896 tptp.int) (BOUND_VARIABLE_1438897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9636 BOUND_VARIABLE_1438894) BOUND_VARIABLE_1438895) BOUND_VARIABLE_1438896) BOUND_VARIABLE_1438897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438895) BOUND_VARIABLE_1438897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438894) BOUND_VARIABLE_1438896)))))))))) (let ((_let_3696 (forall ((BOUND_VARIABLE_1438869 tptp.int) (BOUND_VARIABLE_1438870 tptp.int) (BOUND_VARIABLE_1438871 tptp.int) (BOUND_VARIABLE_1438872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9637 BOUND_VARIABLE_1438869) BOUND_VARIABLE_1438870) BOUND_VARIABLE_1438871) BOUND_VARIABLE_1438872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438870) BOUND_VARIABLE_1438872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438869) BOUND_VARIABLE_1438871)))))))))) (let ((_let_3697 (forall ((BOUND_VARIABLE_1438844 tptp.int) (BOUND_VARIABLE_1438845 tptp.int) (BOUND_VARIABLE_1438846 tptp.int) (BOUND_VARIABLE_1438847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9638 BOUND_VARIABLE_1438844) BOUND_VARIABLE_1438845) BOUND_VARIABLE_1438846) BOUND_VARIABLE_1438847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438845) BOUND_VARIABLE_1438847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438844) BOUND_VARIABLE_1438846)))))))))) (let ((_let_3698 (forall ((BOUND_VARIABLE_1438819 tptp.int) (BOUND_VARIABLE_1438820 tptp.int) (BOUND_VARIABLE_1438821 tptp.int) (BOUND_VARIABLE_1438822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9639 BOUND_VARIABLE_1438819) BOUND_VARIABLE_1438820) BOUND_VARIABLE_1438821) BOUND_VARIABLE_1438822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438820) BOUND_VARIABLE_1438822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438819) BOUND_VARIABLE_1438821)))))))))) (let ((_let_3699 (forall ((BOUND_VARIABLE_1438794 tptp.int) (BOUND_VARIABLE_1438795 tptp.int) (BOUND_VARIABLE_1438796 tptp.int) (BOUND_VARIABLE_1438797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9640 BOUND_VARIABLE_1438794) BOUND_VARIABLE_1438795) BOUND_VARIABLE_1438796) BOUND_VARIABLE_1438797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438795) BOUND_VARIABLE_1438797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438794) BOUND_VARIABLE_1438796)))))))))) (let ((_let_3700 (forall ((BOUND_VARIABLE_1438769 tptp.int) (BOUND_VARIABLE_1438770 tptp.int) (BOUND_VARIABLE_1438771 tptp.int) (BOUND_VARIABLE_1438772 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9641 BOUND_VARIABLE_1438769) BOUND_VARIABLE_1438770) BOUND_VARIABLE_1438771) BOUND_VARIABLE_1438772) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438770) BOUND_VARIABLE_1438772)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438769) BOUND_VARIABLE_1438771)))))))))) (let ((_let_3701 (forall ((BOUND_VARIABLE_1438744 tptp.int) (BOUND_VARIABLE_1438745 tptp.int) (BOUND_VARIABLE_1438746 tptp.int) (BOUND_VARIABLE_1438747 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9642 BOUND_VARIABLE_1438744) BOUND_VARIABLE_1438745) BOUND_VARIABLE_1438746) BOUND_VARIABLE_1438747) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438745) BOUND_VARIABLE_1438747)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438744) BOUND_VARIABLE_1438746)))))))))) (let ((_let_3702 (forall ((BOUND_VARIABLE_1438719 tptp.int) (BOUND_VARIABLE_1438720 tptp.int) (BOUND_VARIABLE_1438721 tptp.int) (BOUND_VARIABLE_1438722 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9643 BOUND_VARIABLE_1438719) BOUND_VARIABLE_1438720) BOUND_VARIABLE_1438721) BOUND_VARIABLE_1438722) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438720) BOUND_VARIABLE_1438722)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438719) BOUND_VARIABLE_1438721)))))))))) (let ((_let_3703 (forall ((BOUND_VARIABLE_1438694 tptp.int) (BOUND_VARIABLE_1438695 tptp.int) (BOUND_VARIABLE_1438696 tptp.int) (BOUND_VARIABLE_1438697 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9644 BOUND_VARIABLE_1438694) BOUND_VARIABLE_1438695) BOUND_VARIABLE_1438696) BOUND_VARIABLE_1438697) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438695) BOUND_VARIABLE_1438697)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438694) BOUND_VARIABLE_1438696)))))))))) (let ((_let_3704 (forall ((BOUND_VARIABLE_1438669 tptp.int) (BOUND_VARIABLE_1438670 tptp.int) (BOUND_VARIABLE_1438671 tptp.int) (BOUND_VARIABLE_1438672 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9645 BOUND_VARIABLE_1438669) BOUND_VARIABLE_1438670) BOUND_VARIABLE_1438671) BOUND_VARIABLE_1438672) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438670) BOUND_VARIABLE_1438672)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438669) BOUND_VARIABLE_1438671)))))))))) (let ((_let_3705 (forall ((BOUND_VARIABLE_1438644 tptp.int) (BOUND_VARIABLE_1438645 tptp.int) (BOUND_VARIABLE_1438646 tptp.int) (BOUND_VARIABLE_1438647 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9646 BOUND_VARIABLE_1438644) BOUND_VARIABLE_1438645) BOUND_VARIABLE_1438646) BOUND_VARIABLE_1438647) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438645) BOUND_VARIABLE_1438647)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438644) BOUND_VARIABLE_1438646)))))))))) (let ((_let_3706 (forall ((BOUND_VARIABLE_1438619 tptp.int) (BOUND_VARIABLE_1438620 tptp.int) (BOUND_VARIABLE_1438621 tptp.int) (BOUND_VARIABLE_1438622 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9647 BOUND_VARIABLE_1438619) BOUND_VARIABLE_1438620) BOUND_VARIABLE_1438621) BOUND_VARIABLE_1438622) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438620) BOUND_VARIABLE_1438622)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438619) BOUND_VARIABLE_1438621)))))))))) (let ((_let_3707 (forall ((BOUND_VARIABLE_1438594 tptp.int) (BOUND_VARIABLE_1438595 tptp.int) (BOUND_VARIABLE_1438596 tptp.int) (BOUND_VARIABLE_1438597 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9648 BOUND_VARIABLE_1438594) BOUND_VARIABLE_1438595) BOUND_VARIABLE_1438596) BOUND_VARIABLE_1438597) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438595) BOUND_VARIABLE_1438597)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438594) BOUND_VARIABLE_1438596)))))))))) (let ((_let_3708 (forall ((BOUND_VARIABLE_1438569 tptp.int) (BOUND_VARIABLE_1438570 tptp.int) (BOUND_VARIABLE_1438571 tptp.int) (BOUND_VARIABLE_1438572 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9649 BOUND_VARIABLE_1438569) BOUND_VARIABLE_1438570) BOUND_VARIABLE_1438571) BOUND_VARIABLE_1438572) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438570) BOUND_VARIABLE_1438572)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438569) BOUND_VARIABLE_1438571)))))))))) (let ((_let_3709 (forall ((BOUND_VARIABLE_1438544 tptp.int) (BOUND_VARIABLE_1438545 tptp.int) (BOUND_VARIABLE_1438546 tptp.int) (BOUND_VARIABLE_1438547 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9650 BOUND_VARIABLE_1438544) BOUND_VARIABLE_1438545) BOUND_VARIABLE_1438546) BOUND_VARIABLE_1438547) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438545) BOUND_VARIABLE_1438547)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438544) BOUND_VARIABLE_1438546)))))))))) (let ((_let_3710 (forall ((BOUND_VARIABLE_1438519 tptp.int) (BOUND_VARIABLE_1438520 tptp.int) (BOUND_VARIABLE_1438521 tptp.int) (BOUND_VARIABLE_1438522 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9651 BOUND_VARIABLE_1438519) BOUND_VARIABLE_1438520) BOUND_VARIABLE_1438521) BOUND_VARIABLE_1438522) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438520) BOUND_VARIABLE_1438522)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438519) BOUND_VARIABLE_1438521)))))))))) (let ((_let_3711 (forall ((BOUND_VARIABLE_1438494 tptp.int) (BOUND_VARIABLE_1438495 tptp.int) (BOUND_VARIABLE_1438496 tptp.int) (BOUND_VARIABLE_1438497 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9652 BOUND_VARIABLE_1438494) BOUND_VARIABLE_1438495) BOUND_VARIABLE_1438496) BOUND_VARIABLE_1438497) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438495) BOUND_VARIABLE_1438497)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438494) BOUND_VARIABLE_1438496)))))))))) (let ((_let_3712 (forall ((BOUND_VARIABLE_1438469 tptp.int) (BOUND_VARIABLE_1438470 tptp.int) (BOUND_VARIABLE_1438471 tptp.int) (BOUND_VARIABLE_1438472 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9653 BOUND_VARIABLE_1438469) BOUND_VARIABLE_1438470) BOUND_VARIABLE_1438471) BOUND_VARIABLE_1438472) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438470) BOUND_VARIABLE_1438472)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438469) BOUND_VARIABLE_1438471)))))))))) (let ((_let_3713 (forall ((BOUND_VARIABLE_1438444 tptp.int) (BOUND_VARIABLE_1438445 tptp.int) (BOUND_VARIABLE_1438446 tptp.int) (BOUND_VARIABLE_1438447 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9654 BOUND_VARIABLE_1438444) BOUND_VARIABLE_1438445) BOUND_VARIABLE_1438446) BOUND_VARIABLE_1438447) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438445) BOUND_VARIABLE_1438447)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438444) BOUND_VARIABLE_1438446)))))))))) (let ((_let_3714 (forall ((BOUND_VARIABLE_1438419 tptp.int) (BOUND_VARIABLE_1438420 tptp.int) (BOUND_VARIABLE_1438421 tptp.int) (BOUND_VARIABLE_1438422 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9655 BOUND_VARIABLE_1438419) BOUND_VARIABLE_1438420) BOUND_VARIABLE_1438421) BOUND_VARIABLE_1438422) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438420) BOUND_VARIABLE_1438422)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438419) BOUND_VARIABLE_1438421)))))))))) (let ((_let_3715 (forall ((BOUND_VARIABLE_1438394 tptp.int) (BOUND_VARIABLE_1438395 tptp.int) (BOUND_VARIABLE_1438396 tptp.int) (BOUND_VARIABLE_1438397 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9656 BOUND_VARIABLE_1438394) BOUND_VARIABLE_1438395) BOUND_VARIABLE_1438396) BOUND_VARIABLE_1438397) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438395) BOUND_VARIABLE_1438397)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438394) BOUND_VARIABLE_1438396)))))))))) (let ((_let_3716 (forall ((BOUND_VARIABLE_1438369 tptp.int) (BOUND_VARIABLE_1438370 tptp.int) (BOUND_VARIABLE_1438371 tptp.int) (BOUND_VARIABLE_1438372 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9657 BOUND_VARIABLE_1438369) BOUND_VARIABLE_1438370) BOUND_VARIABLE_1438371) BOUND_VARIABLE_1438372) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438370) BOUND_VARIABLE_1438372)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438369) BOUND_VARIABLE_1438371)))))))))) (let ((_let_3717 (forall ((BOUND_VARIABLE_1438344 tptp.int) (BOUND_VARIABLE_1438345 tptp.int) (BOUND_VARIABLE_1438346 tptp.int) (BOUND_VARIABLE_1438347 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9658 BOUND_VARIABLE_1438344) BOUND_VARIABLE_1438345) BOUND_VARIABLE_1438346) BOUND_VARIABLE_1438347) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438345) BOUND_VARIABLE_1438347)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438344) BOUND_VARIABLE_1438346)))))))))) (let ((_let_3718 (forall ((BOUND_VARIABLE_1438319 tptp.int) (BOUND_VARIABLE_1438320 tptp.int) (BOUND_VARIABLE_1438321 tptp.int) (BOUND_VARIABLE_1438322 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9659 BOUND_VARIABLE_1438319) BOUND_VARIABLE_1438320) BOUND_VARIABLE_1438321) BOUND_VARIABLE_1438322) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438320) BOUND_VARIABLE_1438322)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438319) BOUND_VARIABLE_1438321)))))))))) (let ((_let_3719 (forall ((BOUND_VARIABLE_1438294 tptp.int) (BOUND_VARIABLE_1438295 tptp.int) (BOUND_VARIABLE_1438296 tptp.int) (BOUND_VARIABLE_1438297 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9660 BOUND_VARIABLE_1438294) BOUND_VARIABLE_1438295) BOUND_VARIABLE_1438296) BOUND_VARIABLE_1438297) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438295) BOUND_VARIABLE_1438297)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438294) BOUND_VARIABLE_1438296)))))))))) (let ((_let_3720 (forall ((BOUND_VARIABLE_1438269 tptp.int) (BOUND_VARIABLE_1438270 tptp.int) (BOUND_VARIABLE_1438271 tptp.int) (BOUND_VARIABLE_1438272 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9661 BOUND_VARIABLE_1438269) BOUND_VARIABLE_1438270) BOUND_VARIABLE_1438271) BOUND_VARIABLE_1438272) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438270) BOUND_VARIABLE_1438272)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438269) BOUND_VARIABLE_1438271)))))))))) (let ((_let_3721 (forall ((BOUND_VARIABLE_1438244 tptp.int) (BOUND_VARIABLE_1438245 tptp.int) (BOUND_VARIABLE_1438246 tptp.int) (BOUND_VARIABLE_1438247 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9662 BOUND_VARIABLE_1438244) BOUND_VARIABLE_1438245) BOUND_VARIABLE_1438246) BOUND_VARIABLE_1438247) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438245) BOUND_VARIABLE_1438247)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438244) BOUND_VARIABLE_1438246)))))))))) (let ((_let_3722 (forall ((BOUND_VARIABLE_1438219 tptp.int) (BOUND_VARIABLE_1438220 tptp.int) (BOUND_VARIABLE_1438221 tptp.int) (BOUND_VARIABLE_1438222 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9663 BOUND_VARIABLE_1438219) BOUND_VARIABLE_1438220) BOUND_VARIABLE_1438221) BOUND_VARIABLE_1438222) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438220) BOUND_VARIABLE_1438222)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438219) BOUND_VARIABLE_1438221)))))))))) (let ((_let_3723 (forall ((BOUND_VARIABLE_1438194 tptp.int) (BOUND_VARIABLE_1438195 tptp.int) (BOUND_VARIABLE_1438196 tptp.int) (BOUND_VARIABLE_1438197 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9664 BOUND_VARIABLE_1438194) BOUND_VARIABLE_1438195) BOUND_VARIABLE_1438196) BOUND_VARIABLE_1438197) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438195) BOUND_VARIABLE_1438197)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438194) BOUND_VARIABLE_1438196)))))))))) (let ((_let_3724 (forall ((BOUND_VARIABLE_1438169 tptp.int) (BOUND_VARIABLE_1438170 tptp.int) (BOUND_VARIABLE_1438171 tptp.int) (BOUND_VARIABLE_1438172 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9665 BOUND_VARIABLE_1438169) BOUND_VARIABLE_1438170) BOUND_VARIABLE_1438171) BOUND_VARIABLE_1438172) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438170) BOUND_VARIABLE_1438172)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438169) BOUND_VARIABLE_1438171)))))))))) (let ((_let_3725 (forall ((BOUND_VARIABLE_1438144 tptp.int) (BOUND_VARIABLE_1438145 tptp.int) (BOUND_VARIABLE_1438146 tptp.int) (BOUND_VARIABLE_1438147 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9666 BOUND_VARIABLE_1438144) BOUND_VARIABLE_1438145) BOUND_VARIABLE_1438146) BOUND_VARIABLE_1438147) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438145) BOUND_VARIABLE_1438147)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438144) BOUND_VARIABLE_1438146)))))))))) (let ((_let_3726 (forall ((BOUND_VARIABLE_1438119 tptp.int) (BOUND_VARIABLE_1438120 tptp.int) (BOUND_VARIABLE_1438121 tptp.int) (BOUND_VARIABLE_1438122 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9667 BOUND_VARIABLE_1438119) BOUND_VARIABLE_1438120) BOUND_VARIABLE_1438121) BOUND_VARIABLE_1438122) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438120) BOUND_VARIABLE_1438122)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438119) BOUND_VARIABLE_1438121)))))))))) (let ((_let_3727 (forall ((BOUND_VARIABLE_1438094 tptp.int) (BOUND_VARIABLE_1438095 tptp.int) (BOUND_VARIABLE_1438096 tptp.int) (BOUND_VARIABLE_1438097 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9668 BOUND_VARIABLE_1438094) BOUND_VARIABLE_1438095) BOUND_VARIABLE_1438096) BOUND_VARIABLE_1438097) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438095) BOUND_VARIABLE_1438097)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438094) BOUND_VARIABLE_1438096)))))))))) (let ((_let_3728 (forall ((BOUND_VARIABLE_1438069 tptp.int) (BOUND_VARIABLE_1438070 tptp.int) (BOUND_VARIABLE_1438071 tptp.int) (BOUND_VARIABLE_1438072 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9669 BOUND_VARIABLE_1438069) BOUND_VARIABLE_1438070) BOUND_VARIABLE_1438071) BOUND_VARIABLE_1438072) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438070) BOUND_VARIABLE_1438072)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438069) BOUND_VARIABLE_1438071)))))))))) (let ((_let_3729 (forall ((BOUND_VARIABLE_1438044 tptp.int) (BOUND_VARIABLE_1438045 tptp.int) (BOUND_VARIABLE_1438046 tptp.int) (BOUND_VARIABLE_1438047 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9670 BOUND_VARIABLE_1438044) BOUND_VARIABLE_1438045) BOUND_VARIABLE_1438046) BOUND_VARIABLE_1438047) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438045) BOUND_VARIABLE_1438047)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438044) BOUND_VARIABLE_1438046)))))))))) (let ((_let_3730 (forall ((BOUND_VARIABLE_1438019 tptp.int) (BOUND_VARIABLE_1438020 tptp.int) (BOUND_VARIABLE_1438021 tptp.int) (BOUND_VARIABLE_1438022 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9671 BOUND_VARIABLE_1438019) BOUND_VARIABLE_1438020) BOUND_VARIABLE_1438021) BOUND_VARIABLE_1438022) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438020) BOUND_VARIABLE_1438022)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1438019) BOUND_VARIABLE_1438021)))))))))) (let ((_let_3731 (forall ((BOUND_VARIABLE_1437994 tptp.int) (BOUND_VARIABLE_1437995 tptp.int) (BOUND_VARIABLE_1437996 tptp.int) (BOUND_VARIABLE_1437997 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9672 BOUND_VARIABLE_1437994) BOUND_VARIABLE_1437995) BOUND_VARIABLE_1437996) BOUND_VARIABLE_1437997) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437995) BOUND_VARIABLE_1437997)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437994) BOUND_VARIABLE_1437996)))))))))) (let ((_let_3732 (forall ((BOUND_VARIABLE_1437969 tptp.int) (BOUND_VARIABLE_1437970 tptp.int) (BOUND_VARIABLE_1437971 tptp.int) (BOUND_VARIABLE_1437972 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9673 BOUND_VARIABLE_1437969) BOUND_VARIABLE_1437970) BOUND_VARIABLE_1437971) BOUND_VARIABLE_1437972) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437970) BOUND_VARIABLE_1437972)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437969) BOUND_VARIABLE_1437971)))))))))) (let ((_let_3733 (forall ((BOUND_VARIABLE_1437944 tptp.int) (BOUND_VARIABLE_1437945 tptp.int) (BOUND_VARIABLE_1437946 tptp.int) (BOUND_VARIABLE_1437947 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9674 BOUND_VARIABLE_1437944) BOUND_VARIABLE_1437945) BOUND_VARIABLE_1437946) BOUND_VARIABLE_1437947) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437945) BOUND_VARIABLE_1437947)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437944) BOUND_VARIABLE_1437946)))))))))) (let ((_let_3734 (forall ((BOUND_VARIABLE_1437919 tptp.int) (BOUND_VARIABLE_1437920 tptp.int) (BOUND_VARIABLE_1437921 tptp.int) (BOUND_VARIABLE_1437922 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9675 BOUND_VARIABLE_1437919) BOUND_VARIABLE_1437920) BOUND_VARIABLE_1437921) BOUND_VARIABLE_1437922) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437920) BOUND_VARIABLE_1437922)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437919) BOUND_VARIABLE_1437921)))))))))) (let ((_let_3735 (forall ((BOUND_VARIABLE_1437894 tptp.int) (BOUND_VARIABLE_1437895 tptp.int) (BOUND_VARIABLE_1437896 tptp.int) (BOUND_VARIABLE_1437897 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9676 BOUND_VARIABLE_1437894) BOUND_VARIABLE_1437895) BOUND_VARIABLE_1437896) BOUND_VARIABLE_1437897) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437895) BOUND_VARIABLE_1437897)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437894) BOUND_VARIABLE_1437896)))))))))) (let ((_let_3736 (forall ((BOUND_VARIABLE_1437869 tptp.int) (BOUND_VARIABLE_1437870 tptp.int) (BOUND_VARIABLE_1437871 tptp.int) (BOUND_VARIABLE_1437872 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9677 BOUND_VARIABLE_1437869) BOUND_VARIABLE_1437870) BOUND_VARIABLE_1437871) BOUND_VARIABLE_1437872) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437870) BOUND_VARIABLE_1437872)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437869) BOUND_VARIABLE_1437871)))))))))) (let ((_let_3737 (forall ((BOUND_VARIABLE_1437844 tptp.int) (BOUND_VARIABLE_1437845 tptp.int) (BOUND_VARIABLE_1437846 tptp.int) (BOUND_VARIABLE_1437847 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9678 BOUND_VARIABLE_1437844) BOUND_VARIABLE_1437845) BOUND_VARIABLE_1437846) BOUND_VARIABLE_1437847) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437845) BOUND_VARIABLE_1437847)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437844) BOUND_VARIABLE_1437846)))))))))) (let ((_let_3738 (forall ((BOUND_VARIABLE_1437819 tptp.int) (BOUND_VARIABLE_1437820 tptp.int) (BOUND_VARIABLE_1437821 tptp.int) (BOUND_VARIABLE_1437822 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9679 BOUND_VARIABLE_1437819) BOUND_VARIABLE_1437820) BOUND_VARIABLE_1437821) BOUND_VARIABLE_1437822) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437820) BOUND_VARIABLE_1437822)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437819) BOUND_VARIABLE_1437821)))))))))) (let ((_let_3739 (forall ((BOUND_VARIABLE_1437794 tptp.int) (BOUND_VARIABLE_1437795 tptp.int) (BOUND_VARIABLE_1437796 tptp.int) (BOUND_VARIABLE_1437797 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9680 BOUND_VARIABLE_1437794) BOUND_VARIABLE_1437795) BOUND_VARIABLE_1437796) BOUND_VARIABLE_1437797) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437795) BOUND_VARIABLE_1437797)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437794) BOUND_VARIABLE_1437796)))))))))) (let ((_let_3740 (forall ((BOUND_VARIABLE_1437752 tptp.rat) (BOUND_VARIABLE_1437753 tptp.int) (BOUND_VARIABLE_1437754 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7609 BOUND_VARIABLE_1437754) BOUND_VARIABLE_1437753)) (ho_7630 k_7629 BOUND_VARIABLE_1437752)) (ho_7496 (ho_7495 (ho_7635 k_9681 BOUND_VARIABLE_1437752) BOUND_VARIABLE_1437753) BOUND_VARIABLE_1437754))))) (let ((_let_3741 (forall ((BOUND_VARIABLE_1437710 tptp.rat) (BOUND_VARIABLE_1437711 tptp.int) (BOUND_VARIABLE_1437712 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7610 BOUND_VARIABLE_1437712) BOUND_VARIABLE_1437711)) (ho_7630 k_7629 BOUND_VARIABLE_1437710)) (ho_7496 (ho_7495 (ho_7635 k_9682 BOUND_VARIABLE_1437710) BOUND_VARIABLE_1437711) BOUND_VARIABLE_1437712))))) (let ((_let_3742 (forall ((BOUND_VARIABLE_1437685 tptp.int) (BOUND_VARIABLE_1437686 tptp.int) (BOUND_VARIABLE_1437687 tptp.int) (BOUND_VARIABLE_1437688 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9683 BOUND_VARIABLE_1437685) BOUND_VARIABLE_1437686) BOUND_VARIABLE_1437687) BOUND_VARIABLE_1437688) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437686) BOUND_VARIABLE_1437688)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437685) BOUND_VARIABLE_1437687)))))))))) (let ((_let_3743 (forall ((BOUND_VARIABLE_1437660 tptp.int) (BOUND_VARIABLE_1437661 tptp.int) (BOUND_VARIABLE_1437662 tptp.int) (BOUND_VARIABLE_1437663 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9684 BOUND_VARIABLE_1437660) BOUND_VARIABLE_1437661) BOUND_VARIABLE_1437662) BOUND_VARIABLE_1437663) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437661) BOUND_VARIABLE_1437663)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437660) BOUND_VARIABLE_1437662)))))))))) (let ((_let_3744 (forall ((BOUND_VARIABLE_1437635 tptp.int) (BOUND_VARIABLE_1437636 tptp.int) (BOUND_VARIABLE_1437637 tptp.int) (BOUND_VARIABLE_1437638 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9685 BOUND_VARIABLE_1437635) BOUND_VARIABLE_1437636) BOUND_VARIABLE_1437637) BOUND_VARIABLE_1437638) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437636) BOUND_VARIABLE_1437638)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437635) BOUND_VARIABLE_1437637)))))))))) (let ((_let_3745 (forall ((BOUND_VARIABLE_1437610 tptp.int) (BOUND_VARIABLE_1437611 tptp.int) (BOUND_VARIABLE_1437612 tptp.int) (BOUND_VARIABLE_1437613 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9686 BOUND_VARIABLE_1437610) BOUND_VARIABLE_1437611) BOUND_VARIABLE_1437612) BOUND_VARIABLE_1437613) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437611) BOUND_VARIABLE_1437613)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437610) BOUND_VARIABLE_1437612)))))))))) (let ((_let_3746 (forall ((BOUND_VARIABLE_1437585 tptp.int) (BOUND_VARIABLE_1437586 tptp.int) (BOUND_VARIABLE_1437587 tptp.int) (BOUND_VARIABLE_1437588 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9687 BOUND_VARIABLE_1437585) BOUND_VARIABLE_1437586) BOUND_VARIABLE_1437587) BOUND_VARIABLE_1437588) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437586) BOUND_VARIABLE_1437588)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437585) BOUND_VARIABLE_1437587)))))))))) (let ((_let_3747 (forall ((BOUND_VARIABLE_1437560 tptp.int) (BOUND_VARIABLE_1437561 tptp.int) (BOUND_VARIABLE_1437562 tptp.int) (BOUND_VARIABLE_1437563 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9688 BOUND_VARIABLE_1437560) BOUND_VARIABLE_1437561) BOUND_VARIABLE_1437562) BOUND_VARIABLE_1437563) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437561) BOUND_VARIABLE_1437563)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437560) BOUND_VARIABLE_1437562)))))))))) (let ((_let_3748 (forall ((BOUND_VARIABLE_1437535 tptp.int) (BOUND_VARIABLE_1437536 tptp.int) (BOUND_VARIABLE_1437537 tptp.int) (BOUND_VARIABLE_1437538 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9689 BOUND_VARIABLE_1437535) BOUND_VARIABLE_1437536) BOUND_VARIABLE_1437537) BOUND_VARIABLE_1437538) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437536) BOUND_VARIABLE_1437538)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437535) BOUND_VARIABLE_1437537)))))))))) (let ((_let_3749 (forall ((BOUND_VARIABLE_1437493 tptp.rat) (BOUND_VARIABLE_1437494 tptp.int) (BOUND_VARIABLE_1437495 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7611 BOUND_VARIABLE_1437495) BOUND_VARIABLE_1437494)) (ho_7630 k_7629 BOUND_VARIABLE_1437493)) (ho_7496 (ho_7495 (ho_7635 k_9690 BOUND_VARIABLE_1437493) BOUND_VARIABLE_1437494) BOUND_VARIABLE_1437495))))) (let ((_let_3750 (forall ((BOUND_VARIABLE_1437451 tptp.rat) (BOUND_VARIABLE_1437452 tptp.int) (BOUND_VARIABLE_1437453 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7612 BOUND_VARIABLE_1437453) BOUND_VARIABLE_1437452)) (ho_7630 k_7629 BOUND_VARIABLE_1437451)) (ho_7496 (ho_7495 (ho_7635 k_9691 BOUND_VARIABLE_1437451) BOUND_VARIABLE_1437452) BOUND_VARIABLE_1437453))))) (let ((_let_3751 (forall ((BOUND_VARIABLE_1437426 tptp.int) (BOUND_VARIABLE_1437427 tptp.int) (BOUND_VARIABLE_1437428 tptp.int) (BOUND_VARIABLE_1437429 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9692 BOUND_VARIABLE_1437426) BOUND_VARIABLE_1437427) BOUND_VARIABLE_1437428) BOUND_VARIABLE_1437429) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437427) BOUND_VARIABLE_1437429)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437426) BOUND_VARIABLE_1437428)))))))))) (let ((_let_3752 (forall ((BOUND_VARIABLE_1437401 tptp.int) (BOUND_VARIABLE_1437402 tptp.int) (BOUND_VARIABLE_1437403 tptp.int) (BOUND_VARIABLE_1437404 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9693 BOUND_VARIABLE_1437401) BOUND_VARIABLE_1437402) BOUND_VARIABLE_1437403) BOUND_VARIABLE_1437404) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437402) BOUND_VARIABLE_1437404)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437401) BOUND_VARIABLE_1437403)))))))))) (let ((_let_3753 (forall ((BOUND_VARIABLE_1437376 tptp.int) (BOUND_VARIABLE_1437377 tptp.int) (BOUND_VARIABLE_1437378 tptp.int) (BOUND_VARIABLE_1437379 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9694 BOUND_VARIABLE_1437376) BOUND_VARIABLE_1437377) BOUND_VARIABLE_1437378) BOUND_VARIABLE_1437379) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437377) BOUND_VARIABLE_1437379)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437376) BOUND_VARIABLE_1437378)))))))))) (let ((_let_3754 (forall ((BOUND_VARIABLE_1437351 tptp.int) (BOUND_VARIABLE_1437352 tptp.int) (BOUND_VARIABLE_1437353 tptp.int) (BOUND_VARIABLE_1437354 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9695 BOUND_VARIABLE_1437351) BOUND_VARIABLE_1437352) BOUND_VARIABLE_1437353) BOUND_VARIABLE_1437354) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437352) BOUND_VARIABLE_1437354)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437351) BOUND_VARIABLE_1437353)))))))))) (let ((_let_3755 (forall ((BOUND_VARIABLE_1437326 tptp.int) (BOUND_VARIABLE_1437327 tptp.int) (BOUND_VARIABLE_1437328 tptp.int) (BOUND_VARIABLE_1437329 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9696 BOUND_VARIABLE_1437326) BOUND_VARIABLE_1437327) BOUND_VARIABLE_1437328) BOUND_VARIABLE_1437329) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437327) BOUND_VARIABLE_1437329)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437326) BOUND_VARIABLE_1437328)))))))))) (let ((_let_3756 (forall ((BOUND_VARIABLE_1437301 tptp.int) (BOUND_VARIABLE_1437302 tptp.int) (BOUND_VARIABLE_1437303 tptp.int) (BOUND_VARIABLE_1437304 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9697 BOUND_VARIABLE_1437301) BOUND_VARIABLE_1437302) BOUND_VARIABLE_1437303) BOUND_VARIABLE_1437304) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437302) BOUND_VARIABLE_1437304)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437301) BOUND_VARIABLE_1437303)))))))))) (let ((_let_3757 (forall ((BOUND_VARIABLE_1437259 tptp.rat) (BOUND_VARIABLE_1437260 tptp.int) (BOUND_VARIABLE_1437261 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7613 BOUND_VARIABLE_1437261) BOUND_VARIABLE_1437260)) (ho_7630 k_7629 BOUND_VARIABLE_1437259)) (ho_7496 (ho_7495 (ho_7635 k_9698 BOUND_VARIABLE_1437259) BOUND_VARIABLE_1437260) BOUND_VARIABLE_1437261))))) (let ((_let_3758 (forall ((BOUND_VARIABLE_1437217 tptp.rat) (BOUND_VARIABLE_1437218 tptp.int) (BOUND_VARIABLE_1437219 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7614 BOUND_VARIABLE_1437219) BOUND_VARIABLE_1437218)) (ho_7630 k_7629 BOUND_VARIABLE_1437217)) (ho_7496 (ho_7495 (ho_7635 k_9699 BOUND_VARIABLE_1437217) BOUND_VARIABLE_1437218) BOUND_VARIABLE_1437219))))) (let ((_let_3759 (forall ((BOUND_VARIABLE_1437192 tptp.int) (BOUND_VARIABLE_1437193 tptp.int) (BOUND_VARIABLE_1437194 tptp.int) (BOUND_VARIABLE_1437195 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9700 BOUND_VARIABLE_1437192) BOUND_VARIABLE_1437193) BOUND_VARIABLE_1437194) BOUND_VARIABLE_1437195) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437193) BOUND_VARIABLE_1437195)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437192) BOUND_VARIABLE_1437194)))))))))) (let ((_let_3760 (forall ((BOUND_VARIABLE_1437167 tptp.int) (BOUND_VARIABLE_1437168 tptp.int) (BOUND_VARIABLE_1437169 tptp.int) (BOUND_VARIABLE_1437170 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9701 BOUND_VARIABLE_1437167) BOUND_VARIABLE_1437168) BOUND_VARIABLE_1437169) BOUND_VARIABLE_1437170) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437168) BOUND_VARIABLE_1437170)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437167) BOUND_VARIABLE_1437169)))))))))) (let ((_let_3761 (forall ((BOUND_VARIABLE_1437142 tptp.int) (BOUND_VARIABLE_1437143 tptp.int) (BOUND_VARIABLE_1437144 tptp.int) (BOUND_VARIABLE_1437145 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9702 BOUND_VARIABLE_1437142) BOUND_VARIABLE_1437143) BOUND_VARIABLE_1437144) BOUND_VARIABLE_1437145) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437143) BOUND_VARIABLE_1437145)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437142) BOUND_VARIABLE_1437144)))))))))) (let ((_let_3762 (forall ((BOUND_VARIABLE_1437117 tptp.int) (BOUND_VARIABLE_1437118 tptp.int) (BOUND_VARIABLE_1437119 tptp.int) (BOUND_VARIABLE_1437120 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9703 BOUND_VARIABLE_1437117) BOUND_VARIABLE_1437118) BOUND_VARIABLE_1437119) BOUND_VARIABLE_1437120) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437118) BOUND_VARIABLE_1437120)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437117) BOUND_VARIABLE_1437119)))))))))) (let ((_let_3763 (forall ((BOUND_VARIABLE_1437092 tptp.int) (BOUND_VARIABLE_1437093 tptp.int) (BOUND_VARIABLE_1437094 tptp.int) (BOUND_VARIABLE_1437095 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9704 BOUND_VARIABLE_1437092) BOUND_VARIABLE_1437093) BOUND_VARIABLE_1437094) BOUND_VARIABLE_1437095) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437093) BOUND_VARIABLE_1437095)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437092) BOUND_VARIABLE_1437094)))))))))) (let ((_let_3764 (forall ((BOUND_VARIABLE_1437067 tptp.int) (BOUND_VARIABLE_1437068 tptp.int) (BOUND_VARIABLE_1437069 tptp.int) (BOUND_VARIABLE_1437070 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9705 BOUND_VARIABLE_1437067) BOUND_VARIABLE_1437068) BOUND_VARIABLE_1437069) BOUND_VARIABLE_1437070) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437068) BOUND_VARIABLE_1437070)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437067) BOUND_VARIABLE_1437069)))))))))) (let ((_let_3765 (forall ((BOUND_VARIABLE_1437042 tptp.int) (BOUND_VARIABLE_1437043 tptp.int) (BOUND_VARIABLE_1437044 tptp.int) (BOUND_VARIABLE_1437045 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9706 BOUND_VARIABLE_1437042) BOUND_VARIABLE_1437043) BOUND_VARIABLE_1437044) BOUND_VARIABLE_1437045) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437043) BOUND_VARIABLE_1437045)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437042) BOUND_VARIABLE_1437044)))))))))) (let ((_let_3766 (forall ((BOUND_VARIABLE_1437017 tptp.int) (BOUND_VARIABLE_1437018 tptp.int) (BOUND_VARIABLE_1437019 tptp.int) (BOUND_VARIABLE_1437020 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9707 BOUND_VARIABLE_1437017) BOUND_VARIABLE_1437018) BOUND_VARIABLE_1437019) BOUND_VARIABLE_1437020) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437018) BOUND_VARIABLE_1437020)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1437017) BOUND_VARIABLE_1437019)))))))))) (let ((_let_3767 (forall ((BOUND_VARIABLE_1436992 tptp.int) (BOUND_VARIABLE_1436993 tptp.int) (BOUND_VARIABLE_1436994 tptp.int) (BOUND_VARIABLE_1436995 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9708 BOUND_VARIABLE_1436992) BOUND_VARIABLE_1436993) BOUND_VARIABLE_1436994) BOUND_VARIABLE_1436995) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436993) BOUND_VARIABLE_1436995)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436992) BOUND_VARIABLE_1436994)))))))))) (let ((_let_3768 (forall ((BOUND_VARIABLE_1436967 tptp.int) (BOUND_VARIABLE_1436968 tptp.int) (BOUND_VARIABLE_1436969 tptp.int) (BOUND_VARIABLE_1436970 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9709 BOUND_VARIABLE_1436967) BOUND_VARIABLE_1436968) BOUND_VARIABLE_1436969) BOUND_VARIABLE_1436970) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436968) BOUND_VARIABLE_1436970)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436967) BOUND_VARIABLE_1436969)))))))))) (let ((_let_3769 (forall ((BOUND_VARIABLE_1436942 tptp.int) (BOUND_VARIABLE_1436943 tptp.int) (BOUND_VARIABLE_1436944 tptp.int) (BOUND_VARIABLE_1436945 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9710 BOUND_VARIABLE_1436942) BOUND_VARIABLE_1436943) BOUND_VARIABLE_1436944) BOUND_VARIABLE_1436945) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436943) BOUND_VARIABLE_1436945)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436942) BOUND_VARIABLE_1436944)))))))))) (let ((_let_3770 (forall ((BOUND_VARIABLE_1436917 tptp.int) (BOUND_VARIABLE_1436918 tptp.int) (BOUND_VARIABLE_1436919 tptp.int) (BOUND_VARIABLE_1436920 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9711 BOUND_VARIABLE_1436917) BOUND_VARIABLE_1436918) BOUND_VARIABLE_1436919) BOUND_VARIABLE_1436920) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436918) BOUND_VARIABLE_1436920)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436917) BOUND_VARIABLE_1436919)))))))))) (let ((_let_3771 (forall ((BOUND_VARIABLE_1436892 tptp.int) (BOUND_VARIABLE_1436893 tptp.int) (BOUND_VARIABLE_1436894 tptp.int) (BOUND_VARIABLE_1436895 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9712 BOUND_VARIABLE_1436892) BOUND_VARIABLE_1436893) BOUND_VARIABLE_1436894) BOUND_VARIABLE_1436895) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436893) BOUND_VARIABLE_1436895)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436892) BOUND_VARIABLE_1436894)))))))))) (let ((_let_3772 (forall ((BOUND_VARIABLE_1436867 tptp.int) (BOUND_VARIABLE_1436868 tptp.int) (BOUND_VARIABLE_1436869 tptp.int) (BOUND_VARIABLE_1436870 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9713 BOUND_VARIABLE_1436867) BOUND_VARIABLE_1436868) BOUND_VARIABLE_1436869) BOUND_VARIABLE_1436870) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436868) BOUND_VARIABLE_1436870)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436867) BOUND_VARIABLE_1436869)))))))))) (let ((_let_3773 (forall ((BOUND_VARIABLE_1436842 tptp.int) (BOUND_VARIABLE_1436843 tptp.int) (BOUND_VARIABLE_1436844 tptp.int) (BOUND_VARIABLE_1436845 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9714 BOUND_VARIABLE_1436842) BOUND_VARIABLE_1436843) BOUND_VARIABLE_1436844) BOUND_VARIABLE_1436845) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436843) BOUND_VARIABLE_1436845)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436842) BOUND_VARIABLE_1436844)))))))))) (let ((_let_3774 (forall ((BOUND_VARIABLE_1436817 tptp.int) (BOUND_VARIABLE_1436818 tptp.int) (BOUND_VARIABLE_1436819 tptp.int) (BOUND_VARIABLE_1436820 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9715 BOUND_VARIABLE_1436817) BOUND_VARIABLE_1436818) BOUND_VARIABLE_1436819) BOUND_VARIABLE_1436820) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436818) BOUND_VARIABLE_1436820)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436817) BOUND_VARIABLE_1436819)))))))))) (let ((_let_3775 (forall ((BOUND_VARIABLE_1436792 tptp.int) (BOUND_VARIABLE_1436793 tptp.int) (BOUND_VARIABLE_1436794 tptp.int) (BOUND_VARIABLE_1436795 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9716 BOUND_VARIABLE_1436792) BOUND_VARIABLE_1436793) BOUND_VARIABLE_1436794) BOUND_VARIABLE_1436795) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436793) BOUND_VARIABLE_1436795)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436792) BOUND_VARIABLE_1436794)))))))))) (let ((_let_3776 (forall ((BOUND_VARIABLE_1436767 tptp.int) (BOUND_VARIABLE_1436768 tptp.int) (BOUND_VARIABLE_1436769 tptp.int) (BOUND_VARIABLE_1436770 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9717 BOUND_VARIABLE_1436767) BOUND_VARIABLE_1436768) BOUND_VARIABLE_1436769) BOUND_VARIABLE_1436770) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436768) BOUND_VARIABLE_1436770)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436767) BOUND_VARIABLE_1436769)))))))))) (let ((_let_3777 (forall ((BOUND_VARIABLE_1436742 tptp.int) (BOUND_VARIABLE_1436743 tptp.int) (BOUND_VARIABLE_1436744 tptp.int) (BOUND_VARIABLE_1436745 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9718 BOUND_VARIABLE_1436742) BOUND_VARIABLE_1436743) BOUND_VARIABLE_1436744) BOUND_VARIABLE_1436745) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436743) BOUND_VARIABLE_1436745)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436742) BOUND_VARIABLE_1436744)))))))))) (let ((_let_3778 (forall ((BOUND_VARIABLE_1436717 tptp.int) (BOUND_VARIABLE_1436718 tptp.int) (BOUND_VARIABLE_1436719 tptp.int) (BOUND_VARIABLE_1436720 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9719 BOUND_VARIABLE_1436717) BOUND_VARIABLE_1436718) BOUND_VARIABLE_1436719) BOUND_VARIABLE_1436720) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436718) BOUND_VARIABLE_1436720)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436717) BOUND_VARIABLE_1436719)))))))))) (let ((_let_3779 (forall ((BOUND_VARIABLE_1436692 tptp.int) (BOUND_VARIABLE_1436693 tptp.int) (BOUND_VARIABLE_1436694 tptp.int) (BOUND_VARIABLE_1436695 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9720 BOUND_VARIABLE_1436692) BOUND_VARIABLE_1436693) BOUND_VARIABLE_1436694) BOUND_VARIABLE_1436695) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436693) BOUND_VARIABLE_1436695)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436692) BOUND_VARIABLE_1436694)))))))))) (let ((_let_3780 (forall ((BOUND_VARIABLE_1436667 tptp.int) (BOUND_VARIABLE_1436668 tptp.int) (BOUND_VARIABLE_1436669 tptp.int) (BOUND_VARIABLE_1436670 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9721 BOUND_VARIABLE_1436667) BOUND_VARIABLE_1436668) BOUND_VARIABLE_1436669) BOUND_VARIABLE_1436670) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436668) BOUND_VARIABLE_1436670)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436667) BOUND_VARIABLE_1436669)))))))))) (let ((_let_3781 (forall ((BOUND_VARIABLE_1436642 tptp.int) (BOUND_VARIABLE_1436643 tptp.int) (BOUND_VARIABLE_1436644 tptp.int) (BOUND_VARIABLE_1436645 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9722 BOUND_VARIABLE_1436642) BOUND_VARIABLE_1436643) BOUND_VARIABLE_1436644) BOUND_VARIABLE_1436645) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436643) BOUND_VARIABLE_1436645)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436642) BOUND_VARIABLE_1436644)))))))))) (let ((_let_3782 (forall ((BOUND_VARIABLE_1436617 tptp.int) (BOUND_VARIABLE_1436618 tptp.int) (BOUND_VARIABLE_1436619 tptp.int) (BOUND_VARIABLE_1436620 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9723 BOUND_VARIABLE_1436617) BOUND_VARIABLE_1436618) BOUND_VARIABLE_1436619) BOUND_VARIABLE_1436620) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436618) BOUND_VARIABLE_1436620)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436617) BOUND_VARIABLE_1436619)))))))))) (let ((_let_3783 (forall ((BOUND_VARIABLE_1436592 tptp.int) (BOUND_VARIABLE_1436593 tptp.int) (BOUND_VARIABLE_1436594 tptp.int) (BOUND_VARIABLE_1436595 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9724 BOUND_VARIABLE_1436592) BOUND_VARIABLE_1436593) BOUND_VARIABLE_1436594) BOUND_VARIABLE_1436595) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436593) BOUND_VARIABLE_1436595)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436592) BOUND_VARIABLE_1436594)))))))))) (let ((_let_3784 (forall ((BOUND_VARIABLE_1436567 tptp.int) (BOUND_VARIABLE_1436568 tptp.int) (BOUND_VARIABLE_1436569 tptp.int) (BOUND_VARIABLE_1436570 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9725 BOUND_VARIABLE_1436567) BOUND_VARIABLE_1436568) BOUND_VARIABLE_1436569) BOUND_VARIABLE_1436570) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436568) BOUND_VARIABLE_1436570)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436567) BOUND_VARIABLE_1436569)))))))))) (let ((_let_3785 (forall ((BOUND_VARIABLE_1436542 tptp.int) (BOUND_VARIABLE_1436543 tptp.int) (BOUND_VARIABLE_1436544 tptp.int) (BOUND_VARIABLE_1436545 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9726 BOUND_VARIABLE_1436542) BOUND_VARIABLE_1436543) BOUND_VARIABLE_1436544) BOUND_VARIABLE_1436545) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436543) BOUND_VARIABLE_1436545)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436542) BOUND_VARIABLE_1436544)))))))))) (let ((_let_3786 (forall ((BOUND_VARIABLE_1436517 tptp.int) (BOUND_VARIABLE_1436518 tptp.int) (BOUND_VARIABLE_1436519 tptp.int) (BOUND_VARIABLE_1436520 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9727 BOUND_VARIABLE_1436517) BOUND_VARIABLE_1436518) BOUND_VARIABLE_1436519) BOUND_VARIABLE_1436520) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436518) BOUND_VARIABLE_1436520)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436517) BOUND_VARIABLE_1436519)))))))))) (let ((_let_3787 (forall ((BOUND_VARIABLE_1436492 tptp.int) (BOUND_VARIABLE_1436493 tptp.int) (BOUND_VARIABLE_1436494 tptp.int) (BOUND_VARIABLE_1436495 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9728 BOUND_VARIABLE_1436492) BOUND_VARIABLE_1436493) BOUND_VARIABLE_1436494) BOUND_VARIABLE_1436495) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436493) BOUND_VARIABLE_1436495)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436492) BOUND_VARIABLE_1436494)))))))))) (let ((_let_3788 (forall ((BOUND_VARIABLE_1436467 tptp.int) (BOUND_VARIABLE_1436468 tptp.int) (BOUND_VARIABLE_1436469 tptp.int) (BOUND_VARIABLE_1436470 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9729 BOUND_VARIABLE_1436467) BOUND_VARIABLE_1436468) BOUND_VARIABLE_1436469) BOUND_VARIABLE_1436470) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436468) BOUND_VARIABLE_1436470)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436467) BOUND_VARIABLE_1436469)))))))))) (let ((_let_3789 (forall ((BOUND_VARIABLE_1436442 tptp.int) (BOUND_VARIABLE_1436443 tptp.int) (BOUND_VARIABLE_1436444 tptp.int) (BOUND_VARIABLE_1436445 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9730 BOUND_VARIABLE_1436442) BOUND_VARIABLE_1436443) BOUND_VARIABLE_1436444) BOUND_VARIABLE_1436445) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436443) BOUND_VARIABLE_1436445)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436442) BOUND_VARIABLE_1436444)))))))))) (let ((_let_3790 (forall ((BOUND_VARIABLE_1436417 tptp.int) (BOUND_VARIABLE_1436418 tptp.int) (BOUND_VARIABLE_1436419 tptp.int) (BOUND_VARIABLE_1436420 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9731 BOUND_VARIABLE_1436417) BOUND_VARIABLE_1436418) BOUND_VARIABLE_1436419) BOUND_VARIABLE_1436420) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436418) BOUND_VARIABLE_1436420)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436417) BOUND_VARIABLE_1436419)))))))))) (let ((_let_3791 (forall ((BOUND_VARIABLE_1436392 tptp.int) (BOUND_VARIABLE_1436393 tptp.int) (BOUND_VARIABLE_1436394 tptp.int) (BOUND_VARIABLE_1436395 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9732 BOUND_VARIABLE_1436392) BOUND_VARIABLE_1436393) BOUND_VARIABLE_1436394) BOUND_VARIABLE_1436395) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436393) BOUND_VARIABLE_1436395)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436392) BOUND_VARIABLE_1436394)))))))))) (let ((_let_3792 (forall ((BOUND_VARIABLE_1436367 tptp.int) (BOUND_VARIABLE_1436368 tptp.int) (BOUND_VARIABLE_1436369 tptp.int) (BOUND_VARIABLE_1436370 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9733 BOUND_VARIABLE_1436367) BOUND_VARIABLE_1436368) BOUND_VARIABLE_1436369) BOUND_VARIABLE_1436370) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436368) BOUND_VARIABLE_1436370)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436367) BOUND_VARIABLE_1436369)))))))))) (let ((_let_3793 (forall ((BOUND_VARIABLE_1436342 tptp.int) (BOUND_VARIABLE_1436343 tptp.int) (BOUND_VARIABLE_1436344 tptp.int) (BOUND_VARIABLE_1436345 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9734 BOUND_VARIABLE_1436342) BOUND_VARIABLE_1436343) BOUND_VARIABLE_1436344) BOUND_VARIABLE_1436345) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436343) BOUND_VARIABLE_1436345)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436342) BOUND_VARIABLE_1436344)))))))))) (let ((_let_3794 (forall ((BOUND_VARIABLE_1436317 tptp.int) (BOUND_VARIABLE_1436318 tptp.int) (BOUND_VARIABLE_1436319 tptp.int) (BOUND_VARIABLE_1436320 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9735 BOUND_VARIABLE_1436317) BOUND_VARIABLE_1436318) BOUND_VARIABLE_1436319) BOUND_VARIABLE_1436320) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436318) BOUND_VARIABLE_1436320)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436317) BOUND_VARIABLE_1436319)))))))))) (let ((_let_3795 (forall ((BOUND_VARIABLE_1436292 tptp.int) (BOUND_VARIABLE_1436293 tptp.int) (BOUND_VARIABLE_1436294 tptp.int) (BOUND_VARIABLE_1436295 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9736 BOUND_VARIABLE_1436292) BOUND_VARIABLE_1436293) BOUND_VARIABLE_1436294) BOUND_VARIABLE_1436295) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436293) BOUND_VARIABLE_1436295)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436292) BOUND_VARIABLE_1436294)))))))))) (let ((_let_3796 (forall ((BOUND_VARIABLE_1436267 tptp.int) (BOUND_VARIABLE_1436268 tptp.int) (BOUND_VARIABLE_1436269 tptp.int) (BOUND_VARIABLE_1436270 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9737 BOUND_VARIABLE_1436267) BOUND_VARIABLE_1436268) BOUND_VARIABLE_1436269) BOUND_VARIABLE_1436270) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436268) BOUND_VARIABLE_1436270)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436267) BOUND_VARIABLE_1436269)))))))))) (let ((_let_3797 (forall ((BOUND_VARIABLE_1436242 tptp.int) (BOUND_VARIABLE_1436243 tptp.int) (BOUND_VARIABLE_1436244 tptp.int) (BOUND_VARIABLE_1436245 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9738 BOUND_VARIABLE_1436242) BOUND_VARIABLE_1436243) BOUND_VARIABLE_1436244) BOUND_VARIABLE_1436245) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436243) BOUND_VARIABLE_1436245)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436242) BOUND_VARIABLE_1436244)))))))))) (let ((_let_3798 (forall ((BOUND_VARIABLE_1436217 tptp.int) (BOUND_VARIABLE_1436218 tptp.int) (BOUND_VARIABLE_1436219 tptp.int) (BOUND_VARIABLE_1436220 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9739 BOUND_VARIABLE_1436217) BOUND_VARIABLE_1436218) BOUND_VARIABLE_1436219) BOUND_VARIABLE_1436220) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436218) BOUND_VARIABLE_1436220)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436217) BOUND_VARIABLE_1436219)))))))))) (let ((_let_3799 (forall ((BOUND_VARIABLE_1436192 tptp.int) (BOUND_VARIABLE_1436193 tptp.int) (BOUND_VARIABLE_1436194 tptp.int) (BOUND_VARIABLE_1436195 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9740 BOUND_VARIABLE_1436192) BOUND_VARIABLE_1436193) BOUND_VARIABLE_1436194) BOUND_VARIABLE_1436195) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436193) BOUND_VARIABLE_1436195)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436192) BOUND_VARIABLE_1436194)))))))))) (let ((_let_3800 (forall ((BOUND_VARIABLE_1436167 tptp.int) (BOUND_VARIABLE_1436168 tptp.int) (BOUND_VARIABLE_1436169 tptp.int) (BOUND_VARIABLE_1436170 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9741 BOUND_VARIABLE_1436167) BOUND_VARIABLE_1436168) BOUND_VARIABLE_1436169) BOUND_VARIABLE_1436170) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436168) BOUND_VARIABLE_1436170)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436167) BOUND_VARIABLE_1436169)))))))))) (let ((_let_3801 (forall ((BOUND_VARIABLE_1436142 tptp.int) (BOUND_VARIABLE_1436143 tptp.int) (BOUND_VARIABLE_1436144 tptp.int) (BOUND_VARIABLE_1436145 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9742 BOUND_VARIABLE_1436142) BOUND_VARIABLE_1436143) BOUND_VARIABLE_1436144) BOUND_VARIABLE_1436145) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436143) BOUND_VARIABLE_1436145)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436142) BOUND_VARIABLE_1436144)))))))))) (let ((_let_3802 (forall ((BOUND_VARIABLE_1436117 tptp.int) (BOUND_VARIABLE_1436118 tptp.int) (BOUND_VARIABLE_1436119 tptp.int) (BOUND_VARIABLE_1436120 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9743 BOUND_VARIABLE_1436117) BOUND_VARIABLE_1436118) BOUND_VARIABLE_1436119) BOUND_VARIABLE_1436120) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436118) BOUND_VARIABLE_1436120)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436117) BOUND_VARIABLE_1436119)))))))))) (let ((_let_3803 (forall ((BOUND_VARIABLE_1436092 tptp.int) (BOUND_VARIABLE_1436093 tptp.int) (BOUND_VARIABLE_1436094 tptp.int) (BOUND_VARIABLE_1436095 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9744 BOUND_VARIABLE_1436092) BOUND_VARIABLE_1436093) BOUND_VARIABLE_1436094) BOUND_VARIABLE_1436095) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436093) BOUND_VARIABLE_1436095)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436092) BOUND_VARIABLE_1436094)))))))))) (let ((_let_3804 (forall ((BOUND_VARIABLE_1436067 tptp.int) (BOUND_VARIABLE_1436068 tptp.int) (BOUND_VARIABLE_1436069 tptp.int) (BOUND_VARIABLE_1436070 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9745 BOUND_VARIABLE_1436067) BOUND_VARIABLE_1436068) BOUND_VARIABLE_1436069) BOUND_VARIABLE_1436070) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436068) BOUND_VARIABLE_1436070)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436067) BOUND_VARIABLE_1436069)))))))))) (let ((_let_3805 (forall ((BOUND_VARIABLE_1436042 tptp.int) (BOUND_VARIABLE_1436043 tptp.int) (BOUND_VARIABLE_1436044 tptp.int) (BOUND_VARIABLE_1436045 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9746 BOUND_VARIABLE_1436042) BOUND_VARIABLE_1436043) BOUND_VARIABLE_1436044) BOUND_VARIABLE_1436045) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436043) BOUND_VARIABLE_1436045)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436042) BOUND_VARIABLE_1436044)))))))))) (let ((_let_3806 (forall ((BOUND_VARIABLE_1436017 tptp.int) (BOUND_VARIABLE_1436018 tptp.int) (BOUND_VARIABLE_1436019 tptp.int) (BOUND_VARIABLE_1436020 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9747 BOUND_VARIABLE_1436017) BOUND_VARIABLE_1436018) BOUND_VARIABLE_1436019) BOUND_VARIABLE_1436020) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436018) BOUND_VARIABLE_1436020)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1436017) BOUND_VARIABLE_1436019)))))))))) (let ((_let_3807 (forall ((BOUND_VARIABLE_1435992 tptp.int) (BOUND_VARIABLE_1435993 tptp.int) (BOUND_VARIABLE_1435994 tptp.int) (BOUND_VARIABLE_1435995 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9748 BOUND_VARIABLE_1435992) BOUND_VARIABLE_1435993) BOUND_VARIABLE_1435994) BOUND_VARIABLE_1435995) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435993) BOUND_VARIABLE_1435995)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435992) BOUND_VARIABLE_1435994)))))))))) (let ((_let_3808 (forall ((BOUND_VARIABLE_1435967 tptp.int) (BOUND_VARIABLE_1435968 tptp.int) (BOUND_VARIABLE_1435969 tptp.int) (BOUND_VARIABLE_1435970 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9749 BOUND_VARIABLE_1435967) BOUND_VARIABLE_1435968) BOUND_VARIABLE_1435969) BOUND_VARIABLE_1435970) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435968) BOUND_VARIABLE_1435970)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435967) BOUND_VARIABLE_1435969)))))))))) (let ((_let_3809 (forall ((BOUND_VARIABLE_1435942 tptp.int) (BOUND_VARIABLE_1435943 tptp.int) (BOUND_VARIABLE_1435944 tptp.int) (BOUND_VARIABLE_1435945 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9750 BOUND_VARIABLE_1435942) BOUND_VARIABLE_1435943) BOUND_VARIABLE_1435944) BOUND_VARIABLE_1435945) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435943) BOUND_VARIABLE_1435945)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435942) BOUND_VARIABLE_1435944)))))))))) (let ((_let_3810 (forall ((BOUND_VARIABLE_1435917 tptp.int) (BOUND_VARIABLE_1435918 tptp.int) (BOUND_VARIABLE_1435919 tptp.int) (BOUND_VARIABLE_1435920 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9751 BOUND_VARIABLE_1435917) BOUND_VARIABLE_1435918) BOUND_VARIABLE_1435919) BOUND_VARIABLE_1435920) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435918) BOUND_VARIABLE_1435920)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435917) BOUND_VARIABLE_1435919)))))))))) (let ((_let_3811 (forall ((BOUND_VARIABLE_1435892 tptp.int) (BOUND_VARIABLE_1435893 tptp.int) (BOUND_VARIABLE_1435894 tptp.int) (BOUND_VARIABLE_1435895 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9752 BOUND_VARIABLE_1435892) BOUND_VARIABLE_1435893) BOUND_VARIABLE_1435894) BOUND_VARIABLE_1435895) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435893) BOUND_VARIABLE_1435895)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435892) BOUND_VARIABLE_1435894)))))))))) (let ((_let_3812 (forall ((BOUND_VARIABLE_1435867 tptp.int) (BOUND_VARIABLE_1435868 tptp.int) (BOUND_VARIABLE_1435869 tptp.int) (BOUND_VARIABLE_1435870 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9753 BOUND_VARIABLE_1435867) BOUND_VARIABLE_1435868) BOUND_VARIABLE_1435869) BOUND_VARIABLE_1435870) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435868) BOUND_VARIABLE_1435870)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435867) BOUND_VARIABLE_1435869)))))))))) (let ((_let_3813 (forall ((BOUND_VARIABLE_1435842 tptp.int) (BOUND_VARIABLE_1435843 tptp.int) (BOUND_VARIABLE_1435844 tptp.int) (BOUND_VARIABLE_1435845 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9754 BOUND_VARIABLE_1435842) BOUND_VARIABLE_1435843) BOUND_VARIABLE_1435844) BOUND_VARIABLE_1435845) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435843) BOUND_VARIABLE_1435845)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435842) BOUND_VARIABLE_1435844)))))))))) (let ((_let_3814 (forall ((BOUND_VARIABLE_1435817 tptp.int) (BOUND_VARIABLE_1435818 tptp.int) (BOUND_VARIABLE_1435819 tptp.int) (BOUND_VARIABLE_1435820 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9755 BOUND_VARIABLE_1435817) BOUND_VARIABLE_1435818) BOUND_VARIABLE_1435819) BOUND_VARIABLE_1435820) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435818) BOUND_VARIABLE_1435820)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435817) BOUND_VARIABLE_1435819)))))))))) (let ((_let_3815 (forall ((BOUND_VARIABLE_1435792 tptp.int) (BOUND_VARIABLE_1435793 tptp.int) (BOUND_VARIABLE_1435794 tptp.int) (BOUND_VARIABLE_1435795 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9756 BOUND_VARIABLE_1435792) BOUND_VARIABLE_1435793) BOUND_VARIABLE_1435794) BOUND_VARIABLE_1435795) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435793) BOUND_VARIABLE_1435795)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435792) BOUND_VARIABLE_1435794)))))))))) (let ((_let_3816 (forall ((BOUND_VARIABLE_1435767 tptp.int) (BOUND_VARIABLE_1435768 tptp.int) (BOUND_VARIABLE_1435769 tptp.int) (BOUND_VARIABLE_1435770 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9757 BOUND_VARIABLE_1435767) BOUND_VARIABLE_1435768) BOUND_VARIABLE_1435769) BOUND_VARIABLE_1435770) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435768) BOUND_VARIABLE_1435770)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435767) BOUND_VARIABLE_1435769)))))))))) (let ((_let_3817 (forall ((BOUND_VARIABLE_1435742 tptp.int) (BOUND_VARIABLE_1435743 tptp.int) (BOUND_VARIABLE_1435744 tptp.int) (BOUND_VARIABLE_1435745 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9758 BOUND_VARIABLE_1435742) BOUND_VARIABLE_1435743) BOUND_VARIABLE_1435744) BOUND_VARIABLE_1435745) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435743) BOUND_VARIABLE_1435745)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435742) BOUND_VARIABLE_1435744)))))))))) (let ((_let_3818 (forall ((BOUND_VARIABLE_1435717 tptp.int) (BOUND_VARIABLE_1435718 tptp.int) (BOUND_VARIABLE_1435719 tptp.int) (BOUND_VARIABLE_1435720 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9759 BOUND_VARIABLE_1435717) BOUND_VARIABLE_1435718) BOUND_VARIABLE_1435719) BOUND_VARIABLE_1435720) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435718) BOUND_VARIABLE_1435720)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435717) BOUND_VARIABLE_1435719)))))))))) (let ((_let_3819 (forall ((BOUND_VARIABLE_1435692 tptp.int) (BOUND_VARIABLE_1435693 tptp.int) (BOUND_VARIABLE_1435694 tptp.int) (BOUND_VARIABLE_1435695 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9760 BOUND_VARIABLE_1435692) BOUND_VARIABLE_1435693) BOUND_VARIABLE_1435694) BOUND_VARIABLE_1435695) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435693) BOUND_VARIABLE_1435695)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435692) BOUND_VARIABLE_1435694)))))))))) (let ((_let_3820 (forall ((BOUND_VARIABLE_1435667 tptp.int) (BOUND_VARIABLE_1435668 tptp.int) (BOUND_VARIABLE_1435669 tptp.int) (BOUND_VARIABLE_1435670 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9761 BOUND_VARIABLE_1435667) BOUND_VARIABLE_1435668) BOUND_VARIABLE_1435669) BOUND_VARIABLE_1435670) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435668) BOUND_VARIABLE_1435670)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435667) BOUND_VARIABLE_1435669)))))))))) (let ((_let_3821 (forall ((BOUND_VARIABLE_1435642 tptp.int) (BOUND_VARIABLE_1435643 tptp.int) (BOUND_VARIABLE_1435644 tptp.int) (BOUND_VARIABLE_1435645 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9762 BOUND_VARIABLE_1435642) BOUND_VARIABLE_1435643) BOUND_VARIABLE_1435644) BOUND_VARIABLE_1435645) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435643) BOUND_VARIABLE_1435645)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435642) BOUND_VARIABLE_1435644)))))))))) (let ((_let_3822 (forall ((BOUND_VARIABLE_1435617 tptp.int) (BOUND_VARIABLE_1435618 tptp.int) (BOUND_VARIABLE_1435619 tptp.int) (BOUND_VARIABLE_1435620 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9763 BOUND_VARIABLE_1435617) BOUND_VARIABLE_1435618) BOUND_VARIABLE_1435619) BOUND_VARIABLE_1435620) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435618) BOUND_VARIABLE_1435620)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435617) BOUND_VARIABLE_1435619)))))))))) (let ((_let_3823 (forall ((BOUND_VARIABLE_1435592 tptp.int) (BOUND_VARIABLE_1435593 tptp.int) (BOUND_VARIABLE_1435594 tptp.int) (BOUND_VARIABLE_1435595 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9764 BOUND_VARIABLE_1435592) BOUND_VARIABLE_1435593) BOUND_VARIABLE_1435594) BOUND_VARIABLE_1435595) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435593) BOUND_VARIABLE_1435595)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435592) BOUND_VARIABLE_1435594)))))))))) (let ((_let_3824 (forall ((BOUND_VARIABLE_1435567 tptp.int) (BOUND_VARIABLE_1435568 tptp.int) (BOUND_VARIABLE_1435569 tptp.int) (BOUND_VARIABLE_1435570 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9765 BOUND_VARIABLE_1435567) BOUND_VARIABLE_1435568) BOUND_VARIABLE_1435569) BOUND_VARIABLE_1435570) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435568) BOUND_VARIABLE_1435570)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435567) BOUND_VARIABLE_1435569)))))))))) (let ((_let_3825 (forall ((BOUND_VARIABLE_1435542 tptp.int) (BOUND_VARIABLE_1435543 tptp.int) (BOUND_VARIABLE_1435544 tptp.int) (BOUND_VARIABLE_1435545 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9766 BOUND_VARIABLE_1435542) BOUND_VARIABLE_1435543) BOUND_VARIABLE_1435544) BOUND_VARIABLE_1435545) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435543) BOUND_VARIABLE_1435545)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435542) BOUND_VARIABLE_1435544)))))))))) (let ((_let_3826 (forall ((BOUND_VARIABLE_1435517 tptp.int) (BOUND_VARIABLE_1435518 tptp.int) (BOUND_VARIABLE_1435519 tptp.int) (BOUND_VARIABLE_1435520 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9767 BOUND_VARIABLE_1435517) BOUND_VARIABLE_1435518) BOUND_VARIABLE_1435519) BOUND_VARIABLE_1435520) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435518) BOUND_VARIABLE_1435520)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435517) BOUND_VARIABLE_1435519)))))))))) (let ((_let_3827 (forall ((BOUND_VARIABLE_1435492 tptp.int) (BOUND_VARIABLE_1435493 tptp.int) (BOUND_VARIABLE_1435494 tptp.int) (BOUND_VARIABLE_1435495 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9768 BOUND_VARIABLE_1435492) BOUND_VARIABLE_1435493) BOUND_VARIABLE_1435494) BOUND_VARIABLE_1435495) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435493) BOUND_VARIABLE_1435495)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435492) BOUND_VARIABLE_1435494)))))))))) (let ((_let_3828 (forall ((BOUND_VARIABLE_1435467 tptp.int) (BOUND_VARIABLE_1435468 tptp.int) (BOUND_VARIABLE_1435469 tptp.int) (BOUND_VARIABLE_1435470 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9769 BOUND_VARIABLE_1435467) BOUND_VARIABLE_1435468) BOUND_VARIABLE_1435469) BOUND_VARIABLE_1435470) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435468) BOUND_VARIABLE_1435470)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435467) BOUND_VARIABLE_1435469)))))))))) (let ((_let_3829 (forall ((BOUND_VARIABLE_1435442 tptp.int) (BOUND_VARIABLE_1435443 tptp.int) (BOUND_VARIABLE_1435444 tptp.int) (BOUND_VARIABLE_1435445 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9770 BOUND_VARIABLE_1435442) BOUND_VARIABLE_1435443) BOUND_VARIABLE_1435444) BOUND_VARIABLE_1435445) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435443) BOUND_VARIABLE_1435445)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435442) BOUND_VARIABLE_1435444)))))))))) (let ((_let_3830 (forall ((BOUND_VARIABLE_1435417 tptp.int) (BOUND_VARIABLE_1435418 tptp.int) (BOUND_VARIABLE_1435419 tptp.int) (BOUND_VARIABLE_1435420 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9771 BOUND_VARIABLE_1435417) BOUND_VARIABLE_1435418) BOUND_VARIABLE_1435419) BOUND_VARIABLE_1435420) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435418) BOUND_VARIABLE_1435420)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435417) BOUND_VARIABLE_1435419)))))))))) (let ((_let_3831 (forall ((BOUND_VARIABLE_1435392 tptp.int) (BOUND_VARIABLE_1435393 tptp.int) (BOUND_VARIABLE_1435394 tptp.int) (BOUND_VARIABLE_1435395 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9772 BOUND_VARIABLE_1435392) BOUND_VARIABLE_1435393) BOUND_VARIABLE_1435394) BOUND_VARIABLE_1435395) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435393) BOUND_VARIABLE_1435395)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435392) BOUND_VARIABLE_1435394)))))))))) (let ((_let_3832 (forall ((BOUND_VARIABLE_1435367 tptp.int) (BOUND_VARIABLE_1435368 tptp.int) (BOUND_VARIABLE_1435369 tptp.int) (BOUND_VARIABLE_1435370 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9773 BOUND_VARIABLE_1435367) BOUND_VARIABLE_1435368) BOUND_VARIABLE_1435369) BOUND_VARIABLE_1435370) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435368) BOUND_VARIABLE_1435370)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435367) BOUND_VARIABLE_1435369)))))))))) (let ((_let_3833 (forall ((BOUND_VARIABLE_1435342 tptp.int) (BOUND_VARIABLE_1435343 tptp.int) (BOUND_VARIABLE_1435344 tptp.int) (BOUND_VARIABLE_1435345 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9774 BOUND_VARIABLE_1435342) BOUND_VARIABLE_1435343) BOUND_VARIABLE_1435344) BOUND_VARIABLE_1435345) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435343) BOUND_VARIABLE_1435345)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435342) BOUND_VARIABLE_1435344)))))))))) (let ((_let_3834 (forall ((BOUND_VARIABLE_1435317 tptp.int) (BOUND_VARIABLE_1435318 tptp.int) (BOUND_VARIABLE_1435319 tptp.int) (BOUND_VARIABLE_1435320 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9775 BOUND_VARIABLE_1435317) BOUND_VARIABLE_1435318) BOUND_VARIABLE_1435319) BOUND_VARIABLE_1435320) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435318) BOUND_VARIABLE_1435320)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435317) BOUND_VARIABLE_1435319)))))))))) (let ((_let_3835 (forall ((BOUND_VARIABLE_1435292 tptp.int) (BOUND_VARIABLE_1435293 tptp.int) (BOUND_VARIABLE_1435294 tptp.int) (BOUND_VARIABLE_1435295 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9776 BOUND_VARIABLE_1435292) BOUND_VARIABLE_1435293) BOUND_VARIABLE_1435294) BOUND_VARIABLE_1435295) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435293) BOUND_VARIABLE_1435295)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435292) BOUND_VARIABLE_1435294)))))))))) (let ((_let_3836 (forall ((BOUND_VARIABLE_1435267 tptp.int) (BOUND_VARIABLE_1435268 tptp.int) (BOUND_VARIABLE_1435269 tptp.int) (BOUND_VARIABLE_1435270 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9777 BOUND_VARIABLE_1435267) BOUND_VARIABLE_1435268) BOUND_VARIABLE_1435269) BOUND_VARIABLE_1435270) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435268) BOUND_VARIABLE_1435270)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435267) BOUND_VARIABLE_1435269)))))))))) (let ((_let_3837 (forall ((BOUND_VARIABLE_1435242 tptp.int) (BOUND_VARIABLE_1435243 tptp.int) (BOUND_VARIABLE_1435244 tptp.int) (BOUND_VARIABLE_1435245 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9778 BOUND_VARIABLE_1435242) BOUND_VARIABLE_1435243) BOUND_VARIABLE_1435244) BOUND_VARIABLE_1435245) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435243) BOUND_VARIABLE_1435245)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435242) BOUND_VARIABLE_1435244)))))))))) (let ((_let_3838 (forall ((BOUND_VARIABLE_1435217 tptp.int) (BOUND_VARIABLE_1435218 tptp.int) (BOUND_VARIABLE_1435219 tptp.int) (BOUND_VARIABLE_1435220 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9779 BOUND_VARIABLE_1435217) BOUND_VARIABLE_1435218) BOUND_VARIABLE_1435219) BOUND_VARIABLE_1435220) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435218) BOUND_VARIABLE_1435220)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435217) BOUND_VARIABLE_1435219)))))))))) (let ((_let_3839 (forall ((BOUND_VARIABLE_1435192 tptp.int) (BOUND_VARIABLE_1435193 tptp.int) (BOUND_VARIABLE_1435194 tptp.int) (BOUND_VARIABLE_1435195 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9780 BOUND_VARIABLE_1435192) BOUND_VARIABLE_1435193) BOUND_VARIABLE_1435194) BOUND_VARIABLE_1435195) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435193) BOUND_VARIABLE_1435195)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435192) BOUND_VARIABLE_1435194)))))))))) (let ((_let_3840 (forall ((BOUND_VARIABLE_1435167 tptp.int) (BOUND_VARIABLE_1435168 tptp.int) (BOUND_VARIABLE_1435169 tptp.int) (BOUND_VARIABLE_1435170 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9781 BOUND_VARIABLE_1435167) BOUND_VARIABLE_1435168) BOUND_VARIABLE_1435169) BOUND_VARIABLE_1435170) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435168) BOUND_VARIABLE_1435170)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435167) BOUND_VARIABLE_1435169)))))))))) (let ((_let_3841 (forall ((BOUND_VARIABLE_1435142 tptp.int) (BOUND_VARIABLE_1435143 tptp.int) (BOUND_VARIABLE_1435144 tptp.int) (BOUND_VARIABLE_1435145 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9782 BOUND_VARIABLE_1435142) BOUND_VARIABLE_1435143) BOUND_VARIABLE_1435144) BOUND_VARIABLE_1435145) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435143) BOUND_VARIABLE_1435145)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435142) BOUND_VARIABLE_1435144)))))))))) (let ((_let_3842 (forall ((BOUND_VARIABLE_1435100 tptp.rat) (BOUND_VARIABLE_1435101 tptp.int) (BOUND_VARIABLE_1435102 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7615 BOUND_VARIABLE_1435102) BOUND_VARIABLE_1435101)) (ho_7630 k_7629 BOUND_VARIABLE_1435100)) (ho_7496 (ho_7495 (ho_7635 k_9783 BOUND_VARIABLE_1435100) BOUND_VARIABLE_1435101) BOUND_VARIABLE_1435102))))) (let ((_let_3843 (forall ((BOUND_VARIABLE_1435058 tptp.rat) (BOUND_VARIABLE_1435059 tptp.int) (BOUND_VARIABLE_1435060 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7616 BOUND_VARIABLE_1435060) BOUND_VARIABLE_1435059)) (ho_7630 k_7629 BOUND_VARIABLE_1435058)) (ho_7496 (ho_7495 (ho_7635 k_9784 BOUND_VARIABLE_1435058) BOUND_VARIABLE_1435059) BOUND_VARIABLE_1435060))))) (let ((_let_3844 (forall ((BOUND_VARIABLE_1435033 tptp.int) (BOUND_VARIABLE_1435034 tptp.int) (BOUND_VARIABLE_1435035 tptp.int) (BOUND_VARIABLE_1435036 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9785 BOUND_VARIABLE_1435033) BOUND_VARIABLE_1435034) BOUND_VARIABLE_1435035) BOUND_VARIABLE_1435036) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435034) BOUND_VARIABLE_1435036)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435033) BOUND_VARIABLE_1435035)))))))))) (let ((_let_3845 (forall ((BOUND_VARIABLE_1435008 tptp.int) (BOUND_VARIABLE_1435009 tptp.int) (BOUND_VARIABLE_1435010 tptp.int) (BOUND_VARIABLE_1435011 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9786 BOUND_VARIABLE_1435008) BOUND_VARIABLE_1435009) BOUND_VARIABLE_1435010) BOUND_VARIABLE_1435011) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435009) BOUND_VARIABLE_1435011)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1435008) BOUND_VARIABLE_1435010)))))))))) (let ((_let_3846 (forall ((BOUND_VARIABLE_1434983 tptp.int) (BOUND_VARIABLE_1434984 tptp.int) (BOUND_VARIABLE_1434985 tptp.int) (BOUND_VARIABLE_1434986 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9787 BOUND_VARIABLE_1434983) BOUND_VARIABLE_1434984) BOUND_VARIABLE_1434985) BOUND_VARIABLE_1434986) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434984) BOUND_VARIABLE_1434986)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434983) BOUND_VARIABLE_1434985)))))))))) (let ((_let_3847 (forall ((BOUND_VARIABLE_1434941 tptp.rat) (BOUND_VARIABLE_1434942 tptp.int) (BOUND_VARIABLE_1434943 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7617 BOUND_VARIABLE_1434943) BOUND_VARIABLE_1434942)) (ho_7630 k_7629 BOUND_VARIABLE_1434941)) (ho_7496 (ho_7495 (ho_7635 k_9788 BOUND_VARIABLE_1434941) BOUND_VARIABLE_1434942) BOUND_VARIABLE_1434943))))) (let ((_let_3848 (forall ((BOUND_VARIABLE_1434899 tptp.rat) (BOUND_VARIABLE_1434900 tptp.int) (BOUND_VARIABLE_1434901 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7618 BOUND_VARIABLE_1434901) BOUND_VARIABLE_1434900)) (ho_7630 k_7629 BOUND_VARIABLE_1434899)) (ho_7496 (ho_7495 (ho_7635 k_9789 BOUND_VARIABLE_1434899) BOUND_VARIABLE_1434900) BOUND_VARIABLE_1434901))))) (let ((_let_3849 (forall ((BOUND_VARIABLE_1434874 tptp.int) (BOUND_VARIABLE_1434875 tptp.int) (BOUND_VARIABLE_1434876 tptp.int) (BOUND_VARIABLE_1434877 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9790 BOUND_VARIABLE_1434874) BOUND_VARIABLE_1434875) BOUND_VARIABLE_1434876) BOUND_VARIABLE_1434877) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434875) BOUND_VARIABLE_1434877)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434874) BOUND_VARIABLE_1434876)))))))))) (let ((_let_3850 (forall ((BOUND_VARIABLE_1434849 tptp.int) (BOUND_VARIABLE_1434850 tptp.int) (BOUND_VARIABLE_1434851 tptp.int) (BOUND_VARIABLE_1434852 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9791 BOUND_VARIABLE_1434849) BOUND_VARIABLE_1434850) BOUND_VARIABLE_1434851) BOUND_VARIABLE_1434852) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434850) BOUND_VARIABLE_1434852)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434849) BOUND_VARIABLE_1434851)))))))))) (let ((_let_3851 (forall ((BOUND_VARIABLE_1434824 tptp.int) (BOUND_VARIABLE_1434825 tptp.int) (BOUND_VARIABLE_1434826 tptp.int) (BOUND_VARIABLE_1434827 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9792 BOUND_VARIABLE_1434824) BOUND_VARIABLE_1434825) BOUND_VARIABLE_1434826) BOUND_VARIABLE_1434827) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434825) BOUND_VARIABLE_1434827)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434824) BOUND_VARIABLE_1434826)))))))))) (let ((_let_3852 (forall ((BOUND_VARIABLE_1434799 tptp.int) (BOUND_VARIABLE_1434800 tptp.int) (BOUND_VARIABLE_1434801 tptp.int) (BOUND_VARIABLE_1434802 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9793 BOUND_VARIABLE_1434799) BOUND_VARIABLE_1434800) BOUND_VARIABLE_1434801) BOUND_VARIABLE_1434802) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434800) BOUND_VARIABLE_1434802)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434799) BOUND_VARIABLE_1434801)))))))))) (let ((_let_3853 (forall ((BOUND_VARIABLE_1434757 tptp.rat) (BOUND_VARIABLE_1434758 tptp.int) (BOUND_VARIABLE_1434759 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7619 BOUND_VARIABLE_1434759) BOUND_VARIABLE_1434758)) (ho_7630 k_7629 BOUND_VARIABLE_1434757)) (ho_7496 (ho_7495 (ho_7635 k_9794 BOUND_VARIABLE_1434757) BOUND_VARIABLE_1434758) BOUND_VARIABLE_1434759))))) (let ((_let_3854 (forall ((BOUND_VARIABLE_1434715 tptp.rat) (BOUND_VARIABLE_1434716 tptp.int) (BOUND_VARIABLE_1434717 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7620 BOUND_VARIABLE_1434717) BOUND_VARIABLE_1434716)) (ho_7630 k_7629 BOUND_VARIABLE_1434715)) (ho_7496 (ho_7495 (ho_7635 k_9795 BOUND_VARIABLE_1434715) BOUND_VARIABLE_1434716) BOUND_VARIABLE_1434717))))) (let ((_let_3855 (forall ((BOUND_VARIABLE_1434690 tptp.int) (BOUND_VARIABLE_1434691 tptp.int) (BOUND_VARIABLE_1434692 tptp.int) (BOUND_VARIABLE_1434693 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9796 BOUND_VARIABLE_1434690) BOUND_VARIABLE_1434691) BOUND_VARIABLE_1434692) BOUND_VARIABLE_1434693) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434691) BOUND_VARIABLE_1434693)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434690) BOUND_VARIABLE_1434692)))))))))) (let ((_let_3856 (forall ((BOUND_VARIABLE_1434665 tptp.int) (BOUND_VARIABLE_1434666 tptp.int) (BOUND_VARIABLE_1434667 tptp.int) (BOUND_VARIABLE_1434668 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9797 BOUND_VARIABLE_1434665) BOUND_VARIABLE_1434666) BOUND_VARIABLE_1434667) BOUND_VARIABLE_1434668) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434666) BOUND_VARIABLE_1434668)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434665) BOUND_VARIABLE_1434667)))))))))) (let ((_let_3857 (forall ((BOUND_VARIABLE_1434640 tptp.int) (BOUND_VARIABLE_1434641 tptp.int) (BOUND_VARIABLE_1434642 tptp.int) (BOUND_VARIABLE_1434643 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9798 BOUND_VARIABLE_1434640) BOUND_VARIABLE_1434641) BOUND_VARIABLE_1434642) BOUND_VARIABLE_1434643) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434641) BOUND_VARIABLE_1434643)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434640) BOUND_VARIABLE_1434642)))))))))) (let ((_let_3858 (forall ((BOUND_VARIABLE_1434615 tptp.int) (BOUND_VARIABLE_1434616 tptp.int) (BOUND_VARIABLE_1434617 tptp.int) (BOUND_VARIABLE_1434618 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9799 BOUND_VARIABLE_1434615) BOUND_VARIABLE_1434616) BOUND_VARIABLE_1434617) BOUND_VARIABLE_1434618) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434616) BOUND_VARIABLE_1434618)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434615) BOUND_VARIABLE_1434617)))))))))) (let ((_let_3859 (forall ((BOUND_VARIABLE_1434590 tptp.int) (BOUND_VARIABLE_1434591 tptp.int) (BOUND_VARIABLE_1434592 tptp.int) (BOUND_VARIABLE_1434593 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9800 BOUND_VARIABLE_1434590) BOUND_VARIABLE_1434591) BOUND_VARIABLE_1434592) BOUND_VARIABLE_1434593) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434591) BOUND_VARIABLE_1434593)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434590) BOUND_VARIABLE_1434592)))))))))) (let ((_let_3860 (forall ((BOUND_VARIABLE_1434565 tptp.int) (BOUND_VARIABLE_1434566 tptp.int) (BOUND_VARIABLE_1434567 tptp.int) (BOUND_VARIABLE_1434568 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9801 BOUND_VARIABLE_1434565) BOUND_VARIABLE_1434566) BOUND_VARIABLE_1434567) BOUND_VARIABLE_1434568) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434566) BOUND_VARIABLE_1434568)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434565) BOUND_VARIABLE_1434567)))))))))) (let ((_let_3861 (forall ((BOUND_VARIABLE_1434523 tptp.rat) (BOUND_VARIABLE_1434524 tptp.int) (BOUND_VARIABLE_1434525 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7621 BOUND_VARIABLE_1434525) BOUND_VARIABLE_1434524)) (ho_7630 k_7629 BOUND_VARIABLE_1434523)) (ho_7496 (ho_7495 (ho_7635 k_9802 BOUND_VARIABLE_1434523) BOUND_VARIABLE_1434524) BOUND_VARIABLE_1434525))))) (let ((_let_3862 (forall ((BOUND_VARIABLE_1434481 tptp.rat) (BOUND_VARIABLE_1434482 tptp.int) (BOUND_VARIABLE_1434483 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7622 BOUND_VARIABLE_1434483) BOUND_VARIABLE_1434482)) (ho_7630 k_7629 BOUND_VARIABLE_1434481)) (ho_7496 (ho_7495 (ho_7635 k_9803 BOUND_VARIABLE_1434481) BOUND_VARIABLE_1434482) BOUND_VARIABLE_1434483))))) (let ((_let_3863 (forall ((BOUND_VARIABLE_1434456 tptp.int) (BOUND_VARIABLE_1434457 tptp.int) (BOUND_VARIABLE_1434458 tptp.int) (BOUND_VARIABLE_1434459 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9804 BOUND_VARIABLE_1434456) BOUND_VARIABLE_1434457) BOUND_VARIABLE_1434458) BOUND_VARIABLE_1434459) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434457) BOUND_VARIABLE_1434459)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434456) BOUND_VARIABLE_1434458)))))))))) (let ((_let_3864 (forall ((BOUND_VARIABLE_1434431 tptp.int) (BOUND_VARIABLE_1434432 tptp.int) (BOUND_VARIABLE_1434433 tptp.int) (BOUND_VARIABLE_1434434 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9805 BOUND_VARIABLE_1434431) BOUND_VARIABLE_1434432) BOUND_VARIABLE_1434433) BOUND_VARIABLE_1434434) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434432) BOUND_VARIABLE_1434434)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434431) BOUND_VARIABLE_1434433)))))))))) (let ((_let_3865 (forall ((BOUND_VARIABLE_1434406 tptp.int) (BOUND_VARIABLE_1434407 tptp.int) (BOUND_VARIABLE_1434408 tptp.int) (BOUND_VARIABLE_1434409 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9806 BOUND_VARIABLE_1434406) BOUND_VARIABLE_1434407) BOUND_VARIABLE_1434408) BOUND_VARIABLE_1434409) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434407) BOUND_VARIABLE_1434409)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434406) BOUND_VARIABLE_1434408)))))))))) (let ((_let_3866 (forall ((BOUND_VARIABLE_1434381 tptp.int) (BOUND_VARIABLE_1434382 tptp.int) (BOUND_VARIABLE_1434383 tptp.int) (BOUND_VARIABLE_1434384 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9807 BOUND_VARIABLE_1434381) BOUND_VARIABLE_1434382) BOUND_VARIABLE_1434383) BOUND_VARIABLE_1434384) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434382) BOUND_VARIABLE_1434384)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434381) BOUND_VARIABLE_1434383)))))))))) (let ((_let_3867 (forall ((BOUND_VARIABLE_1434339 tptp.rat) (BOUND_VARIABLE_1434340 tptp.int) (BOUND_VARIABLE_1434341 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7623 BOUND_VARIABLE_1434341) BOUND_VARIABLE_1434340)) (ho_7630 k_7629 BOUND_VARIABLE_1434339)) (ho_7496 (ho_7495 (ho_7635 k_9808 BOUND_VARIABLE_1434339) BOUND_VARIABLE_1434340) BOUND_VARIABLE_1434341))))) (let ((_let_3868 (forall ((BOUND_VARIABLE_1434297 tptp.rat) (BOUND_VARIABLE_1434298 tptp.int) (BOUND_VARIABLE_1434299 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7624 BOUND_VARIABLE_1434299) BOUND_VARIABLE_1434298)) (ho_7630 k_7629 BOUND_VARIABLE_1434297)) (ho_7496 (ho_7495 (ho_7635 k_9809 BOUND_VARIABLE_1434297) BOUND_VARIABLE_1434298) BOUND_VARIABLE_1434299))))) (let ((_let_3869 (forall ((BOUND_VARIABLE_1434255 tptp.rat) (BOUND_VARIABLE_1434256 tptp.int) (BOUND_VARIABLE_1434257 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7625 BOUND_VARIABLE_1434257) BOUND_VARIABLE_1434256)) (ho_7630 k_7629 BOUND_VARIABLE_1434255)) (ho_7496 (ho_7495 (ho_7635 k_9810 BOUND_VARIABLE_1434255) BOUND_VARIABLE_1434256) BOUND_VARIABLE_1434257))))) (let ((_let_3870 (forall ((BOUND_VARIABLE_1434213 tptp.rat) (BOUND_VARIABLE_1434214 tptp.int) (BOUND_VARIABLE_1434215 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7626 BOUND_VARIABLE_1434215) BOUND_VARIABLE_1434214)) (ho_7630 k_7629 BOUND_VARIABLE_1434213)) (ho_7496 (ho_7495 (ho_7635 k_9811 BOUND_VARIABLE_1434213) BOUND_VARIABLE_1434214) BOUND_VARIABLE_1434215))))) (let ((_let_3871 (forall ((BOUND_VARIABLE_1434171 tptp.rat) (BOUND_VARIABLE_1434172 tptp.int) (BOUND_VARIABLE_1434173 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7627 BOUND_VARIABLE_1434173) BOUND_VARIABLE_1434172)) (ho_7630 k_7629 BOUND_VARIABLE_1434171)) (ho_7496 (ho_7495 (ho_7635 k_9812 BOUND_VARIABLE_1434171) BOUND_VARIABLE_1434172) BOUND_VARIABLE_1434173))))) (let ((_let_3872 (forall ((BOUND_VARIABLE_1434146 tptp.int) (BOUND_VARIABLE_1434147 tptp.int) (BOUND_VARIABLE_1434148 tptp.int) (BOUND_VARIABLE_1434149 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9813 BOUND_VARIABLE_1434146) BOUND_VARIABLE_1434147) BOUND_VARIABLE_1434148) BOUND_VARIABLE_1434149) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434147) BOUND_VARIABLE_1434149)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434146) BOUND_VARIABLE_1434148)))))))))) (let ((_let_3873 (forall ((BOUND_VARIABLE_1434121 tptp.int) (BOUND_VARIABLE_1434122 tptp.int) (BOUND_VARIABLE_1434123 tptp.int) (BOUND_VARIABLE_1434124 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9814 BOUND_VARIABLE_1434121) BOUND_VARIABLE_1434122) BOUND_VARIABLE_1434123) BOUND_VARIABLE_1434124) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434122) BOUND_VARIABLE_1434124)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434121) BOUND_VARIABLE_1434123)))))))))) (let ((_let_3874 (forall ((BOUND_VARIABLE_1434096 tptp.int) (BOUND_VARIABLE_1434097 tptp.int) (BOUND_VARIABLE_1434098 tptp.int) (BOUND_VARIABLE_1434099 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9815 BOUND_VARIABLE_1434096) BOUND_VARIABLE_1434097) BOUND_VARIABLE_1434098) BOUND_VARIABLE_1434099) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434097) BOUND_VARIABLE_1434099)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434096) BOUND_VARIABLE_1434098)))))))))) (let ((_let_3875 (forall ((BOUND_VARIABLE_1434071 tptp.int) (BOUND_VARIABLE_1434072 tptp.int) (BOUND_VARIABLE_1434073 tptp.int) (BOUND_VARIABLE_1434074 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9816 BOUND_VARIABLE_1434071) BOUND_VARIABLE_1434072) BOUND_VARIABLE_1434073) BOUND_VARIABLE_1434074) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434072) BOUND_VARIABLE_1434074)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434071) BOUND_VARIABLE_1434073)))))))))) (let ((_let_3876 (forall ((BOUND_VARIABLE_1434046 tptp.int) (BOUND_VARIABLE_1434047 tptp.int) (BOUND_VARIABLE_1434048 tptp.int) (BOUND_VARIABLE_1434049 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9817 BOUND_VARIABLE_1434046) BOUND_VARIABLE_1434047) BOUND_VARIABLE_1434048) BOUND_VARIABLE_1434049) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434047) BOUND_VARIABLE_1434049)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434046) BOUND_VARIABLE_1434048)))))))))) (let ((_let_3877 (forall ((BOUND_VARIABLE_1434021 tptp.int) (BOUND_VARIABLE_1434022 tptp.int) (BOUND_VARIABLE_1434023 tptp.int) (BOUND_VARIABLE_1434024 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9818 BOUND_VARIABLE_1434021) BOUND_VARIABLE_1434022) BOUND_VARIABLE_1434023) BOUND_VARIABLE_1434024) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434022) BOUND_VARIABLE_1434024)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1434021) BOUND_VARIABLE_1434023)))))))))) (let ((_let_3878 (forall ((BOUND_VARIABLE_1433996 tptp.int) (BOUND_VARIABLE_1433997 tptp.int) (BOUND_VARIABLE_1433998 tptp.int) (BOUND_VARIABLE_1433999 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9819 BOUND_VARIABLE_1433996) BOUND_VARIABLE_1433997) BOUND_VARIABLE_1433998) BOUND_VARIABLE_1433999) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433997) BOUND_VARIABLE_1433999)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433996) BOUND_VARIABLE_1433998)))))))))) (let ((_let_3879 (forall ((BOUND_VARIABLE_1433971 tptp.int) (BOUND_VARIABLE_1433972 tptp.int) (BOUND_VARIABLE_1433973 tptp.int) (BOUND_VARIABLE_1433974 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9820 BOUND_VARIABLE_1433971) BOUND_VARIABLE_1433972) BOUND_VARIABLE_1433973) BOUND_VARIABLE_1433974) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433972) BOUND_VARIABLE_1433974)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433971) BOUND_VARIABLE_1433973)))))))))) (let ((_let_3880 (forall ((BOUND_VARIABLE_1433946 tptp.int) (BOUND_VARIABLE_1433947 tptp.int) (BOUND_VARIABLE_1433948 tptp.int) (BOUND_VARIABLE_1433949 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9821 BOUND_VARIABLE_1433946) BOUND_VARIABLE_1433947) BOUND_VARIABLE_1433948) BOUND_VARIABLE_1433949) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433947) BOUND_VARIABLE_1433949)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433946) BOUND_VARIABLE_1433948)))))))))) (let ((_let_3881 (forall ((BOUND_VARIABLE_1433921 tptp.int) (BOUND_VARIABLE_1433922 tptp.int) (BOUND_VARIABLE_1433923 tptp.int) (BOUND_VARIABLE_1433924 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9822 BOUND_VARIABLE_1433921) BOUND_VARIABLE_1433922) BOUND_VARIABLE_1433923) BOUND_VARIABLE_1433924) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433922) BOUND_VARIABLE_1433924)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433921) BOUND_VARIABLE_1433923)))))))))) (let ((_let_3882 (forall ((BOUND_VARIABLE_1433896 tptp.int) (BOUND_VARIABLE_1433897 tptp.int) (BOUND_VARIABLE_1433898 tptp.int) (BOUND_VARIABLE_1433899 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9823 BOUND_VARIABLE_1433896) BOUND_VARIABLE_1433897) BOUND_VARIABLE_1433898) BOUND_VARIABLE_1433899) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433897) BOUND_VARIABLE_1433899)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433896) BOUND_VARIABLE_1433898)))))))))) (let ((_let_3883 (forall ((BOUND_VARIABLE_1433871 tptp.int) (BOUND_VARIABLE_1433872 tptp.int) (BOUND_VARIABLE_1433873 tptp.int) (BOUND_VARIABLE_1433874 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9824 BOUND_VARIABLE_1433871) BOUND_VARIABLE_1433872) BOUND_VARIABLE_1433873) BOUND_VARIABLE_1433874) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433872) BOUND_VARIABLE_1433874)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433871) BOUND_VARIABLE_1433873)))))))))) (let ((_let_3884 (forall ((BOUND_VARIABLE_1433846 tptp.int) (BOUND_VARIABLE_1433847 tptp.int) (BOUND_VARIABLE_1433848 tptp.int) (BOUND_VARIABLE_1433849 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9825 BOUND_VARIABLE_1433846) BOUND_VARIABLE_1433847) BOUND_VARIABLE_1433848) BOUND_VARIABLE_1433849) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433847) BOUND_VARIABLE_1433849)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433846) BOUND_VARIABLE_1433848)))))))))) (let ((_let_3885 (forall ((BOUND_VARIABLE_1433821 tptp.int) (BOUND_VARIABLE_1433822 tptp.int) (BOUND_VARIABLE_1433823 tptp.int) (BOUND_VARIABLE_1433824 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9826 BOUND_VARIABLE_1433821) BOUND_VARIABLE_1433822) BOUND_VARIABLE_1433823) BOUND_VARIABLE_1433824) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433822) BOUND_VARIABLE_1433824)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433821) BOUND_VARIABLE_1433823)))))))))) (let ((_let_3886 (forall ((BOUND_VARIABLE_1433796 tptp.int) (BOUND_VARIABLE_1433797 tptp.int) (BOUND_VARIABLE_1433798 tptp.int) (BOUND_VARIABLE_1433799 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9827 BOUND_VARIABLE_1433796) BOUND_VARIABLE_1433797) BOUND_VARIABLE_1433798) BOUND_VARIABLE_1433799) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433797) BOUND_VARIABLE_1433799)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433796) BOUND_VARIABLE_1433798)))))))))) (let ((_let_3887 (forall ((BOUND_VARIABLE_1433771 tptp.int) (BOUND_VARIABLE_1433772 tptp.int) (BOUND_VARIABLE_1433773 tptp.int) (BOUND_VARIABLE_1433774 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9828 BOUND_VARIABLE_1433771) BOUND_VARIABLE_1433772) BOUND_VARIABLE_1433773) BOUND_VARIABLE_1433774) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433772) BOUND_VARIABLE_1433774)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433771) BOUND_VARIABLE_1433773)))))))))) (let ((_let_3888 (forall ((BOUND_VARIABLE_1433746 tptp.int) (BOUND_VARIABLE_1433747 tptp.int) (BOUND_VARIABLE_1433748 tptp.int) (BOUND_VARIABLE_1433749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9829 BOUND_VARIABLE_1433746) BOUND_VARIABLE_1433747) BOUND_VARIABLE_1433748) BOUND_VARIABLE_1433749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433747) BOUND_VARIABLE_1433749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433746) BOUND_VARIABLE_1433748)))))))))) (let ((_let_3889 (forall ((BOUND_VARIABLE_1433721 tptp.int) (BOUND_VARIABLE_1433722 tptp.int) (BOUND_VARIABLE_1433723 tptp.int) (BOUND_VARIABLE_1433724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9830 BOUND_VARIABLE_1433721) BOUND_VARIABLE_1433722) BOUND_VARIABLE_1433723) BOUND_VARIABLE_1433724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433722) BOUND_VARIABLE_1433724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433721) BOUND_VARIABLE_1433723)))))))))) (let ((_let_3890 (forall ((BOUND_VARIABLE_1433696 tptp.int) (BOUND_VARIABLE_1433697 tptp.int) (BOUND_VARIABLE_1433698 tptp.int) (BOUND_VARIABLE_1433699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9831 BOUND_VARIABLE_1433696) BOUND_VARIABLE_1433697) BOUND_VARIABLE_1433698) BOUND_VARIABLE_1433699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433697) BOUND_VARIABLE_1433699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433696) BOUND_VARIABLE_1433698)))))))))) (let ((_let_3891 (forall ((BOUND_VARIABLE_1433671 tptp.int) (BOUND_VARIABLE_1433672 tptp.int) (BOUND_VARIABLE_1433673 tptp.int) (BOUND_VARIABLE_1433674 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9832 BOUND_VARIABLE_1433671) BOUND_VARIABLE_1433672) BOUND_VARIABLE_1433673) BOUND_VARIABLE_1433674) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433672) BOUND_VARIABLE_1433674)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433671) BOUND_VARIABLE_1433673)))))))))) (let ((_let_3892 (forall ((BOUND_VARIABLE_1433646 tptp.int) (BOUND_VARIABLE_1433647 tptp.int) (BOUND_VARIABLE_1433648 tptp.int) (BOUND_VARIABLE_1433649 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9833 BOUND_VARIABLE_1433646) BOUND_VARIABLE_1433647) BOUND_VARIABLE_1433648) BOUND_VARIABLE_1433649) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433647) BOUND_VARIABLE_1433649)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433646) BOUND_VARIABLE_1433648)))))))))) (let ((_let_3893 (forall ((BOUND_VARIABLE_1433621 tptp.int) (BOUND_VARIABLE_1433622 tptp.int) (BOUND_VARIABLE_1433623 tptp.int) (BOUND_VARIABLE_1433624 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9834 BOUND_VARIABLE_1433621) BOUND_VARIABLE_1433622) BOUND_VARIABLE_1433623) BOUND_VARIABLE_1433624) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433622) BOUND_VARIABLE_1433624)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433621) BOUND_VARIABLE_1433623)))))))))) (let ((_let_3894 (forall ((BOUND_VARIABLE_1433596 tptp.int) (BOUND_VARIABLE_1433597 tptp.int) (BOUND_VARIABLE_1433598 tptp.int) (BOUND_VARIABLE_1433599 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9835 BOUND_VARIABLE_1433596) BOUND_VARIABLE_1433597) BOUND_VARIABLE_1433598) BOUND_VARIABLE_1433599) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433597) BOUND_VARIABLE_1433599)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433596) BOUND_VARIABLE_1433598)))))))))) (let ((_let_3895 (forall ((BOUND_VARIABLE_1433571 tptp.int) (BOUND_VARIABLE_1433572 tptp.int) (BOUND_VARIABLE_1433573 tptp.int) (BOUND_VARIABLE_1433574 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9836 BOUND_VARIABLE_1433571) BOUND_VARIABLE_1433572) BOUND_VARIABLE_1433573) BOUND_VARIABLE_1433574) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433572) BOUND_VARIABLE_1433574)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433571) BOUND_VARIABLE_1433573)))))))))) (let ((_let_3896 (forall ((BOUND_VARIABLE_1433546 tptp.int) (BOUND_VARIABLE_1433547 tptp.int) (BOUND_VARIABLE_1433548 tptp.int) (BOUND_VARIABLE_1433549 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9837 BOUND_VARIABLE_1433546) BOUND_VARIABLE_1433547) BOUND_VARIABLE_1433548) BOUND_VARIABLE_1433549) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433547) BOUND_VARIABLE_1433549)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433546) BOUND_VARIABLE_1433548)))))))))) (let ((_let_3897 (forall ((BOUND_VARIABLE_1433521 tptp.int) (BOUND_VARIABLE_1433522 tptp.int) (BOUND_VARIABLE_1433523 tptp.int) (BOUND_VARIABLE_1433524 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9838 BOUND_VARIABLE_1433521) BOUND_VARIABLE_1433522) BOUND_VARIABLE_1433523) BOUND_VARIABLE_1433524) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433522) BOUND_VARIABLE_1433524)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433521) BOUND_VARIABLE_1433523)))))))))) (let ((_let_3898 (forall ((BOUND_VARIABLE_1433496 tptp.int) (BOUND_VARIABLE_1433497 tptp.int) (BOUND_VARIABLE_1433498 tptp.int) (BOUND_VARIABLE_1433499 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9839 BOUND_VARIABLE_1433496) BOUND_VARIABLE_1433497) BOUND_VARIABLE_1433498) BOUND_VARIABLE_1433499) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433497) BOUND_VARIABLE_1433499)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433496) BOUND_VARIABLE_1433498)))))))))) (let ((_let_3899 (forall ((BOUND_VARIABLE_1433471 tptp.int) (BOUND_VARIABLE_1433472 tptp.int) (BOUND_VARIABLE_1433473 tptp.int) (BOUND_VARIABLE_1433474 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9840 BOUND_VARIABLE_1433471) BOUND_VARIABLE_1433472) BOUND_VARIABLE_1433473) BOUND_VARIABLE_1433474) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433472) BOUND_VARIABLE_1433474)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433471) BOUND_VARIABLE_1433473)))))))))) (let ((_let_3900 (forall ((BOUND_VARIABLE_1433446 tptp.int) (BOUND_VARIABLE_1433447 tptp.int) (BOUND_VARIABLE_1433448 tptp.int) (BOUND_VARIABLE_1433449 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9841 BOUND_VARIABLE_1433446) BOUND_VARIABLE_1433447) BOUND_VARIABLE_1433448) BOUND_VARIABLE_1433449) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433447) BOUND_VARIABLE_1433449)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433446) BOUND_VARIABLE_1433448)))))))))) (let ((_let_3901 (forall ((BOUND_VARIABLE_1433421 tptp.int) (BOUND_VARIABLE_1433422 tptp.int) (BOUND_VARIABLE_1433423 tptp.int) (BOUND_VARIABLE_1433424 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9842 BOUND_VARIABLE_1433421) BOUND_VARIABLE_1433422) BOUND_VARIABLE_1433423) BOUND_VARIABLE_1433424) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433422) BOUND_VARIABLE_1433424)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433421) BOUND_VARIABLE_1433423)))))))))) (let ((_let_3902 (forall ((BOUND_VARIABLE_1433396 tptp.int) (BOUND_VARIABLE_1433397 tptp.int) (BOUND_VARIABLE_1433398 tptp.int) (BOUND_VARIABLE_1433399 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9843 BOUND_VARIABLE_1433396) BOUND_VARIABLE_1433397) BOUND_VARIABLE_1433398) BOUND_VARIABLE_1433399) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433397) BOUND_VARIABLE_1433399)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433396) BOUND_VARIABLE_1433398)))))))))) (let ((_let_3903 (forall ((BOUND_VARIABLE_1433371 tptp.int) (BOUND_VARIABLE_1433372 tptp.int) (BOUND_VARIABLE_1433373 tptp.int) (BOUND_VARIABLE_1433374 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9844 BOUND_VARIABLE_1433371) BOUND_VARIABLE_1433372) BOUND_VARIABLE_1433373) BOUND_VARIABLE_1433374) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433372) BOUND_VARIABLE_1433374)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433371) BOUND_VARIABLE_1433373)))))))))) (let ((_let_3904 (forall ((BOUND_VARIABLE_1433346 tptp.int) (BOUND_VARIABLE_1433347 tptp.int) (BOUND_VARIABLE_1433348 tptp.int) (BOUND_VARIABLE_1433349 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9845 BOUND_VARIABLE_1433346) BOUND_VARIABLE_1433347) BOUND_VARIABLE_1433348) BOUND_VARIABLE_1433349) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433347) BOUND_VARIABLE_1433349)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433346) BOUND_VARIABLE_1433348)))))))))) (let ((_let_3905 (forall ((BOUND_VARIABLE_1433321 tptp.int) (BOUND_VARIABLE_1433322 tptp.int) (BOUND_VARIABLE_1433323 tptp.int) (BOUND_VARIABLE_1433324 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9846 BOUND_VARIABLE_1433321) BOUND_VARIABLE_1433322) BOUND_VARIABLE_1433323) BOUND_VARIABLE_1433324) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433322) BOUND_VARIABLE_1433324)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433321) BOUND_VARIABLE_1433323)))))))))) (let ((_let_3906 (forall ((BOUND_VARIABLE_1433296 tptp.int) (BOUND_VARIABLE_1433297 tptp.int) (BOUND_VARIABLE_1433298 tptp.int) (BOUND_VARIABLE_1433299 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9847 BOUND_VARIABLE_1433296) BOUND_VARIABLE_1433297) BOUND_VARIABLE_1433298) BOUND_VARIABLE_1433299) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433297) BOUND_VARIABLE_1433299)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433296) BOUND_VARIABLE_1433298)))))))))) (let ((_let_3907 (forall ((BOUND_VARIABLE_1433271 tptp.int) (BOUND_VARIABLE_1433272 tptp.int) (BOUND_VARIABLE_1433273 tptp.int) (BOUND_VARIABLE_1433274 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9848 BOUND_VARIABLE_1433271) BOUND_VARIABLE_1433272) BOUND_VARIABLE_1433273) BOUND_VARIABLE_1433274) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433272) BOUND_VARIABLE_1433274)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433271) BOUND_VARIABLE_1433273)))))))))) (let ((_let_3908 (forall ((BOUND_VARIABLE_1433246 tptp.int) (BOUND_VARIABLE_1433247 tptp.int) (BOUND_VARIABLE_1433248 tptp.int) (BOUND_VARIABLE_1433249 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9849 BOUND_VARIABLE_1433246) BOUND_VARIABLE_1433247) BOUND_VARIABLE_1433248) BOUND_VARIABLE_1433249) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433247) BOUND_VARIABLE_1433249)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433246) BOUND_VARIABLE_1433248)))))))))) (let ((_let_3909 (forall ((BOUND_VARIABLE_1433221 tptp.int) (BOUND_VARIABLE_1433222 tptp.int) (BOUND_VARIABLE_1433223 tptp.int) (BOUND_VARIABLE_1433224 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9850 BOUND_VARIABLE_1433221) BOUND_VARIABLE_1433222) BOUND_VARIABLE_1433223) BOUND_VARIABLE_1433224) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433222) BOUND_VARIABLE_1433224)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433221) BOUND_VARIABLE_1433223)))))))))) (let ((_let_3910 (forall ((BOUND_VARIABLE_1433196 tptp.int) (BOUND_VARIABLE_1433197 tptp.int) (BOUND_VARIABLE_1433198 tptp.int) (BOUND_VARIABLE_1433199 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9851 BOUND_VARIABLE_1433196) BOUND_VARIABLE_1433197) BOUND_VARIABLE_1433198) BOUND_VARIABLE_1433199) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433197) BOUND_VARIABLE_1433199)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433196) BOUND_VARIABLE_1433198)))))))))) (let ((_let_3911 (forall ((BOUND_VARIABLE_1433171 tptp.int) (BOUND_VARIABLE_1433172 tptp.int) (BOUND_VARIABLE_1433173 tptp.int) (BOUND_VARIABLE_1433174 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9852 BOUND_VARIABLE_1433171) BOUND_VARIABLE_1433172) BOUND_VARIABLE_1433173) BOUND_VARIABLE_1433174) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433172) BOUND_VARIABLE_1433174)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433171) BOUND_VARIABLE_1433173)))))))))) (let ((_let_3912 (forall ((BOUND_VARIABLE_1433146 tptp.int) (BOUND_VARIABLE_1433147 tptp.int) (BOUND_VARIABLE_1433148 tptp.int) (BOUND_VARIABLE_1433149 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9853 BOUND_VARIABLE_1433146) BOUND_VARIABLE_1433147) BOUND_VARIABLE_1433148) BOUND_VARIABLE_1433149) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433147) BOUND_VARIABLE_1433149)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433146) BOUND_VARIABLE_1433148)))))))))) (let ((_let_3913 (forall ((BOUND_VARIABLE_1433121 tptp.int) (BOUND_VARIABLE_1433122 tptp.int) (BOUND_VARIABLE_1433123 tptp.int) (BOUND_VARIABLE_1433124 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9854 BOUND_VARIABLE_1433121) BOUND_VARIABLE_1433122) BOUND_VARIABLE_1433123) BOUND_VARIABLE_1433124) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433122) BOUND_VARIABLE_1433124)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433121) BOUND_VARIABLE_1433123)))))))))) (let ((_let_3914 (forall ((BOUND_VARIABLE_1433096 tptp.int) (BOUND_VARIABLE_1433097 tptp.int) (BOUND_VARIABLE_1433098 tptp.int) (BOUND_VARIABLE_1433099 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9855 BOUND_VARIABLE_1433096) BOUND_VARIABLE_1433097) BOUND_VARIABLE_1433098) BOUND_VARIABLE_1433099) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433097) BOUND_VARIABLE_1433099)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433096) BOUND_VARIABLE_1433098)))))))))) (let ((_let_3915 (forall ((BOUND_VARIABLE_1433071 tptp.int) (BOUND_VARIABLE_1433072 tptp.int) (BOUND_VARIABLE_1433073 tptp.int) (BOUND_VARIABLE_1433074 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9856 BOUND_VARIABLE_1433071) BOUND_VARIABLE_1433072) BOUND_VARIABLE_1433073) BOUND_VARIABLE_1433074) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433072) BOUND_VARIABLE_1433074)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433071) BOUND_VARIABLE_1433073)))))))))) (let ((_let_3916 (forall ((BOUND_VARIABLE_1433046 tptp.int) (BOUND_VARIABLE_1433047 tptp.int) (BOUND_VARIABLE_1433048 tptp.int) (BOUND_VARIABLE_1433049 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9857 BOUND_VARIABLE_1433046) BOUND_VARIABLE_1433047) BOUND_VARIABLE_1433048) BOUND_VARIABLE_1433049) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433047) BOUND_VARIABLE_1433049)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433046) BOUND_VARIABLE_1433048)))))))))) (let ((_let_3917 (forall ((BOUND_VARIABLE_1433021 tptp.int) (BOUND_VARIABLE_1433022 tptp.int) (BOUND_VARIABLE_1433023 tptp.int) (BOUND_VARIABLE_1433024 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9858 BOUND_VARIABLE_1433021) BOUND_VARIABLE_1433022) BOUND_VARIABLE_1433023) BOUND_VARIABLE_1433024) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433022) BOUND_VARIABLE_1433024)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1433021) BOUND_VARIABLE_1433023)))))))))) (let ((_let_3918 (forall ((BOUND_VARIABLE_1432996 tptp.int) (BOUND_VARIABLE_1432997 tptp.int) (BOUND_VARIABLE_1432998 tptp.int) (BOUND_VARIABLE_1432999 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9859 BOUND_VARIABLE_1432996) BOUND_VARIABLE_1432997) BOUND_VARIABLE_1432998) BOUND_VARIABLE_1432999) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432997) BOUND_VARIABLE_1432999)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432996) BOUND_VARIABLE_1432998)))))))))) (let ((_let_3919 (forall ((BOUND_VARIABLE_1432971 tptp.int) (BOUND_VARIABLE_1432972 tptp.int) (BOUND_VARIABLE_1432973 tptp.int) (BOUND_VARIABLE_1432974 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9860 BOUND_VARIABLE_1432971) BOUND_VARIABLE_1432972) BOUND_VARIABLE_1432973) BOUND_VARIABLE_1432974) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432972) BOUND_VARIABLE_1432974)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432971) BOUND_VARIABLE_1432973)))))))))) (let ((_let_3920 (forall ((BOUND_VARIABLE_1432946 tptp.int) (BOUND_VARIABLE_1432947 tptp.int) (BOUND_VARIABLE_1432948 tptp.int) (BOUND_VARIABLE_1432949 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9861 BOUND_VARIABLE_1432946) BOUND_VARIABLE_1432947) BOUND_VARIABLE_1432948) BOUND_VARIABLE_1432949) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432947) BOUND_VARIABLE_1432949)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432946) BOUND_VARIABLE_1432948)))))))))) (let ((_let_3921 (forall ((BOUND_VARIABLE_1432921 tptp.int) (BOUND_VARIABLE_1432922 tptp.int) (BOUND_VARIABLE_1432923 tptp.int) (BOUND_VARIABLE_1432924 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9862 BOUND_VARIABLE_1432921) BOUND_VARIABLE_1432922) BOUND_VARIABLE_1432923) BOUND_VARIABLE_1432924) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432922) BOUND_VARIABLE_1432924)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432921) BOUND_VARIABLE_1432923)))))))))) (let ((_let_3922 (forall ((BOUND_VARIABLE_1432896 tptp.int) (BOUND_VARIABLE_1432897 tptp.int) (BOUND_VARIABLE_1432898 tptp.int) (BOUND_VARIABLE_1432899 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9863 BOUND_VARIABLE_1432896) BOUND_VARIABLE_1432897) BOUND_VARIABLE_1432898) BOUND_VARIABLE_1432899) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432897) BOUND_VARIABLE_1432899)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432896) BOUND_VARIABLE_1432898)))))))))) (let ((_let_3923 (forall ((BOUND_VARIABLE_1432871 tptp.int) (BOUND_VARIABLE_1432872 tptp.int) (BOUND_VARIABLE_1432873 tptp.int) (BOUND_VARIABLE_1432874 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9864 BOUND_VARIABLE_1432871) BOUND_VARIABLE_1432872) BOUND_VARIABLE_1432873) BOUND_VARIABLE_1432874) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432872) BOUND_VARIABLE_1432874)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432871) BOUND_VARIABLE_1432873)))))))))) (let ((_let_3924 (forall ((BOUND_VARIABLE_1432846 tptp.int) (BOUND_VARIABLE_1432847 tptp.int) (BOUND_VARIABLE_1432848 tptp.int) (BOUND_VARIABLE_1432849 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9865 BOUND_VARIABLE_1432846) BOUND_VARIABLE_1432847) BOUND_VARIABLE_1432848) BOUND_VARIABLE_1432849) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432847) BOUND_VARIABLE_1432849)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432846) BOUND_VARIABLE_1432848)))))))))) (let ((_let_3925 (forall ((BOUND_VARIABLE_1432821 tptp.int) (BOUND_VARIABLE_1432822 tptp.int) (BOUND_VARIABLE_1432823 tptp.int) (BOUND_VARIABLE_1432824 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9866 BOUND_VARIABLE_1432821) BOUND_VARIABLE_1432822) BOUND_VARIABLE_1432823) BOUND_VARIABLE_1432824) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432822) BOUND_VARIABLE_1432824)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432821) BOUND_VARIABLE_1432823)))))))))) (let ((_let_3926 (forall ((BOUND_VARIABLE_1432796 tptp.int) (BOUND_VARIABLE_1432797 tptp.int) (BOUND_VARIABLE_1432798 tptp.int) (BOUND_VARIABLE_1432799 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9867 BOUND_VARIABLE_1432796) BOUND_VARIABLE_1432797) BOUND_VARIABLE_1432798) BOUND_VARIABLE_1432799) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432797) BOUND_VARIABLE_1432799)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432796) BOUND_VARIABLE_1432798)))))))))) (let ((_let_3927 (forall ((BOUND_VARIABLE_1432771 tptp.int) (BOUND_VARIABLE_1432772 tptp.int) (BOUND_VARIABLE_1432773 tptp.int) (BOUND_VARIABLE_1432774 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9868 BOUND_VARIABLE_1432771) BOUND_VARIABLE_1432772) BOUND_VARIABLE_1432773) BOUND_VARIABLE_1432774) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432772) BOUND_VARIABLE_1432774)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432771) BOUND_VARIABLE_1432773)))))))))) (let ((_let_3928 (forall ((BOUND_VARIABLE_1432746 tptp.int) (BOUND_VARIABLE_1432747 tptp.int) (BOUND_VARIABLE_1432748 tptp.int) (BOUND_VARIABLE_1432749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9869 BOUND_VARIABLE_1432746) BOUND_VARIABLE_1432747) BOUND_VARIABLE_1432748) BOUND_VARIABLE_1432749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432747) BOUND_VARIABLE_1432749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432746) BOUND_VARIABLE_1432748)))))))))) (let ((_let_3929 (forall ((BOUND_VARIABLE_1432721 tptp.int) (BOUND_VARIABLE_1432722 tptp.int) (BOUND_VARIABLE_1432723 tptp.int) (BOUND_VARIABLE_1432724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9870 BOUND_VARIABLE_1432721) BOUND_VARIABLE_1432722) BOUND_VARIABLE_1432723) BOUND_VARIABLE_1432724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432722) BOUND_VARIABLE_1432724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432721) BOUND_VARIABLE_1432723)))))))))) (let ((_let_3930 (forall ((BOUND_VARIABLE_1432696 tptp.int) (BOUND_VARIABLE_1432697 tptp.int) (BOUND_VARIABLE_1432698 tptp.int) (BOUND_VARIABLE_1432699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9871 BOUND_VARIABLE_1432696) BOUND_VARIABLE_1432697) BOUND_VARIABLE_1432698) BOUND_VARIABLE_1432699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432697) BOUND_VARIABLE_1432699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432696) BOUND_VARIABLE_1432698)))))))))) (let ((_let_3931 (forall ((BOUND_VARIABLE_1432671 tptp.int) (BOUND_VARIABLE_1432672 tptp.int) (BOUND_VARIABLE_1432673 tptp.int) (BOUND_VARIABLE_1432674 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9872 BOUND_VARIABLE_1432671) BOUND_VARIABLE_1432672) BOUND_VARIABLE_1432673) BOUND_VARIABLE_1432674) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432672) BOUND_VARIABLE_1432674)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432671) BOUND_VARIABLE_1432673)))))))))) (let ((_let_3932 (forall ((BOUND_VARIABLE_1432646 tptp.int) (BOUND_VARIABLE_1432647 tptp.int) (BOUND_VARIABLE_1432648 tptp.int) (BOUND_VARIABLE_1432649 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9873 BOUND_VARIABLE_1432646) BOUND_VARIABLE_1432647) BOUND_VARIABLE_1432648) BOUND_VARIABLE_1432649) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432647) BOUND_VARIABLE_1432649)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432646) BOUND_VARIABLE_1432648)))))))))) (let ((_let_3933 (forall ((BOUND_VARIABLE_1432621 tptp.int) (BOUND_VARIABLE_1432622 tptp.int) (BOUND_VARIABLE_1432623 tptp.int) (BOUND_VARIABLE_1432624 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9874 BOUND_VARIABLE_1432621) BOUND_VARIABLE_1432622) BOUND_VARIABLE_1432623) BOUND_VARIABLE_1432624) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432622) BOUND_VARIABLE_1432624)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432621) BOUND_VARIABLE_1432623)))))))))) (let ((_let_3934 (forall ((BOUND_VARIABLE_1432596 tptp.int) (BOUND_VARIABLE_1432597 tptp.int) (BOUND_VARIABLE_1432598 tptp.int) (BOUND_VARIABLE_1432599 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9875 BOUND_VARIABLE_1432596) BOUND_VARIABLE_1432597) BOUND_VARIABLE_1432598) BOUND_VARIABLE_1432599) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432597) BOUND_VARIABLE_1432599)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432596) BOUND_VARIABLE_1432598)))))))))) (let ((_let_3935 (forall ((BOUND_VARIABLE_1432571 tptp.int) (BOUND_VARIABLE_1432572 tptp.int) (BOUND_VARIABLE_1432573 tptp.int) (BOUND_VARIABLE_1432574 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9876 BOUND_VARIABLE_1432571) BOUND_VARIABLE_1432572) BOUND_VARIABLE_1432573) BOUND_VARIABLE_1432574) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432572) BOUND_VARIABLE_1432574)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432571) BOUND_VARIABLE_1432573)))))))))) (let ((_let_3936 (forall ((BOUND_VARIABLE_1432546 tptp.int) (BOUND_VARIABLE_1432547 tptp.int) (BOUND_VARIABLE_1432548 tptp.int) (BOUND_VARIABLE_1432549 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9877 BOUND_VARIABLE_1432546) BOUND_VARIABLE_1432547) BOUND_VARIABLE_1432548) BOUND_VARIABLE_1432549) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432547) BOUND_VARIABLE_1432549)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432546) BOUND_VARIABLE_1432548)))))))))) (let ((_let_3937 (forall ((BOUND_VARIABLE_1432521 tptp.int) (BOUND_VARIABLE_1432522 tptp.int) (BOUND_VARIABLE_1432523 tptp.int) (BOUND_VARIABLE_1432524 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9878 BOUND_VARIABLE_1432521) BOUND_VARIABLE_1432522) BOUND_VARIABLE_1432523) BOUND_VARIABLE_1432524) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432522) BOUND_VARIABLE_1432524)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432521) BOUND_VARIABLE_1432523)))))))))) (let ((_let_3938 (forall ((BOUND_VARIABLE_1432496 tptp.int) (BOUND_VARIABLE_1432497 tptp.int) (BOUND_VARIABLE_1432498 tptp.int) (BOUND_VARIABLE_1432499 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9879 BOUND_VARIABLE_1432496) BOUND_VARIABLE_1432497) BOUND_VARIABLE_1432498) BOUND_VARIABLE_1432499) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432497) BOUND_VARIABLE_1432499)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432496) BOUND_VARIABLE_1432498)))))))))) (let ((_let_3939 (forall ((BOUND_VARIABLE_1432471 tptp.int) (BOUND_VARIABLE_1432472 tptp.int) (BOUND_VARIABLE_1432473 tptp.int) (BOUND_VARIABLE_1432474 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9880 BOUND_VARIABLE_1432471) BOUND_VARIABLE_1432472) BOUND_VARIABLE_1432473) BOUND_VARIABLE_1432474) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432472) BOUND_VARIABLE_1432474)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432471) BOUND_VARIABLE_1432473)))))))))) (let ((_let_3940 (forall ((BOUND_VARIABLE_1432446 tptp.int) (BOUND_VARIABLE_1432447 tptp.int) (BOUND_VARIABLE_1432448 tptp.int) (BOUND_VARIABLE_1432449 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9881 BOUND_VARIABLE_1432446) BOUND_VARIABLE_1432447) BOUND_VARIABLE_1432448) BOUND_VARIABLE_1432449) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432447) BOUND_VARIABLE_1432449)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432446) BOUND_VARIABLE_1432448)))))))))) (let ((_let_3941 (forall ((BOUND_VARIABLE_1432421 tptp.int) (BOUND_VARIABLE_1432422 tptp.int) (BOUND_VARIABLE_1432423 tptp.int) (BOUND_VARIABLE_1432424 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9882 BOUND_VARIABLE_1432421) BOUND_VARIABLE_1432422) BOUND_VARIABLE_1432423) BOUND_VARIABLE_1432424) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432422) BOUND_VARIABLE_1432424)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432421) BOUND_VARIABLE_1432423)))))))))) (let ((_let_3942 (forall ((BOUND_VARIABLE_1432396 tptp.int) (BOUND_VARIABLE_1432397 tptp.int) (BOUND_VARIABLE_1432398 tptp.int) (BOUND_VARIABLE_1432399 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9883 BOUND_VARIABLE_1432396) BOUND_VARIABLE_1432397) BOUND_VARIABLE_1432398) BOUND_VARIABLE_1432399) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432397) BOUND_VARIABLE_1432399)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432396) BOUND_VARIABLE_1432398)))))))))) (let ((_let_3943 (forall ((BOUND_VARIABLE_1432371 tptp.int) (BOUND_VARIABLE_1432372 tptp.int) (BOUND_VARIABLE_1432373 tptp.int) (BOUND_VARIABLE_1432374 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9884 BOUND_VARIABLE_1432371) BOUND_VARIABLE_1432372) BOUND_VARIABLE_1432373) BOUND_VARIABLE_1432374) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432372) BOUND_VARIABLE_1432374)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432371) BOUND_VARIABLE_1432373)))))))))) (let ((_let_3944 (forall ((BOUND_VARIABLE_1432346 tptp.int) (BOUND_VARIABLE_1432347 tptp.int) (BOUND_VARIABLE_1432348 tptp.int) (BOUND_VARIABLE_1432349 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9885 BOUND_VARIABLE_1432346) BOUND_VARIABLE_1432347) BOUND_VARIABLE_1432348) BOUND_VARIABLE_1432349) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432347) BOUND_VARIABLE_1432349)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432346) BOUND_VARIABLE_1432348)))))))))) (let ((_let_3945 (forall ((BOUND_VARIABLE_1432321 tptp.int) (BOUND_VARIABLE_1432322 tptp.int) (BOUND_VARIABLE_1432323 tptp.int) (BOUND_VARIABLE_1432324 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9886 BOUND_VARIABLE_1432321) BOUND_VARIABLE_1432322) BOUND_VARIABLE_1432323) BOUND_VARIABLE_1432324) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432322) BOUND_VARIABLE_1432324)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432321) BOUND_VARIABLE_1432323)))))))))) (let ((_let_3946 (forall ((BOUND_VARIABLE_1432296 tptp.int) (BOUND_VARIABLE_1432297 tptp.int) (BOUND_VARIABLE_1432298 tptp.int) (BOUND_VARIABLE_1432299 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9887 BOUND_VARIABLE_1432296) BOUND_VARIABLE_1432297) BOUND_VARIABLE_1432298) BOUND_VARIABLE_1432299) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432297) BOUND_VARIABLE_1432299)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432296) BOUND_VARIABLE_1432298)))))))))) (let ((_let_3947 (forall ((BOUND_VARIABLE_1432271 tptp.int) (BOUND_VARIABLE_1432272 tptp.int) (BOUND_VARIABLE_1432273 tptp.int) (BOUND_VARIABLE_1432274 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9888 BOUND_VARIABLE_1432271) BOUND_VARIABLE_1432272) BOUND_VARIABLE_1432273) BOUND_VARIABLE_1432274) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432272) BOUND_VARIABLE_1432274)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432271) BOUND_VARIABLE_1432273)))))))))) (let ((_let_3948 (forall ((BOUND_VARIABLE_1432246 tptp.int) (BOUND_VARIABLE_1432247 tptp.int) (BOUND_VARIABLE_1432248 tptp.int) (BOUND_VARIABLE_1432249 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9889 BOUND_VARIABLE_1432246) BOUND_VARIABLE_1432247) BOUND_VARIABLE_1432248) BOUND_VARIABLE_1432249) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432247) BOUND_VARIABLE_1432249)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432246) BOUND_VARIABLE_1432248)))))))))) (let ((_let_3949 (forall ((BOUND_VARIABLE_1432221 tptp.int) (BOUND_VARIABLE_1432222 tptp.int) (BOUND_VARIABLE_1432223 tptp.int) (BOUND_VARIABLE_1432224 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9890 BOUND_VARIABLE_1432221) BOUND_VARIABLE_1432222) BOUND_VARIABLE_1432223) BOUND_VARIABLE_1432224) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432222) BOUND_VARIABLE_1432224)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432221) BOUND_VARIABLE_1432223)))))))))) (let ((_let_3950 (forall ((BOUND_VARIABLE_1432196 tptp.int) (BOUND_VARIABLE_1432197 tptp.int) (BOUND_VARIABLE_1432198 tptp.int) (BOUND_VARIABLE_1432199 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9891 BOUND_VARIABLE_1432196) BOUND_VARIABLE_1432197) BOUND_VARIABLE_1432198) BOUND_VARIABLE_1432199) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432197) BOUND_VARIABLE_1432199)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432196) BOUND_VARIABLE_1432198)))))))))) (let ((_let_3951 (forall ((BOUND_VARIABLE_1432171 tptp.int) (BOUND_VARIABLE_1432172 tptp.int) (BOUND_VARIABLE_1432173 tptp.int) (BOUND_VARIABLE_1432174 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9892 BOUND_VARIABLE_1432171) BOUND_VARIABLE_1432172) BOUND_VARIABLE_1432173) BOUND_VARIABLE_1432174) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432172) BOUND_VARIABLE_1432174)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432171) BOUND_VARIABLE_1432173)))))))))) (let ((_let_3952 (forall ((BOUND_VARIABLE_1432146 tptp.int) (BOUND_VARIABLE_1432147 tptp.int) (BOUND_VARIABLE_1432148 tptp.int) (BOUND_VARIABLE_1432149 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9893 BOUND_VARIABLE_1432146) BOUND_VARIABLE_1432147) BOUND_VARIABLE_1432148) BOUND_VARIABLE_1432149) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432147) BOUND_VARIABLE_1432149)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432146) BOUND_VARIABLE_1432148)))))))))) (let ((_let_3953 (forall ((BOUND_VARIABLE_1432121 tptp.int) (BOUND_VARIABLE_1432122 tptp.int) (BOUND_VARIABLE_1432123 tptp.int) (BOUND_VARIABLE_1432124 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9894 BOUND_VARIABLE_1432121) BOUND_VARIABLE_1432122) BOUND_VARIABLE_1432123) BOUND_VARIABLE_1432124) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432122) BOUND_VARIABLE_1432124)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432121) BOUND_VARIABLE_1432123)))))))))) (let ((_let_3954 (forall ((BOUND_VARIABLE_1432096 tptp.int) (BOUND_VARIABLE_1432097 tptp.int) (BOUND_VARIABLE_1432098 tptp.int) (BOUND_VARIABLE_1432099 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9895 BOUND_VARIABLE_1432096) BOUND_VARIABLE_1432097) BOUND_VARIABLE_1432098) BOUND_VARIABLE_1432099) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432097) BOUND_VARIABLE_1432099)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432096) BOUND_VARIABLE_1432098)))))))))) (let ((_let_3955 (forall ((BOUND_VARIABLE_1432071 tptp.int) (BOUND_VARIABLE_1432072 tptp.int) (BOUND_VARIABLE_1432073 tptp.int) (BOUND_VARIABLE_1432074 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9896 BOUND_VARIABLE_1432071) BOUND_VARIABLE_1432072) BOUND_VARIABLE_1432073) BOUND_VARIABLE_1432074) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432072) BOUND_VARIABLE_1432074)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432071) BOUND_VARIABLE_1432073)))))))))) (let ((_let_3956 (forall ((BOUND_VARIABLE_1432046 tptp.int) (BOUND_VARIABLE_1432047 tptp.int) (BOUND_VARIABLE_1432048 tptp.int) (BOUND_VARIABLE_1432049 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9897 BOUND_VARIABLE_1432046) BOUND_VARIABLE_1432047) BOUND_VARIABLE_1432048) BOUND_VARIABLE_1432049) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432047) BOUND_VARIABLE_1432049)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432046) BOUND_VARIABLE_1432048)))))))))) (let ((_let_3957 (forall ((BOUND_VARIABLE_1432021 tptp.int) (BOUND_VARIABLE_1432022 tptp.int) (BOUND_VARIABLE_1432023 tptp.int) (BOUND_VARIABLE_1432024 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9898 BOUND_VARIABLE_1432021) BOUND_VARIABLE_1432022) BOUND_VARIABLE_1432023) BOUND_VARIABLE_1432024) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432022) BOUND_VARIABLE_1432024)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1432021) BOUND_VARIABLE_1432023)))))))))) (let ((_let_3958 (forall ((BOUND_VARIABLE_1431996 tptp.int) (BOUND_VARIABLE_1431997 tptp.int) (BOUND_VARIABLE_1431998 tptp.int) (BOUND_VARIABLE_1431999 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9899 BOUND_VARIABLE_1431996) BOUND_VARIABLE_1431997) BOUND_VARIABLE_1431998) BOUND_VARIABLE_1431999) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431997) BOUND_VARIABLE_1431999)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431996) BOUND_VARIABLE_1431998)))))))))) (let ((_let_3959 (forall ((BOUND_VARIABLE_1431971 tptp.int) (BOUND_VARIABLE_1431972 tptp.int) (BOUND_VARIABLE_1431973 tptp.int) (BOUND_VARIABLE_1431974 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9900 BOUND_VARIABLE_1431971) BOUND_VARIABLE_1431972) BOUND_VARIABLE_1431973) BOUND_VARIABLE_1431974) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431972) BOUND_VARIABLE_1431974)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431971) BOUND_VARIABLE_1431973)))))))))) (let ((_let_3960 (forall ((BOUND_VARIABLE_1431946 tptp.int) (BOUND_VARIABLE_1431947 tptp.int) (BOUND_VARIABLE_1431948 tptp.int) (BOUND_VARIABLE_1431949 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9901 BOUND_VARIABLE_1431946) BOUND_VARIABLE_1431947) BOUND_VARIABLE_1431948) BOUND_VARIABLE_1431949) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431947) BOUND_VARIABLE_1431949)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431946) BOUND_VARIABLE_1431948)))))))))) (let ((_let_3961 (forall ((BOUND_VARIABLE_1431921 tptp.int) (BOUND_VARIABLE_1431922 tptp.int) (BOUND_VARIABLE_1431923 tptp.int) (BOUND_VARIABLE_1431924 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9902 BOUND_VARIABLE_1431921) BOUND_VARIABLE_1431922) BOUND_VARIABLE_1431923) BOUND_VARIABLE_1431924) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431922) BOUND_VARIABLE_1431924)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431921) BOUND_VARIABLE_1431923)))))))))) (let ((_let_3962 (forall ((BOUND_VARIABLE_1431896 tptp.int) (BOUND_VARIABLE_1431897 tptp.int) (BOUND_VARIABLE_1431898 tptp.int) (BOUND_VARIABLE_1431899 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9903 BOUND_VARIABLE_1431896) BOUND_VARIABLE_1431897) BOUND_VARIABLE_1431898) BOUND_VARIABLE_1431899) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431897) BOUND_VARIABLE_1431899)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431896) BOUND_VARIABLE_1431898)))))))))) (let ((_let_3963 (forall ((BOUND_VARIABLE_1431871 tptp.int) (BOUND_VARIABLE_1431872 tptp.int) (BOUND_VARIABLE_1431873 tptp.int) (BOUND_VARIABLE_1431874 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9904 BOUND_VARIABLE_1431871) BOUND_VARIABLE_1431872) BOUND_VARIABLE_1431873) BOUND_VARIABLE_1431874) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431872) BOUND_VARIABLE_1431874)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431871) BOUND_VARIABLE_1431873)))))))))) (let ((_let_3964 (forall ((BOUND_VARIABLE_1431846 tptp.int) (BOUND_VARIABLE_1431847 tptp.int) (BOUND_VARIABLE_1431848 tptp.int) (BOUND_VARIABLE_1431849 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9905 BOUND_VARIABLE_1431846) BOUND_VARIABLE_1431847) BOUND_VARIABLE_1431848) BOUND_VARIABLE_1431849) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431847) BOUND_VARIABLE_1431849)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431846) BOUND_VARIABLE_1431848)))))))))) (let ((_let_3965 (forall ((BOUND_VARIABLE_1431821 tptp.int) (BOUND_VARIABLE_1431822 tptp.int) (BOUND_VARIABLE_1431823 tptp.int) (BOUND_VARIABLE_1431824 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9906 BOUND_VARIABLE_1431821) BOUND_VARIABLE_1431822) BOUND_VARIABLE_1431823) BOUND_VARIABLE_1431824) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431822) BOUND_VARIABLE_1431824)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431821) BOUND_VARIABLE_1431823)))))))))) (let ((_let_3966 (forall ((BOUND_VARIABLE_1431796 tptp.int) (BOUND_VARIABLE_1431797 tptp.int) (BOUND_VARIABLE_1431798 tptp.int) (BOUND_VARIABLE_1431799 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9907 BOUND_VARIABLE_1431796) BOUND_VARIABLE_1431797) BOUND_VARIABLE_1431798) BOUND_VARIABLE_1431799) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431797) BOUND_VARIABLE_1431799)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431796) BOUND_VARIABLE_1431798)))))))))) (let ((_let_3967 (forall ((BOUND_VARIABLE_1431771 tptp.int) (BOUND_VARIABLE_1431772 tptp.int) (BOUND_VARIABLE_1431773 tptp.int) (BOUND_VARIABLE_1431774 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9908 BOUND_VARIABLE_1431771) BOUND_VARIABLE_1431772) BOUND_VARIABLE_1431773) BOUND_VARIABLE_1431774) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431772) BOUND_VARIABLE_1431774)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431771) BOUND_VARIABLE_1431773)))))))))) (let ((_let_3968 (forall ((BOUND_VARIABLE_1431746 tptp.int) (BOUND_VARIABLE_1431747 tptp.int) (BOUND_VARIABLE_1431748 tptp.int) (BOUND_VARIABLE_1431749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9909 BOUND_VARIABLE_1431746) BOUND_VARIABLE_1431747) BOUND_VARIABLE_1431748) BOUND_VARIABLE_1431749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431747) BOUND_VARIABLE_1431749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431746) BOUND_VARIABLE_1431748)))))))))) (let ((_let_3969 (forall ((BOUND_VARIABLE_1431721 tptp.int) (BOUND_VARIABLE_1431722 tptp.int) (BOUND_VARIABLE_1431723 tptp.int) (BOUND_VARIABLE_1431724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9910 BOUND_VARIABLE_1431721) BOUND_VARIABLE_1431722) BOUND_VARIABLE_1431723) BOUND_VARIABLE_1431724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431722) BOUND_VARIABLE_1431724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431721) BOUND_VARIABLE_1431723)))))))))) (let ((_let_3970 (forall ((BOUND_VARIABLE_1431696 tptp.int) (BOUND_VARIABLE_1431697 tptp.int) (BOUND_VARIABLE_1431698 tptp.int) (BOUND_VARIABLE_1431699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9911 BOUND_VARIABLE_1431696) BOUND_VARIABLE_1431697) BOUND_VARIABLE_1431698) BOUND_VARIABLE_1431699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431697) BOUND_VARIABLE_1431699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431696) BOUND_VARIABLE_1431698)))))))))) (let ((_let_3971 (forall ((BOUND_VARIABLE_1431671 tptp.int) (BOUND_VARIABLE_1431672 tptp.int) (BOUND_VARIABLE_1431673 tptp.int) (BOUND_VARIABLE_1431674 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9912 BOUND_VARIABLE_1431671) BOUND_VARIABLE_1431672) BOUND_VARIABLE_1431673) BOUND_VARIABLE_1431674) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431672) BOUND_VARIABLE_1431674)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431671) BOUND_VARIABLE_1431673)))))))))) (let ((_let_3972 (forall ((BOUND_VARIABLE_1431646 tptp.int) (BOUND_VARIABLE_1431647 tptp.int) (BOUND_VARIABLE_1431648 tptp.int) (BOUND_VARIABLE_1431649 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9913 BOUND_VARIABLE_1431646) BOUND_VARIABLE_1431647) BOUND_VARIABLE_1431648) BOUND_VARIABLE_1431649) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431647) BOUND_VARIABLE_1431649)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431646) BOUND_VARIABLE_1431648)))))))))) (let ((_let_3973 (forall ((BOUND_VARIABLE_1431621 tptp.int) (BOUND_VARIABLE_1431622 tptp.int) (BOUND_VARIABLE_1431623 tptp.int) (BOUND_VARIABLE_1431624 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9914 BOUND_VARIABLE_1431621) BOUND_VARIABLE_1431622) BOUND_VARIABLE_1431623) BOUND_VARIABLE_1431624) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431622) BOUND_VARIABLE_1431624)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431621) BOUND_VARIABLE_1431623)))))))))) (let ((_let_3974 (forall ((BOUND_VARIABLE_1431596 tptp.int) (BOUND_VARIABLE_1431597 tptp.int) (BOUND_VARIABLE_1431598 tptp.int) (BOUND_VARIABLE_1431599 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9915 BOUND_VARIABLE_1431596) BOUND_VARIABLE_1431597) BOUND_VARIABLE_1431598) BOUND_VARIABLE_1431599) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431597) BOUND_VARIABLE_1431599)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431596) BOUND_VARIABLE_1431598)))))))))) (let ((_let_3975 (forall ((BOUND_VARIABLE_1431571 tptp.int) (BOUND_VARIABLE_1431572 tptp.int) (BOUND_VARIABLE_1431573 tptp.int) (BOUND_VARIABLE_1431574 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9916 BOUND_VARIABLE_1431571) BOUND_VARIABLE_1431572) BOUND_VARIABLE_1431573) BOUND_VARIABLE_1431574) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431572) BOUND_VARIABLE_1431574)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431571) BOUND_VARIABLE_1431573)))))))))) (let ((_let_3976 (forall ((BOUND_VARIABLE_1431546 tptp.int) (BOUND_VARIABLE_1431547 tptp.int) (BOUND_VARIABLE_1431548 tptp.int) (BOUND_VARIABLE_1431549 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9917 BOUND_VARIABLE_1431546) BOUND_VARIABLE_1431547) BOUND_VARIABLE_1431548) BOUND_VARIABLE_1431549) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431547) BOUND_VARIABLE_1431549)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431546) BOUND_VARIABLE_1431548)))))))))) (let ((_let_3977 (forall ((BOUND_VARIABLE_1431521 tptp.int) (BOUND_VARIABLE_1431522 tptp.int) (BOUND_VARIABLE_1431523 tptp.int) (BOUND_VARIABLE_1431524 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9918 BOUND_VARIABLE_1431521) BOUND_VARIABLE_1431522) BOUND_VARIABLE_1431523) BOUND_VARIABLE_1431524) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431522) BOUND_VARIABLE_1431524)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431521) BOUND_VARIABLE_1431523)))))))))) (let ((_let_3978 (forall ((BOUND_VARIABLE_1431496 tptp.int) (BOUND_VARIABLE_1431497 tptp.int) (BOUND_VARIABLE_1431498 tptp.int) (BOUND_VARIABLE_1431499 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9919 BOUND_VARIABLE_1431496) BOUND_VARIABLE_1431497) BOUND_VARIABLE_1431498) BOUND_VARIABLE_1431499) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431497) BOUND_VARIABLE_1431499)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431496) BOUND_VARIABLE_1431498)))))))))) (let ((_let_3979 (forall ((BOUND_VARIABLE_1431471 tptp.int) (BOUND_VARIABLE_1431472 tptp.int) (BOUND_VARIABLE_1431473 tptp.int) (BOUND_VARIABLE_1431474 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9920 BOUND_VARIABLE_1431471) BOUND_VARIABLE_1431472) BOUND_VARIABLE_1431473) BOUND_VARIABLE_1431474) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431472) BOUND_VARIABLE_1431474)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431471) BOUND_VARIABLE_1431473)))))))))) (let ((_let_3980 (forall ((BOUND_VARIABLE_1431446 tptp.int) (BOUND_VARIABLE_1431447 tptp.int) (BOUND_VARIABLE_1431448 tptp.int) (BOUND_VARIABLE_1431449 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9921 BOUND_VARIABLE_1431446) BOUND_VARIABLE_1431447) BOUND_VARIABLE_1431448) BOUND_VARIABLE_1431449) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431447) BOUND_VARIABLE_1431449)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431446) BOUND_VARIABLE_1431448)))))))))) (let ((_let_3981 (forall ((BOUND_VARIABLE_1431421 tptp.int) (BOUND_VARIABLE_1431422 tptp.int) (BOUND_VARIABLE_1431423 tptp.int) (BOUND_VARIABLE_1431424 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9922 BOUND_VARIABLE_1431421) BOUND_VARIABLE_1431422) BOUND_VARIABLE_1431423) BOUND_VARIABLE_1431424) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431422) BOUND_VARIABLE_1431424)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431421) BOUND_VARIABLE_1431423)))))))))) (let ((_let_3982 (forall ((BOUND_VARIABLE_1431396 tptp.int) (BOUND_VARIABLE_1431397 tptp.int) (BOUND_VARIABLE_1431398 tptp.int) (BOUND_VARIABLE_1431399 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9923 BOUND_VARIABLE_1431396) BOUND_VARIABLE_1431397) BOUND_VARIABLE_1431398) BOUND_VARIABLE_1431399) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431397) BOUND_VARIABLE_1431399)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431396) BOUND_VARIABLE_1431398)))))))))) (let ((_let_3983 (forall ((BOUND_VARIABLE_1431371 tptp.int) (BOUND_VARIABLE_1431372 tptp.int) (BOUND_VARIABLE_1431373 tptp.int) (BOUND_VARIABLE_1431374 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9924 BOUND_VARIABLE_1431371) BOUND_VARIABLE_1431372) BOUND_VARIABLE_1431373) BOUND_VARIABLE_1431374) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431372) BOUND_VARIABLE_1431374)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431371) BOUND_VARIABLE_1431373)))))))))) (let ((_let_3984 (forall ((BOUND_VARIABLE_1431346 tptp.int) (BOUND_VARIABLE_1431347 tptp.int) (BOUND_VARIABLE_1431348 tptp.int) (BOUND_VARIABLE_1431349 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9925 BOUND_VARIABLE_1431346) BOUND_VARIABLE_1431347) BOUND_VARIABLE_1431348) BOUND_VARIABLE_1431349) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431347) BOUND_VARIABLE_1431349)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431346) BOUND_VARIABLE_1431348)))))))))) (let ((_let_3985 (forall ((BOUND_VARIABLE_1431321 tptp.int) (BOUND_VARIABLE_1431322 tptp.int) (BOUND_VARIABLE_1431323 tptp.int) (BOUND_VARIABLE_1431324 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9926 BOUND_VARIABLE_1431321) BOUND_VARIABLE_1431322) BOUND_VARIABLE_1431323) BOUND_VARIABLE_1431324) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431322) BOUND_VARIABLE_1431324)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431321) BOUND_VARIABLE_1431323)))))))))) (let ((_let_3986 (forall ((BOUND_VARIABLE_1431296 tptp.int) (BOUND_VARIABLE_1431297 tptp.int) (BOUND_VARIABLE_1431298 tptp.int) (BOUND_VARIABLE_1431299 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9927 BOUND_VARIABLE_1431296) BOUND_VARIABLE_1431297) BOUND_VARIABLE_1431298) BOUND_VARIABLE_1431299) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431297) BOUND_VARIABLE_1431299)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431296) BOUND_VARIABLE_1431298)))))))))) (let ((_let_3987 (forall ((BOUND_VARIABLE_1431271 tptp.int) (BOUND_VARIABLE_1431272 tptp.int) (BOUND_VARIABLE_1431273 tptp.int) (BOUND_VARIABLE_1431274 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9928 BOUND_VARIABLE_1431271) BOUND_VARIABLE_1431272) BOUND_VARIABLE_1431273) BOUND_VARIABLE_1431274) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431272) BOUND_VARIABLE_1431274)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431271) BOUND_VARIABLE_1431273)))))))))) (let ((_let_3988 (forall ((BOUND_VARIABLE_1431246 tptp.int) (BOUND_VARIABLE_1431247 tptp.int) (BOUND_VARIABLE_1431248 tptp.int) (BOUND_VARIABLE_1431249 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9929 BOUND_VARIABLE_1431246) BOUND_VARIABLE_1431247) BOUND_VARIABLE_1431248) BOUND_VARIABLE_1431249) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431247) BOUND_VARIABLE_1431249)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431246) BOUND_VARIABLE_1431248)))))))))) (let ((_let_3989 (forall ((BOUND_VARIABLE_1431221 tptp.int) (BOUND_VARIABLE_1431222 tptp.int) (BOUND_VARIABLE_1431223 tptp.int) (BOUND_VARIABLE_1431224 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9930 BOUND_VARIABLE_1431221) BOUND_VARIABLE_1431222) BOUND_VARIABLE_1431223) BOUND_VARIABLE_1431224) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431222) BOUND_VARIABLE_1431224)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431221) BOUND_VARIABLE_1431223)))))))))) (let ((_let_3990 (forall ((BOUND_VARIABLE_1431196 tptp.int) (BOUND_VARIABLE_1431197 tptp.int) (BOUND_VARIABLE_1431198 tptp.int) (BOUND_VARIABLE_1431199 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9931 BOUND_VARIABLE_1431196) BOUND_VARIABLE_1431197) BOUND_VARIABLE_1431198) BOUND_VARIABLE_1431199) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431197) BOUND_VARIABLE_1431199)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431196) BOUND_VARIABLE_1431198)))))))))) (let ((_let_3991 (forall ((BOUND_VARIABLE_1431171 tptp.int) (BOUND_VARIABLE_1431172 tptp.int) (BOUND_VARIABLE_1431173 tptp.int) (BOUND_VARIABLE_1431174 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9932 BOUND_VARIABLE_1431171) BOUND_VARIABLE_1431172) BOUND_VARIABLE_1431173) BOUND_VARIABLE_1431174) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431172) BOUND_VARIABLE_1431174)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431171) BOUND_VARIABLE_1431173)))))))))) (let ((_let_3992 (forall ((BOUND_VARIABLE_1431146 tptp.int) (BOUND_VARIABLE_1431147 tptp.int) (BOUND_VARIABLE_1431148 tptp.int) (BOUND_VARIABLE_1431149 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9933 BOUND_VARIABLE_1431146) BOUND_VARIABLE_1431147) BOUND_VARIABLE_1431148) BOUND_VARIABLE_1431149) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431147) BOUND_VARIABLE_1431149)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431146) BOUND_VARIABLE_1431148)))))))))) (let ((_let_3993 (forall ((BOUND_VARIABLE_1431121 tptp.int) (BOUND_VARIABLE_1431122 tptp.int) (BOUND_VARIABLE_1431123 tptp.int) (BOUND_VARIABLE_1431124 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9934 BOUND_VARIABLE_1431121) BOUND_VARIABLE_1431122) BOUND_VARIABLE_1431123) BOUND_VARIABLE_1431124) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431122) BOUND_VARIABLE_1431124)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431121) BOUND_VARIABLE_1431123)))))))))) (let ((_let_3994 (forall ((BOUND_VARIABLE_1431096 tptp.int) (BOUND_VARIABLE_1431097 tptp.int) (BOUND_VARIABLE_1431098 tptp.int) (BOUND_VARIABLE_1431099 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9935 BOUND_VARIABLE_1431096) BOUND_VARIABLE_1431097) BOUND_VARIABLE_1431098) BOUND_VARIABLE_1431099) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431097) BOUND_VARIABLE_1431099)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431096) BOUND_VARIABLE_1431098)))))))))) (let ((_let_3995 (forall ((BOUND_VARIABLE_1431071 tptp.int) (BOUND_VARIABLE_1431072 tptp.int) (BOUND_VARIABLE_1431073 tptp.int) (BOUND_VARIABLE_1431074 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9936 BOUND_VARIABLE_1431071) BOUND_VARIABLE_1431072) BOUND_VARIABLE_1431073) BOUND_VARIABLE_1431074) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431072) BOUND_VARIABLE_1431074)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431071) BOUND_VARIABLE_1431073)))))))))) (let ((_let_3996 (forall ((BOUND_VARIABLE_1431046 tptp.int) (BOUND_VARIABLE_1431047 tptp.int) (BOUND_VARIABLE_1431048 tptp.int) (BOUND_VARIABLE_1431049 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9937 BOUND_VARIABLE_1431046) BOUND_VARIABLE_1431047) BOUND_VARIABLE_1431048) BOUND_VARIABLE_1431049) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431047) BOUND_VARIABLE_1431049)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431046) BOUND_VARIABLE_1431048)))))))))) (let ((_let_3997 (forall ((BOUND_VARIABLE_1431021 tptp.int) (BOUND_VARIABLE_1431022 tptp.int) (BOUND_VARIABLE_1431023 tptp.int) (BOUND_VARIABLE_1431024 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9938 BOUND_VARIABLE_1431021) BOUND_VARIABLE_1431022) BOUND_VARIABLE_1431023) BOUND_VARIABLE_1431024) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431022) BOUND_VARIABLE_1431024)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1431021) BOUND_VARIABLE_1431023)))))))))) (let ((_let_3998 (forall ((BOUND_VARIABLE_1430996 tptp.int) (BOUND_VARIABLE_1430997 tptp.int) (BOUND_VARIABLE_1430998 tptp.int) (BOUND_VARIABLE_1430999 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9939 BOUND_VARIABLE_1430996) BOUND_VARIABLE_1430997) BOUND_VARIABLE_1430998) BOUND_VARIABLE_1430999) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430997) BOUND_VARIABLE_1430999)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430996) BOUND_VARIABLE_1430998)))))))))) (let ((_let_3999 (forall ((BOUND_VARIABLE_1430971 tptp.int) (BOUND_VARIABLE_1430972 tptp.int) (BOUND_VARIABLE_1430973 tptp.int) (BOUND_VARIABLE_1430974 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9940 BOUND_VARIABLE_1430971) BOUND_VARIABLE_1430972) BOUND_VARIABLE_1430973) BOUND_VARIABLE_1430974) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430972) BOUND_VARIABLE_1430974)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430971) BOUND_VARIABLE_1430973)))))))))) (let ((_let_4000 (forall ((BOUND_VARIABLE_1430946 tptp.int) (BOUND_VARIABLE_1430947 tptp.int) (BOUND_VARIABLE_1430948 tptp.int) (BOUND_VARIABLE_1430949 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9941 BOUND_VARIABLE_1430946) BOUND_VARIABLE_1430947) BOUND_VARIABLE_1430948) BOUND_VARIABLE_1430949) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430947) BOUND_VARIABLE_1430949)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430946) BOUND_VARIABLE_1430948)))))))))) (let ((_let_4001 (forall ((BOUND_VARIABLE_1430921 tptp.int) (BOUND_VARIABLE_1430922 tptp.int) (BOUND_VARIABLE_1430923 tptp.int) (BOUND_VARIABLE_1430924 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9942 BOUND_VARIABLE_1430921) BOUND_VARIABLE_1430922) BOUND_VARIABLE_1430923) BOUND_VARIABLE_1430924) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430922) BOUND_VARIABLE_1430924)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430921) BOUND_VARIABLE_1430923)))))))))) (let ((_let_4002 (forall ((BOUND_VARIABLE_1430896 tptp.int) (BOUND_VARIABLE_1430897 tptp.int) (BOUND_VARIABLE_1430898 tptp.int) (BOUND_VARIABLE_1430899 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9943 BOUND_VARIABLE_1430896) BOUND_VARIABLE_1430897) BOUND_VARIABLE_1430898) BOUND_VARIABLE_1430899) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430897) BOUND_VARIABLE_1430899)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430896) BOUND_VARIABLE_1430898)))))))))) (let ((_let_4003 (forall ((BOUND_VARIABLE_1430871 tptp.int) (BOUND_VARIABLE_1430872 tptp.int) (BOUND_VARIABLE_1430873 tptp.int) (BOUND_VARIABLE_1430874 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9944 BOUND_VARIABLE_1430871) BOUND_VARIABLE_1430872) BOUND_VARIABLE_1430873) BOUND_VARIABLE_1430874) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430872) BOUND_VARIABLE_1430874)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430871) BOUND_VARIABLE_1430873)))))))))) (let ((_let_4004 (forall ((BOUND_VARIABLE_1430846 tptp.int) (BOUND_VARIABLE_1430847 tptp.int) (BOUND_VARIABLE_1430848 tptp.int) (BOUND_VARIABLE_1430849 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9945 BOUND_VARIABLE_1430846) BOUND_VARIABLE_1430847) BOUND_VARIABLE_1430848) BOUND_VARIABLE_1430849) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430847) BOUND_VARIABLE_1430849)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430846) BOUND_VARIABLE_1430848)))))))))) (let ((_let_4005 (forall ((BOUND_VARIABLE_1430821 tptp.int) (BOUND_VARIABLE_1430822 tptp.int) (BOUND_VARIABLE_1430823 tptp.int) (BOUND_VARIABLE_1430824 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9946 BOUND_VARIABLE_1430821) BOUND_VARIABLE_1430822) BOUND_VARIABLE_1430823) BOUND_VARIABLE_1430824) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430822) BOUND_VARIABLE_1430824)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430821) BOUND_VARIABLE_1430823)))))))))) (let ((_let_4006 (forall ((BOUND_VARIABLE_1430796 tptp.int) (BOUND_VARIABLE_1430797 tptp.int) (BOUND_VARIABLE_1430798 tptp.int) (BOUND_VARIABLE_1430799 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9947 BOUND_VARIABLE_1430796) BOUND_VARIABLE_1430797) BOUND_VARIABLE_1430798) BOUND_VARIABLE_1430799) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430797) BOUND_VARIABLE_1430799)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430796) BOUND_VARIABLE_1430798)))))))))) (let ((_let_4007 (forall ((BOUND_VARIABLE_1430771 tptp.int) (BOUND_VARIABLE_1430772 tptp.int) (BOUND_VARIABLE_1430773 tptp.int) (BOUND_VARIABLE_1430774 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9948 BOUND_VARIABLE_1430771) BOUND_VARIABLE_1430772) BOUND_VARIABLE_1430773) BOUND_VARIABLE_1430774) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430772) BOUND_VARIABLE_1430774)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430771) BOUND_VARIABLE_1430773)))))))))) (let ((_let_4008 (forall ((BOUND_VARIABLE_1430746 tptp.int) (BOUND_VARIABLE_1430747 tptp.int) (BOUND_VARIABLE_1430748 tptp.int) (BOUND_VARIABLE_1430749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9949 BOUND_VARIABLE_1430746) BOUND_VARIABLE_1430747) BOUND_VARIABLE_1430748) BOUND_VARIABLE_1430749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430747) BOUND_VARIABLE_1430749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430746) BOUND_VARIABLE_1430748)))))))))) (let ((_let_4009 (forall ((BOUND_VARIABLE_1430721 tptp.int) (BOUND_VARIABLE_1430722 tptp.int) (BOUND_VARIABLE_1430723 tptp.int) (BOUND_VARIABLE_1430724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9950 BOUND_VARIABLE_1430721) BOUND_VARIABLE_1430722) BOUND_VARIABLE_1430723) BOUND_VARIABLE_1430724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430722) BOUND_VARIABLE_1430724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430721) BOUND_VARIABLE_1430723)))))))))) (let ((_let_4010 (forall ((BOUND_VARIABLE_1430696 tptp.int) (BOUND_VARIABLE_1430697 tptp.int) (BOUND_VARIABLE_1430698 tptp.int) (BOUND_VARIABLE_1430699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9951 BOUND_VARIABLE_1430696) BOUND_VARIABLE_1430697) BOUND_VARIABLE_1430698) BOUND_VARIABLE_1430699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430697) BOUND_VARIABLE_1430699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430696) BOUND_VARIABLE_1430698)))))))))) (let ((_let_4011 (forall ((BOUND_VARIABLE_1430671 tptp.int) (BOUND_VARIABLE_1430672 tptp.int) (BOUND_VARIABLE_1430673 tptp.int) (BOUND_VARIABLE_1430674 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9952 BOUND_VARIABLE_1430671) BOUND_VARIABLE_1430672) BOUND_VARIABLE_1430673) BOUND_VARIABLE_1430674) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430672) BOUND_VARIABLE_1430674)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430671) BOUND_VARIABLE_1430673)))))))))) (let ((_let_4012 (forall ((BOUND_VARIABLE_1430646 tptp.int) (BOUND_VARIABLE_1430647 tptp.int) (BOUND_VARIABLE_1430648 tptp.int) (BOUND_VARIABLE_1430649 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9953 BOUND_VARIABLE_1430646) BOUND_VARIABLE_1430647) BOUND_VARIABLE_1430648) BOUND_VARIABLE_1430649) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430647) BOUND_VARIABLE_1430649)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430646) BOUND_VARIABLE_1430648)))))))))) (let ((_let_4013 (forall ((BOUND_VARIABLE_1430621 tptp.int) (BOUND_VARIABLE_1430622 tptp.int) (BOUND_VARIABLE_1430623 tptp.int) (BOUND_VARIABLE_1430624 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9954 BOUND_VARIABLE_1430621) BOUND_VARIABLE_1430622) BOUND_VARIABLE_1430623) BOUND_VARIABLE_1430624) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430622) BOUND_VARIABLE_1430624)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430621) BOUND_VARIABLE_1430623)))))))))) (let ((_let_4014 (forall ((BOUND_VARIABLE_1430596 tptp.int) (BOUND_VARIABLE_1430597 tptp.int) (BOUND_VARIABLE_1430598 tptp.int) (BOUND_VARIABLE_1430599 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9955 BOUND_VARIABLE_1430596) BOUND_VARIABLE_1430597) BOUND_VARIABLE_1430598) BOUND_VARIABLE_1430599) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430597) BOUND_VARIABLE_1430599)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430596) BOUND_VARIABLE_1430598)))))))))) (let ((_let_4015 (forall ((BOUND_VARIABLE_1430571 tptp.int) (BOUND_VARIABLE_1430572 tptp.int) (BOUND_VARIABLE_1430573 tptp.int) (BOUND_VARIABLE_1430574 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9956 BOUND_VARIABLE_1430571) BOUND_VARIABLE_1430572) BOUND_VARIABLE_1430573) BOUND_VARIABLE_1430574) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430572) BOUND_VARIABLE_1430574)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430571) BOUND_VARIABLE_1430573)))))))))) (let ((_let_4016 (forall ((BOUND_VARIABLE_1430546 tptp.int) (BOUND_VARIABLE_1430547 tptp.int) (BOUND_VARIABLE_1430548 tptp.int) (BOUND_VARIABLE_1430549 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9957 BOUND_VARIABLE_1430546) BOUND_VARIABLE_1430547) BOUND_VARIABLE_1430548) BOUND_VARIABLE_1430549) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430547) BOUND_VARIABLE_1430549)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430546) BOUND_VARIABLE_1430548)))))))))) (let ((_let_4017 (forall ((BOUND_VARIABLE_1430521 tptp.int) (BOUND_VARIABLE_1430522 tptp.int) (BOUND_VARIABLE_1430523 tptp.int) (BOUND_VARIABLE_1430524 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9958 BOUND_VARIABLE_1430521) BOUND_VARIABLE_1430522) BOUND_VARIABLE_1430523) BOUND_VARIABLE_1430524) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430522) BOUND_VARIABLE_1430524)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430521) BOUND_VARIABLE_1430523)))))))))) (let ((_let_4018 (forall ((BOUND_VARIABLE_1430496 tptp.int) (BOUND_VARIABLE_1430497 tptp.int) (BOUND_VARIABLE_1430498 tptp.int) (BOUND_VARIABLE_1430499 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9959 BOUND_VARIABLE_1430496) BOUND_VARIABLE_1430497) BOUND_VARIABLE_1430498) BOUND_VARIABLE_1430499) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430497) BOUND_VARIABLE_1430499)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430496) BOUND_VARIABLE_1430498)))))))))) (let ((_let_4019 (forall ((BOUND_VARIABLE_1430471 tptp.int) (BOUND_VARIABLE_1430472 tptp.int) (BOUND_VARIABLE_1430473 tptp.int) (BOUND_VARIABLE_1430474 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9960 BOUND_VARIABLE_1430471) BOUND_VARIABLE_1430472) BOUND_VARIABLE_1430473) BOUND_VARIABLE_1430474) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430472) BOUND_VARIABLE_1430474)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430471) BOUND_VARIABLE_1430473)))))))))) (let ((_let_4020 (forall ((BOUND_VARIABLE_1430446 tptp.int) (BOUND_VARIABLE_1430447 tptp.int) (BOUND_VARIABLE_1430448 tptp.int) (BOUND_VARIABLE_1430449 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9961 BOUND_VARIABLE_1430446) BOUND_VARIABLE_1430447) BOUND_VARIABLE_1430448) BOUND_VARIABLE_1430449) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430447) BOUND_VARIABLE_1430449)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430446) BOUND_VARIABLE_1430448)))))))))) (let ((_let_4021 (forall ((BOUND_VARIABLE_1430421 tptp.int) (BOUND_VARIABLE_1430422 tptp.int) (BOUND_VARIABLE_1430423 tptp.int) (BOUND_VARIABLE_1430424 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9962 BOUND_VARIABLE_1430421) BOUND_VARIABLE_1430422) BOUND_VARIABLE_1430423) BOUND_VARIABLE_1430424) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430422) BOUND_VARIABLE_1430424)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430421) BOUND_VARIABLE_1430423)))))))))) (let ((_let_4022 (forall ((BOUND_VARIABLE_1430396 tptp.int) (BOUND_VARIABLE_1430397 tptp.int) (BOUND_VARIABLE_1430398 tptp.int) (BOUND_VARIABLE_1430399 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9963 BOUND_VARIABLE_1430396) BOUND_VARIABLE_1430397) BOUND_VARIABLE_1430398) BOUND_VARIABLE_1430399) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430397) BOUND_VARIABLE_1430399)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430396) BOUND_VARIABLE_1430398)))))))))) (let ((_let_4023 (forall ((BOUND_VARIABLE_1430371 tptp.int) (BOUND_VARIABLE_1430372 tptp.int) (BOUND_VARIABLE_1430373 tptp.int) (BOUND_VARIABLE_1430374 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9964 BOUND_VARIABLE_1430371) BOUND_VARIABLE_1430372) BOUND_VARIABLE_1430373) BOUND_VARIABLE_1430374) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430372) BOUND_VARIABLE_1430374)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430371) BOUND_VARIABLE_1430373)))))))))) (let ((_let_4024 (forall ((BOUND_VARIABLE_1430346 tptp.int) (BOUND_VARIABLE_1430347 tptp.int) (BOUND_VARIABLE_1430348 tptp.int) (BOUND_VARIABLE_1430349 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9965 BOUND_VARIABLE_1430346) BOUND_VARIABLE_1430347) BOUND_VARIABLE_1430348) BOUND_VARIABLE_1430349) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430347) BOUND_VARIABLE_1430349)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430346) BOUND_VARIABLE_1430348)))))))))) (let ((_let_4025 (forall ((BOUND_VARIABLE_1430321 tptp.int) (BOUND_VARIABLE_1430322 tptp.int) (BOUND_VARIABLE_1430323 tptp.int) (BOUND_VARIABLE_1430324 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9966 BOUND_VARIABLE_1430321) BOUND_VARIABLE_1430322) BOUND_VARIABLE_1430323) BOUND_VARIABLE_1430324) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430322) BOUND_VARIABLE_1430324)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430321) BOUND_VARIABLE_1430323)))))))))) (let ((_let_4026 (forall ((BOUND_VARIABLE_1430296 tptp.int) (BOUND_VARIABLE_1430297 tptp.int) (BOUND_VARIABLE_1430298 tptp.int) (BOUND_VARIABLE_1430299 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9967 BOUND_VARIABLE_1430296) BOUND_VARIABLE_1430297) BOUND_VARIABLE_1430298) BOUND_VARIABLE_1430299) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430297) BOUND_VARIABLE_1430299)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430296) BOUND_VARIABLE_1430298)))))))))) (let ((_let_4027 (forall ((BOUND_VARIABLE_1430271 tptp.int) (BOUND_VARIABLE_1430272 tptp.int) (BOUND_VARIABLE_1430273 tptp.int) (BOUND_VARIABLE_1430274 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9968 BOUND_VARIABLE_1430271) BOUND_VARIABLE_1430272) BOUND_VARIABLE_1430273) BOUND_VARIABLE_1430274) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430272) BOUND_VARIABLE_1430274)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430271) BOUND_VARIABLE_1430273)))))))))) (let ((_let_4028 (forall ((BOUND_VARIABLE_1430246 tptp.int) (BOUND_VARIABLE_1430247 tptp.int) (BOUND_VARIABLE_1430248 tptp.int) (BOUND_VARIABLE_1430249 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9969 BOUND_VARIABLE_1430246) BOUND_VARIABLE_1430247) BOUND_VARIABLE_1430248) BOUND_VARIABLE_1430249) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430247) BOUND_VARIABLE_1430249)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430246) BOUND_VARIABLE_1430248)))))))))) (let ((_let_4029 (forall ((BOUND_VARIABLE_1430221 tptp.int) (BOUND_VARIABLE_1430222 tptp.int) (BOUND_VARIABLE_1430223 tptp.int) (BOUND_VARIABLE_1430224 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9970 BOUND_VARIABLE_1430221) BOUND_VARIABLE_1430222) BOUND_VARIABLE_1430223) BOUND_VARIABLE_1430224) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430222) BOUND_VARIABLE_1430224)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430221) BOUND_VARIABLE_1430223)))))))))) (let ((_let_4030 (forall ((BOUND_VARIABLE_1430196 tptp.int) (BOUND_VARIABLE_1430197 tptp.int) (BOUND_VARIABLE_1430198 tptp.int) (BOUND_VARIABLE_1430199 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9971 BOUND_VARIABLE_1430196) BOUND_VARIABLE_1430197) BOUND_VARIABLE_1430198) BOUND_VARIABLE_1430199) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430197) BOUND_VARIABLE_1430199)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430196) BOUND_VARIABLE_1430198)))))))))) (let ((_let_4031 (forall ((BOUND_VARIABLE_1430171 tptp.int) (BOUND_VARIABLE_1430172 tptp.int) (BOUND_VARIABLE_1430173 tptp.int) (BOUND_VARIABLE_1430174 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9972 BOUND_VARIABLE_1430171) BOUND_VARIABLE_1430172) BOUND_VARIABLE_1430173) BOUND_VARIABLE_1430174) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430172) BOUND_VARIABLE_1430174)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430171) BOUND_VARIABLE_1430173)))))))))) (let ((_let_4032 (forall ((BOUND_VARIABLE_1430146 tptp.int) (BOUND_VARIABLE_1430147 tptp.int) (BOUND_VARIABLE_1430148 tptp.int) (BOUND_VARIABLE_1430149 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9973 BOUND_VARIABLE_1430146) BOUND_VARIABLE_1430147) BOUND_VARIABLE_1430148) BOUND_VARIABLE_1430149) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430147) BOUND_VARIABLE_1430149)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430146) BOUND_VARIABLE_1430148)))))))))) (let ((_let_4033 (forall ((BOUND_VARIABLE_1430121 tptp.int) (BOUND_VARIABLE_1430122 tptp.int) (BOUND_VARIABLE_1430123 tptp.int) (BOUND_VARIABLE_1430124 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9974 BOUND_VARIABLE_1430121) BOUND_VARIABLE_1430122) BOUND_VARIABLE_1430123) BOUND_VARIABLE_1430124) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430122) BOUND_VARIABLE_1430124)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430121) BOUND_VARIABLE_1430123)))))))))) (let ((_let_4034 (forall ((BOUND_VARIABLE_1430096 tptp.int) (BOUND_VARIABLE_1430097 tptp.int) (BOUND_VARIABLE_1430098 tptp.int) (BOUND_VARIABLE_1430099 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9975 BOUND_VARIABLE_1430096) BOUND_VARIABLE_1430097) BOUND_VARIABLE_1430098) BOUND_VARIABLE_1430099) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430097) BOUND_VARIABLE_1430099)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430096) BOUND_VARIABLE_1430098)))))))))) (let ((_let_4035 (forall ((BOUND_VARIABLE_1430071 tptp.int) (BOUND_VARIABLE_1430072 tptp.int) (BOUND_VARIABLE_1430073 tptp.int) (BOUND_VARIABLE_1430074 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9976 BOUND_VARIABLE_1430071) BOUND_VARIABLE_1430072) BOUND_VARIABLE_1430073) BOUND_VARIABLE_1430074) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430072) BOUND_VARIABLE_1430074)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430071) BOUND_VARIABLE_1430073)))))))))) (let ((_let_4036 (forall ((BOUND_VARIABLE_1430046 tptp.int) (BOUND_VARIABLE_1430047 tptp.int) (BOUND_VARIABLE_1430048 tptp.int) (BOUND_VARIABLE_1430049 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9977 BOUND_VARIABLE_1430046) BOUND_VARIABLE_1430047) BOUND_VARIABLE_1430048) BOUND_VARIABLE_1430049) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430047) BOUND_VARIABLE_1430049)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430046) BOUND_VARIABLE_1430048)))))))))) (let ((_let_4037 (forall ((BOUND_VARIABLE_1430021 tptp.int) (BOUND_VARIABLE_1430022 tptp.int) (BOUND_VARIABLE_1430023 tptp.int) (BOUND_VARIABLE_1430024 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9978 BOUND_VARIABLE_1430021) BOUND_VARIABLE_1430022) BOUND_VARIABLE_1430023) BOUND_VARIABLE_1430024) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430022) BOUND_VARIABLE_1430024)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1430021) BOUND_VARIABLE_1430023)))))))))) (let ((_let_4038 (forall ((BOUND_VARIABLE_1429996 tptp.int) (BOUND_VARIABLE_1429997 tptp.int) (BOUND_VARIABLE_1429998 tptp.int) (BOUND_VARIABLE_1429999 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9979 BOUND_VARIABLE_1429996) BOUND_VARIABLE_1429997) BOUND_VARIABLE_1429998) BOUND_VARIABLE_1429999) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429997) BOUND_VARIABLE_1429999)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429996) BOUND_VARIABLE_1429998)))))))))) (let ((_let_4039 (forall ((BOUND_VARIABLE_1429971 tptp.int) (BOUND_VARIABLE_1429972 tptp.int) (BOUND_VARIABLE_1429973 tptp.int) (BOUND_VARIABLE_1429974 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9980 BOUND_VARIABLE_1429971) BOUND_VARIABLE_1429972) BOUND_VARIABLE_1429973) BOUND_VARIABLE_1429974) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429972) BOUND_VARIABLE_1429974)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429971) BOUND_VARIABLE_1429973)))))))))) (let ((_let_4040 (forall ((BOUND_VARIABLE_1429946 tptp.int) (BOUND_VARIABLE_1429947 tptp.int) (BOUND_VARIABLE_1429948 tptp.int) (BOUND_VARIABLE_1429949 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9981 BOUND_VARIABLE_1429946) BOUND_VARIABLE_1429947) BOUND_VARIABLE_1429948) BOUND_VARIABLE_1429949) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429947) BOUND_VARIABLE_1429949)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429946) BOUND_VARIABLE_1429948)))))))))) (let ((_let_4041 (forall ((BOUND_VARIABLE_1429921 tptp.int) (BOUND_VARIABLE_1429922 tptp.int) (BOUND_VARIABLE_1429923 tptp.int) (BOUND_VARIABLE_1429924 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9982 BOUND_VARIABLE_1429921) BOUND_VARIABLE_1429922) BOUND_VARIABLE_1429923) BOUND_VARIABLE_1429924) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429922) BOUND_VARIABLE_1429924)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429921) BOUND_VARIABLE_1429923)))))))))) (let ((_let_4042 (forall ((BOUND_VARIABLE_1429896 tptp.int) (BOUND_VARIABLE_1429897 tptp.int) (BOUND_VARIABLE_1429898 tptp.int) (BOUND_VARIABLE_1429899 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9983 BOUND_VARIABLE_1429896) BOUND_VARIABLE_1429897) BOUND_VARIABLE_1429898) BOUND_VARIABLE_1429899) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429897) BOUND_VARIABLE_1429899)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429896) BOUND_VARIABLE_1429898)))))))))) (let ((_let_4043 (forall ((BOUND_VARIABLE_1429871 tptp.int) (BOUND_VARIABLE_1429872 tptp.int) (BOUND_VARIABLE_1429873 tptp.int) (BOUND_VARIABLE_1429874 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9984 BOUND_VARIABLE_1429871) BOUND_VARIABLE_1429872) BOUND_VARIABLE_1429873) BOUND_VARIABLE_1429874) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429872) BOUND_VARIABLE_1429874)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429871) BOUND_VARIABLE_1429873)))))))))) (let ((_let_4044 (forall ((BOUND_VARIABLE_1429846 tptp.int) (BOUND_VARIABLE_1429847 tptp.int) (BOUND_VARIABLE_1429848 tptp.int) (BOUND_VARIABLE_1429849 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9985 BOUND_VARIABLE_1429846) BOUND_VARIABLE_1429847) BOUND_VARIABLE_1429848) BOUND_VARIABLE_1429849) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429847) BOUND_VARIABLE_1429849)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429846) BOUND_VARIABLE_1429848)))))))))) (let ((_let_4045 (forall ((BOUND_VARIABLE_1429821 tptp.int) (BOUND_VARIABLE_1429822 tptp.int) (BOUND_VARIABLE_1429823 tptp.int) (BOUND_VARIABLE_1429824 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9986 BOUND_VARIABLE_1429821) BOUND_VARIABLE_1429822) BOUND_VARIABLE_1429823) BOUND_VARIABLE_1429824) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429822) BOUND_VARIABLE_1429824)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429821) BOUND_VARIABLE_1429823)))))))))) (let ((_let_4046 (forall ((BOUND_VARIABLE_1429796 tptp.int) (BOUND_VARIABLE_1429797 tptp.int) (BOUND_VARIABLE_1429798 tptp.int) (BOUND_VARIABLE_1429799 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9987 BOUND_VARIABLE_1429796) BOUND_VARIABLE_1429797) BOUND_VARIABLE_1429798) BOUND_VARIABLE_1429799) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429797) BOUND_VARIABLE_1429799)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429796) BOUND_VARIABLE_1429798)))))))))) (let ((_let_4047 (forall ((BOUND_VARIABLE_1429771 tptp.int) (BOUND_VARIABLE_1429772 tptp.int) (BOUND_VARIABLE_1429773 tptp.int) (BOUND_VARIABLE_1429774 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9988 BOUND_VARIABLE_1429771) BOUND_VARIABLE_1429772) BOUND_VARIABLE_1429773) BOUND_VARIABLE_1429774) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429772) BOUND_VARIABLE_1429774)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429771) BOUND_VARIABLE_1429773)))))))))) (let ((_let_4048 (forall ((BOUND_VARIABLE_1429746 tptp.int) (BOUND_VARIABLE_1429747 tptp.int) (BOUND_VARIABLE_1429748 tptp.int) (BOUND_VARIABLE_1429749 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9989 BOUND_VARIABLE_1429746) BOUND_VARIABLE_1429747) BOUND_VARIABLE_1429748) BOUND_VARIABLE_1429749) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429747) BOUND_VARIABLE_1429749)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429746) BOUND_VARIABLE_1429748)))))))))) (let ((_let_4049 (forall ((BOUND_VARIABLE_1429721 tptp.int) (BOUND_VARIABLE_1429722 tptp.int) (BOUND_VARIABLE_1429723 tptp.int) (BOUND_VARIABLE_1429724 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9990 BOUND_VARIABLE_1429721) BOUND_VARIABLE_1429722) BOUND_VARIABLE_1429723) BOUND_VARIABLE_1429724) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429722) BOUND_VARIABLE_1429724)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429721) BOUND_VARIABLE_1429723)))))))))) (let ((_let_4050 (forall ((BOUND_VARIABLE_1429696 tptp.int) (BOUND_VARIABLE_1429697 tptp.int) (BOUND_VARIABLE_1429698 tptp.int) (BOUND_VARIABLE_1429699 tptp.int)) (= (ho_7496 (ho_7495 (ho_7494 (ho_7493 k_9991 BOUND_VARIABLE_1429696) BOUND_VARIABLE_1429697) BOUND_VARIABLE_1429698) BOUND_VARIABLE_1429699) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429697) BOUND_VARIABLE_1429699)) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (ho_7459 (ho_7461 k_7472 BOUND_VARIABLE_1429696) BOUND_VARIABLE_1429698)))))))))) (let ((_let_4051 (forall ((BOUND_VARIABLE_1429666 tptp.nat) (BOUND_VARIABLE_1429667 tptp.nat) (BOUND_VARIABLE_1429668 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1429667) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1429668) _let_2))))) (ho_7533 k_7532 BOUND_VARIABLE_1429666)) (ho_7541 (ho_7540 (ho_7539 k_9992 BOUND_VARIABLE_1429666) BOUND_VARIABLE_1429667) BOUND_VARIABLE_1429668)))))))) (let ((_let_4052 (forall ((BOUND_VARIABLE_1429656 tptp.nat) (BOUND_VARIABLE_1429657 tptp.nat)) (= (ho_7541 (ho_7540 k_9993 BOUND_VARIABLE_1429656) BOUND_VARIABLE_1429657) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1429657)) (ho_7533 k_7532 BOUND_VARIABLE_1429656)))))) (let ((_let_4053 (forall ((BOUND_VARIABLE_1429618 tptp.nat) (BOUND_VARIABLE_1429619 tptp.nat)) (= (ho_9995 k_9994 (ho_7540 (ho_7539 k_7628 BOUND_VARIABLE_1429618) BOUND_VARIABLE_1429619)) (ho_9998 (ho_9997 k_9996 BOUND_VARIABLE_1429618) BOUND_VARIABLE_1429619))))) (let ((_let_4054 (forall ((BOUND_VARIABLE_1568188 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_232918 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (or (not (ho_7633 (ho_7632 k_7631 (ho_7635 k_7634 R5)) (ho_7630 k_7629 _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (or (not (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_232918)) (ho_7533 k_7532 N2))) (and (ho_7633 (ho_7632 k_7631 (ho_7639 (ho_7638 k_7637 BOUND_VARIABLE_1568188) N2)) (ho_7630 k_7629 R5)) (not (= R5 (ho_7636 BOUND_VARIABLE_1568188 N2))))))))))))))) (ho_10000 k_9999 BOUND_VARIABLE_1568188))))) (let ((_let_4055 (forall ((BOUND_VARIABLE_1429541 tptp.product_prod_int_int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429541)) (ho_7907 k_7906 BOUND_VARIABLE_1429541)))))))) (not (= (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429541)) (ho_7907 k_7906 BOUND_VARIABLE_1429541))))) (ho_7633 k_10001 BOUND_VARIABLE_1429541)))))) (let ((_let_4056 (forall ((BOUND_VARIABLE_1429522 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7908 BOUND_VARIABLE_1429522))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (= (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_3 _let_1)) (ho_7698 (ho_7697 k_7696 _let_3) _let_2)) (ho_7698 (ho_7697 k_7696 (ho_7907 k_7906 BOUND_VARIABLE_1429522)) _let_1)) (ho_7702 k_10002 BOUND_VARIABLE_1429522)))))))) (let ((_let_4057 (forall ((BOUND_VARIABLE_1429503 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7908 BOUND_VARIABLE_1429503))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (= (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_3 _let_1)) (ho_7698 (ho_7697 k_7696 _let_3) _let_2)) (ho_7698 (ho_7697 k_7696 (ho_7907 k_7906 BOUND_VARIABLE_1429503)) _let_1)) (ho_7702 k_10003 BOUND_VARIABLE_1429503)))))))) (let ((_let_4058 (forall ((BOUND_VARIABLE_1429496 Bool) (BOUND_VARIABLE_1429497 Bool)) (= (= BOUND_VARIABLE_1429496 BOUND_VARIABLE_1429497) (ho_8986 (ho_10005 k_10004 BOUND_VARIABLE_1429496) BOUND_VARIABLE_1429497))))) (let ((_let_4059 (forall ((BOUND_VARIABLE_1429471 tptp.product_prod_int_int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429471)) (ho_7907 k_7906 BOUND_VARIABLE_1429471)))))))) (not (= (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429471)) (ho_7907 k_7906 BOUND_VARIABLE_1429471))))) (ho_7633 k_10006 BOUND_VARIABLE_1429471)))))) (let ((_let_4060 (forall ((BOUND_VARIABLE_1429446 tptp.product_prod_int_int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429446)) (ho_7907 k_7906 BOUND_VARIABLE_1429446)))))))) (not (= (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429446)) (ho_7907 k_7906 BOUND_VARIABLE_1429446))))) (ho_7633 k_10007 BOUND_VARIABLE_1429446)))))) (let ((_let_4061 (forall ((BOUND_VARIABLE_1429430 tptp.product_prod_int_int) (BOUND_VARIABLE_1429431 tptp.product_prod_int_int)) (= (ho_7702 (ho_7701 k_10008 BOUND_VARIABLE_1429430) BOUND_VARIABLE_1429431) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429430)) (ho_7907 k_7908 BOUND_VARIABLE_1429431))) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7906 BOUND_VARIABLE_1429430)) (ho_7907 k_7906 BOUND_VARIABLE_1429431))))))) (let ((_let_4062 (forall ((BOUND_VARIABLE_1429414 tptp.product_prod_int_int) (BOUND_VARIABLE_1429415 tptp.product_prod_int_int)) (= (ho_7702 (ho_7701 k_10009 BOUND_VARIABLE_1429414) BOUND_VARIABLE_1429415) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429414)) (ho_7907 k_7908 BOUND_VARIABLE_1429415))) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7906 BOUND_VARIABLE_1429414)) (ho_7907 k_7906 BOUND_VARIABLE_1429415))))))) (let ((_let_4063 (forall ((BOUND_VARIABLE_1429399 tptp.product_prod_int_int)) (= (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7907 k_7908 BOUND_VARIABLE_1429399))) (ho_7907 k_7906 BOUND_VARIABLE_1429399)) (ho_7702 k_10010 BOUND_VARIABLE_1429399))))) (let ((_let_4064 (forall ((BOUND_VARIABLE_1429384 tptp.product_prod_int_int)) (= (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7907 k_7908 BOUND_VARIABLE_1429384))) (ho_7907 k_7906 BOUND_VARIABLE_1429384)) (ho_7702 k_10011 BOUND_VARIABLE_1429384))))) (let ((_let_4065 (forall ((BOUND_VARIABLE_1429357 tptp.product_prod_int_int) (BOUND_VARIABLE_1429358 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7906 BOUND_VARIABLE_1429358))) (let ((_let_2 (ho_7907 k_7906 BOUND_VARIABLE_1429357))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_3)))) (= (ho_7633 (ho_10013 k_10012 BOUND_VARIABLE_1429357) BOUND_VARIABLE_1429358) (and (not (= _let_4 _let_2)) (not (= _let_4 _let_1)) (= (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429358)) _let_2) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429357)) _let_1))))))))))) (let ((_let_4066 (forall ((BOUND_VARIABLE_1429350 tptp.int) (BOUND_VARIABLE_1429351 tptp.int)) (= (= BOUND_VARIABLE_1429350 BOUND_VARIABLE_1429351) (ho_7496 (ho_7495 k_10014 BOUND_VARIABLE_1429350) BOUND_VARIABLE_1429351))))) (let ((_let_4067 (forall ((BOUND_VARIABLE_1429343 tptp.int) (BOUND_VARIABLE_1429344 tptp.int)) (= (= BOUND_VARIABLE_1429343 BOUND_VARIABLE_1429344) (ho_7496 (ho_7495 k_10015 BOUND_VARIABLE_1429343) BOUND_VARIABLE_1429344))))) (let ((_let_4068 (forall ((BOUND_VARIABLE_1429325 tptp.int) (BOUND_VARIABLE_1429326 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7698 (ho_7697 k_10016 BOUND_VARIABLE_1429325) BOUND_VARIABLE_1429326) (ho_7702 (ho_7701 (ho_7700 k_7699 (= BOUND_VARIABLE_1429326 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 BOUND_VARIABLE_1429325) BOUND_VARIABLE_1429326)))))))) (let ((_let_4069 (forall ((BOUND_VARIABLE_1429307 tptp.int) (BOUND_VARIABLE_1429308 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7698 (ho_7697 k_10017 BOUND_VARIABLE_1429307) BOUND_VARIABLE_1429308) (ho_7702 (ho_7701 (ho_7700 k_7699 (= BOUND_VARIABLE_1429308 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 BOUND_VARIABLE_1429307) BOUND_VARIABLE_1429308)))))))) (let ((_let_4070 (forall ((BOUND_VARIABLE_1429280 tptp.product_prod_int_int) (BOUND_VARIABLE_1429281 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7906 BOUND_VARIABLE_1429281))) (let ((_let_2 (ho_7907 k_7906 BOUND_VARIABLE_1429280))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_3)))) (= (ho_7633 (ho_10013 k_10018 BOUND_VARIABLE_1429280) BOUND_VARIABLE_1429281) (and (not (= _let_4 _let_2)) (not (= _let_4 _let_1)) (= (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429281)) _let_2) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429280)) _let_1))))))))))) (let ((_let_4071 (forall ((BOUND_VARIABLE_1429260 tptp.product_prod_int_int) (BOUND_VARIABLE_1429261 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7906 BOUND_VARIABLE_1429261))) (let ((_let_2 (ho_7907 k_7906 BOUND_VARIABLE_1429260))) (= (ho_7702 (ho_7701 k_10019 BOUND_VARIABLE_1429260) BOUND_VARIABLE_1429261) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429260)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429261)) _let_2))) (ho_7459 (ho_7461 k_7472 _let_2) _let_1)))))))) (let ((_let_4072 (forall ((BOUND_VARIABLE_1429240 tptp.product_prod_int_int) (BOUND_VARIABLE_1429241 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7906 BOUND_VARIABLE_1429241))) (let ((_let_2 (ho_7907 k_7906 BOUND_VARIABLE_1429240))) (= (ho_7702 (ho_7701 k_10020 BOUND_VARIABLE_1429240) BOUND_VARIABLE_1429241) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429240)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1429241)) _let_2))) (ho_7459 (ho_7461 k_7472 _let_2) _let_1)))))))) (let ((_let_4073 (forall ((BOUND_VARIABLE_1429195 tptp.nat) (BOUND_VARIABLE_1429196 tptp.nat) (BOUND_VARIABLE_1429197 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7642 BOUND_VARIABLE_1429195) BOUND_VARIABLE_1429196)) BOUND_VARIABLE_1429197) (ho_8535 (ho_10023 (ho_10022 k_10021 BOUND_VARIABLE_1429195) BOUND_VARIABLE_1429196) BOUND_VARIABLE_1429197))))) (let ((_let_4074 (forall ((BOUND_VARIABLE_1429150 tptp.nat) (BOUND_VARIABLE_1429151 tptp.nat) (BOUND_VARIABLE_1429152 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7645 BOUND_VARIABLE_1429150) BOUND_VARIABLE_1429151)) BOUND_VARIABLE_1429152) (ho_8535 (ho_10023 (ho_10022 k_10024 BOUND_VARIABLE_1429150) BOUND_VARIABLE_1429151) BOUND_VARIABLE_1429152))))) (let ((_let_4075 (forall ((BOUND_VARIABLE_1429105 tptp.nat) (BOUND_VARIABLE_1429106 tptp.nat) (BOUND_VARIABLE_1429107 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7646 BOUND_VARIABLE_1429105) BOUND_VARIABLE_1429106)) BOUND_VARIABLE_1429107) (ho_8535 (ho_10023 (ho_10022 k_10025 BOUND_VARIABLE_1429105) BOUND_VARIABLE_1429106) BOUND_VARIABLE_1429107))))) (let ((_let_4076 (forall ((BOUND_VARIABLE_1429060 tptp.nat) (BOUND_VARIABLE_1429061 tptp.nat) (BOUND_VARIABLE_1429062 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7647 BOUND_VARIABLE_1429060) BOUND_VARIABLE_1429061)) BOUND_VARIABLE_1429062) (ho_8535 (ho_10023 (ho_10022 k_10026 BOUND_VARIABLE_1429060) BOUND_VARIABLE_1429061) BOUND_VARIABLE_1429062))))) (let ((_let_4077 (forall ((BOUND_VARIABLE_1429053 Bool) (BOUND_VARIABLE_1429054 Bool)) (= (= BOUND_VARIABLE_1429053 BOUND_VARIABLE_1429054) (ho_8986 (ho_10005 k_10027 BOUND_VARIABLE_1429053) BOUND_VARIABLE_1429054))))) (let ((_let_4078 (forall ((BOUND_VARIABLE_1429006 tptp.nat) (BOUND_VARIABLE_1429007 tptp.nat) (BOUND_VARIABLE_1429008 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7648 BOUND_VARIABLE_1429006) BOUND_VARIABLE_1429007)) BOUND_VARIABLE_1429008) (ho_7834 (ho_7837 (ho_7836 k_10028 BOUND_VARIABLE_1429006) BOUND_VARIABLE_1429007) BOUND_VARIABLE_1429008))))) (let ((_let_4079 (forall ((BOUND_VARIABLE_1428959 tptp.nat) (BOUND_VARIABLE_1428960 tptp.nat) (BOUND_VARIABLE_1428961 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7649 BOUND_VARIABLE_1428959) BOUND_VARIABLE_1428960)) BOUND_VARIABLE_1428961) (ho_7834 (ho_7837 (ho_7836 k_10029 BOUND_VARIABLE_1428959) BOUND_VARIABLE_1428960) BOUND_VARIABLE_1428961))))) (let ((_let_4080 (forall ((BOUND_VARIABLE_1428952 Bool) (BOUND_VARIABLE_1428953 Bool)) (= (= BOUND_VARIABLE_1428952 BOUND_VARIABLE_1428953) (ho_8986 (ho_10005 k_10030 BOUND_VARIABLE_1428952) BOUND_VARIABLE_1428953))))) (let ((_let_4081 (forall ((BOUND_VARIABLE_1428905 tptp.nat) (BOUND_VARIABLE_1428906 tptp.nat) (BOUND_VARIABLE_1428907 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7650 BOUND_VARIABLE_1428905) BOUND_VARIABLE_1428906)) BOUND_VARIABLE_1428907) (ho_7834 (ho_7837 (ho_7836 k_10031 BOUND_VARIABLE_1428905) BOUND_VARIABLE_1428906) BOUND_VARIABLE_1428907))))) (let ((_let_4082 (forall ((BOUND_VARIABLE_1428858 tptp.nat) (BOUND_VARIABLE_1428859 tptp.nat) (BOUND_VARIABLE_1428860 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7651 BOUND_VARIABLE_1428858) BOUND_VARIABLE_1428859)) BOUND_VARIABLE_1428860) (ho_7834 (ho_7837 (ho_7836 k_10032 BOUND_VARIABLE_1428858) BOUND_VARIABLE_1428859) BOUND_VARIABLE_1428860))))) (let ((_let_4083 (forall ((BOUND_VARIABLE_1428850 tptp.nat) (BOUND_VARIABLE_1428851 tptp.nat)) (= (ho_7641 (ho_7448 k_10033 BOUND_VARIABLE_1428850) BOUND_VARIABLE_1428851) (ho_7641 (ho_7448 k_7640 BOUND_VARIABLE_1428851) BOUND_VARIABLE_1428850))))) (let ((_let_4084 (forall ((BOUND_VARIABLE_1428842 tptp.nat) (BOUND_VARIABLE_1428843 tptp.nat)) (= (ho_7641 (ho_7448 k_10034 BOUND_VARIABLE_1428842) BOUND_VARIABLE_1428843) (ho_7641 (ho_7448 k_7640 BOUND_VARIABLE_1428843) BOUND_VARIABLE_1428842))))) (let ((_let_4085 (forall ((BOUND_VARIABLE_1428801 tptp.nat) (BOUND_VARIABLE_1428802 tptp.nat) (BOUND_VARIABLE_1428803 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7652 BOUND_VARIABLE_1428801) BOUND_VARIABLE_1428802)) BOUND_VARIABLE_1428803) (ho_7834 (ho_7837 (ho_7836 k_10035 BOUND_VARIABLE_1428801) BOUND_VARIABLE_1428802) BOUND_VARIABLE_1428803))))) (let ((_let_4086 (forall ((BOUND_VARIABLE_1428720 tptp.nat) (BOUND_VARIABLE_1428721 tptp.nat) (BOUND_VARIABLE_1428722 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7653 BOUND_VARIABLE_1428720) BOUND_VARIABLE_1428721)) BOUND_VARIABLE_1428722) (ho_8535 (ho_10023 (ho_10022 k_10036 BOUND_VARIABLE_1428720) BOUND_VARIABLE_1428721) BOUND_VARIABLE_1428722))))) (let ((_let_4087 (forall ((BOUND_VARIABLE_1428639 tptp.nat) (BOUND_VARIABLE_1428640 tptp.nat) (BOUND_VARIABLE_1428641 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7654 BOUND_VARIABLE_1428639) BOUND_VARIABLE_1428640)) BOUND_VARIABLE_1428641) (ho_8535 (ho_10023 (ho_10022 k_10037 BOUND_VARIABLE_1428639) BOUND_VARIABLE_1428640) BOUND_VARIABLE_1428641))))) (let ((_let_4088 (forall ((BOUND_VARIABLE_1428594 tptp.nat) (BOUND_VARIABLE_1428595 tptp.nat) (BOUND_VARIABLE_1428596 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7655 BOUND_VARIABLE_1428594) BOUND_VARIABLE_1428595)) BOUND_VARIABLE_1428596) (ho_8535 (ho_10023 (ho_10022 k_10038 BOUND_VARIABLE_1428594) BOUND_VARIABLE_1428595) BOUND_VARIABLE_1428596))))) (let ((_let_4089 (forall ((BOUND_VARIABLE_1428587 Bool) (BOUND_VARIABLE_1428588 Bool)) (= (= BOUND_VARIABLE_1428587 BOUND_VARIABLE_1428588) (ho_8986 (ho_10005 k_10039 BOUND_VARIABLE_1428587) BOUND_VARIABLE_1428588))))) (let ((_let_4090 (forall ((BOUND_VARIABLE_1428540 tptp.nat) (BOUND_VARIABLE_1428541 tptp.nat) (BOUND_VARIABLE_1428542 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7656 BOUND_VARIABLE_1428540) BOUND_VARIABLE_1428541)) BOUND_VARIABLE_1428542) (ho_7834 (ho_7837 (ho_7836 k_10040 BOUND_VARIABLE_1428540) BOUND_VARIABLE_1428541) BOUND_VARIABLE_1428542))))) (let ((_let_4091 (forall ((BOUND_VARIABLE_1428533 Bool) (BOUND_VARIABLE_1428534 Bool)) (= (= BOUND_VARIABLE_1428533 BOUND_VARIABLE_1428534) (ho_8986 (ho_10005 k_10041 BOUND_VARIABLE_1428533) BOUND_VARIABLE_1428534))))) (let ((_let_4092 (forall ((BOUND_VARIABLE_1428486 tptp.nat) (BOUND_VARIABLE_1428487 tptp.nat) (BOUND_VARIABLE_1428488 tptp.product_prod_nat_nat)) (= (ho_7834 (ho_7833 k_7832 (ho_7539 (ho_7538 k_7657 BOUND_VARIABLE_1428486) BOUND_VARIABLE_1428487)) BOUND_VARIABLE_1428488) (ho_7834 (ho_7837 (ho_7836 k_10042 BOUND_VARIABLE_1428486) BOUND_VARIABLE_1428487) BOUND_VARIABLE_1428488))))) (let ((_let_4093 (forall ((BOUND_VARIABLE_1428478 tptp.nat) (BOUND_VARIABLE_1428479 tptp.nat)) (= (ho_7641 (ho_7448 k_10043 BOUND_VARIABLE_1428478) BOUND_VARIABLE_1428479) (ho_7641 (ho_7448 k_7640 BOUND_VARIABLE_1428479) BOUND_VARIABLE_1428478))))) (let ((_let_4094 (forall ((BOUND_VARIABLE_1428471 tptp.nat) (BOUND_VARIABLE_1428472 tptp.nat)) (= (= BOUND_VARIABLE_1428471 BOUND_VARIABLE_1428472) (ho_7541 (ho_7540 k_10044 BOUND_VARIABLE_1428471) BOUND_VARIABLE_1428472))))) (let ((_let_4095 (forall ((BOUND_VARIABLE_1428464 tptp.nat)) (= (ho_7641 k_10045 BOUND_VARIABLE_1428464) (ho_7641 (ho_7448 k_7640 BOUND_VARIABLE_1428464) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))))))) (let ((_let_4096 (forall ((BOUND_VARIABLE_1428419 tptp.nat) (BOUND_VARIABLE_1428420 tptp.nat) (BOUND_VARIABLE_1428421 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7658 BOUND_VARIABLE_1428419) BOUND_VARIABLE_1428420)) BOUND_VARIABLE_1428421) (ho_8535 (ho_10023 (ho_10022 k_10046 BOUND_VARIABLE_1428419) BOUND_VARIABLE_1428420) BOUND_VARIABLE_1428421))))) (let ((_let_4097 (forall ((BOUND_VARIABLE_1428338 tptp.nat) (BOUND_VARIABLE_1428339 tptp.nat) (BOUND_VARIABLE_1428340 tptp.product_prod_nat_nat)) (= (ho_8535 (ho_7450 k_7449 (ho_7644 (ho_7643 k_7659 BOUND_VARIABLE_1428338) BOUND_VARIABLE_1428339)) BOUND_VARIABLE_1428340) (ho_8535 (ho_10023 (ho_10022 k_10047 BOUND_VARIABLE_1428338) BOUND_VARIABLE_1428339) BOUND_VARIABLE_1428340))))) (let ((_let_4098 (forall ((BOUND_VARIABLE_1428319 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7908 BOUND_VARIABLE_1428319))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (= (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_3 _let_1)) (ho_7698 (ho_7697 k_7696 _let_3) _let_2)) (ho_7698 (ho_7697 k_7696 (ho_7907 k_7906 BOUND_VARIABLE_1428319)) _let_1)) (ho_7702 k_10048 BOUND_VARIABLE_1428319)))))))) (let ((_let_4099 (forall ((BOUND_VARIABLE_1428312 Bool) (BOUND_VARIABLE_1428313 Bool)) (= (= BOUND_VARIABLE_1428312 BOUND_VARIABLE_1428313) (ho_8986 (ho_10005 k_10049 BOUND_VARIABLE_1428312) BOUND_VARIABLE_1428313))))) (let ((_let_4100 (forall ((BOUND_VARIABLE_1428287 tptp.product_prod_int_int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (= (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_2)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1428287)) (ho_7907 k_7906 BOUND_VARIABLE_1428287)))))))) (not (= (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1428287)) (ho_7907 k_7906 BOUND_VARIABLE_1428287))))) (ho_7633 k_10050 BOUND_VARIABLE_1428287)))))) (let ((_let_4101 (forall ((BOUND_VARIABLE_1428261 tptp.rat)) (let ((_let_1 (ho_7630 k_7706 BOUND_VARIABLE_1428261))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (= (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7630 k_7706 BOUND_VARIABLE_1428261))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (not (= (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) _let_3)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))))))) (not (= (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 _let_1)) (ho_7907 k_7906 _let_1))))) (ho_10052 k_10051 BOUND_VARIABLE_1428261))))))) (let ((_let_4102 (forall ((BOUND_VARIABLE_1428245 tptp.product_prod_int_int) (BOUND_VARIABLE_1428246 tptp.product_prod_int_int)) (= (ho_7702 (ho_7701 k_10053 BOUND_VARIABLE_1428245) BOUND_VARIABLE_1428246) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1428245)) (ho_7907 k_7908 BOUND_VARIABLE_1428246))) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7906 BOUND_VARIABLE_1428245)) (ho_7907 k_7906 BOUND_VARIABLE_1428246))))))) (let ((_let_4103 (forall ((BOUND_VARIABLE_1428230 tptp.product_prod_int_int)) (= (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7907 k_7908 BOUND_VARIABLE_1428230))) (ho_7907 k_7906 BOUND_VARIABLE_1428230)) (ho_7702 k_10054 BOUND_VARIABLE_1428230))))) (let ((_let_4104 (forall ((BOUND_VARIABLE_1428223 tptp.int) (BOUND_VARIABLE_1428224 tptp.int)) (= (= BOUND_VARIABLE_1428223 BOUND_VARIABLE_1428224) (ho_7496 (ho_7495 k_10055 BOUND_VARIABLE_1428223) BOUND_VARIABLE_1428224))))) (let ((_let_4105 (forall ((BOUND_VARIABLE_1428216 tptp.int) (BOUND_VARIABLE_1428217 tptp.int)) (= (= BOUND_VARIABLE_1428216 BOUND_VARIABLE_1428217) (ho_7496 (ho_7495 k_10056 BOUND_VARIABLE_1428216) BOUND_VARIABLE_1428217))))) (let ((_let_4106 (forall ((BOUND_VARIABLE_1428198 tptp.int) (BOUND_VARIABLE_1428199 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7698 (ho_7697 k_10057 BOUND_VARIABLE_1428198) BOUND_VARIABLE_1428199) (ho_7702 (ho_7701 (ho_7700 k_7699 (= BOUND_VARIABLE_1428199 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 BOUND_VARIABLE_1428198) BOUND_VARIABLE_1428199)))))))) (let ((_let_4107 (forall ((BOUND_VARIABLE_1428178 tptp.int) (BOUND_VARIABLE_1428179 tptp.int)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_10060 (ho_10059 k_10058 BOUND_VARIABLE_1428178) BOUND_VARIABLE_1428179) (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= BOUND_VARIABLE_1428179 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 BOUND_VARIABLE_1428178) BOUND_VARIABLE_1428179))))))))) (let ((_let_4108 (forall ((BOUND_VARIABLE_1568904 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1568902 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1428165 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1568904 BOUND_VARIABLE_1428165)) (ho_7636 BOUND_VARIABLE_1568902 BOUND_VARIABLE_1428165)) (ho_7636 (ho_10063 (ho_10062 k_10061 BOUND_VARIABLE_1568904) BOUND_VARIABLE_1568902) BOUND_VARIABLE_1428165))))) (let ((_let_4109 (forall ((BOUND_VARIABLE_1568927 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1568925 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1428150 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_7712) (ho_7636 BOUND_VARIABLE_1568927 BOUND_VARIABLE_1428150)) (ho_7636 BOUND_VARIABLE_1568925 BOUND_VARIABLE_1428150)) (ho_7636 (ho_10063 (ho_10062 k_10064 BOUND_VARIABLE_1568927) BOUND_VARIABLE_1568925) BOUND_VARIABLE_1428150))))) (let ((_let_4110 (forall ((BOUND_VARIABLE_1428141 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))) (ho_7636 k_10065 BOUND_VARIABLE_1428141))))))) (let ((_let_4111 (forall ((BOUND_VARIABLE_1428121 tptp.product_prod_int_int) (BOUND_VARIABLE_1428122 tptp.product_prod_int_int)) (let ((_let_1 (ho_7907 k_7906 BOUND_VARIABLE_1428122))) (let ((_let_2 (ho_7907 k_7906 BOUND_VARIABLE_1428121))) (= (ho_7702 (ho_7701 k_10066 BOUND_VARIABLE_1428121) BOUND_VARIABLE_1428122) (ho_7698 (ho_7697 k_7696 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1428121)) _let_1)) (ho_7459 (ho_7461 k_7472 (ho_7907 k_7908 BOUND_VARIABLE_1428122)) _let_2))) (ho_7459 (ho_7461 k_7472 _let_2) _let_1)))))))) (let ((_let_4112 (forall ((BOUND_VARIABLE_1428114 Bool) (BOUND_VARIABLE_1428115 Bool)) (= (= BOUND_VARIABLE_1428114 BOUND_VARIABLE_1428115) (ho_8986 (ho_10005 k_10067 BOUND_VARIABLE_1428114) BOUND_VARIABLE_1428115))))) (let ((_let_4113 (forall ((BOUND_VARIABLE_1568974 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_232619 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (or (not (ho_7633 (ho_7632 k_7631 (ho_7635 k_7660 R5)) (ho_7630 k_7629 _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (or (not (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_232619)) (ho_7533 k_7532 N2))) (and (ho_7633 (ho_7632 k_7631 (ho_7639 (ho_7638 k_7661 BOUND_VARIABLE_1568974) N2)) (ho_7630 k_7629 R5)) (not (= R5 (ho_7636 BOUND_VARIABLE_1568974 N2))))))))))))))) (ho_10000 k_10068 BOUND_VARIABLE_1568974))))) (let ((_let_4114 (forall ((BOUND_VARIABLE_1428019 tptp.real)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_232339 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (or (not (ho_7633 (ho_7632 k_7631 (ho_7635 k_10069 R5)) (ho_7630 k_7629 _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (or (not (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_232339)) (ho_7533 k_7532 N2))) (and (ho_7633 (ho_7632 k_7631 (ho_7639 (ho_7665 k_7664 BOUND_VARIABLE_1428019) N2)) (ho_7630 k_7629 R5)) (not (= R5 (ho_7636 (ho_7663 k_7662 BOUND_VARIABLE_1428019) N2))))))))))))))) (ho_7781 k_10070 BOUND_VARIABLE_1428019))))) (let ((_let_4115 (forall ((BOUND_VARIABLE_1428012 tptp.int) (BOUND_VARIABLE_1428013 tptp.int)) (= (= BOUND_VARIABLE_1428012 BOUND_VARIABLE_1428013) (ho_7496 (ho_7495 k_10071 BOUND_VARIABLE_1428012) BOUND_VARIABLE_1428013))))) (let ((_let_4116 (forall ((BOUND_VARIABLE_1428005 tptp.int) (BOUND_VARIABLE_1428006 tptp.int)) (= (= BOUND_VARIABLE_1428005 BOUND_VARIABLE_1428006) (ho_7496 (ho_7495 k_10072 BOUND_VARIABLE_1428005) BOUND_VARIABLE_1428006))))) (let ((_let_4117 (forall ((BOUND_VARIABLE_1427998 tptp.int)) (= (ho_7459 k_10073 BOUND_VARIABLE_1427998) (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1427998) BOUND_VARIABLE_1427998))))) (let ((_let_4118 (forall ((BOUND_VARIABLE_1427991 tptp.int)) (= (ho_7459 k_10074 BOUND_VARIABLE_1427991) (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1427991) BOUND_VARIABLE_1427991))))) (let ((_let_4119 (forall ((BOUND_VARIABLE_1427984 tptp.nat) (BOUND_VARIABLE_1427985 tptp.nat)) (= (= BOUND_VARIABLE_1427984 BOUND_VARIABLE_1427985) (ho_7541 (ho_7540 k_10075 BOUND_VARIABLE_1427984) BOUND_VARIABLE_1427985))))) (let ((_let_4120 (forall ((BOUND_VARIABLE_1427977 tptp.nat) (BOUND_VARIABLE_1427978 tptp.nat)) (= (= BOUND_VARIABLE_1427977 BOUND_VARIABLE_1427978) (ho_7541 (ho_7540 k_10076 BOUND_VARIABLE_1427977) BOUND_VARIABLE_1427978))))) (let ((_let_4121 (forall ((BOUND_VARIABLE_1427970 tptp.nat) (BOUND_VARIABLE_1427971 tptp.nat)) (= (= BOUND_VARIABLE_1427970 BOUND_VARIABLE_1427971) (ho_7541 (ho_7540 k_10077 BOUND_VARIABLE_1427970) BOUND_VARIABLE_1427971))))) (let ((_let_4122 (forall ((BOUND_VARIABLE_1427963 tptp.nat) (BOUND_VARIABLE_1427964 tptp.nat)) (= (= BOUND_VARIABLE_1427963 BOUND_VARIABLE_1427964) (ho_7541 (ho_7540 k_10078 BOUND_VARIABLE_1427963) BOUND_VARIABLE_1427964))))) (let ((_let_4123 (forall ((BOUND_VARIABLE_1427956 tptp.nat) (BOUND_VARIABLE_1427957 tptp.nat)) (= (= BOUND_VARIABLE_1427956 BOUND_VARIABLE_1427957) (ho_7541 (ho_7540 k_10079 BOUND_VARIABLE_1427956) BOUND_VARIABLE_1427957))))) (let ((_let_4124 (forall ((BOUND_VARIABLE_1427949 Bool) (BOUND_VARIABLE_1427950 Bool)) (= (= BOUND_VARIABLE_1427949 BOUND_VARIABLE_1427950) (ho_8986 (ho_10005 k_10080 BOUND_VARIABLE_1427949) BOUND_VARIABLE_1427950))))) (let ((_let_4125 (forall ((BOUND_VARIABLE_1427942 tptp.nat) (BOUND_VARIABLE_1427943 tptp.nat)) (= (= BOUND_VARIABLE_1427942 BOUND_VARIABLE_1427943) (ho_7541 (ho_7540 k_10081 BOUND_VARIABLE_1427942) BOUND_VARIABLE_1427943))))) (let ((_let_4126 (forall ((BOUND_VARIABLE_1427935 tptp.nat) (BOUND_VARIABLE_1427936 tptp.nat)) (= (= BOUND_VARIABLE_1427935 BOUND_VARIABLE_1427936) (ho_7541 (ho_7540 k_10082 BOUND_VARIABLE_1427935) BOUND_VARIABLE_1427936))))) (let ((_let_4127 (forall ((BOUND_VARIABLE_1427928 tptp.nat) (BOUND_VARIABLE_1427929 tptp.nat)) (= (= BOUND_VARIABLE_1427928 BOUND_VARIABLE_1427929) (ho_7541 (ho_7540 k_10083 BOUND_VARIABLE_1427928) BOUND_VARIABLE_1427929))))) (let ((_let_4128 (forall ((BOUND_VARIABLE_1427921 tptp.int) (BOUND_VARIABLE_1427922 tptp.int)) (= (= BOUND_VARIABLE_1427921 BOUND_VARIABLE_1427922) (ho_7496 (ho_7495 k_10084 BOUND_VARIABLE_1427921) BOUND_VARIABLE_1427922))))) (let ((_let_4129 (forall ((BOUND_VARIABLE_1427914 tptp.int) (BOUND_VARIABLE_1427915 tptp.int)) (= (= BOUND_VARIABLE_1427914 BOUND_VARIABLE_1427915) (ho_7496 (ho_7495 k_10085 BOUND_VARIABLE_1427914) BOUND_VARIABLE_1427915))))) (let ((_let_4130 (forall ((BOUND_VARIABLE_1427907 tptp.int) (BOUND_VARIABLE_1427908 tptp.int)) (= (= BOUND_VARIABLE_1427907 BOUND_VARIABLE_1427908) (ho_7496 (ho_7495 k_10086 BOUND_VARIABLE_1427907) BOUND_VARIABLE_1427908))))) (let ((_let_4131 (forall ((BOUND_VARIABLE_1427900 tptp.nat) (BOUND_VARIABLE_1427901 tptp.nat)) (= (= BOUND_VARIABLE_1427900 BOUND_VARIABLE_1427901) (ho_7541 (ho_7540 k_10087 BOUND_VARIABLE_1427900) BOUND_VARIABLE_1427901))))) (let ((_let_4132 (forall ((BOUND_VARIABLE_1427893 tptp.nat) (BOUND_VARIABLE_1427894 tptp.nat)) (= (= BOUND_VARIABLE_1427893 BOUND_VARIABLE_1427894) (ho_7541 (ho_7540 k_10088 BOUND_VARIABLE_1427893) BOUND_VARIABLE_1427894))))) (let ((_let_4133 (forall ((BOUND_VARIABLE_1427886 tptp.int) (BOUND_VARIABLE_1427887 tptp.int)) (= (= BOUND_VARIABLE_1427886 BOUND_VARIABLE_1427887) (ho_7496 (ho_7495 k_10089 BOUND_VARIABLE_1427886) BOUND_VARIABLE_1427887))))) (let ((_let_4134 (forall ((BOUND_VARIABLE_1427879 tptp.int) (BOUND_VARIABLE_1427880 tptp.int)) (= (= BOUND_VARIABLE_1427879 BOUND_VARIABLE_1427880) (ho_7496 (ho_7495 k_10090 BOUND_VARIABLE_1427879) BOUND_VARIABLE_1427880))))) (let ((_let_4135 (forall ((BOUND_VARIABLE_1427872 tptp.int) (BOUND_VARIABLE_1427873 tptp.int)) (= (= BOUND_VARIABLE_1427872 BOUND_VARIABLE_1427873) (ho_7496 (ho_7495 k_10091 BOUND_VARIABLE_1427872) BOUND_VARIABLE_1427873))))) (let ((_let_4136 (forall ((BOUND_VARIABLE_1427865 tptp.nat) (BOUND_VARIABLE_1427866 tptp.nat)) (= (= BOUND_VARIABLE_1427865 BOUND_VARIABLE_1427866) (ho_7541 (ho_7540 k_10092 BOUND_VARIABLE_1427865) BOUND_VARIABLE_1427866))))) (let ((_let_4137 (forall ((BOUND_VARIABLE_1427858 tptp.nat) (BOUND_VARIABLE_1427859 tptp.nat)) (= (= BOUND_VARIABLE_1427858 BOUND_VARIABLE_1427859) (ho_7541 (ho_7540 k_10093 BOUND_VARIABLE_1427858) BOUND_VARIABLE_1427859))))) (let ((_let_4138 (forall ((BOUND_VARIABLE_1427851 tptp.nat) (BOUND_VARIABLE_1427852 tptp.nat)) (= (= BOUND_VARIABLE_1427851 BOUND_VARIABLE_1427852) (ho_7541 (ho_7540 k_10094 BOUND_VARIABLE_1427851) BOUND_VARIABLE_1427852))))) (let ((_let_4139 (forall ((BOUND_VARIABLE_1427844 tptp.nat) (BOUND_VARIABLE_1427845 tptp.nat)) (= (= BOUND_VARIABLE_1427844 BOUND_VARIABLE_1427845) (ho_7541 (ho_7540 k_10095 BOUND_VARIABLE_1427844) BOUND_VARIABLE_1427845))))) (let ((_let_4140 (forall ((BOUND_VARIABLE_1427837 tptp.nat) (BOUND_VARIABLE_1427838 tptp.nat)) (= (= BOUND_VARIABLE_1427837 BOUND_VARIABLE_1427838) (ho_7541 (ho_7540 k_10096 BOUND_VARIABLE_1427837) BOUND_VARIABLE_1427838))))) (let ((_let_4141 (forall ((BOUND_VARIABLE_1427830 Bool) (BOUND_VARIABLE_1427831 Bool)) (= (= BOUND_VARIABLE_1427830 BOUND_VARIABLE_1427831) (ho_8986 (ho_10005 k_10097 BOUND_VARIABLE_1427830) BOUND_VARIABLE_1427831))))) (let ((_let_4142 (forall ((BOUND_VARIABLE_1569229 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569227 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427817 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_7712) (ho_7636 BOUND_VARIABLE_1569229 BOUND_VARIABLE_1427817)) (ho_7636 BOUND_VARIABLE_1569227 BOUND_VARIABLE_1427817)) (ho_7636 (ho_10063 (ho_10062 k_10098 BOUND_VARIABLE_1569229) BOUND_VARIABLE_1569227) BOUND_VARIABLE_1427817))))) (let ((_let_4143 (forall ((BOUND_VARIABLE_1569245 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569243 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427802 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_7712) (ho_7636 BOUND_VARIABLE_1569245 BOUND_VARIABLE_1427802)) (ho_7636 BOUND_VARIABLE_1569243 BOUND_VARIABLE_1427802)) (ho_7636 (ho_10063 (ho_10062 k_10099 BOUND_VARIABLE_1569245) BOUND_VARIABLE_1569243) BOUND_VARIABLE_1427802))))) (let ((_let_4144 (forall ((BOUND_VARIABLE_1569261 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569259 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427787 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1569261 BOUND_VARIABLE_1427787)) (ho_7636 BOUND_VARIABLE_1569259 BOUND_VARIABLE_1427787)) (ho_7636 (ho_10063 (ho_10062 k_10100 BOUND_VARIABLE_1569261) BOUND_VARIABLE_1569259) BOUND_VARIABLE_1427787))))) (let ((_let_4145 (forall ((BOUND_VARIABLE_1569277 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569275 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427772 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1569277 BOUND_VARIABLE_1427772)) (ho_7636 BOUND_VARIABLE_1569275 BOUND_VARIABLE_1427772)) (ho_7636 (ho_10063 (ho_10062 k_10101 BOUND_VARIABLE_1569277) BOUND_VARIABLE_1569275) BOUND_VARIABLE_1427772))))) (let ((_let_4146 (forall ((BOUND_VARIABLE_1427763 Bool) (BOUND_VARIABLE_1427764 Bool)) (= (= BOUND_VARIABLE_1427763 BOUND_VARIABLE_1427764) (ho_8986 (ho_10005 k_10102 BOUND_VARIABLE_1427763) BOUND_VARIABLE_1427764))))) (let ((_let_4147 (forall ((BOUND_VARIABLE_1569298 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_232490 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (or (not (ho_7633 (ho_7632 k_7631 (ho_7635 k_7666 R5)) (ho_7630 k_7629 _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (or (not (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_232490)) (ho_7533 k_7532 N2))) (and (ho_7633 (ho_7632 k_7631 (ho_7639 (ho_7638 k_7667 BOUND_VARIABLE_1569298) N2)) (ho_7630 k_7629 R5)) (not (= R5 (ho_7636 BOUND_VARIABLE_1569298 N2))))))))))))))) (ho_10000 k_10103 BOUND_VARIABLE_1569298))))) (let ((_let_4148 (forall ((BOUND_VARIABLE_1569330 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_232519 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))))) (let ((_let_4 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_5 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_4) k_7712) _let_3) (ho_7711 (ho_7710 _let_4 k_7705) _let_3)))) (or (not (ho_7633 (ho_7632 k_7631 (ho_7635 k_7668 R5)) (ho_7630 k_7629 _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (or (not (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_232519)) (ho_7533 k_7532 N2))) (and (ho_7633 (ho_7632 k_7631 (ho_7639 (ho_7638 k_7669 BOUND_VARIABLE_1569330) N2)) (ho_7630 k_7629 R5)) (not (= R5 (ho_7636 BOUND_VARIABLE_1569330 N2))))))))))))))) (ho_10000 k_10104 BOUND_VARIABLE_1569330))))) (let ((_let_4149 (forall ((BOUND_VARIABLE_1569364 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569362 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427646 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1569364 BOUND_VARIABLE_1427646)) (ho_7636 BOUND_VARIABLE_1569362 BOUND_VARIABLE_1427646)) (ho_7636 (ho_10063 (ho_10062 k_10105 BOUND_VARIABLE_1569364) BOUND_VARIABLE_1569362) BOUND_VARIABLE_1427646))))) (let ((_let_4150 (forall ((BOUND_VARIABLE_1569380 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569378 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427631 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_7712) (ho_7636 BOUND_VARIABLE_1569380 BOUND_VARIABLE_1427631)) (ho_7636 BOUND_VARIABLE_1569378 BOUND_VARIABLE_1427631)) (ho_7636 (ho_10063 (ho_10062 k_10106 BOUND_VARIABLE_1569380) BOUND_VARIABLE_1569378) BOUND_VARIABLE_1427631))))) (let ((_let_4151 (forall ((BOUND_VARIABLE_1427622 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))) (ho_7636 k_10107 BOUND_VARIABLE_1427622))))))) (let ((_let_4152 (forall ((BOUND_VARIABLE_1427615 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))) (ho_7636 k_10108 BOUND_VARIABLE_1427615))))))) (let ((_let_4153 (forall ((BOUND_VARIABLE_1427573 tptp.rat) (BOUND_VARIABLE_1427574 tptp.int) (BOUND_VARIABLE_1427575 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7670 BOUND_VARIABLE_1427575) BOUND_VARIABLE_1427574)) (ho_7630 k_7629 BOUND_VARIABLE_1427573)) (ho_7496 (ho_7495 (ho_7635 k_10109 BOUND_VARIABLE_1427573) BOUND_VARIABLE_1427574) BOUND_VARIABLE_1427575))))) (let ((_let_4154 (forall ((BOUND_VARIABLE_1569418 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427530 tptp.nat) (BOUND_VARIABLE_1427531 tptp.int) (BOUND_VARIABLE_1427532 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7671 BOUND_VARIABLE_1427532) BOUND_VARIABLE_1427531)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1569418 BOUND_VARIABLE_1427530))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_10110 BOUND_VARIABLE_1569418) BOUND_VARIABLE_1427530) BOUND_VARIABLE_1427531) BOUND_VARIABLE_1427532))))) (let ((_let_4155 (forall ((BOUND_VARIABLE_1569437 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1427484 tptp.nat) (BOUND_VARIABLE_1427485 tptp.int) (BOUND_VARIABLE_1427486 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7672 BOUND_VARIABLE_1427486) BOUND_VARIABLE_1427485)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 (ho_10112 k_10111 BOUND_VARIABLE_1569437)) BOUND_VARIABLE_1427484))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_10113 BOUND_VARIABLE_1569437) BOUND_VARIABLE_1427484) BOUND_VARIABLE_1427485) BOUND_VARIABLE_1427486))))) (let ((_let_4156 (forall ((BOUND_VARIABLE_1427475 tptp.real) (BOUND_VARIABLE_1427476 tptp.real)) (= (ho_7516 (ho_7519 k_10114 BOUND_VARIABLE_1427475) BOUND_VARIABLE_1427476) (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1427476) BOUND_VARIABLE_1427475))))) (let ((_let_4157 (forall ((BOUND_VARIABLE_1427439 tptp.nat) (BOUND_VARIABLE_1427440 tptp.nat)) (let ((_let_1 (ho_10116 k_10115 BOUND_VARIABLE_1427440))) (let ((_let_2 (ho_7846 k_7845 true))) (let ((_let_3 (ho_7848 (ho_7850 k_7849 (ho_7848 k_7847 _let_2)) _let_2))) (let ((_let_4 (ho_7848 (ho_7850 (ho_7855 k_7854 (ho_7853 (ho_7852 k_7851 _let_1) _let_3)) (ho_7848 k_7847 _let_1)) _let_1))) (let ((_let_5 (ho_10116 k_10115 BOUND_VARIABLE_1427439))) (let ((_let_6 (ho_7848 (ho_7850 (ho_7855 k_7854 (ho_7853 (ho_7852 k_7851 _let_5) _let_3)) (ho_7848 k_7847 _let_5)) _let_5))) (let ((_let_7 (ho_7858 k_7857 _let_3))) (= (ho_10122 (ho_10121 (ho_10120 k_10119 k_7875) k_7875) (ho_7863 (ho_7862 (ho_7861 k_7860 (= _let_3 _let_5)) (ho_7859 _let_7 _let_3)) (ho_7863 (ho_7862 (ho_7861 k_7860 (= _let_3 _let_1)) (ho_7859 _let_7 _let_5)) (ho_7859 (ho_7858 k_7857 (ho_7848 (ho_7850 k_10118 _let_6) _let_4)) (ho_7848 (ho_7850 k_10117 _let_6) _let_4))))) (ho_7641 (ho_7448 k_10123 BOUND_VARIABLE_1427439) BOUND_VARIABLE_1427440)))))))))))) (let ((_let_4158 (forall ((BOUND_VARIABLE_1569535 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1427422 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7541 BOUND_VARIABLE_1569535 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1427422) _let_2)))) (ho_7541 (ho_10125 k_10124 BOUND_VARIABLE_1569535) BOUND_VARIABLE_1427422)))))))) (let ((_let_4159 (forall ((BOUND_VARIABLE_1427373 tptp.real) (BOUND_VARIABLE_1427374 tptp.real) (BOUND_VARIABLE_1427375 tptp.nat) (BOUND_VARIABLE_1427376 tptp.int) (BOUND_VARIABLE_1427377 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7673 BOUND_VARIABLE_1427377) BOUND_VARIABLE_1427376)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1427373) BOUND_VARIABLE_1427374)) BOUND_VARIABLE_1427375))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 (ho_10127 k_10126 BOUND_VARIABLE_1427373) BOUND_VARIABLE_1427374) BOUND_VARIABLE_1427375) BOUND_VARIABLE_1427376) BOUND_VARIABLE_1427377))))) (let ((_let_4160 (forall ((BOUND_VARIABLE_1427331 tptp.rat) (BOUND_VARIABLE_1427332 tptp.int) (BOUND_VARIABLE_1427333 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7674 BOUND_VARIABLE_1427333) BOUND_VARIABLE_1427332)) (ho_7630 k_7629 BOUND_VARIABLE_1427331)) (ho_7496 (ho_7495 (ho_7635 k_10128 BOUND_VARIABLE_1427331) BOUND_VARIABLE_1427332) BOUND_VARIABLE_1427333))))) (let ((_let_4161 (forall ((BOUND_VARIABLE_1427286 tptp.real) (BOUND_VARIABLE_1427287 tptp.nat) (BOUND_VARIABLE_1427288 tptp.int) (BOUND_VARIABLE_1427289 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7675 BOUND_VARIABLE_1427289) BOUND_VARIABLE_1427288)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 BOUND_VARIABLE_1427286) BOUND_VARIABLE_1427287))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 k_10129 BOUND_VARIABLE_1427286) BOUND_VARIABLE_1427287) BOUND_VARIABLE_1427288) BOUND_VARIABLE_1427289))))) (let ((_let_4162 (forall ((BOUND_VARIABLE_1427244 tptp.rat) (BOUND_VARIABLE_1427245 tptp.int) (BOUND_VARIABLE_1427246 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7676 BOUND_VARIABLE_1427246) BOUND_VARIABLE_1427245)) (ho_7630 k_7629 BOUND_VARIABLE_1427244)) (ho_7496 (ho_7495 (ho_7635 k_10130 BOUND_VARIABLE_1427244) BOUND_VARIABLE_1427245) BOUND_VARIABLE_1427246))))) (let ((_let_4163 (forall ((BOUND_VARIABLE_1427199 tptp.real) (BOUND_VARIABLE_1427200 tptp.nat) (BOUND_VARIABLE_1427201 tptp.int) (BOUND_VARIABLE_1427202 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7677 BOUND_VARIABLE_1427202) BOUND_VARIABLE_1427201)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 BOUND_VARIABLE_1427199) BOUND_VARIABLE_1427200))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 k_10131 BOUND_VARIABLE_1427199) BOUND_VARIABLE_1427200) BOUND_VARIABLE_1427201) BOUND_VARIABLE_1427202))))) (let ((_let_4164 (forall ((BOUND_VARIABLE_1427151 tptp.real) (BOUND_VARIABLE_1427152 tptp.real) (BOUND_VARIABLE_1427153 tptp.nat) (BOUND_VARIABLE_1427154 tptp.int) (BOUND_VARIABLE_1427155 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7678 BOUND_VARIABLE_1427155) BOUND_VARIABLE_1427154)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1427151) BOUND_VARIABLE_1427152)) BOUND_VARIABLE_1427153))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 (ho_10127 k_10132 BOUND_VARIABLE_1427151) BOUND_VARIABLE_1427152) BOUND_VARIABLE_1427153) BOUND_VARIABLE_1427154) BOUND_VARIABLE_1427155))))) (let ((_let_4165 (forall ((BOUND_VARIABLE_1427109 tptp.rat) (BOUND_VARIABLE_1427110 tptp.int) (BOUND_VARIABLE_1427111 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7679 BOUND_VARIABLE_1427111) BOUND_VARIABLE_1427110)) (ho_7630 k_7629 BOUND_VARIABLE_1427109)) (ho_7496 (ho_7495 (ho_7635 k_10133 BOUND_VARIABLE_1427109) BOUND_VARIABLE_1427110) BOUND_VARIABLE_1427111))))) (let ((_let_4166 (forall ((BOUND_VARIABLE_1427064 tptp.real) (BOUND_VARIABLE_1427065 tptp.nat) (BOUND_VARIABLE_1427066 tptp.int) (BOUND_VARIABLE_1427067 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7680 BOUND_VARIABLE_1427067) BOUND_VARIABLE_1427066)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 BOUND_VARIABLE_1427064) BOUND_VARIABLE_1427065))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 k_10134 BOUND_VARIABLE_1427064) BOUND_VARIABLE_1427065) BOUND_VARIABLE_1427066) BOUND_VARIABLE_1427067))))) (let ((_let_4167 (forall ((BOUND_VARIABLE_1427022 tptp.rat) (BOUND_VARIABLE_1427023 tptp.int) (BOUND_VARIABLE_1427024 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7681 BOUND_VARIABLE_1427024) BOUND_VARIABLE_1427023)) (ho_7630 k_7629 BOUND_VARIABLE_1427022)) (ho_7496 (ho_7495 (ho_7635 k_10135 BOUND_VARIABLE_1427022) BOUND_VARIABLE_1427023) BOUND_VARIABLE_1427024))))) (let ((_let_4168 (forall ((BOUND_VARIABLE_1426977 tptp.real) (BOUND_VARIABLE_1426978 tptp.nat) (BOUND_VARIABLE_1426979 tptp.int) (BOUND_VARIABLE_1426980 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7682 BOUND_VARIABLE_1426980) BOUND_VARIABLE_1426979)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 BOUND_VARIABLE_1426977) BOUND_VARIABLE_1426978))) (ho_7496 (ho_7495 (ho_7639 (ho_7665 k_10136 BOUND_VARIABLE_1426977) BOUND_VARIABLE_1426978) BOUND_VARIABLE_1426979) BOUND_VARIABLE_1426980))))) (let ((_let_4169 (forall ((BOUND_VARIABLE_1426935 tptp.rat) (BOUND_VARIABLE_1426936 tptp.int) (BOUND_VARIABLE_1426937 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7683 BOUND_VARIABLE_1426937) BOUND_VARIABLE_1426936)) (ho_7630 k_7629 BOUND_VARIABLE_1426935)) (ho_7496 (ho_7495 (ho_7635 k_10137 BOUND_VARIABLE_1426935) BOUND_VARIABLE_1426936) BOUND_VARIABLE_1426937))))) (let ((_let_4170 (forall ((BOUND_VARIABLE_1569737 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426892 tptp.nat) (BOUND_VARIABLE_1426893 tptp.int) (BOUND_VARIABLE_1426894 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7684 BOUND_VARIABLE_1426894) BOUND_VARIABLE_1426893)) (ho_7630 k_7629 (ho_7636 BOUND_VARIABLE_1569737 BOUND_VARIABLE_1426892))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_10138 BOUND_VARIABLE_1569737) BOUND_VARIABLE_1426892) BOUND_VARIABLE_1426893) BOUND_VARIABLE_1426894))))) (let ((_let_4171 (forall ((BOUND_VARIABLE_1569756 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426846 tptp.nat) (BOUND_VARIABLE_1426847 tptp.int) (BOUND_VARIABLE_1426848 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7685 BOUND_VARIABLE_1426848) BOUND_VARIABLE_1426847)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 (ho_10112 k_10111 BOUND_VARIABLE_1569756)) BOUND_VARIABLE_1426846))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_10139 BOUND_VARIABLE_1569756) BOUND_VARIABLE_1426846) BOUND_VARIABLE_1426847) BOUND_VARIABLE_1426848))))) (let ((_let_4172 (forall ((BOUND_VARIABLE_1426803 tptp.rat) (BOUND_VARIABLE_1426804 tptp.int) (BOUND_VARIABLE_1426805 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7686 BOUND_VARIABLE_1426805) BOUND_VARIABLE_1426804)) (ho_7630 k_7629 BOUND_VARIABLE_1426803)) (ho_7496 (ho_7495 (ho_7635 k_10140 BOUND_VARIABLE_1426803) BOUND_VARIABLE_1426804) BOUND_VARIABLE_1426805))))) (let ((_let_4173 (forall ((BOUND_VARIABLE_1426761 tptp.rat) (BOUND_VARIABLE_1426762 tptp.int) (BOUND_VARIABLE_1426763 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7687 BOUND_VARIABLE_1426763) BOUND_VARIABLE_1426762)) (ho_7630 k_7629 BOUND_VARIABLE_1426761)) (ho_7496 (ho_7495 (ho_7635 k_10069 BOUND_VARIABLE_1426761) BOUND_VARIABLE_1426762) BOUND_VARIABLE_1426763))))) (let ((_let_4174 (forall ((BOUND_VARIABLE_1569804 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426716 tptp.nat) (BOUND_VARIABLE_1426717 tptp.int) (BOUND_VARIABLE_1426718 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7688 BOUND_VARIABLE_1426718) BOUND_VARIABLE_1426717)) (ho_7630 k_7629 (ho_7636 (ho_7663 k_7662 (ho_10112 k_10111 BOUND_VARIABLE_1569804)) BOUND_VARIABLE_1426716))) (ho_7496 (ho_7495 (ho_7639 (ho_7638 k_10141 BOUND_VARIABLE_1569804) BOUND_VARIABLE_1426716) BOUND_VARIABLE_1426717) BOUND_VARIABLE_1426718))))) (let ((_let_4175 (forall ((BOUND_VARIABLE_1569827 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569825 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426702 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_8019) (ho_7636 BOUND_VARIABLE_1569827 BOUND_VARIABLE_1426702)) (ho_7636 BOUND_VARIABLE_1569825 BOUND_VARIABLE_1426702)) (ho_7636 (ho_10063 (ho_10062 k_10142 BOUND_VARIABLE_1569827) BOUND_VARIABLE_1569825) BOUND_VARIABLE_1426702))))) (let ((_let_4176 (forall ((BOUND_VARIABLE_1569843 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1569841 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426687 tptp.nat)) (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_7712) (ho_7636 BOUND_VARIABLE_1569843 BOUND_VARIABLE_1426687)) (ho_7636 BOUND_VARIABLE_1569841 BOUND_VARIABLE_1426687)) (ho_7636 (ho_10063 (ho_10062 k_10143 BOUND_VARIABLE_1569843) BOUND_VARIABLE_1569841) BOUND_VARIABLE_1426687))))) (let ((_let_4177 (forall ((BOUND_VARIABLE_1426678 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (= (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_1 _let_2)) (ho_7698 (ho_7697 k_7696 _let_2) _let_1)) (ho_7698 (ho_7697 k_7696 _let_1) _let_1))) (ho_7636 k_10144 BOUND_VARIABLE_1426678))))))) (let ((_let_4178 (forall ((BOUND_VARIABLE_1426636 tptp.rat) (BOUND_VARIABLE_1426637 tptp.int) (BOUND_VARIABLE_1426638 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7689 BOUND_VARIABLE_1426638) BOUND_VARIABLE_1426637)) (ho_7630 k_7629 BOUND_VARIABLE_1426636)) (ho_7496 (ho_7495 (ho_7635 k_10145 BOUND_VARIABLE_1426636) BOUND_VARIABLE_1426637) BOUND_VARIABLE_1426638))))) (let ((_let_4179 (forall ((BOUND_VARIABLE_1569876 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426587 tptp.nat) (BOUND_VARIABLE_1426588 tptp.rat) (BOUND_VARIABLE_1426589 tptp.int) (BOUND_VARIABLE_1426590 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7690 BOUND_VARIABLE_1426590) BOUND_VARIABLE_1426589)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) (ho_7709 (ho_7708 k_7707 k_7706) k_7703)) k_7712) (ho_7636 BOUND_VARIABLE_1569876 BOUND_VARIABLE_1426587)) BOUND_VARIABLE_1426588))) (ho_7496 (ho_7495 (ho_7635 (ho_10148 (ho_10147 k_10146 BOUND_VARIABLE_1569876) BOUND_VARIABLE_1426587) BOUND_VARIABLE_1426588) BOUND_VARIABLE_1426589) BOUND_VARIABLE_1426590))))) (let ((_let_4180 (forall ((BOUND_VARIABLE_1426544 tptp.rat) (BOUND_VARIABLE_1426545 tptp.int) (BOUND_VARIABLE_1426546 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7691 BOUND_VARIABLE_1426546) BOUND_VARIABLE_1426545)) (ho_7630 k_7629 BOUND_VARIABLE_1426544)) (ho_7496 (ho_7495 (ho_7635 k_10149 BOUND_VARIABLE_1426544) BOUND_VARIABLE_1426545) BOUND_VARIABLE_1426546))))) (let ((_let_4181 (forall ((BOUND_VARIABLE_1426502 tptp.rat) (BOUND_VARIABLE_1426503 tptp.int) (BOUND_VARIABLE_1426504 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7692 BOUND_VARIABLE_1426504) BOUND_VARIABLE_1426503)) (ho_7630 k_7629 BOUND_VARIABLE_1426502)) (ho_7496 (ho_7495 (ho_7635 k_10150 BOUND_VARIABLE_1426502) BOUND_VARIABLE_1426503) BOUND_VARIABLE_1426504))))) (let ((_let_4182 (forall ((BOUND_VARIABLE_1426460 tptp.rat) (BOUND_VARIABLE_1426461 tptp.int) (BOUND_VARIABLE_1426462 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7693 BOUND_VARIABLE_1426462) BOUND_VARIABLE_1426461)) (ho_7630 k_7629 BOUND_VARIABLE_1426460)) (ho_7496 (ho_7495 (ho_7635 k_10151 BOUND_VARIABLE_1426460) BOUND_VARIABLE_1426461) BOUND_VARIABLE_1426462))))) (let ((_let_4183 (forall ((BOUND_VARIABLE_1426418 tptp.rat) (BOUND_VARIABLE_1426419 tptp.int) (BOUND_VARIABLE_1426420 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7694 BOUND_VARIABLE_1426420) BOUND_VARIABLE_1426419)) (ho_7630 k_7629 BOUND_VARIABLE_1426418)) (ho_7496 (ho_7495 (ho_7635 k_10152 BOUND_VARIABLE_1426418) BOUND_VARIABLE_1426419) BOUND_VARIABLE_1426420))))) (let ((_let_4184 (forall ((BOUND_VARIABLE_1569962 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1426355 tptp.nat) (BOUND_VARIABLE_1426356 tptp.int) (BOUND_VARIABLE_1426357 tptp.int)) (let ((_let_1 (ho_7636 BOUND_VARIABLE_1569962 BOUND_VARIABLE_1426355))) (let ((_let_2 (ho_7709 (ho_7708 k_7707 k_7706) k_7703))) (let ((_let_3 (ho_7710 _let_2 k_7705))) (let ((_let_4 (ho_7446 k_7445 tptp.one))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_4)))) (let ((_let_6 (ho_7704 k_7703 (ho_7702 (ho_7701 (ho_7700 k_7699 (= _let_4 _let_5)) (ho_7698 (ho_7697 k_7696 _let_5) _let_4)) (ho_7698 (ho_7697 k_7696 _let_4) _let_4))))) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7695 BOUND_VARIABLE_1426357) BOUND_VARIABLE_1426356)) (ho_7630 k_7629 (ho_7711 (ho_7717 (ho_8510 k_8509 (and (ho_7633 (ho_7632 k_7631 k_7718) (ho_7630 k_7629 _let_1)) (not (= (ho_7711 (ho_7717 (ho_7716 (ho_7715 (ho_7714 k_7713 k_7706) _let_2) k_7712) _let_6) (ho_7711 _let_3 _let_6)) _let_1)))) (ho_7711 _let_3 _let_1)) 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BOUND_VARIABLE_1426182))))) (let ((_let_4189 (forall ((BOUND_VARIABLE_1426137 tptp.rat) (BOUND_VARIABLE_1426138 tptp.int) (BOUND_VARIABLE_1426139 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7723 BOUND_VARIABLE_1426139) BOUND_VARIABLE_1426138)) (ho_7630 k_7629 BOUND_VARIABLE_1426137)) (ho_7496 (ho_7495 (ho_7635 k_10158 BOUND_VARIABLE_1426137) BOUND_VARIABLE_1426138) BOUND_VARIABLE_1426139))))) (let ((_let_4190 (forall ((BOUND_VARIABLE_1426095 tptp.rat) (BOUND_VARIABLE_1426096 tptp.int) (BOUND_VARIABLE_1426097 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7724 BOUND_VARIABLE_1426097) BOUND_VARIABLE_1426096)) (ho_7630 k_7629 BOUND_VARIABLE_1426095)) (ho_7496 (ho_7495 (ho_7635 k_10159 BOUND_VARIABLE_1426095) BOUND_VARIABLE_1426096) BOUND_VARIABLE_1426097))))) (let ((_let_4191 (forall ((BOUND_VARIABLE_1426053 tptp.rat) (BOUND_VARIABLE_1426054 tptp.int) (BOUND_VARIABLE_1426055 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7725 BOUND_VARIABLE_1426055) 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(ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10164 BOUND_VARIABLE_1425911) BOUND_VARIABLE_1425912)))))))))))))))))))))) (let ((_let_4196 (forall ((BOUND_VARIABLE_1425814 tptp.nat) (BOUND_VARIABLE_1425815 tptp.real) (BOUND_VARIABLE_1425816 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1425816) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7516 (ho_7519 k_7523 _let_7) (ho_7516 k_7521 _let_7)))) (let ((_let_9 (ho_7728 k_7727 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1425814) _let_8)) BOUND_VARIABLE_1425815)))) (let ((_let_10 (ho_7730 k_7729 _let_9))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 _let_8) _let_7))) (let ((_let_12 (ho_7519 k_7522 (ho_7730 k_7733 _let_11)))) (let ((_let_13 (ho_7730 k_7733 _let_9))) (let ((_let_14 (ho_7519 k_7522 (ho_7730 k_7729 _let_11)))) (let ((_let_15 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_10)) (ho_7516 k_7521 (ho_7516 _let_12 _let_13)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_14 _let_13)) (ho_7516 _let_12 _let_10)))) _let_6))) (let ((_let_16 (ho_7463 k_7462 _let_1))) (let ((_let_17 (ho_7466 (ho_7465 k_7471 _let_16) _let_4))) (let ((_let_18 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_17 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_17) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 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k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10167 BOUND_VARIABLE_1425741) BOUND_VARIABLE_1425742)))))))))))))))))))))) (let ((_let_4198 (forall ((BOUND_VARIABLE_1425668 tptp.real) (BOUND_VARIABLE_1425669 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1425669) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 BOUND_VARIABLE_1425668))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10168 BOUND_VARIABLE_1425668) BOUND_VARIABLE_1425669)))))))))))))))))))))) (let ((_let_4199 (forall ((BOUND_VARIABLE_1425592 tptp.real) (BOUND_VARIABLE_1425593 tptp.real) (BOUND_VARIABLE_1425594 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1425594) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1425592) BOUND_VARIABLE_1425593)))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 (ho_10170 k_10169 BOUND_VARIABLE_1425592) BOUND_VARIABLE_1425593) BOUND_VARIABLE_1425594)))))))))))))))))))))) (let ((_let_4200 (forall ((BOUND_VARIABLE_1425511 tptp.real)) (let ((_let_1 (ho_10172 k_10171 (ho_7738 k_7737 BOUND_VARIABLE_1425511)))) (let ((_let_2 (ho_7728 k_7727 BOUND_VARIABLE_1425511))) (let ((_let_3 (ho_7730 k_7729 _let_2))) (let ((_let_4 (ho_7510 k_7509 tptp.one))) (let ((_let_5 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_4) (ho_7516 k_7521 _let_4))) _let_4))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7733 _let_5)))) (let ((_let_7 (ho_7730 k_7733 _let_2))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7729 _let_5)))) (let ((_let_9 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_8 _let_3)) (ho_7516 k_7521 (ho_7516 _let_6 _let_7)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_8 _let_7)) (ho_7516 _let_6 _let_3))))) (let ((_let_10 (ho_7985 k_7984 tptp.one))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_10)) (ho_7730 k_7729 _let_9))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_10)) (ho_7730 k_7733 _let_9))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_11)) (ho_7730 k_7729 _let_1))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_11)) (ho_7730 k_7733 _let_1))) (ho_7728 k_10173 BOUND_VARIABLE_1425511)))))))))))))))) (let ((_let_4201 (forall ((BOUND_VARIABLE_1425404 tptp.real)) (let ((_let_1 (ho_10172 k_10171 (ho_7738 k_7739 BOUND_VARIABLE_1425404)))) (let ((_let_2 (ho_7728 k_7727 BOUND_VARIABLE_1425404))) (let ((_let_3 (ho_7730 k_7729 _let_2))) (let ((_let_4 (ho_7510 k_7509 tptp.one))) (let ((_let_5 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_4) (ho_7516 k_7521 _let_4))) _let_4))) (let ((_let_6 (ho_7519 k_7522 (ho_7730 k_7733 _let_5)))) (let ((_let_7 (ho_7730 k_7733 _let_2))) (let ((_let_8 (ho_7519 k_7522 (ho_7730 k_7729 _let_5)))) (let ((_let_9 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_8 _let_3)) (ho_7516 k_7521 (ho_7516 _let_6 _let_7)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_8 _let_7)) (ho_7516 _let_6 _let_3))))) (let ((_let_10 (ho_7985 k_7984 tptp.one))) (let ((_let_11 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_10)) (ho_7730 k_7729 _let_9))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_10)) (ho_7730 k_7733 _let_9))))) (let ((_let_12 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7730 k_7729 _let_11)) (ho_7730 k_7729 _let_1))) (ho_7516 (ho_7519 k_7523 (ho_7730 k_7733 _let_11)) (ho_7730 k_7733 _let_1))))) (let ((_let_13 (ho_7730 k_7729 _let_12))) (let ((_let_14 (ho_7728 k_7727 _let_4))) (let ((_let_15 (ho_7519 k_7522 (ho_7730 k_7733 _let_14)))) (let ((_let_16 (ho_7730 k_7733 _let_12))) (let ((_let_17 (ho_7519 k_7522 (ho_7730 k_7729 _let_14)))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_17 _let_13)) (ho_7516 k_7521 (ho_7516 _let_15 _let_16)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_17 _let_16)) (ho_7516 _let_15 _let_13))) (ho_7728 k_10174 BOUND_VARIABLE_1425404)))))))))))))))))))))) (let ((_let_4202 (forall ((BOUND_VARIABLE_1425341 tptp.real) (BOUND_VARIABLE_1425342 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1425342) _let_4)))) (let ((_let_9 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_10 (ho_7466 (ho_7465 k_7471 _let_5) _let_9))) (let ((_let_11 (ho_7516 k_7521 _let_1))) (= (ho_7508 (ho_7507 k_10175 BOUND_VARIABLE_1425341) BOUND_VARIABLE_1425342) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1425342 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_11)) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_11) (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 _let_10) _let_4)))) _let_4))))) _let_9))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1425342 _let_10)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_10) (ho_7463 k_7462 (ho_7459 _let_8 (ho_7459 _let_3 _let_7)))) _let_1)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1425341) BOUND_VARIABLE_1425342))))))))))))))))) (let ((_let_4203 (forall ((BOUND_VARIABLE_1425268 tptp.real) (BOUND_VARIABLE_1425269 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1425269) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 BOUND_VARIABLE_1425268))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10176 BOUND_VARIABLE_1425268) BOUND_VARIABLE_1425269)))))))))))))))))))))) (let ((_let_4204 (forall ((BOUND_VARIABLE_1425213 tptp.real) (BOUND_VARIABLE_1425214 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_5 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 _let_4 _let_3)))) (let ((_let_6 (ho_7463 k_7462 _let_3))) (let ((_let_7 (ho_7469 k_7468 k_7467))) (let ((_let_8 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_6) _let_8))) (= (ho_7508 (ho_7507 k_10177 BOUND_VARIABLE_1425213) BOUND_VARIABLE_1425214) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1425214 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 _let_2) (ho_7466 (ho_7465 k_7471 BOUND_VARIABLE_1425214) _let_8))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1425214 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_7 BOUND_VARIABLE_1425214) _let_5)) (ho_7459 _let_4 (ho_7459 (ho_7470 _let_7 _let_6) _let_5))))) _let_1))))) (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1425213) BOUND_VARIABLE_1425214))))))))))))))) (let ((_let_4205 (forall ((BOUND_VARIABLE_1425140 tptp.real) (BOUND_VARIABLE_1425141 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1425141) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 BOUND_VARIABLE_1425140))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10178 BOUND_VARIABLE_1425140) BOUND_VARIABLE_1425141)))))))))))))))))))))) (let ((_let_4206 (forall ((BOUND_VARIABLE_1425067 tptp.real) (BOUND_VARIABLE_1425068 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1425068) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 BOUND_VARIABLE_1425067))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10179 BOUND_VARIABLE_1425067) BOUND_VARIABLE_1425068)))))))))))))))))))))) (let ((_let_4207 (forall ((BOUND_VARIABLE_1424993 tptp.real) (BOUND_VARIABLE_1424994 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1424994) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7728 k_7727 (ho_7516 k_7521 BOUND_VARIABLE_1424993)))) (let ((_let_8 (ho_7730 k_7729 _let_7))) (let ((_let_9 (ho_7510 k_7509 tptp.one))) (let ((_let_10 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 _let_9) (ho_7516 k_7521 _let_9))) _let_9))) (let ((_let_11 (ho_7519 k_7522 (ho_7730 k_7733 _let_10)))) (let ((_let_12 (ho_7730 k_7733 _let_7))) (let ((_let_13 (ho_7519 k_7522 (ho_7730 k_7729 _let_10)))) (let ((_let_14 (ho_7736 (ho_7735 k_7734 (ho_7728 (ho_7732 k_7731 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_8)) (ho_7516 k_7521 (ho_7516 _let_11 _let_12)))) (ho_7516 (ho_7519 k_7523 (ho_7516 _let_13 _let_12)) (ho_7516 _let_11 _let_8)))) _let_6))) (let ((_let_15 (ho_7463 k_7462 _let_1))) (let ((_let_16 (ho_7466 (ho_7465 k_7471 _let_15) _let_4))) (let ((_let_17 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_16 _let_6)) _let_9) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_16) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_15) _let_3))))) _let_9)))))) (= (ho_7728 (ho_7732 k_7731 (ho_7516 _let_17 (ho_7730 k_7729 _let_14))) (ho_7516 _let_17 (ho_7730 k_7733 _let_14))) (ho_7736 (ho_7738 k_10180 BOUND_VARIABLE_1424993) BOUND_VARIABLE_1424994)))))))))))))))))))))) (let ((_let_4208 (forall ((BOUND_VARIABLE_1424986 tptp.num)) (= (ho_7441 k_10181 BOUND_VARIABLE_1424986) (ho_7441 k_7444 (ho_7443 k_7486 BOUND_VARIABLE_1424986)))))) (let ((_let_4209 (forall ((BOUND_VARIABLE_1424979 tptp.num)) (= (ho_7441 k_10182 BOUND_VARIABLE_1424979) (ho_7441 k_7444 (ho_7443 k_7486 BOUND_VARIABLE_1424979)))))) (let ((_let_4210 (forall ((BOUND_VARIABLE_1424937 tptp.rat) (BOUND_VARIABLE_1424938 tptp.int) (BOUND_VARIABLE_1424939 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7740 BOUND_VARIABLE_1424939) BOUND_VARIABLE_1424938)) (ho_7630 k_7629 BOUND_VARIABLE_1424937)) (ho_7496 (ho_7495 (ho_7635 k_10183 BOUND_VARIABLE_1424937) BOUND_VARIABLE_1424938) BOUND_VARIABLE_1424939))))) (let ((_let_4211 (forall ((BOUND_VARIABLE_1424895 tptp.rat) (BOUND_VARIABLE_1424896 tptp.int) (BOUND_VARIABLE_1424897 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7741 BOUND_VARIABLE_1424897) BOUND_VARIABLE_1424896)) (ho_7630 k_7629 BOUND_VARIABLE_1424895)) (ho_7496 (ho_7495 (ho_7635 k_10184 BOUND_VARIABLE_1424895) BOUND_VARIABLE_1424896) BOUND_VARIABLE_1424897))))) (let ((_let_4212 (forall ((BOUND_VARIABLE_1424853 tptp.rat) (BOUND_VARIABLE_1424854 tptp.int) (BOUND_VARIABLE_1424855 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7742 BOUND_VARIABLE_1424855) BOUND_VARIABLE_1424854)) (ho_7630 k_7629 BOUND_VARIABLE_1424853)) (ho_7496 (ho_7495 (ho_7635 k_10185 BOUND_VARIABLE_1424853) BOUND_VARIABLE_1424854) BOUND_VARIABLE_1424855))))) (let ((_let_4213 (forall ((BOUND_VARIABLE_1424811 tptp.rat) (BOUND_VARIABLE_1424812 tptp.int) (BOUND_VARIABLE_1424813 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7743 BOUND_VARIABLE_1424813) BOUND_VARIABLE_1424812)) (ho_7630 k_7629 BOUND_VARIABLE_1424811)) (ho_7496 (ho_7495 (ho_7635 k_10186 BOUND_VARIABLE_1424811) BOUND_VARIABLE_1424812) BOUND_VARIABLE_1424813))))) (let ((_let_4214 (forall ((BOUND_VARIABLE_1424769 tptp.rat) (BOUND_VARIABLE_1424770 tptp.int) (BOUND_VARIABLE_1424771 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7744 BOUND_VARIABLE_1424771) BOUND_VARIABLE_1424770)) (ho_7630 k_7629 BOUND_VARIABLE_1424769)) (ho_7496 (ho_7495 (ho_7635 k_10187 BOUND_VARIABLE_1424769) BOUND_VARIABLE_1424770) BOUND_VARIABLE_1424771))))) (let ((_let_4215 (forall ((BOUND_VARIABLE_1424727 tptp.rat) (BOUND_VARIABLE_1424728 tptp.int) (BOUND_VARIABLE_1424729 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7745 BOUND_VARIABLE_1424729) BOUND_VARIABLE_1424728)) (ho_7630 k_7629 BOUND_VARIABLE_1424727)) (ho_7496 (ho_7495 (ho_7635 k_10188 BOUND_VARIABLE_1424727) BOUND_VARIABLE_1424728) BOUND_VARIABLE_1424729))))) (let ((_let_4216 (forall ((BOUND_VARIABLE_1424685 tptp.rat) (BOUND_VARIABLE_1424686 tptp.int) (BOUND_VARIABLE_1424687 tptp.int)) (= (ho_7633 (ho_7632 k_7631 (ho_7494 (ho_7493 k_7746 BOUND_VARIABLE_1424687) BOUND_VARIABLE_1424686)) (ho_7630 k_7629 BOUND_VARIABLE_1424685)) (ho_7496 (ho_7495 (ho_7635 k_10189 BOUND_VARIABLE_1424685) BOUND_VARIABLE_1424686) BOUND_VARIABLE_1424687))))) (let ((_let_4217 (forall ((BOUND_VARIABLE_1424668 tptp.list_nat) (BOUND_VARIABLE_1424669 tptp.nat)) (= (ho_7541 (ho_8981 k_10190 BOUND_VARIABLE_1424668) BOUND_VARIABLE_1424669) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1424669 (ho_7466 (ho_7754 k_7753 BOUND_VARIABLE_1424668) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 BOUND_VARIABLE_1424668))))))))))) (let ((_let_4218 (forall ((BOUND_VARIABLE_1424651 tptp.list_int) (BOUND_VARIABLE_1424652 tptp.int)) (= (ho_7496 (ho_8983 k_10191 BOUND_VARIABLE_1424651) BOUND_VARIABLE_1424652) (not (forall ((I4 tptp.nat)) (or (not (= BOUND_VARIABLE_1424652 (ho_7927 (ho_7926 k_7925 BOUND_VARIABLE_1424651) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7924 k_7923 BOUND_VARIABLE_1424651))))))))))) (let ((_let_4219 (forall ((BOUND_VARIABLE_1424597 tptp.nat) (BOUND_VARIABLE_1424598 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424597) _let_2))) (let ((_let_5 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_4) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424598) _let_2)))) _let_2))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 _let_5) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) _let_5))) _let_2)))) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) _let_2)) _let_4)) (ho_7466 (ho_7465 k_10192 BOUND_VARIABLE_1424597) BOUND_VARIABLE_1424598)))))))))) (let ((_let_4220 (forall ((BOUND_VARIABLE_1424585 tptp.nat) (BOUND_VARIABLE_1424586 tptp.nat) (BOUND_VARIABLE_1424587 tptp.list_nat)) (= (ho_10196 (ho_10195 (ho_10194 k_10193 BOUND_VARIABLE_1424585) BOUND_VARIABLE_1424586) BOUND_VARIABLE_1424587) (and (= BOUND_VARIABLE_1424585 (ho_7752 k_7751 BOUND_VARIABLE_1424587)) (= BOUND_VARIABLE_1424586 (ho_7752 k_10197 BOUND_VARIABLE_1424587))))))) (let ((_let_4221 (forall ((BOUND_VARIABLE_1424573 tptp.nat) (BOUND_VARIABLE_1424574 tptp.nat) (BOUND_VARIABLE_1424575 tptp.list_nat)) (= (ho_10196 (ho_10195 (ho_10194 k_10198 BOUND_VARIABLE_1424573) BOUND_VARIABLE_1424574) BOUND_VARIABLE_1424575) (and (= BOUND_VARIABLE_1424573 (ho_7752 k_7751 BOUND_VARIABLE_1424575)) (= BOUND_VARIABLE_1424574 (ho_7752 k_10197 BOUND_VARIABLE_1424575))))))) (let ((_let_4222 (forall ((BOUND_VARIABLE_1424547 tptp.nat) (BOUND_VARIABLE_1424548 tptp.nat) (BOUND_VARIABLE_1424549 tptp.list_nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_10196 (ho_10195 (ho_10194 k_10199 BOUND_VARIABLE_1424547) BOUND_VARIABLE_1424548) BOUND_VARIABLE_1424549) (and (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1424547) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))) (ho_7752 k_7751 BOUND_VARIABLE_1424549)) (= BOUND_VARIABLE_1424548 (ho_7752 k_10197 BOUND_VARIABLE_1424549))))))))))) (let ((_let_4223 (forall ((BOUND_VARIABLE_1424521 tptp.nat) (BOUND_VARIABLE_1424522 tptp.nat) (BOUND_VARIABLE_1424523 tptp.list_nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (and (= BOUND_VARIABLE_1424521 (ho_7752 k_7751 BOUND_VARIABLE_1424523)) (= BOUND_VARIABLE_1424522 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7752 k_10197 BOUND_VARIABLE_1424523)) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_10196 (ho_10195 (ho_10194 k_10200 BOUND_VARIABLE_1424521) BOUND_VARIABLE_1424522) BOUND_VARIABLE_1424523)))))))) (let ((_let_4224 (forall ((BOUND_VARIABLE_1424516 tptp.nat)) (= BOUND_VARIABLE_1424516 (ho_7466 k_10201 BOUND_VARIABLE_1424516))))) (let ((_let_4225 (forall ((BOUND_VARIABLE_1424496 tptp.nat) (BOUND_VARIABLE_1424497 tptp.nat) (BOUND_VARIABLE_1424498 tptp.nat)) (= (ho_7541 (ho_7540 (ho_7539 k_10202 BOUND_VARIABLE_1424496) BOUND_VARIABLE_1424497) BOUND_VARIABLE_1424498) (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7750 (ho_7749 k_7748 BOUND_VARIABLE_1424496) BOUND_VARIABLE_1424497))) (or (not (= BOUND_VARIABLE_1424498 (ho_7466 (ho_7754 k_7753 _let_1) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_1)))))))))))) (let ((_let_4226 (forall ((BOUND_VARIABLE_1424464 tptp.nat) (BOUND_VARIABLE_1424465 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_10205 (ho_10208 (ho_10207 k_10206 (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1424464)) (ho_7533 k_7532 BOUND_VARIABLE_1424465))) (ho_10205 (ho_10204 k_10203 BOUND_VARIABLE_1424464) (ho_7750 (ho_7749 k_7748 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424464) _let_2)))) BOUND_VARIABLE_1424465))) tptp.nil_nat) (ho_7750 (ho_7749 k_10209 BOUND_VARIABLE_1424464) BOUND_VARIABLE_1424465)))))))) (let ((_let_4227 (forall ((BOUND_VARIABLE_1424447 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 _let_1))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1424447) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_4) _let_3)) (ho_7459 (ho_7470 _let_5 (ho_7466 (ho_7465 k_7471 _let_4) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) _let_3)))) _let_3)))) (ho_7466 k_10210 BOUND_VARIABLE_1424447)))))))))) (let ((_let_4228 (forall ((BOUND_VARIABLE_1424428 tptp.nat)) (= (ho_9995 k_9994 (ho_7540 k_7747 BOUND_VARIABLE_1424428)) (ho_9998 k_10211 BOUND_VARIABLE_1424428))))) (let ((_let_4229 (forall ((BOUND_VARIABLE_1424381 tptp.nat)) (= (ho_9995 k_9994 (ho_7540 k_7755 BOUND_VARIABLE_1424381)) (ho_9998 k_10212 BOUND_VARIABLE_1424381))))) (let ((_let_4230 (forall ((BOUND_VARIABLE_1424362 tptp.nat)) (= (ho_9995 k_9994 (ho_7540 k_7756 BOUND_VARIABLE_1424362)) (ho_9998 k_10213 BOUND_VARIABLE_1424362))))) (let ((_let_4231 (forall ((BOUND_VARIABLE_1424323 tptp.nat)) (= (ho_9995 k_9994 (ho_7540 k_7757 BOUND_VARIABLE_1424323)) (ho_9998 k_10214 BOUND_VARIABLE_1424323))))) (let ((_let_4232 (forall ((BOUND_VARIABLE_1424301 tptp.nat) (BOUND_VARIABLE_1424302 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424302) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424301) _let_2))) (ho_7466 (ho_7465 k_10215 BOUND_VARIABLE_1424301) BOUND_VARIABLE_1424302)))))))) (let ((_let_4233 (forall ((BOUND_VARIABLE_1424283 tptp.nat) (BOUND_VARIABLE_1424284 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (= BOUND_VARIABLE_1424284 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424283) _let_2)))) (ho_7541 (ho_7540 k_10216 BOUND_VARIABLE_1424283) BOUND_VARIABLE_1424284)))))))) (let ((_let_4234 (forall ((BOUND_VARIABLE_1424234 tptp.nat) (BOUND_VARIABLE_1424235 tptp.nat) (BOUND_VARIABLE_1424236 tptp.nat) (BOUND_VARIABLE_1424237 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7750 (ho_7749 k_7748 BOUND_VARIABLE_1424234) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424235) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424236) _let_2)))))) (or (not (= BOUND_VARIABLE_1424237 (ho_7466 (ho_7754 k_7753 _let_4) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_4))))))))))) (ho_7541 (ho_7540 (ho_7539 (ho_7538 k_10217 BOUND_VARIABLE_1424234) BOUND_VARIABLE_1424235) BOUND_VARIABLE_1424236) BOUND_VARIABLE_1424237))))) (let ((_let_4235 (forall ((BOUND_VARIABLE_1424214 tptp.nat) (BOUND_VARIABLE_1424215 tptp.nat) (BOUND_VARIABLE_1424216 tptp.nat)) (= (ho_7541 (ho_7540 (ho_7539 k_10218 BOUND_VARIABLE_1424214) BOUND_VARIABLE_1424215) BOUND_VARIABLE_1424216) (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7750 (ho_7749 k_7748 BOUND_VARIABLE_1424214) BOUND_VARIABLE_1424215))) (or (not (= BOUND_VARIABLE_1424216 (ho_7466 (ho_7754 k_7753 _let_1) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_1)))))))))))) (let ((_let_4236 (forall ((BOUND_VARIABLE_1424166 tptp.nat) (BOUND_VARIABLE_1424167 tptp.nat) (BOUND_VARIABLE_1424168 tptp.nat)) (= (not (forall ((I4 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7750 (ho_7749 k_7748 BOUND_VARIABLE_1424166) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424166) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424167) _let_2)))))) (or (not (= BOUND_VARIABLE_1424168 (ho_7466 (ho_7754 k_7753 _let_4) I4))) (not (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 I4)) (ho_7533 k_7532 (ho_7752 k_7751 _let_4))))))))))) (ho_7541 (ho_7540 (ho_7539 k_10219 BOUND_VARIABLE_1424166) BOUND_VARIABLE_1424167) BOUND_VARIABLE_1424168))))) (let ((_let_4237 (forall ((BOUND_VARIABLE_1424148 tptp.nat) (BOUND_VARIABLE_1424149 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7466 (ho_7465 k_10220 BOUND_VARIABLE_1424149) BOUND_VARIABLE_1424148)) _let_2))) (ho_7466 (ho_7465 k_10221 BOUND_VARIABLE_1424148) BOUND_VARIABLE_1424149)))))))) (let ((_let_4238 (forall ((BOUND_VARIABLE_1424130 tptp.nat) (BOUND_VARIABLE_1424131 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7466 (ho_7465 k_10220 BOUND_VARIABLE_1424130) BOUND_VARIABLE_1424131)) _let_2))) (ho_7466 (ho_7465 k_10222 BOUND_VARIABLE_1424130) BOUND_VARIABLE_1424131)))))))) (let ((_let_4239 (forall ((BOUND_VARIABLE_1424106 tptp.nat) (BOUND_VARIABLE_1424107 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1424107) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1424106) _let_3)))) (ho_7466 (ho_7465 k_10223 BOUND_VARIABLE_1424106) BOUND_VARIABLE_1424107))))))))) (let ((_let_4240 (forall ((BOUND_VARIABLE_1424079 tptp.nat) (BOUND_VARIABLE_1424080 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 k_7521 _let_1))) (let ((_let_3 (ho_7516 (ho_7519 k_7523 _let_1) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1424080 _let_3))) (let ((_let_5 (not _let_4))) (= (ho_7516 (ho_7512 k_10224 BOUND_VARIABLE_1424079) BOUND_VARIABLE_1424080) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 (ho_7518 k_7517 _let_4) _let_3) (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 _let_3) BOUND_VARIABLE_1424080) _let_5)) _let_1) _let_2))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 (ho_7518 k_7517 (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1424080) _let_3) _let_5)) (ho_7516 k_7521 BOUND_VARIABLE_1424080)) BOUND_VARIABLE_1424080)) BOUND_VARIABLE_1424079))))))))))) (let ((_let_4241 (forall ((BOUND_VARIABLE_1424053 tptp.nat) (BOUND_VARIABLE_1424054 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7466 (ho_7465 k_7464 BOUND_VARIABLE_1424053) BOUND_VARIABLE_1424054)) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1424054) _let_3)))) (ho_7466 (ho_7465 k_10225 BOUND_VARIABLE_1424053) BOUND_VARIABLE_1424054))))))))) (let ((_let_4242 (forall ((BOUND_VARIABLE_1424031 tptp.nat) (BOUND_VARIABLE_1424032 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424031) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1424032) _let_2))) (ho_7466 (ho_7465 k_10226 BOUND_VARIABLE_1424031) BOUND_VARIABLE_1424032)))))))) (let ((_let_4243 (forall ((BOUND_VARIABLE_1571317 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1424011 tptp.real)) (let ((_let_1 (ho_7516 BOUND_VARIABLE_1571317 BOUND_VARIABLE_1424011))) (let ((_let_2 (ho_7510 k_7509 tptp.one))) (let ((_let_3 (ho_7519 k_7523 _let_2))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_10228 (ho_7516 (ho_7519 k_7523 (ho_7516 _let_3 _let_2)) (ho_7795 k_7794 k_10227))) (ho_7516 (ho_7519 k_7522 (ho_7516 _let_3 _let_1)) (ho_7516 k_7520 (ho_7516 _let_3 (ho_7516 k_7521 _let_1)))))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))) (ho_7516 (ho_8397 k_10229 BOUND_VARIABLE_1571317) BOUND_VARIABLE_1424011)))))))) (let ((_let_4244 (forall ((BOUND_VARIABLE_1571345 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1424003 tptp.real)) (= (ho_7516 (ho_8397 k_10230 BOUND_VARIABLE_1571345) BOUND_VARIABLE_1424003) (ho_7516 k_10231 (ho_7516 BOUND_VARIABLE_1571345 BOUND_VARIABLE_1424003)))))) (let ((_let_4245 (forall ((BOUND_VARIABLE_1423965 tptp.nat) (BOUND_VARIABLE_1423966 tptp.nat) (BOUND_VARIABLE_1423967 tptp.nat)) (= (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1423965 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423967) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2)))))))))) (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (not (= BOUND_VARIABLE_1423966 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423967) _let_2)) (ho_7459 (ho_7470 _let_3 K3) _let_2))))))))))) (ho_7541 (ho_7540 (ho_7539 k_10232 BOUND_VARIABLE_1423965) BOUND_VARIABLE_1423966) BOUND_VARIABLE_1423967))))) (let ((_let_4246 (forall ((BOUND_VARIABLE_1423924 tptp.nat) (BOUND_VARIABLE_1423925 tptp.nat)) (let ((_let_1 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7466 (ho_7465 k_10235 BOUND_VARIABLE_1423924) BOUND_VARIABLE_1423925) (ho_7466 (ho_7465 (ho_7878 k_7877 (= BOUND_VARIABLE_1423925 _let_1)) _let_1) (ho_10234 k_10233 (ho_9995 k_9994 (ho_7540 (ho_7539 k_7758 BOUND_VARIABLE_1423925) BOUND_VARIABLE_1423924))))))))) (let ((_let_4247 (forall ((BOUND_VARIABLE_1423901 tptp.nat)) (= (ho_9995 k_9994 (ho_7540 k_7759 BOUND_VARIABLE_1423901)) (ho_9998 k_10236 BOUND_VARIABLE_1423901))))) (let ((_let_4248 (forall ((BOUND_VARIABLE_1571408 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1423881 tptp.nat) (BOUND_VARIABLE_1423882 tptp.real)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7508 (ho_7507 k_7506 (ho_7516 BOUND_VARIABLE_1571408 BOUND_VARIABLE_1423882)) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423881) _let_2)))) (ho_7516 (ho_7512 (ho_7788 k_10237 BOUND_VARIABLE_1571408) BOUND_VARIABLE_1423881) BOUND_VARIABLE_1423882)))))))) (let ((_let_4249 (forall ((BOUND_VARIABLE_1571425 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1423871 tptp.nat) (BOUND_VARIABLE_1423872 tptp.real)) (= (ho_7516 (ho_7512 (ho_7788 k_10238 BOUND_VARIABLE_1571425) BOUND_VARIABLE_1423871) BOUND_VARIABLE_1423872) (ho_7508 (ho_7507 k_7506 (ho_7516 BOUND_VARIABLE_1571425 BOUND_VARIABLE_1423872)) BOUND_VARIABLE_1423871))))) (let ((_let_4250 (forall ((BOUND_VARIABLE_1571439 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_1423861 tptp.real) (BOUND_VARIABLE_1423862 tptp.real)) (= (ho_7781 (ho_7780 (ho_10240 k_10239 BOUND_VARIABLE_1571439) BOUND_VARIABLE_1423861) BOUND_VARIABLE_1423862) (ho_7781 BOUND_VARIABLE_1571439 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1423862) BOUND_VARIABLE_1423861)))))) (let ((_let_4251 (forall ((BOUND_VARIABLE_1423847 tptp.real) (BOUND_VARIABLE_1423848 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_10241 BOUND_VARIABLE_1423847) BOUND_VARIABLE_1423848) (ho_7516 (ho_7519 k_10242 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1423847) BOUND_VARIABLE_1423848))) (ho_7516 (ho_7519 k_7522 _let_1) (ho_7516 k_7520 BOUND_VARIABLE_1423848)))))))) (let ((_let_4252 (forall ((BOUND_VARIABLE_1423798 tptp.real) (BOUND_VARIABLE_1423799 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1423799) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1423798) _let_6)) (ho_7508 (ho_7507 k_10243 BOUND_VARIABLE_1423798) BOUND_VARIABLE_1423799)))))))))))))) (let ((_let_4253 (forall ((BOUND_VARIABLE_1423788 tptp.real)) (let ((_let_1 (ho_7516 (ho_7519 k_7522 (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one)))) (ho_7516 k_7520 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one)))))) (= (ho_7781 k_10244 BOUND_VARIABLE_1423788) (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1423788) _let_1) (not (= BOUND_VARIABLE_1423788 _let_1)))))))) (let ((_let_4254 (forall ((BOUND_VARIABLE_1423776 tptp.real) (BOUND_VARIABLE_1423777 tptp.real)) (= (ho_7516 (ho_7519 k_10245 BOUND_VARIABLE_1423776) BOUND_VARIABLE_1423777) (ho_7516 (ho_7519 k_10242 (ho_7516 (ho_7519 k_7523 (ho_7510 k_7509 tptp.one)) (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1423776) (ho_7516 k_7520 BOUND_VARIABLE_1423777)))) BOUND_VARIABLE_1423777))))) (let ((_let_4255 (forall ((BOUND_VARIABLE_1423727 tptp.real) (BOUND_VARIABLE_1423728 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1423728) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1423727) _let_6)) (ho_7508 (ho_7507 k_10246 BOUND_VARIABLE_1423727) BOUND_VARIABLE_1423728)))))))))))))) (let ((_let_4256 (forall ((BOUND_VARIABLE_1423717 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7781 k_10247 BOUND_VARIABLE_1423717) (and (ho_7781 (ho_7780 k_7779 BOUND_VARIABLE_1423717) _let_1) (not (= BOUND_VARIABLE_1423717 _let_1)))))))) (let ((_let_4257 (forall ((BOUND_VARIABLE_1571565 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1423693 tptp.nat) (BOUND_VARIABLE_1423694 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7541 BOUND_VARIABLE_1571565 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423694) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423693) _let_2)))) (ho_7541 (ho_7540 (ho_10249 k_10248 BOUND_VARIABLE_1571565) BOUND_VARIABLE_1423693) BOUND_VARIABLE_1423694)))))))) (let ((_let_4258 (forall ((BOUND_VARIABLE_1423682 tptp.nat) (BOUND_VARIABLE_1423683 tptp.nat)) (= (ho_7541 (ho_7540 k_10250 BOUND_VARIABLE_1423682) BOUND_VARIABLE_1423683) (ho_7536 (ho_7535 k_7542 (ho_7533 k_7532 BOUND_VARIABLE_1423682)) (ho_7533 k_7532 BOUND_VARIABLE_1423683)))))) (let ((_let_4259 (forall ((BOUND_VARIABLE_1571599 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1423658 tptp.nat) (BOUND_VARIABLE_1423659 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7541 BOUND_VARIABLE_1571599 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423659) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423658) _let_2)))) (ho_7541 (ho_7540 (ho_10249 k_10251 BOUND_VARIABLE_1571599) BOUND_VARIABLE_1423658) BOUND_VARIABLE_1423659)))))))) (let ((_let_4260 (forall ((BOUND_VARIABLE_1571615 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1423640 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7541 BOUND_VARIABLE_1571615 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423640) _let_2)))) (ho_7541 (ho_10125 k_10252 BOUND_VARIABLE_1571615) BOUND_VARIABLE_1423640)))))))) (let ((_let_4261 (forall ((BOUND_VARIABLE_1571627 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423630 tptp.nat)) (= (ho_7508 (ho_7761 k_10253 BOUND_VARIABLE_1571627) BOUND_VARIABLE_1423630) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423630)) (ho_7508 BOUND_VARIABLE_1571627 BOUND_VARIABLE_1423630)))))) (let ((_let_4262 (forall ((BOUND_VARIABLE_1571640 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423620 tptp.nat)) (= (ho_7508 (ho_7761 k_10254 BOUND_VARIABLE_1571640) BOUND_VARIABLE_1423620) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423620)) (ho_7508 BOUND_VARIABLE_1571640 BOUND_VARIABLE_1423620)))))) (let ((_let_4263 (forall ((BOUND_VARIABLE_1423587 tptp.nat) (BOUND_VARIABLE_1423588 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1423588)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423587) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_10255 BOUND_VARIABLE_1423587) BOUND_VARIABLE_1423588)))))))) (let ((_let_4264 (forall ((BOUND_VARIABLE_1571673 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423536 tptp.nat)) (= (ho_10258 (ho_10257 k_10256 (ho_7761 k_7760 BOUND_VARIABLE_1571673)) (ho_9995 k_9994 (ho_7540 k_7762 BOUND_VARIABLE_1423536))) (ho_7508 (ho_7761 k_10259 BOUND_VARIABLE_1571673) BOUND_VARIABLE_1423536))))) (let ((_let_4265 (forall ((BOUND_VARIABLE_1571695 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423526 tptp.nat)) (= (ho_7508 (ho_7761 k_10260 BOUND_VARIABLE_1571695) BOUND_VARIABLE_1423526) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423526)) (ho_7508 BOUND_VARIABLE_1571695 BOUND_VARIABLE_1423526)))))) (let ((_let_4266 (forall ((BOUND_VARIABLE_1571708 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423474 tptp.nat)) (= (ho_10258 (ho_10257 k_10256 (ho_7761 k_7763 BOUND_VARIABLE_1571708)) (ho_9995 k_9994 (ho_7540 k_7764 BOUND_VARIABLE_1423474))) (ho_7508 (ho_7761 k_10261 BOUND_VARIABLE_1571708) BOUND_VARIABLE_1423474))))) (let ((_let_4267 (forall ((BOUND_VARIABLE_1571722 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423464 tptp.nat)) (= (ho_7508 (ho_7761 k_10262 BOUND_VARIABLE_1571722) BOUND_VARIABLE_1423464) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423464)) (ho_7508 BOUND_VARIABLE_1571722 BOUND_VARIABLE_1423464)))))) (let ((_let_4268 (forall ((BOUND_VARIABLE_1571735 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423454 tptp.nat)) (= (ho_7508 (ho_7761 k_10263 BOUND_VARIABLE_1571735) BOUND_VARIABLE_1423454) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423454)) (ho_7508 BOUND_VARIABLE_1571735 BOUND_VARIABLE_1423454)))))) (let ((_let_4269 (forall ((BOUND_VARIABLE_1423431 tptp.nat) (BOUND_VARIABLE_1423432 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1423432)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423431) _let_2))))) (ho_7541 (ho_7540 k_10264 BOUND_VARIABLE_1423431) BOUND_VARIABLE_1423432)))))))) (let ((_let_4270 (forall ((BOUND_VARIABLE_1571763 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423390 tptp.nat)) (= (ho_10258 (ho_10257 k_10256 (ho_7761 k_7765 BOUND_VARIABLE_1571763)) (ho_9995 k_9994 (ho_7540 k_7766 BOUND_VARIABLE_1423390))) (ho_7508 (ho_7761 k_10265 BOUND_VARIABLE_1571763) BOUND_VARIABLE_1423390))))) (let ((_let_4271 (forall ((BOUND_VARIABLE_1571777 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423380 tptp.nat)) (= (ho_7508 (ho_7761 k_10266 BOUND_VARIABLE_1571777) BOUND_VARIABLE_1423380) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423380)) (ho_7508 BOUND_VARIABLE_1571777 BOUND_VARIABLE_1423380)))))) (let ((_let_4272 (forall ((BOUND_VARIABLE_1423347 tptp.nat) (BOUND_VARIABLE_1423348 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1423348)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423347) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_10267 BOUND_VARIABLE_1423347) BOUND_VARIABLE_1423348)))))))) (let ((_let_4273 (forall ((BOUND_VARIABLE_1571810 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423296 tptp.nat)) (= (ho_10258 (ho_10257 k_10256 (ho_7761 k_7767 BOUND_VARIABLE_1571810)) (ho_9995 k_9994 (ho_7540 k_7768 BOUND_VARIABLE_1423296))) (ho_7508 (ho_7761 k_10268 BOUND_VARIABLE_1571810) BOUND_VARIABLE_1423296))))) (let ((_let_4274 (forall ((BOUND_VARIABLE_1571824 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423254 tptp.nat)) (= (ho_10258 (ho_10257 k_10256 (ho_7761 k_7769 BOUND_VARIABLE_1571824)) (ho_9995 k_9994 (ho_7540 k_7770 BOUND_VARIABLE_1423254))) (ho_7508 (ho_7761 k_10269 BOUND_VARIABLE_1571824) BOUND_VARIABLE_1423254))))) (let ((_let_4275 (forall ((BOUND_VARIABLE_1571838 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423244 tptp.nat)) (= (ho_7508 (ho_7761 k_10270 BOUND_VARIABLE_1571838) BOUND_VARIABLE_1423244) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423244)) (ho_7508 BOUND_VARIABLE_1571838 BOUND_VARIABLE_1423244)))))) (let ((_let_4276 (forall ((BOUND_VARIABLE_1571851 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423234 tptp.nat)) (= (ho_7508 (ho_7761 k_10271 BOUND_VARIABLE_1571851) BOUND_VARIABLE_1423234) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423234)) (ho_7508 BOUND_VARIABLE_1571851 BOUND_VARIABLE_1423234)))))) (let ((_let_4277 (forall ((BOUND_VARIABLE_1423211 tptp.nat) (BOUND_VARIABLE_1423212 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1423212)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423211) _let_2))))) (ho_7541 (ho_7540 k_10272 BOUND_VARIABLE_1423211) BOUND_VARIABLE_1423212)))))))) (let ((_let_4278 (forall ((BOUND_VARIABLE_1571879 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423202 tptp.nat)) (= (ho_7508 (ho_7761 k_10273 BOUND_VARIABLE_1571879) BOUND_VARIABLE_1423202) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423202)) (ho_7508 BOUND_VARIABLE_1571879 BOUND_VARIABLE_1423202)))))) (let ((_let_4279 (forall ((BOUND_VARIABLE_1423158 tptp.real) (BOUND_VARIABLE_1423159 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (let ((_let_4 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1423159) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (let ((_let_5 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 _let_5) (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) _let_4) (ho_7516 (ho_7519 k_7523 _let_5) (ho_7516 k_7521 _let_5)))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1423158) _let_4)) (ho_7508 (ho_7507 k_10274 BOUND_VARIABLE_1423158) BOUND_VARIABLE_1423159)))))))))) (let ((_let_4280 (forall ((BOUND_VARIABLE_1571917 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423117 tptp.nat)) (= (ho_10258 (ho_10257 k_10256 (ho_7761 k_7771 BOUND_VARIABLE_1571917)) (ho_9995 k_9994 (ho_7540 k_7772 BOUND_VARIABLE_1423117))) (ho_7508 (ho_7761 k_10275 BOUND_VARIABLE_1571917) BOUND_VARIABLE_1423117))))) (let ((_let_4281 (forall ((BOUND_VARIABLE_1571931 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423107 tptp.nat)) (= (ho_7508 (ho_7761 k_10276 BOUND_VARIABLE_1571931) BOUND_VARIABLE_1423107) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423107)) (ho_7508 BOUND_VARIABLE_1571931 BOUND_VARIABLE_1423107)))))) (let ((_let_4282 (forall ((BOUND_VARIABLE_1571942 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423081 tptp.nat)) (= (ho_7795 k_7794 (ho_7775 (ho_7774 k_7773 BOUND_VARIABLE_1571942) BOUND_VARIABLE_1423081)) (ho_7508 (ho_7761 k_10277 BOUND_VARIABLE_1571942) BOUND_VARIABLE_1423081))))) (let ((_let_4283 (forall ((BOUND_VARIABLE_1571958 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1571957 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1423067 tptp.nat)) (= (ho_7508 (ho_10280 (ho_10279 k_10278 BOUND_VARIABLE_1571958) BOUND_VARIABLE_1571957) BOUND_VARIABLE_1423067) (ho_7516 (ho_7519 k_7523 (ho_7508 BOUND_VARIABLE_1571958 BOUND_VARIABLE_1423067)) (ho_7516 k_7521 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7927 BOUND_VARIABLE_1571957 BOUND_VARIABLE_1423067))) (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one))) (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))))))))))) (let ((_let_4284 (forall ((BOUND_VARIABLE_1571982 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423031 tptp.real) (BOUND_VARIABLE_1423032 tptp.nat)) (= (ho_7795 k_7794 (ho_7507 (ho_7778 (ho_7777 k_7776 BOUND_VARIABLE_1571982) BOUND_VARIABLE_1423032) BOUND_VARIABLE_1423031)) (ho_7508 (ho_7507 (ho_7800 k_10281 BOUND_VARIABLE_1571982) BOUND_VARIABLE_1423031) BOUND_VARIABLE_1423032))))) (let ((_let_4285 (forall ((BOUND_VARIABLE_1572001 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1572000 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1423017 tptp.nat)) (= (ho_7508 (ho_10280 (ho_10279 k_10282 BOUND_VARIABLE_1572001) BOUND_VARIABLE_1572000) BOUND_VARIABLE_1423017) (ho_7516 (ho_7519 k_7523 (ho_7508 BOUND_VARIABLE_1572001 BOUND_VARIABLE_1423017)) (ho_7516 k_7521 (ho_7516 (ho_7519 k_7522 (ho_7990 k_7989 (ho_7927 BOUND_VARIABLE_1572000 BOUND_VARIABLE_1423017))) (ho_7516 (ho_7519 k_7522 (ho_7510 k_7509 (ho_7443 k_7442 tptp.one))) (ho_7516 k_7796 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))))))))))) (let ((_let_4286 (forall ((BOUND_VARIABLE_1572019 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1423006 tptp.nat)) (= (ho_7508 (ho_7761 k_10283 BOUND_VARIABLE_1572019) BOUND_VARIABLE_1423006) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1423006)) (ho_7508 BOUND_VARIABLE_1572019 BOUND_VARIABLE_1423006)))))) (let ((_let_4287 (forall ((BOUND_VARIABLE_1572032 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422996 tptp.nat)) (= (ho_7508 (ho_7761 k_10284 BOUND_VARIABLE_1572032) BOUND_VARIABLE_1422996) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422996)) (ho_7508 BOUND_VARIABLE_1572032 BOUND_VARIABLE_1422996)))))) (let ((_let_4288 (forall ((BOUND_VARIABLE_1422966 tptp.real) (BOUND_VARIABLE_1422967 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7519 k_7523 _let_1))) (let ((_let_3 (ho_7446 k_7445 tptp.one))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_3) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_3)))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1422966) (ho_7516 _let_2 (ho_7516 k_7521 (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 (ho_7463 k_7462 _let_3)) _let_4)) (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1422967) _let_4)))) (ho_7516 _let_2 (ho_7516 k_7521 _let_1))))))) (ho_7508 (ho_7507 k_10285 BOUND_VARIABLE_1422966) BOUND_VARIABLE_1422967)))))))))) (let ((_let_4289 (forall ((BOUND_VARIABLE_1422943 tptp.real) (BOUND_VARIABLE_1422944 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7519 k_7523 _let_1))) (= (ho_7508 (ho_7507 k_7506 (ho_7516 _let_2 (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1422943) (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1422944) (ho_7516 _let_2 (ho_7516 k_7521 _let_1))))))) BOUND_VARIABLE_1422944) (ho_7508 (ho_7507 k_10286 BOUND_VARIABLE_1422943) BOUND_VARIABLE_1422944))))))) (let ((_let_4290 (forall ((BOUND_VARIABLE_1422894 tptp.real) (BOUND_VARIABLE_1422895 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one))))) (let ((_let_5 (ho_7469 k_7468 k_7467))) (let ((_let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 BOUND_VARIABLE_1422895) _let_3)) (ho_7459 (ho_7470 _let_5 _let_4) _let_3))))) (let ((_let_7 (ho_7510 k_7509 tptp.one))) (let ((_let_8 (ho_7463 k_7462 _let_1))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_8) _let_4))) (= (ho_7516 (ho_7519 k_7522 (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_6)) _let_7) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_5 _let_6) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_5 _let_8) _let_3))))) _let_7)))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1422894) _let_6)) (ho_7508 (ho_7507 k_10287 BOUND_VARIABLE_1422894) BOUND_VARIABLE_1422895)))))))))))))) (let ((_let_4291 (forall ((BOUND_VARIABLE_1422867 tptp.real) (BOUND_VARIABLE_1422868 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1422867) (ho_7516 k_7521 (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_2)) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1422868) _let_3)))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))))) (ho_7508 (ho_7507 k_10288 BOUND_VARIABLE_1422867) BOUND_VARIABLE_1422868))))))))) (let ((_let_4292 (forall ((BOUND_VARIABLE_1422858 tptp.real) (BOUND_VARIABLE_1422859 tptp.nat)) (= (ho_7508 (ho_7507 k_10289 BOUND_VARIABLE_1422858) BOUND_VARIABLE_1422859) (ho_7516 k_7520 (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1422858) BOUND_VARIABLE_1422859)))))) (let ((_let_4293 (forall ((BOUND_VARIABLE_1422846 tptp.real) (BOUND_VARIABLE_1422847 tptp.real) (BOUND_VARIABLE_1422848 tptp.nat)) (= (ho_7508 (ho_7507 (ho_10291 k_10290 BOUND_VARIABLE_1422846) BOUND_VARIABLE_1422847) BOUND_VARIABLE_1422848) (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1422846) (ho_7516 k_7520 (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1422847) BOUND_VARIABLE_1422848))))))) (let ((_let_4294 (forall ((BOUND_VARIABLE_1422821 tptp.real) (BOUND_VARIABLE_1422822 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1422821) (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_2)) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1422822) _let_3)))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) (ho_7508 (ho_7507 k_10292 BOUND_VARIABLE_1422821) BOUND_VARIABLE_1422822))))))))) (let ((_let_4295 (forall ((BOUND_VARIABLE_1422800 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_2)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (= (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_2)) _let_3)) (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1422800) _let_3)))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (ho_7508 k_10293 BOUND_VARIABLE_1422800))))))))) (let ((_let_4296 (forall ((BOUND_VARIABLE_1422773 tptp.real) (BOUND_VARIABLE_1422774 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7508 (ho_7507 k_10294 BOUND_VARIABLE_1422773) BOUND_VARIABLE_1422774) (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1422774 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))) (ho_7516 (ho_8397 (ho_8396 k_8395 tptp.top_top_set_real) (ho_7512 k_7782 BOUND_VARIABLE_1422774)) BOUND_VARIABLE_1422773))))))) (let ((_let_4297 (forall ((BOUND_VARIABLE_1422758 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (= (ho_7516 (ho_7519 k_7522 _let_1) (ho_7516 k_7520 (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1422758) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1))))) (ho_7508 k_10295 BOUND_VARIABLE_1422758)))))) (let ((_let_4298 (forall ((BOUND_VARIABLE_1572201 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422751 tptp.nat)) (= (ho_7508 (ho_7761 k_10296 BOUND_VARIABLE_1572201) BOUND_VARIABLE_1422751) (ho_7516 k_7520 (ho_7508 BOUND_VARIABLE_1572201 BOUND_VARIABLE_1422751)))))) (let ((_let_4299 (forall ((BOUND_VARIABLE_1572214 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1572213 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422740 tptp.nat)) (= (ho_7508 (ho_7761 (ho_10298 k_10297 BOUND_VARIABLE_1572214) BOUND_VARIABLE_1572213) BOUND_VARIABLE_1422740) (ho_7516 (ho_7519 k_7523 (ho_7508 BOUND_VARIABLE_1572214 BOUND_VARIABLE_1422740)) (ho_7516 k_7521 (ho_7508 BOUND_VARIABLE_1572213 BOUND_VARIABLE_1422740))))))) (let ((_let_4300 (forall ((BOUND_VARIABLE_1422708 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (= (ho_7508 k_10299 BOUND_VARIABLE_1422708) (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1422708 (ho_7466 (ho_7465 k_7471 (ho_7463 k_7462 (ho_7446 k_7445 tptp.one))) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) _let_2) (ho_7516 (ho_8397 (ho_8396 k_8395 tptp.top_top_set_real) (ho_7512 k_7783 BOUND_VARIABLE_1422708)) (ho_7516 (ho_7512 (ho_7788 k_7787 k_7786) BOUND_VARIABLE_1422708) _let_2))))))))) (let ((_let_4301 (forall ((BOUND_VARIABLE_1422686 tptp.nat) (BOUND_VARIABLE_1422687 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422687) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422686) _let_2))) (ho_7466 (ho_7465 k_10300 BOUND_VARIABLE_1422686) BOUND_VARIABLE_1422687)))))))) (let ((_let_4302 (forall ((BOUND_VARIABLE_1422664 tptp.nat) (BOUND_VARIABLE_1422665 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422664) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422665) _let_2))) (ho_7466 (ho_7465 k_10301 BOUND_VARIABLE_1422664) BOUND_VARIABLE_1422665)))))))) (let ((_let_4303 (forall ((BOUND_VARIABLE_1572275 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422655 tptp.nat)) (= (ho_7508 (ho_7761 k_10302 BOUND_VARIABLE_1572275) BOUND_VARIABLE_1422655) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422655)) (ho_7508 BOUND_VARIABLE_1572275 BOUND_VARIABLE_1422655)))))) (let ((_let_4304 (forall ((BOUND_VARIABLE_1572288 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422645 tptp.nat)) (= (ho_7508 (ho_7761 k_10303 BOUND_VARIABLE_1572288) BOUND_VARIABLE_1422645) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422645)) (ho_7508 BOUND_VARIABLE_1572288 BOUND_VARIABLE_1422645)))))) (let ((_let_4305 (forall ((BOUND_VARIABLE_1422612 tptp.nat) (BOUND_VARIABLE_1422613 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1422613)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422612) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_10304 BOUND_VARIABLE_1422612) BOUND_VARIABLE_1422613)))))))) (let ((_let_4306 (forall ((BOUND_VARIABLE_1572321 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422603 tptp.nat)) (= (ho_7508 (ho_7761 k_10305 BOUND_VARIABLE_1572321) BOUND_VARIABLE_1422603) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422603)) (ho_7508 BOUND_VARIABLE_1572321 BOUND_VARIABLE_1422603)))))) (let ((_let_4307 (forall ((BOUND_VARIABLE_1422580 tptp.nat) (BOUND_VARIABLE_1422581 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1422581)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422580) _let_2))))) (ho_7541 (ho_7540 k_10306 BOUND_VARIABLE_1422580) BOUND_VARIABLE_1422581)))))))) (let ((_let_4308 (forall ((BOUND_VARIABLE_1572349 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422571 tptp.nat)) (= (ho_7508 (ho_7761 k_10307 BOUND_VARIABLE_1572349) BOUND_VARIABLE_1422571) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422571)) (ho_7508 BOUND_VARIABLE_1572349 BOUND_VARIABLE_1422571)))))) (let ((_let_4309 (forall ((BOUND_VARIABLE_1572362 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422561 tptp.nat)) (= (ho_7508 (ho_7761 k_10308 BOUND_VARIABLE_1572362) BOUND_VARIABLE_1422561) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422561)) (ho_7508 BOUND_VARIABLE_1572362 BOUND_VARIABLE_1422561)))))) (let ((_let_4310 (forall ((BOUND_VARIABLE_1422538 tptp.nat) (BOUND_VARIABLE_1422539 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1422539)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422538) _let_2))))) (ho_7541 (ho_7540 k_10309 BOUND_VARIABLE_1422538) BOUND_VARIABLE_1422539)))))))) (let ((_let_4311 (forall ((BOUND_VARIABLE_1572390 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1422529 tptp.nat)) (= (ho_7508 (ho_7761 k_10310 BOUND_VARIABLE_1572390) BOUND_VARIABLE_1422529) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422529)) (ho_7508 BOUND_VARIABLE_1572390 BOUND_VARIABLE_1422529)))))) (let ((_let_4312 (forall ((BOUND_VARIABLE_1422496 tptp.nat) (BOUND_VARIABLE_1422497 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1422497)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2)) (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422496) _let_2)))) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 _let_1)) _let_2))))) (ho_7541 (ho_7540 k_10311 BOUND_VARIABLE_1422496) BOUND_VARIABLE_1422497)))))))) (let ((_let_4313 (forall ((BOUND_VARIABLE_1422456 tptp.real)) (= (ho_7516 (ho_7519 k_7522 (ho_7795 k_7794 (ho_7507 k_7784 BOUND_VARIABLE_1422456))) (ho_7516 k_7520 (ho_7795 k_7794 (ho_7507 k_7785 BOUND_VARIABLE_1422456)))) (ho_7516 k_10312 BOUND_VARIABLE_1422456))))) (let ((_let_4314 (forall ((BOUND_VARIABLE_1422426 tptp.int) (BOUND_VARIABLE_1422427 tptp.int)) (= (ho_10315 (ho_10318 (ho_10317 k_10316 (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= BOUND_VARIABLE_1422427 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1422426) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))))))))) (ho_10315 (ho_10314 k_10313 BOUND_VARIABLE_1422426) (ho_7922 (ho_7921 k_7920 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1422426) (ho_7446 k_7445 tptp.one))) BOUND_VARIABLE_1422427))) tptp.nil_int) (ho_7922 (ho_7921 k_10319 BOUND_VARIABLE_1422426) BOUND_VARIABLE_1422427))))) (let ((_let_4315 (forall ((BOUND_VARIABLE_1422387 tptp.int) (BOUND_VARIABLE_1422388 tptp.int) (BOUND_VARIABLE_1422389 tptp.list_int)) (= (ho_10315 (ho_10318 (ho_10317 k_10316 (and (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (not (= BOUND_VARIABLE_1422387 (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1422388) (ho_7459 (ho_7470 (ho_7469 k_7468 k_7467) N2) (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1))))))))) (not (= BOUND_VARIABLE_1422387 BOUND_VARIABLE_1422388)))) BOUND_VARIABLE_1422389) (ho_10315 (ho_10314 (ho_10321 k_10320 BOUND_VARIABLE_1422387) (ho_7459 (ho_7461 k_7460 BOUND_VARIABLE_1422388) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) (ho_7446 k_7445 tptp.one)))) (ho_10315 (ho_10314 k_10313 BOUND_VARIABLE_1422388) BOUND_VARIABLE_1422389))) (ho_10315 (ho_10314 (ho_10321 k_10322 BOUND_VARIABLE_1422387) BOUND_VARIABLE_1422388) BOUND_VARIABLE_1422389))))) (let ((_let_4316 (forall ((BOUND_VARIABLE_1422364 tptp.real)) (= (ho_7795 k_7794 (ho_7507 k_7789 BOUND_VARIABLE_1422364)) (ho_7516 k_10323 BOUND_VARIABLE_1422364))))) (let ((_let_4317 (forall ((BOUND_VARIABLE_1422339 tptp.real) (BOUND_VARIABLE_1422340 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)) _let_1)))) (let ((_let_3 (ho_7469 k_7468 k_7467))) (= (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 (ho_7516 k_7521 (ho_7510 k_7509 tptp.one))) BOUND_VARIABLE_1422340)) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1422339) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7472 (ho_7459 (ho_7470 _let_3 BOUND_VARIABLE_1422340) _let_2)) (ho_7459 (ho_7470 _let_3 (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))) _let_2))))) (ho_7508 (ho_7507 k_10324 BOUND_VARIABLE_1422339) BOUND_VARIABLE_1422340)))))))) (let ((_let_4318 (forall ((BOUND_VARIABLE_1572554 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1422197 tptp.real) (BOUND_VARIABLE_1422198 tptp.nat) (BOUND_VARIABLE_1422199 tptp.nat) (BOUND_VARIABLE_1422200 tptp.real)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1422198) _let_4)))) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1422199) _let_4)))))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7516 (ho_7519 k_7523 (ho_7516 (ho_7512 BOUND_VARIABLE_1572554 BOUND_VARIABLE_1422199) BOUND_VARIABLE_1422200)) (ho_7516 k_7521 (ho_7516 (ho_7519 k_7523 (ho_10258 (ho_10257 k_10256 (ho_7507 (ho_7778 (ho_7791 k_7790 BOUND_VARIABLE_1572554) BOUND_VARIABLE_1422199) BOUND_VARIABLE_1422200)) (ho_9995 k_9994 (ho_7540 (ho_7539 k_7792 BOUND_VARIABLE_1422198) BOUND_VARIABLE_1422199)))) (ho_7516 (ho_7519 k_7522 BOUND_VARIABLE_1422197) (ho_7516 (ho_7519 k_7522 (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1422200) _let_8)) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= _let_9 _let_8)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 _let_8) _let_4)) (ho_7459 _let_3 _let_7)))) _let_1)))))))) (ho_7516 (ho_7512 (ho_7515 (ho_8158 (ho_10326 k_10325 BOUND_VARIABLE_1572554) BOUND_VARIABLE_1422197) BOUND_VARIABLE_1422198) BOUND_VARIABLE_1422199) BOUND_VARIABLE_1422200)))))))))))))) (let ((_let_4319 (forall ((BOUND_VARIABLE_1572608 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1422134 tptp.nat) (BOUND_VARIABLE_1422135 tptp.real) (BOUND_VARIABLE_1422136 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))) (let ((_let_8 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1422136) _let_4))) (let ((_let_9 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_7778 (ho_7791 k_10327 BOUND_VARIABLE_1572608) BOUND_VARIABLE_1422134) BOUND_VARIABLE_1422135) BOUND_VARIABLE_1422136) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1572608 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_7) (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1422134) _let_4)))) _let_4)) _let_8))) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1422136 _let_9)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_9) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 _let_8) (ho_7459 _let_3 _let_7)))) _let_1))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1422135) BOUND_VARIABLE_1422136))))))))))))))) (let ((_let_4320 (forall ((BOUND_VARIABLE_1422086 tptp.nat) (BOUND_VARIABLE_1422087 tptp.nat) (BOUND_VARIABLE_1422088 tptp.nat)) (let ((_let_1 (ho_7446 k_7445 tptp.one))) (let ((_let_2 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_3 (ho_7459 (ho_7461 k_7460 _let_1) (ho_7459 _let_2 _let_1)))) (let ((_let_4 (ho_7469 k_7468 k_7467))) (let ((_let_5 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 _let_1)) _let_3)))) (= (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1422088)) (ho_7533 k_7532 (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 _let_5 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1422086) _let_3)))) _let_3)) (ho_7459 _let_2 (ho_7459 (ho_7470 _let_4 (ho_7463 k_7462 (ho_7459 _let_5 (ho_7459 (ho_7470 _let_4 BOUND_VARIABLE_1422087) _let_3)))) _let_3)))))) (ho_7541 (ho_7540 (ho_7539 k_10328 BOUND_VARIABLE_1422086) BOUND_VARIABLE_1422087) BOUND_VARIABLE_1422088)))))))))) (let ((_let_4321 (forall ((BOUND_VARIABLE_1572673 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1422042 tptp.real) (BOUND_VARIABLE_1422043 tptp.real) (BOUND_VARIABLE_1422044 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_10291 (ho_10330 k_10329 BOUND_VARIABLE_1572673) BOUND_VARIABLE_1422042) BOUND_VARIABLE_1422043) BOUND_VARIABLE_1422044) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1572673 BOUND_VARIABLE_1422044) BOUND_VARIABLE_1422043)) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1422044 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1422044) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1))))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1422042) (ho_7516 k_7521 BOUND_VARIABLE_1422043))) BOUND_VARIABLE_1422044))))))))))))) (let ((_let_4322 (forall ((BOUND_VARIABLE_1422031 tptp.nat) (BOUND_VARIABLE_1422032 tptp.nat)) (= (ho_7541 (ho_7540 k_10331 BOUND_VARIABLE_1422031) BOUND_VARIABLE_1422032) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1422032)) (ho_7533 k_7532 BOUND_VARIABLE_1422031)))))) (let ((_let_4323 (forall ((BOUND_VARIABLE_1572724 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1421987 tptp.real) (BOUND_VARIABLE_1421988 tptp.real) (BOUND_VARIABLE_1421989 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_10291 (ho_10330 k_10332 BOUND_VARIABLE_1572724) BOUND_VARIABLE_1421987) BOUND_VARIABLE_1421988) BOUND_VARIABLE_1421989) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1572724 BOUND_VARIABLE_1421989) BOUND_VARIABLE_1421988)) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1421989 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1421989) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1))))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1421987) (ho_7516 k_7521 BOUND_VARIABLE_1421988))) BOUND_VARIABLE_1421989))))))))))))) (let ((_let_4324 (forall ((BOUND_VARIABLE_1421976 tptp.nat) (BOUND_VARIABLE_1421977 tptp.nat)) (= (ho_7541 (ho_7540 k_10333 BOUND_VARIABLE_1421976) BOUND_VARIABLE_1421977) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1421977)) (ho_7533 k_7532 BOUND_VARIABLE_1421976)))))) (let ((_let_4325 (forall ((BOUND_VARIABLE_1572771 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1421932 tptp.real) (BOUND_VARIABLE_1421933 tptp.real) (BOUND_VARIABLE_1421934 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_10291 (ho_10330 k_10334 BOUND_VARIABLE_1572771) BOUND_VARIABLE_1421932) BOUND_VARIABLE_1421933) BOUND_VARIABLE_1421934) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1572771 BOUND_VARIABLE_1421934) BOUND_VARIABLE_1421933)) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1421934 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1421934) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1))))) (ho_7508 (ho_7507 k_7506 (ho_7516 (ho_7519 k_7523 BOUND_VARIABLE_1421932) (ho_7516 k_7521 BOUND_VARIABLE_1421933))) BOUND_VARIABLE_1421934))))))))))))) (let ((_let_4326 (forall ((BOUND_VARIABLE_1421921 tptp.nat) (BOUND_VARIABLE_1421922 tptp.nat)) (= (ho_7541 (ho_7540 k_10335 BOUND_VARIABLE_1421921) BOUND_VARIABLE_1421922) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1421922)) (ho_7533 k_7532 BOUND_VARIABLE_1421921)))))) (let ((_let_4327 (forall ((BOUND_VARIABLE_1572815 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1421881 tptp.real) (BOUND_VARIABLE_1421882 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_10337 k_10336 BOUND_VARIABLE_1572815) BOUND_VARIABLE_1421881) BOUND_VARIABLE_1421882) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1572815 BOUND_VARIABLE_1421882) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1421882 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7514 k_7513 k_7511) _let_7) (ho_7463 k_7462 (ho_7459 (ho_7461 k_7460 (ho_7459 (ho_7470 _let_6 BOUND_VARIABLE_1421882) _let_4)) (ho_7459 _let_3 (ho_7459 (ho_7470 _let_6 _let_5) _let_4))))) _let_1))))) (ho_7508 (ho_7507 k_7506 BOUND_VARIABLE_1421881) BOUND_VARIABLE_1421882))))))))))))) (let ((_let_4328 (forall ((BOUND_VARIABLE_1421870 tptp.nat) (BOUND_VARIABLE_1421871 tptp.nat)) (= (ho_7541 (ho_7540 k_10338 BOUND_VARIABLE_1421870) BOUND_VARIABLE_1421871) (ho_7536 (ho_7535 k_7534 (ho_7533 k_7532 BOUND_VARIABLE_1421871)) (ho_7533 k_7532 BOUND_VARIABLE_1421870)))))) (let ((_let_4329 (forall ((BOUND_VARIABLE_1572861 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1421830 tptp.real) (BOUND_VARIABLE_1421831 tptp.nat)) (let ((_let_1 (ho_7510 k_7509 tptp.one))) (let ((_let_2 (ho_7446 k_7445 tptp.one))) (let ((_let_3 (ho_7458 (ho_7457 (ho_7456 k_7455 k_7453) k_7451) (ho_7450 k_7449 k_7447)))) (let ((_let_4 (ho_7459 (ho_7461 k_7460 _let_2) (ho_7459 _let_3 _let_2)))) (let ((_let_5 (ho_7463 k_7462 _let_2))) (let ((_let_6 (ho_7469 k_7468 k_7467))) (let ((_let_7 (ho_7466 (ho_7465 k_7471 _let_5) (ho_7463 k_7462 (ho_7446 k_7445 (ho_7443 k_7442 tptp.one)))))) (= (ho_7508 (ho_7507 (ho_10337 k_10339 BOUND_VARIABLE_1572861) BOUND_VARIABLE_1421830) BOUND_VARIABLE_1421831) (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7519 k_7522 (ho_7516 (ho_7512 BOUND_VARIABLE_1572861 BOUND_VARIABLE_1421831) (ho_7516 (ho_7519 k_7523 _let_1) (ho_7516 k_7521 _let_1)))) (ho_7516 k_7520 (ho_7516 (ho_7519 (ho_7518 k_7517 (= BOUND_VARIABLE_1421831 _let_7)) _let_1) (ho_7516 (ho_7512 (ho_7515 (ho_7